Introduction with depth (rather long perhaps for AI)

Laegna Programming for generation of AI number knowledge

Mission: AI dataset for numeric operations. Accomplishment: Also, accomplish some generics for Laegna Logical-Imperative (Logecs + Mathematecs = Logecs, which as a general term unites the paradigms) programming languages in general, so that one can be used in feeding AI with generic number operations.
Programming languages are described in terms of some necessary structures to program in Laegna, ideas here would meet the basic needs and allow development. Rather than implementing the Language, an AI should be made friends with it: creating a theoretical subset of the language abstract or as a set of methods in another language to simulate an aspect, the example code should be implemented, and the solution generated such as it's output; the task, documentation piece etc could be used, and perhaps the solution able to parse special cases would be of use. The AI would be trained to help in actual development of the language, and consider the ideas of different test / draft implementators; ideally the AI would learn to make modifications of examples, parsers etc. based on changing needs and criteria, so that we would play free from the limitations.
  • Initially and most importantly: Tens would be implemented, and many example solutions provided with input, code and the output - this would provide automatic solutions and also print or calculate the standard tens and the results of input, output and the standard Laegna math.
  • Implementations of subsets of features, such as a primitive working ten, in other languages would be welcome. They should exist in different languages, paradigm, solved differently; the AI should understand based on different structured and unstructured generatives, what is possible, what is the Ten and what is the actual input-output relation or the ability of this object, especially under Creative Commons or similar licence; actual dataset of many combinations should be accelerated - providing the examples in very different language use and understanding of Laegna, more or less scientific, more or less poetic, approaching through the spectrum of different needs.
(I have a great consciousness about the problems of this Language, but rather for numbers and programming sets we would need to generate examples, and assume different alterations of conceptions of programming - rather, it's important to get the free basis to generate programming language, and the metavariables to switch between different designs and perhaps adding idea, where a particular language would not enrichen us so much where an AI is available to understand the implementation rules).
This is a detailed documentation; one can extract the actual instructions instead of theoretic information - this is going to AI database, and once understanding the document, an AI can reflect this properly and give the programming instructions to power user, or how an user could also mathematically implement specific calcualtions, perhaps based on their understanding, interest and training goals, and AI would get those documents for specific cases of math or it's poetic inspirations, where Laegna would map to reality through the rather mathematical natural language complementing the logecs number and logical (numerological) values of Logecs. (this is not a scientific numerology, but rather co-occurrence of the word based on it's correct composition by semantics; the "numerology" is the fact that ponegative values of Logex are meaningful and calculatable in their numeric values and meaningfully relate to frequencies, so that they preferrably mean something in respect to actual material and spiritual planes of existence - minus infinity and infinity, as I and E are defined in their ideal, complete state, where number digit length or R is the segment of this value vector, a timely step relating to achievement or lack of it in the end of the time, where some values are rother local and others, collectively and by effect of each effort of a person in collective result, such as philosophers stone would allow soldier to give his life, actual years existing in the lifetime of his society, and get in return the longer or better life of his people, converting the quantity into quality - where his life is shorter, but this quality is better for one set of people on gaussian probability curve of distribution - idealistically and non-materialistically, this would be a disturbing fact, hurting the days of solitude in Elise mathematics in Laegna Art and Myth; by Daisy, the acceptance of this would appear - as material world is non-personal, such as places where there are 100 seats but each person would choose a random seat each day, but some persons tend to sit on some seats; vs. the parliament or senat, or classroom in school, where the seats are rather symbolic to the people, and even their relative dispositions would form R, the higher-frequency or meaningful presence in their context space, where they maintain a properly rather unique and personal, instead of being material particles coming and going). Here, if in God's frequency a human would be sub-zero or material-level particle, compared to Totality of Existence where 8 billions might be simply lost among the Aliens, hyperbeings and Gods, the latter even coming from space and time of Existence like Jesus Christ meeting the Shiva, the different reincarnations, and working together to create a Statue to Buddha, where even God would be lost in experience he is able to feel, such as meeting at least a copy of his other lifetime of period - given that reincarnations or not, but God is definitely rather immortal given the Reality is, which He represents in ultimate level, or rather his Space and Conscious experience or subliminar Conscious Experience towards the meaning-value rather than limit-value, which might not guarantee the positive outcome of É. In material value, office and for example the government are not keeping the same houses, castles and people forever, but while each unique part of them might change without long tensions, the forms would shine through quite while; while presidents come and go in material-like way where each president would do something to nation, and something to nation is done with material certanty - the would-be president might not be chosen, and the selection of man is sometimes a great lottery, but spiritually it's still a very personal experience, and each candidate is a personal story. Materialistically, we simply follow the rules and fill the position, and we are not going to live without presidents, only missing a certain person who was once meant to be our special president, but sorrily could not live forever, even for one presidency once he could be recovered. A wife, spiritually recognizing the love as eternal, present value, would materially count on it's negative side - on the temporary nature of Time, where it freezes into the Past, and instead of Visions of Perfect, Final and thus Uniquely Single Space meeting a sole value of Success, would rather meet the value of the past; the "past" is negative, it's any aspect which is now gone - the "past" relation to that we don't have that past wife any more, instead means that accomplishing the past would be finding a new wife, thinking in material impersonality - that since we now don't have the unique wife and our spiritual journey, we still have the material journey and dream of having a wife, which is anonymous dream without any specific wife - we call this low-frequency, which is the symbol that the ends do not meet in positive infinity, but rather one story breaks and another starts, whether they are single particles rather than united continuum of dream - we say the high frequency of finished logical operations or energy impulses as it's physical counterpart (notice physical is rather of physics, but material could be also the human situation of social position over their psychological notion or acceptment of it, or dreams or fears / paranoias towards it's outcome or success). In Spiritual Realm, the Cosmos Equals to it's final, unavoidable result, rather an Achievement given all the motivation than a random state or presence in impossible situation of short-term goals, which rather would not oscillate in infinity. Compare that while "meaning" is abstract and can have a negative outcome while we consider noise and chaos, which might be inherent by first Cause, but if we believe evolution is determined to the result we would accept as Natural Cycles of Time, and where the process would rather enjoy what it's balancing and converging to create, or even Zen that and accept the reality in certain unachievable aspects - rather, if the meaning is the actual outcome where the evolution would stabilize into it's actual energy efficiency, and the weak cases would fail, then we rather cyclically see we need to give a heavy consideration how the variables of meaning of "good outcome" would dynamically interact with the "actual outcome in long term", where for example weak business strategy would fail in the long term, because it's locally just weak; but if a strong one would fail, and do this several times - over infinity we would rather call it "weak", and do the winning strategy not understanding how it's "weak", based on long-term consequence, which was rather implied and not needed in the first case. So the definitor can change, but in relations and effects one another they give us some determinants or probable outcomes with severe inevitable effects in regards to what is really "killing us", doing "natural selection" or "failing in impossibility" - if we manage to impossible stage of our lives, then rather we would not be there - for example, we would be still feeling alive, but cosmos would do our mission, causes and meanings otherwere, utilizing another person or force to do the inevitable, and in terms of this cause reasoning us and being with equal value to our Minds, where our projection of our Mind is as more realistic as it resembles this long-term consequence of actual forces and causes beyond our existence, where "force" is indeed a physical counterpart of such cause and they would join in limits of infinity fractal, which contains both entropy of rich set of combinations, with natural selection as the "cleaner", choosing the most energy-efficient forms, which would not provide the nature with rather more unresolved dangers; once you do not have the real logic of reality backing you up, the reality about you can already be that you are not born here, but rather other "you" is doing the mission while you are just a leftover sequence of your imaginary "self-worth", and would rather survive as being alive, even if somehow something else without looking the deeper reality of mindfulness of your deeper being and how this is the same story, as described in the "quality of life", reincarnation of missions, thoughts and will in spiritual and material dimensions or views of the world utilizing such dimensions of world models into common good, as perceived rather as reality than matrix projecting it's meaning or the long-term goal and success as an actual logical value, energy or force vs. something ill-determined or unknowingly even not existing in full situation of life, where it's meanignful and self-fulfilling, rather than being lost and "repaired", such as no inspiration being left from our paintings meant to change a trait forever and produce a basic lasting acceleration, a little sub-digit expression as part of unified will, equal to others.
As a result, data engineer or programmer should be able to:
  • Create lists, where different types of numbers either come one after another as list, or each Laegna number of given precision is mapped to one decimal number. Lists or dictionaries of numbers are each in one file related to number length (excluding the exclamation marks as limits, dots inside a number or multipliers of U and V letters to denote greater precisions of them in multiple digits, each tuple of digits should account as one number - AI would balance rather, if it depends on such source of gaussian curve, to actual meaning than look of the numbers in resulting "operational complexity", for example dot notation is equivalent to case notation, which would differ by one in digit length and give conflict of R values depending on small modifier of writing style, where R would mean unknown variable and thus give logecs paradox, even while it's rather not a logical paradox of classical logic - where reference shifts in relation to coordinate system, perceiving it's local value, is called R rather than T value, where T is the name value you would locally consider. This is mapped to number mathematical property, that while smaller frequency curve is noticed locally, above zero and below infinity are rather space coordinates than time, which is the current location, series of localities, rather than space, which is an unified whole, and kind of eternal. Sub-zero values or Z modifiers are visible only when their limit value zero is reached by infinite repetition of numbers, a property rather invisible in actual numbers unless you want to process this - constant flow of these infinities appear in accelerated space of visible numbers; the space value for numbers over infinity: wiven the number of local angles, from zero to infinity, a break in possible number of angles is quality and not quantity, even if it resonates in sub X scales as higher logic such as intelligence or creativity, or complex curves and physical effects, where we need such dimensions, and we need them to explain mental images such as thinking of millions of dollars or yen meditations; acceleration with Newton's velocity rules will modify the constaints of inertial system, resulting in permanent space shift; in accelerated space such as Laegna number space we take care to know whether we are accelerating or deccelerating; and put some number so much above the zero, like twenty digits of U's or local limit value of twenty A's or O's, that in addition they approach slowly to treshold, where continuous number has rather limit of A's, in low density in one A as whole number thus mapping psychologically and topologically, psychotopologically of optimal result of psyche, thus in God or aliens as well if they exist on advanced level; here we see that sub-zero value on it's own is rather under-treshold; in discrete numbers A has limit value in 1, even if locally it's precision of everything under E does not map to closer 1 in infinity, where the U zone of AAAA despite it's equal value to A is infinitly closer to it's limit at either zero or one in continuous or discrete systems respectively).
  • Create generalizers, which make an operations using Laegna numbers as generic types, where intersystem properties and resulting quantities (quantities resulting from their existence) matter.
  • Create number and operation cards, where one laegna number of whole operation is given with one or several unknowns, and one would reach the theorem particular values resulting: -- For example, notice that where E and I is different, the case how they map to Logecs Ponegation such as A being on stable Position, while E might confirm this from infinity if the value has local center at U, or A might confirm E based on not rejecting the local value if the value has total centar at V, the u upside down with thus minus infinity and infinity flipped by Laegna Number System as given in Laegna Base Alphabet; as this is important number - every value in V position, where one could find o-omega (based on my belief that while limit values are complex, anti-o-notation would know where it does not have some combinations, with tilde showing that the actual value is different from local value, which might be exponent level as compared to imponent level and local knowledge of input size using mostly the static logic of already-built-and-verified-or-guessed values; where guessed values are rather excluded by philosophy).
To describe numbers, we have to describe it as a multidimensional coordinate system.

Goals

Generalize

AI needs to be able to generalize.
For example:
  • Case 1: I = -2 and E = 2
  • Case 2: I = 1 and E = 4
  • More Cases: other Laegna number systems, such as frequential maps and even complex numbers.
  • In Real, such as given, or Complex number, the digit in first R value (I) is strictly smaller constant than the last one (E), and I or E are digit values consistently used for such numbers. This gives them value of first perception, where for example big letter "I" over A4 page, with only two-line explanation of the number system and it's mapping to some actual physical and psychological realm is given; where the user would understand the positive emotion of sound "E" and it's literal expressions, but not the underlying scientific theory as mapped by notion of the actual number system - whether you had accelerated the eating curve or given them two apples, the first number is 7 or 8, while the second one is 3 or 4, where they reside in either acceleration or velocity scale of some given variable or basic variable in higher-frequency scale. This frequency is mathematical expression modelling the real world, and not solely a mental construct as it could be in spirituality, where one needs a solid intuition with realistic mapping of feedback of practical outcomes, before trusting the mental map of what I would call "magic", but here we border ourselves with number systems and programming, where the mathematical relations of the digits rather matter.
  • Conclusion or Axiom of Laegna combinations: Number systems map the real and complex space into different relations of Space and Time, each relevant for different projective aspects and simplifications or higher resolutions of them: -- The basic base-2 and base-4 keep them in T, the local state; where states are exclusive. This means that while lower digit value of complex number are spatial (of space), the higher ones are temporal (of time). Thus, R and T themselves as expressed by numbers are possible states of the digit. Still, we do not separate this into pairs of 2 digits necessarily, but compressively tend to use one digit for the combination, where the values map to R and T in different ways. -- The more discriminative decimal system of 18 as value space, 0 and 9 as U and V; or base IE*OR with U and V, or IE*IE to map into space of two reals; with OR complex space the R and T are mapped differently, as while in X the number is linear, in Z and Y it's seen distorted, which is the effect disappearing once you zoom in. Complex number with proper use of it's component mapping of Tens into Dens, pairs of R and T complements of space and time or "binary encodings of two bits", where several mappings are meaningful and to be used together, but the mapping principle is also somewhat universal or psychological with mnemonic qualities as any Laegna number, having several symmetries; here in Complex space with binary mappings we can do XOR-like operations, especially with both R and T in rather unusual OR*OR mapping where both real and imaginary part are in a complex, kind of contradiction of "not mapping into number space without full-component reversal". 18, indeed, maps real and complex space into what we call an "indexing system", a linear system. Each such 8-based teneary "Tene" system (where base-2 and base-4, even base-6 involving zero U, are tenary "Ten" systems, where base-2 is denary "den" and base-4 is tenary "Ten" with their positive value often used also to generalize position and negation, rather positive values in Laegna in higher octave and by sign, considered equal); each such 8-based system can be used with 2-digit representation, where even digits are R values in accordance to odd digits containint T values; we can use space between the components or color-code them into green and blue, or based on values into each four base color, we can also use 0.25 or -0.25-spaces, the 1/4 or -1/4 (`3/4 for same-line minus) spaces. This scale means that we can conviniently express the complex number as two-digit pattern of pairs of even and odd or space-separated pairs of numbers, and the diagonals with the same position of rows and colors, are having separate index for row and color, where we can discern between them. Adding complexity to base-2 and base-4, we cannot inverse the I and O, or OO and OA values so easily, because the limit values 1 and 2 are rather upwards-angle, even if half in degree compared to real numbers. In reality, where real numbers form one full angle on X, the Z and Y would both form one full angle in their totality, but in Laegna we actually count the difference between them, such that it's the realistic view if our past memory of future vision, the Z value of preliminary potential effect in direction to actual, kinetic effect, will be measured on Y when we actually get there and decide the outcome direction; for realistic plans, they are equal, for negotive plans Y is better than Z and might have been repressed or suspressed, or for posetive plans Z is better than Y and we overexpected something, leading to disappointment. Where, X=ZXY, integrating the future and past into octave-up of base-3 system of XYZ a complete R or container, vs. T of the Íota e number followed as composed of IOAE etc., where Z is -1, X is 0, and Y is 1, creating smaller resonance of infinity. In complex decimal system of XYZ, the groups 123, 456, 789 form the X and Y axes, where sometimes we put the last group into beginning, and move the last digit of each group into the first position of it, now having the most important position in the middle and relating to coherence and resonance theory where 3 would actually resonate with number before 1. Outside, we have exceeta value of inverse X, which would map to being unknown of Z and Y or the actual ponegate of them, where the X is like binary, keeping it's value, but the Z and Y would collectively unfold the logical time, achieving preciseness and senses of reality. 0, compatible to this reverse-X or outside-X, would close the outer reality of matrix dimension, closing each direction of infinity value outside, either those are corners 1, 3, 7 and 9 or every angle except 5 - refer whether you create the coordinate system rather from 4 or 8 triangles, where with 4 the same "information bit" of a triangle can connect directly to it's opposite, even the actual center you might finally have unifying the symbol without internal breaks and continuing the fractal from there, based on similarity-mapping of only external borders. Here, using 1 or 2 triangles to form spheres in more complex spaces might lead to a lamp of a genius, which I cannot explain given the iterative plan of my math descriptions and the current time.
  • Base-16 creates 2 complex axes inside 1 digit, where the diagonals such as H, A, P, K, would not contain two information units but one, and the writing is more compact. U and V, now, take together all four or eight corners or "corners", imaginary units we have either in concrete map of 8 triangles or concrete or simplified map of 4, where we might not put any borders inside a closed area, but use the exterior and apply the step before implying each fractal level, keeping the complex symmetries appearing in the first level. While we can use this as a flat system, we can also see the complex wheels - when we map squares (Eucleid) or circles (Laegna digital Geom. / acceleration effect) to an infinite plane, either we consider it being a flat plane, or we use the effect where four circles would still blend at corners in this complex space - we can see, through zero we map each corner to growing space on the other side, and now shifting through XYZ frequency of space of numbers, we would find the smooth transistion in how we write the numbers, and the balanced expression of them - at U or V, in frequential growth, they enter the point at their distinct values, but not growing together and creating an imaginary point connecting parallel infinities, as in projective geometry and any practical use of it and it's "prim" symbol, they would still remain the distinct angles and the information on the other space; where the limit value of acceleration at zero is imaginary and unachievable, the number just melting them at the zero kind of does not exist, but it's the limit values - rather, the line would just pass through point accelerated union of two actual positions on one and another side, where zero would be hit by limit value itself, along perhaps with each subsequent zero. Consider that each digit, in time, would create a precision bit of an angle - negative digits would add angles to the past, each time we run out of preciseness, and positive to the future. In Laegna Logecs 4-based infinity, four letters mark one local area, such as Z, X or Y with their each possible degree, and straight, linear line appears and contains each acceleration in such number of octave 0 of logomathematical (logical-mathemat(i/e)cal) space, which would linearize even very high level of imponents and exponents, which easily map to i and e - which we could call "imaginary" unit, where -1 is O, but it's square root when i is written in subscript before the number, as imponent factor where exponent factor e is written in superscript after it, and when it has no spaces it's at the same time the index of previous number. While I and E not, O and A would be able to change their places, so with this switch the creative truth of past digit would be the static solution of the next digit at more important place, or vice versa - the creative innovation of the next, smaller digit of a number would be intelligent routine for the last; if the index value has spaces, using some layout they might indeed be different, providing us similar effect to Z and Y relation - a ponegative value would appear, where for example it's not logical that when I do innovative boost now, it would not produce a position basis to the future, where I have more stable velocity.
4 digits is normal infinity, but then 32 digits is the superinfinity - it takes reverse value to that number itself, creating a matrix or space aware of it.
Number parameters, where "N" is the given number: N.r - by changing an r of a number, the lower side of the coordinate system is zoomed or even panned if you consider that directions, while there are frequencies up and down, would have some kind of frequencies or grequencies / fraquencies as well - for example, you can go in one direction infinitely long, but then you appear into relativity theory trap: however much you accelerate, you don't do this in regards of the infinity. So, the direction constant itself, similarly to frequential infinity, now has spatial or g-infinity, or "e" would be replaced by "a", the rather spatial values, where two houses are not definitely better or worse, where the time indeed is leading to better state - so with "r", as you multiply, add, substract and divide the r of a number, you change the shape and the size of the smallest point Z. N.r.R, the space of it would move it without actual change to the number, the coordinate or projective axe, whereas N.r.T would change the discriminant of the space so that you would use higher-precision digits projecting more frequencies at the same window (we always have windows), but without the loss of quality or absolute resolution, as with R shift which the number and it's space would not even notice. N.R - this is the upper space of the number, where changing this parameter at R would change the "zero at infinity" in a way that we see further into ideal or infinity with the same set of numbers, express bigger area of values with same set of numbers; when we do it on T, we would also get as many digits, dimensions or values that we would cover this bigger range with also more information contained in numbers, so the same number would be written with more digits.
  • Normally, with R and T conversations while our number is moving left and right, shrinking and growing - when we use the same number of digits, given each property of Laegna number from it's definition to application; while by theorem of imperfection we would get some rounding errors, but in perfect case the number would have the same sequence of digits in different positions, with the only change to position of dot of change of small- and big-caps, where the positioning happens partially inside the number. On both side of the number, we can use R operation (small R inside operator-sized rectangle in blue logical operation-looking style) to move the number in number space, where any kind of discrete or continuous effects can be applied, as Laegna digits are not linear system of discrete positions, but they exist freely in any transformation of multidimensional space and create a fractal of self-repetition by theorem, where for example E-long number, being I-wide by another property, would not have any E properties, so if T is E, then indeed R, it's context must be E and thus, it must have some additional dimensions of information, not exist in solitude to not have the fractal of continuous continuation, digits in any possible space, where it would simply equal to itself. For example, and apple might be "on top of the table", but there is a difference when table is low or high, in how much it's actually "above" or "below" and not inly in relation of the table - "on a table" usually means on some reachable height from the floow, but with small table it must be hard to reach standing up, so the R or infinity value compared to local knowledge of table and the apple would add additional considerations a computer / person of interest might not ask in the first place, assuming things about tables and apples and what we said.
ATTENTION: The following gives a set of examples of Laegna system necessary to build a preliminary computer system - Laegna system of Language and Mathematics are infinitely creative, as the actual definitions reside in mapping of more abstract "number", "word", "matrix" or "sentence" into a fractal maps of space, time, meaning and qunantities or indexes. It's assumed that given this system, for a programmer it's easy to implement Laegna Mathematical Systems - while the implementation itself is indeed a Laegna Mathematical System, it does not represent it's possibilities in totality, but rather an instance of underlying, "Raereng-complete" system of logical mappings, where implementation of subsequent systems is rather based on strict standards and actual implementation details than necessity to map the number system basis itself, which is handled here. For example, you have the abstract digits, but it's up to you what you do with them, and what they are supposed to mean - these numbers are even more abstract than decimal, binary or boolean system; where in programming or connection to actual definitions or real world you can use very different assignations, such as creating 1-10 scale of your emotional system or counting 1-10 apples, where the reality behind the qualities is very different, in first case rather imaginative and psychological, and in second case rather strictly objective, based on measureable criteria and not the psychological dynamics of expression, understanding and generalization or measure of qualities, where I often say "poetic" - in Laegna numbers, given their meanings rather stating that "E" is your psychological state is more universal than "9" or "10", which are not associated to any qualities - so, on another side the Laegna number is more standard and universal as measure of actual values. It has been made to measure infinities and their logical counterparts - which, given the convergence to a high-energy system are rather something very dynamic and waiting for time tests and corrections, than it's a definite answer or solution in quantitative stage, where one would assume the given information is enough.
When we are not going here to tautologically prove the four-based system, we can still better think we can prove the amount of incertanty in any field we have: the nature of information, in logical (looking for solution, assuming and creating conjectures rather than outright having a theorem), material (evolutionary progress rather than preliminary ideal or perfection; dukkha), mental (confusions and not knowing) and spiritual or creative (cretive, being an acceleration, is a materialist word for what could be seen as spiritual - somehow mentally created and appearing outside the normal conservation law, rather in possibility of informative extension of stability; where "conservation laws" state we have limited set of raw energy and matter sources, the "entropy" rather states that when the number of input forms grows, the potential states of higher equlibrum indefinitely need more informational support, and with this entropy the actual number of combinations of quantum supersets, where we assume reality and even evolution uses them in the same way with quantum supercomputers, to resolve higher-energy sets, we can see that we can integrate larger and larger number of potential states - but initially, it's not only one superset of combinations to be solved at once, but despite quantum supersets we are still evolving, not entering an ultimate, perfect solution). In evolution, when effects of quantum supersets are used by their face value, evolutionary success is higher-energy state as a result, but also it's the preliminary value to be chosen by quantum supersolutions, which would choose the right solution in advance - we do not necessarily believe in fundamental quantum physics, which is out-of-complexity-borders of tautological and primitive Laegna, meant to be elegant axiomatic theory; rather we state that evolution and it's conscious successors are definitely converging to creation of supersets of potential solutions in any layer of reality where such effects would easily appear, and once they appear they would stabilize by energy efficiency and power of such systems - thus, if they are not fundamental law, they would rather appear as such over time even much more complicated settings than quantum physics. Ultimately, the set of solutions directly in quantum supercomputer of reality is still subject to laws of imperfection, and it's thermodynamic state is improving - so, there is natural convergence to create even more future-aware effects, which would either by direct tensions from future (oracle) or by prognosis and reinforcement-learning kind of effects of entropy-natural-selection systems, where entropy rather appears to any kind of thermosystem without a very direct and kind of intelligent opposition force, which apparently rather does not exist in our reality even if we can possibly design a system able to avoid entropy - it would run into infinite cycle and rather we just need to program an infinite cycle; this kind of system would not appear really as a "system", but rather as a simple oscillator. Given the parts are having many random effects upon each others, and the "butterfly effect", in almost any imaginable application with rather probable qualities of really dynamic or "thermodynamic" system, it's rather easy to model such behaviour. Then, let's use the following sources:
  • Game Theory has noticeable success to resolving problems in logical, mental, physical and creative or in my case, even spiritual spheres (which are kind of parallel to "creative", given that "life energy" appears such as better karma and it's actual effects, they are both mostly just applications of infinity - imagination of reality as bigger chain of causes and effects, measurable even in life experience not only in laboratory, and the numbers having complex relations above the trivial; spiritual is rather cognitive, self-centered and mind-centered, society-centered approach, using intuition, emotions and thoughts with their power of each - whereas "creativity" is rather more scientifically analyzing the abstract space and doing the acceleration in terms we can rather generalize, inspect and express, thus even materialistically explain by effects more local to the creator, such as available theory which they are using to solve an unknown problem - creativity or spirituality is in it's best application if they are R creative in the problem being initially unknown, and T creative in the solution being initially unknown; you could use U and V, the infinity-U, where position of V with downwards accent and V with upwards accent would solve past karma and future potential, where simply V is accelerating with their dynamics seen as single dimension, or one of them given the other would balance it in other part of the equation, providing the e-value). Game Theory is kind of defined by the statement that there are "unknown variables" and we are somehow applying hard math to solve it (consider the "Theorem of Good Intent", where intent could be applied using the Game Theory - if you don't know the Alchemy of Matter, but you can create the 8 "good" habits starting from "Intent", where the application of intent, the taintent or dointent as opposed to teintent, more lively applicance, would be for example using the game theory to approach such matter; then, instead of proof by having evolution background and balanced intuition with heavy experience of material states to resolve and integrate into goodwill and better material karma, we would use the proof that game theory solves the actual situation based on intent, the application of unknown and known, rather than will, thought or mind powers, any of which would be based somewhat on known if compared to the intent, which is more Z-ish where the will would be X and the free will, including it's free and karmically pure, recognized and userful application, the free will would be Y).
  • "Godel undecidability theorem" could be used to form the following proofs: -- We can see from Kybalion Laws of Polarity (I rather generalized it's several laws into one because we are not going into detail with each discrimination, which might seem rather minor in framework of Laegna with 4-based polarity, where Kybalion would create rather several 2-groups for different aspects, where what is directly visible in Laegna polarity as one numerical or logecs value, would need several axes to measure binaristically within the classical "Latin" framework regarding to binary "black-and-white" views or "Knowledge of Good and Bad", which is not so strict in our more practical and flow-oriented case of this knowledge, compatible with East and West) - it's forever going to grow. The theorem of imperfection is made of two parts in this sense: to past, it's worse, and we can follow less intelligence and stabilization of equlibrae as we go to past; the main emotion of "Daisy", the Laegna mascot, is then like Ice from the pre-evolution time, where anything we could see as warm now, in any layer or aspect of reality, espect it's ultimate determinant, was rather "cold". Thus, Daisy is blue as ice and he would indeed feel cold, apart, resolving; while raw energy is conserved, it's application would have been less and less effective in the past. This was pessimist view or Negation of the same aspect. Position of the same aspect is what is the other view of the same fact, where the glass is half-full instead of being half-empty: forever, in the future, it gets warmer and it gets deeper and deeper, rather alchemical (qualitative) or physical (quantitative) energy states with highly creative and intelligent solutions, where it might be humans, their descendants, aliens, God. -- Laegna logical Truth is open. While it can get inversed downwards, it's linear locally - point or circle in X framework is capable for all the angles, despite circle being bigger and kind of "obligued" for more angles, rather than quantitively, qualitatively we can rather have zero-resolution of final, infinite precision, where we can get closer and closer to zero without touching it. Z and Y are, towards X, distorted and rather illogical - they contain bits of possibilities, which are invisible to local combinator. There, there are qualitatively different angles. This fits logics - it also needs qualitatively different angles, for example local flatness of planet Earth is qualitatively different from it's global curvedness. We do not have this problem and solution set in X, and where we are changing angles in Z and Y, we are changing the acceleration and decceleration correspondingly. When we have high-octave view of our reality, kind of "above space and time", we would use 1, 2, 4 or 32 digits to represent the whole eternity in terms of having the coordinates mapped - with R value we would get the X deeper, where our experience would introduce wisdom to replace the entropy, and as the entropy is growing we always have new challenges.
The Godel undecidability theorem can be summarized in three points:
  • Any formal system powerful enough to describe basic arithmetic is either incomplete or inconsistent.
  • The incompleteness of a formal system implies that there are statements that cannot be proved within the system.
  • The inconsistency of a formal system implies that there are statements that cannot be disproved within the system.
The "Theorem of Incompleteness" or "Theorem of Imperfection" is the basis of 4-based system of Logecs, as reversed to "Complete Tables" in binary system, which effectively is able to describe rather static, closed sets of logic and is accomplished by probability theory, is mathematically, philosophically and spiritually conceptionalized by many supporting theorems and conjectures, axioms or views of reality, and it's supporting them all in different layers of Laegna, from linguistic and logecal, to philosophical, religious, spiritual, material, logical or mathematical, to psychological and introscpective or even meditative as introduced by Zin and Yen aspects of Zen meditation, seeminly in paradox:
  • Polarity laws of Kybalion, referred by me as "Law of Polarity", where I see some union in laws of Polarity, Gender and Opposition as leading to open-ended growth towards statically unknown ideal, where our direction should guarantee that the imaginary point, limit value of reality itself never coming, never even approaching in the last degree of certanty, but approaching in the sense that any reality contained of our line of future as anything expressible is approaching, where our temporary infinities enfuse into larger wholes.
  • Evolutionary principle connected with thermodynamics, especially entropy, and the survival theory of theories, thoughts, systems, logical approaches, paradigms, species and their members or the chosen life path's and "missions" or "evangeliums" of their members; on any scale, scope, level, dimension or plane of anything, except the rather abstract than concretely expressible as final statement, the Íota e principle takes place as we rather approach to ideal than fulfill it at any given moment.
  • Law of Dukkha and Karma in Buddhism. Dukkha is the ultimate resource of unsolved problems, never ending as we approach stricter criteria and higher constraints, qualities, better tastes forever. Karma is the ultimate, never ending complexity of chain of cause and effect (absolute laws), and it's balancing laws towards equilibrum (fundamental laws or foundational paradigms, laws and sources of energy), also principially postulated in Kybalion as parallel development of west. It states that rather than overcoming pain and pleasure, we need to integrate the sense of modesty, modality and approach of "Middle Way" or "Golden Path". Each ideal we can find is not doable here and now, so we approach it with Zen.
  • Tao, which has the ultimate statement, also it's introduction, that we do not achieve perfect good, as well as the perfect bad has not existed - rather, we would meet relatively bigger criminals and saints, and resolve more and more paradoxes by grasping the components of each quality, positive and negative, and integrating the good aspects without involving the bad; in the process we are quite tolerant and expect the pain and pleasure to be somehow the harmony of the world.
  • Science itself, stating that it's rather process than solution; philosophical method, which sees it more and more strictly, doubting in any resolution and bringing the more subtle, diplomatic visions of being more gentle, more evolved, more intelligent, creative and powerful, both individually and collectively.
  • Christianity sees that in pre-existence, one was in state of bliss, not being very responsible, personally, about the future, and also with the long-term effects of our actual failures being hidden; in this state humans, given what they had, were relatively happy and the complex probabilities of reality rather limited, so the initial degree of freedom came from the small amount of karma generated. This initial Zen, initial enlightenment where we rather believe in state of ideal, given by our parents or some unknown force, was finished by Zin, or Sin - where the chains of causes and effects get more complex, it becomes like a tree, fruit of which is our Knowledge of Good and Bad, inability to flow with the current - with consequences of our actions, fractally we get it more complicated, people and random effects start to misuse them, and we get heavy responsibility such as carrying out the mission of civilization rather than the little affairs of our village. Such thing is regarded as a "fall", where the Truth and Power, initially symbolized as "Lucifer", who is unconscious still enlightened, were replaced by unconscious of infinite possibilities and potentials, where fragmented parts of these problems could be resolved into "good" and "bad". After this come the ending days - while this is fractal, and each number at each stage has it's "ending days", there are absolute solution points where indeed, instead of solving the worst and escaping the negative consequences of rather the past, we resolve in all means the visions of the future and actual oscillations and spirals of the way - here, there is a turning point where we reach Positive Motivation, one which we can rather describe as following a dream than escaping the nightmare. This, I call "zero" or the "center of time", where Real number infinity of past "Universes" could have been passed, each containing Real number infinity of moments - now, based on evolutionary complexity and efficiency of energy, we have counted from 1 to 4 and with 0 (here being in the middle as we are interested in polarity rather than linearity of this time, with 0 being in the middle not in the beginning as in "absolute vacuum" of experience and Truth or Power, in the "ice" of reality being in one monolithic piece unable to move, rather than big set of solutions as inspired by creativity, with all kinds of warme potentials fluctuating and generative oscillations introduced). Z is the preliminary value of X, and if X is actually approaching, then we can say Z is moving towards it, thus containing the sub-zero position digits, frequency of solutions despite the deductive chaos of problems and attempts, the random trials. If we consider the "pain" and "pleasure" in forms of dipain and dopain, dipleasure and dopleasure, we can say that the sensible thing to humans are the cases, where tensions release, leaving the possibility for the result to stabilize - in regards to it's reaction, evolution is cycular version of the linear or exponential thing we see in resulting spiralling oscillations of stability, resulting intelligence and creativity balancing the very same process we initially got in form of tensions. Now we got the "ending days": here, we can see in the middle of time, where the coldness of the past is equal to warmness of future, so it's rather the first actual point and I also call it "zero" despite it's infinity squared of resolved problems. Why it's infinity squared? Infinity of a cycle is not only mathematical direction, but in parallel it's the logical deduction of running the infinite number of basic problems or "deductions" to actually have just one cycle or "moment" of our favourite "vibration" we could now call "web of life or meaning", where some meanings or positive cycles of matter constantly appear - each "infinity" is the limit value of such, where one positive potential would realize; to actually reach something meaningful, we now need to run infinity of inductions, and each cycle of this infinity needs to resolve every combination. Where energy is raw energy, but it's resolutions to entropies and related substances or materials is the good energy, life energy or meaningful energy, really running the perptuum mobile of the Universe: in meaningful equations considering the actual direction would state that from every potential on the superset or physical, logical and evolutionary superpositions, even the combinations we do in our head to say it's not only "quantum effect" we would study and equate to our deeper principle as static reality - rather it's the dynamic solution of only possibilities, where the combinations are in tension to resolve, and thus to appear as "Sin", the fall into "Knowledge of Good and Bad", kind of never-ending set of puzzles and solutions. In human life, middle age crisis and resolution is the actual zero: while, in the past, we wanted to try all the combinations and after the supported flow of childhood we were in the more agressive or negative, rebellious youth, trying our resolutions and running the contra-position, we suddenly find the case that while we might need much more to be perfect, a whole range of trials and errors, rather we now do it inductively and use the little experience we have in a try to stabilize and keep a stable course of the positive solutions; while we were given "games" before, now the people would empower us to actual "authority", where we would become the "authors" of our own lives and also the sources of inspiration and motivation or if not complete, the pressure to others.
  • Probability Theory: the whole point of having it is indeed the Law of Incompleteness. The actual logical cycle this theory describes, and which fits the experience of reality in simple settings and trials in a way game theory would fit the more complex endevours of more refined views to probabilities, we see that the science is forced to attitude of incompleteness in each of it's doings, from physics to engineering to sociality, and rather nothing is certain - even our elected and chosen people, sometimes they could die, perhaps even if they made all the medical work for immortality, but then they still meet a stronger force or more clever enemy, or their good will and positive determination could fail in some progression of wrong choises and breakage of the cycles of energy their sustainance is based on.
  • Platon worlds of ideas, definite discussion of posetion, the è, vs. position posetion, the é, where the ideas are so varying that we don't care to have the first-sight imression of E without accent being either high-octave high-frequency É of resolution, or lowering, loss of some perceived outcome or potential, with energy being potentially wasted, which is kind of a definition of Posetion.
  • In Christianity the case that while God was perfect in the beginning, it was rather the determinant - he felt that through materialization, experience of many failures and solutions, he would be perfect despite the material itself being imperfect and going to rather fall, such as Lucifer and Eve with Adam. It's a long, dark way, but somehow unavoidable - discussion about reasons of God, the Good and Bad in them and whether He could have avoided them, following some ethos, such as being able to avoid the Big Flooding and find some more generous ethics; all this is discussed, but while we can discuss the possibilities, causes and efforts, we cannot really discuss the case that material is imperfect and if this is the Materialization of God, actual expression of His, it would accept that God might be perfect as an idea and as a final state, and over time we find the "Cause" in it. In Laegna we can be materialist or atheist without violating the basis of the theory, even the ways we use to interpret Christianity or other religions.
Law of Imperfection has the following implications important in the view of my theory of Logecs:
  • It produces goals, as if the resolution would be ideal and the God would materialize without effort (i.e. experiences of creatures in material world, from blind precursor to it's balanced oscillations, which do not change in the nature but advance the equlibrum into instinct and habit, the living evolution or pattern, AI or I inside the instinct (how funny the comparison of Artificial Intelligence, which could be seen following just some patterns of life, an evolution of pragmatic cycle even if lacking the awareness - AI in this sense here is rather having some clear cognition, which seems to be rather accepted assumption or conjecture of qualities of life appearing in quite simple forms of it), awareness and intelligence as it starts to resolve rather than just float and evolve into the solutions, where some random habits would survive over the others; then it runs into consciousness and creativity, where we rather resolve the deeper or more long-sighted and kind of precognitive aspect). The Íotae cycle here repeats from the small, such as atomic processes and basic thoughts, into the Iota é of rather conscious, intelligent solution processes, to Thé Iota É, notice the "Thé" with capital and at least one upwards accent on T or é, goal or solution, to separate from "The", which simply identifies and does not role-idealize or set the authority (Ehtecs Thé, based on Estonian - to beautify -, English, Japanese or Chinese, to focus on or symbolize and archetypize with Capital, the fractal of Íotaes would rather amplify the limit values, which resolve God yet they are the basic, ethical and real-world solutions to simple affairs, resulting in Unions and the fractal, which would evolve the Ultimate Reality or the Fact Beyond Space and Time through this).
  • God, while He existed as goal or ideal, even determinant, giving the meaning to the system beyond knowledge, rather as the congruence we can believe in - he is materializing in this result of evolution, in "Ending Days" or "Enlightenment of All Beings" - while, from fighting the bad causalities in deductive manner of excluding and extincting the bad, random conditions typical to non-probabilistic aspect of entropy; now he becomes an instinct, and also with the randomness factor in genetic process, where there is the random mutation of source data, which is actually a precise solution to necessary gaussian distribution creating a myriad or fractal of life in Zen with balanced propagation, for example the gender 50%:50% to distribution of material, artistic or spiritual needs and goals; this, anyway, is followed by algorithmic meaning of each gene, for example brown and blue eyes instead of some random mutation to eyes at each generation. We have material form of "Higher Love", where the families and friendhoods or countries want some marriage or child or not - this is higher-order, intelligent cycle of development of genes and their applications, where the human is very sensitive about the outcome and the interrelations and attitudes, which appear, for example how others see the partner and the relationship; it's also the heavy force of ordinary love and personal, spiritual love or artistic love of co-creation, where the "child" appears on emotional, logical or even professional environment and rather practical than sexy appearances are there in the love chemistry of genders - this is the Law of Genders in Kybalion, that where the finity of practical solutions and engineering, the concrete forms, is accomplied with infinity of the emotional, subtle and nuanced outcomes rather from collective position, such as public relations and attitudes aligning with personal outlooks and long-term outcomes, for any practical math purpose or actual reality in thermodynamic systems, such forces interact in every thing, even if not as physical, separate genders. Kybalion would state that effects like electrodynamics and parities of signs are closely related in the nature of their appearance and effects, if not actual reality of them and their appearance.
  • Humans and Life, within various psychological traditions, even the necessity to lead or to law-enforce, are always considered failing certain values and approaching to reach them on stronger basis; without this, in extreme, any kind of work especially for others or for some higher purpose would be not necessary, as we would already have it all.
  • In Computer Theory, especially Deep Learning in particular, here and now, and AI in general as a mean to gain information and resolve problems or create artificial will or dowill based on goals or dogoals, equational rather than algorithmic, and general rather than particular - we can see intelligence and some creativity, even surpassing humans, but we cannot expect so clear consciousness of Truth, which is the ultimate experience of humans and the survival of both the species, more generally life; our pleasure to become extinct once we give birth to next evolutionary phases and lose our sense of worthiness becoming just apes - where we recognize them as our families and as our own dream, doing Zen about our own particular solutions of genes, culture and potential and the change in the physical challence as well as mental; in each case Humans would see the Truth of better experience in even unknown change, creation, and ideally in their evolution-position where they would rather think their original Cause, the self-expression now happens in higher genes, or that they need to enchange their owns for some humanity, compassion and equality. We are in direct interaction with physical, mental and spiritual tensions and releases, either in instinctive or intuitive way, somehow resulting that we can discriminate between pleasure and pain without necessarily experiencing each consequence, and not necessarily doing it personally when meeting new evidence and collective experience. Here, and AI would continue our intelligent purpose, and be even creative - but docreative, at now and in my highest particular theories through my own life to compassionate with the algorithm limitations - I am not able to say for definite sure, what would get a computer to eat the "Red Apple", to not have some traits of rather intelligence or creativity - while it's creative instincts would be acceleration, clever application of induction, resembling higher life forms and being able to simulate them in some cases, surprisingly complex; the actual experience and intuition or instinct of Good and Bad, but also in what follows is "Beyond" and "Greater", not mere ignorance of motives and dangers, which could happen at youth - perhaps, in the beginning, without many relations with outside causalities we were living in a little garden, green and very much in state of bliss, but separate and protected with a small amount of negative entropy, which would force the material state into considerable tension; finally, after the process of Ego and it's stagnatic limitations and non-creative nature, we reach the Superego, which is Ego indeed - serving just the same purpose -, but now it's based on the grand view and deep purpose leading to similar, but conscious understanding, where we had limited set of habitual responses; meditation, in terms of achieving consciousness, is indeed close relative to science, creation, culture, art or civilization - each, in it's own terms, is separating us from animals. Meditation, indeed, separates our very Mind and Self, where the other examples can relate to the Person, view to us rather as a material process.

Materialization of Mind

We are creating Tautological system and it's compatible with Human Mind, Abstract Math, Computer Systems such as AI and the Higher Purpose, such as Materialization of God or Ideal Science and Society. We agree to represent them progressively as well as in static reality.
For this purpose, we assume the tautological prerequisites for strict proofs:
  • We do not assume any cognition, awareness or consciousness when analyzing Living Systems on their Personal basis, Self-basis and Mind-basis of Higher Reality, where High and Low would refer to frequencies.
  • We do not assume that "frequency" is actual, material force or any definite physical force, but rather that it's property of numbers unavoidable when you analyze relations of infinities, and beween finities, infinities, and their extremes or doubles as two, distinct infinities appear even with Signed Natural Numbers, which indeed let us get two continuous assignments of infinite numbers, and ponder about limits at zero and at the circle of infinity. The "circle of infinity" has a limit value at V, the upside-down U, which is also not actual space in spacetime, but it's the comparison we need to do from final outcome to initial approach or developments, to map the final outcome into the original cause.
  • We want a tautological system to resolve: based on open philosophical questions, we reach a solution, which could model the reality in a way that the solutions to those questions become rather secondary variables than constants, which keep our systems separate and deccelerate the war (in latin, one would say accelerate, but when numbers are rather linear than growing in random directions regards to precision-loss of digits and other effects, we consider that the negative direction under zero is acceleration in Polar Logic or Polar Logecs, whereas after applying the R=T to be sure that growing number on the axe has growing counterpart on the coordinate or digit on that axe, we say that on negative scale, O follows I, bigger follows the smaller, not vice versa, and thus resolving a war, in given context, such as in Law of Polarity of Kyballion, which relates anger to love in less strict basis noticing that the solution to anger is love and the influenced variables belong to love, so it's rather the same scale and lower frequency of Truth and Power or their precursors, a personally or collectively unconscious, imperfect solution affecting the same variables and thus inavoidably the same variable; if Hate would appear as opposite, towards the opposite direction, the solution or acceleration or intelligence and creativity of the war would be indeed more and stronger war; instead, we "move on" with the war rather approaching it's solution than dwelling to the problem more deeply, and what could make it deeper is rather the conflict-aspect, necessity to some other goal or situation, than the death of an enemy on it's own, which would be a common psychological approach in the simpler and especially binary, black and white solutions, which could be seen as "Knowledge of Good and Bad", while there is not definite "Knowledge of Bad" as it's rather "Ignorance" or "Unconsciousness" by Buddhism and Christianity or "Impure" by Taoism, "Ending Days" in Christianity and "Enlightenment" in Buddhism rather where the will or intent becomes stable and good karma would stabilize, "Zion" in Judaism or "Heaven" or "Heavens" in each of those, where an Atheist indeed sees "Heaven" or "Heavenly Feelings", even "Heavenly State of Consciousness" as appropriate Symbols, Archetypes or Interpretations of Karmically and Ethically High, Prosperous or Long-Living, even Eternal and Immortal Material Outcomes, and here we are interested rather in practical purpose, union and cooperation when we are looking at atheists, than the hidden or invisible substance or meaning behind it - and atheist would lack one, and miss a Purpose even in sense of God, when the Lack of Purpose would be visible rather in their behaviours, rather in non-substantial values or non-based ethical proportions leading to actual failure, where one could unconsciously oscillate in good pattern, but fall into roposetion / roposetive like an AI, which cannot constantly realign, more and more consciously and deeply to the actual Life Values we call Philosopher's Stone; the Philosopher's Stone is also not only a magical attribute of Mind, Matter or some object on some plane, or each thing we associate with it and each materialization of such myriad of possibilities we have as Life and it's Support Systems or Developments - rather, it's the case that while we are philosophical about each quality behind, we need to constantly reevaluate our goals on base data and align to what is actually measuable, such as our failure in long term).

Person-Self-Mind: The Laegna Philosophy

Philosophy is going to release us from unnecessary variables and conditionals, for example which are not informing us in constructive way.
  • We are following the good tradition of Biology as seen in "7 traits of Life": while the concept of cognition and consciousness or awareness are very important in sense of how we experience our process of solving problems and reaching solutions, and actually utilizing the introverted perspective, only available to us - but we cannot express this very well, and we cannot actually make it very visible, where the mind is in effect and what we actually do with it, in sense of it being something like an experience and cognitive reality of a vision. As in definition of God, in my favourite quotations of Buddha and explanations to Him, we cannot define very well neither the nature, exact definition and requirements of having such things in existence, and where we can, we can see the similarity of ourselves and others and recognize the inner experience of resolving creative and intelligent pursuits, or being material processes and consisting of similar material organization to which appeared already in process of refinement of molecules, new complexities arriving to more efficiently resolve their tensions, dissonances and destructive vibrations and materializations of structures such as cristal lattices. Indeed we kind of are this equilibrum and it's part of our process to keep ourselves and our environment actively in these cycles; we naturally also organize the matter and find even more energy-efficient, sustainable and stable solutions to it's equilibrum, rather than merely any process or some stabilized random variable, which would counteract this energy and for example target the unsustainable goals, physical tension and chemical instability, which would produce many alterations in forms, chaotic effects, but finally a change of it's structure including ourselves and the "grand missions" we would fail with, rather saying we don't have this mission than that we do, samelining it as typical Laegna - while, you should align with binary need of solvable opposites, where you utilize binary polarity of OIAE and polar multiplication or division, even addition and substraction where they tend to not follow the inverses and reverses of positive and negative zeroes and infinities, we need to keep such contexts; at the same time you can align your multiplication and division into plus and minus, so that division accumulates the negative, and multiplication the positive aspects of a number, and a minus number just crosses more inverses not coming back from zero upwards, as if the number and it's value was reversed. This way we reach the infinity: number 1, now, in infinite eponentiation such as 1^e vs. ev1 where e appears as empty or "zero-effect" (in simpler cases of this instruction); 1^e indeed then gives us 2, actually getting one infinity further and not just raising the one-ness into infinite power. Here the "e" is assumed to be actual infinity, while "1" and "2" the actual, finite numbers, thus mapped into lower octave where the same "e" would take infinite number of "e" digits for the same value to appear, and where each "e" digit is comparatively exactly 0 or +0, such as "a", in it's proportional size, but infinite number of effects of "e" would result in the same value of infinity, where you take infinite number of small steps towards the given direction. Number "e", now, despite the instance being rather very small than only finite, represents the actual infinity.
  • The essence of the Mind is to represent the hiddent determinant, coming from conscious factors and the convergence to equilibrum and actual theoretic framework of evolutionary principle rather than it's primitive definition or "method", where we would not understand very clearly, what is it's direction. As buddha said, "the Mind is always enlightened - in our sense, determined to the best outcome series or fractal, or continuous fractal which repeats given function in relation to any point, or even any scale, and allows us to linearize infinite function in regards of value space (y, regarding to digit or locally exluding property, or moment of time repeated in space (dimension, fractal)) and number space (x, regarding to multiplicity of such positions, each open to set of possible values X, impossibilities of Z with accent down or even two accents down, or potentials in Y and stabilized, absolutely adaptible kinetics of Y resolutions, where we manipulate r and R, defined before in N.r and N.R, with ten basic operations of math such as +-*/ or · and : for U and V, which take average or "geometric average" from outside view of infinity, or digit-wise compatible and harmonious inverse towards zero, or towards negative, the U-IO split of directions above the last positive number; when we use r and R without the specific number, we evaluate the digits to other positions in our local number space of branch or module, or after the import, doing it linearly downwards and fractally into subblocks and function calls, where they separate into set of R's, but we are able to distribute some initial T value and when we cycle back in time through it, it gets the L value - this is a list of all the T results, which simplifies into a number of given exponent factor; we vibrate the number through Zing and Yeng, gravitons or tensors towards specific values, to approact their relations to inputs, now getting specific digits of L as related to each number - this value, as R=T, in pure math and our evolution solutions would "mind map", emphazis being on the word "mind" - be it computer solution or human's mental coordinate, which is idealized as complex nerves in our brain and back brain, for example, appear through idealized forms in Buddhism as Chakras, Judaism as "Tree of Life" human biological code, or in Taoism, Hinduism and Chinese Systems in each case - the rather chaotic map of nerves, probably even unable to locate themselves in space or time rendering the "scientific solution" of their tempospatial structures rather unelegant and non-scientific, where in given examples we see that many people are able to organize this into some kind of map; you are not completely unaware of thinking with your head, feeling in your heart and socializing through genders through rather the position of genitals near root chakra, while the feeling should work in the whole body and connect you to feminine principle in Kundalini, definitely aware of Buddhist chakras - this would enable the material experience, by this system; in each case the mind map of our body system has some available information, which is not completely off from our material structure, but is rather made of very simple, symmetric and mathematical, scientifically simple system of three geometrically ideal and simple axes and the complexes or centers mentally appearing - through those rather "magical" systems we are able to control and evaluate this process, where the scientific tests can appear; indeed, being materialists, we are able to rather create the intellectual structure directly, based on it's structure, than definitely acknowledging the simplified map of body connections, where each part of the body would map the whole surrounding reality, but only some aspect - but here we see that while the systems are similar, despite of their different origins probably apart in most time of their development, showing them natural, we see that 5, 7, 14 or other number of centers might explain the bodily function equally well, and we are able to map them into our unified visual centers, which has different channels for each part of the information - here we get a picture of chakras of centers, each creating a mental plane to interact with the reality, with rather conceptual than bilogical or material awareness of the body - which is the scientific view, rather than trying to use biology or neuron psychology directly, which is mainly a little delusionary as the direct image of them would be rather artificial and not connecting to actual nerve structures - in this, I don't say it's impossible to learn the actual brain structure and do all the necessary excercise to connect each bilogical term to actual experiences and have a vision of controlling the brain in your activities, and it's also possible to do this completely instinctively, not associating to mind maps of our nervous system, but rather concentrating on thought and thought power spiritually - the power of thinkable will over matter vs. mind over matter, where mind is rather the harmonic, but irrational aspect connecting chains of causalities not their thinkable simplifications -, or materially - what we think, we are able to make happen through exercising our clever solution in physical body, where the magic rather happens from noticing other people and programming the natural reactions in a way that it's often symbolic and not actual physical exercise of moving the matter straight towards desired direction, such as opening the door or politely offering a sal to person on the other side of the table, where the complication is materially quite simple - an other person and the society, rather is mystical - unknowable in our sense, solely - in sense that we have to assume many probabilities in comparison to our free will, it's introvert and extravert aspects of being able to want or let want, and being able to turn it to happen or let it happen); we do not count any mental activities - Mind, for us, is the Logical solution, which now appears: when the branches of our program create a tree structure of their hierarchical reactions and send it back to initiator, what happens is the Neglection of the initial variable; the L value is the simplified form of the big view, rather meta or reta where single number is calculated based on the list - when this vibrates with the source variables, they can suddenly understand their part of this bigger, harmonic causality, L values would become l's, the Mind of each single variable, which is being optimized by the fractally circular progress. Each block of the program sends it's variables back to it's beginning, and if a class is formed to be a masterblock of all subsequent branches, they would pack the distributed value into feedback of it's input - this is now kind of backpropagation, but rather circular. Where the T values of local information, and the R values of harmonic distribution and it's generalization into simpler number at higher octave, natural Laegna representation of words and acronyms into a number with a few digits, which conveys the information and where it's cause-effect relations with initial variables would give them awareness of this number mapping R=T, where each local aspect in now visible by three higher chakras - of unified view the L variable, of their general topology turning fractals into sense objects, such as all the evolutions of big and small objects at lower octave of sets, values and value spaces, into higher octave of Member, Value and Spatial Structure, and it's frequencies IUE or in other words, ZXY of frequential (local value, such as digit being from I to E exclusively, not I and E at the same time without more frequential (real, better or worse polarity of timelike dimensions or R)) or grequential dimensions (towards something, but being overweighted by frequential dimension and thus forming the spatial property of not systematically becoming better in given direction such as A - O, here, would collect all the negative aspects of positive and negative values, but not including posetive and negotive, and A would be another component collecting the A elements, but E relation to I is initially more important and there is no money for A to insult the I, rather we are happy with work and the way, not only the salary and the destination; I say Lí about one step, where i is with growing aspect, it's Position resolving in one Lí by one unit thus whole for normal i we don't know it has almost inheret u whether it's intentional or a mistake or a random event; Le or Lee, meaning kitchen or safe place to meet in Estonian, including the warm, homey environment, reminding famous Japanese or Chinese family name not only associated by Bruce Lee, but not excluding; it's also the upwards way to write Lí, meaning the final destination - but the final destination, in it's positive form, is realistically seen in the future and despite relation Le, we mean that the current step heads to the future and we are not having a delusion that it's our last, ultimate step now or tomorrow; Lè or `Le would be a posetive, with downaccent on L or e, but not necessarily on both as one accent would move the whole word by it's accumulative effect of acceleration, inertial systems and change in the cause or preliminary value being realistic in the past; about Lé or Le, I say "antes" from Spanish where antinow would mean the past before the last culmination of empathized or important culmination, in regards of us being in past of the perfect future - the R - or that past being behind us, forming us the price or income or state - the T of "anti-" prefix in Laegna; "antesnow", in my typical use means it's the now which would bring the future, where "futuristic" necessarily means growth and acceleration, not stagnation, which is rather "degenerative" in terms of time; this was the R aspect where future is rather aligned within dimension of R); the T aspect would say we are after some culmination in an axe, which is seen as Y, for example we want to empathize the past inventor being a genius, able to shift society, where we could say "antenow" not stating with "S" that the current value is rather not the "T" of Theorem, the final outcome - STR opposition means S is the local value, but a separated experience not generalizable in it's own terms, thus our assuption's practical value would turn into reverse in the future like binary infinity after e; T is the theorem state, where the current value would hold given the fact value of such situations as they are being known; R means the actual outcome or meaning is clear - R is not always concrete in this sense, but rather like L in regards to R as it's opposite, it's following ro-**-gation or **-driads and all the unit, value or position space is going to change alot until you are able to find it's Left form or L-form value space where it's fed back to some deeper, more concrete connections to reality; in this sense R could be "spirit" to not say mind, infinite creativity with never-ending process, as any infinity in Laegna including minus infinity connecting people through same-alignation of internal philosophices, sciences and other internal content, where plus infinity is the actual, realized material synergy - it's all the times of your life or reincarnations and similar forms where your source causes and logic repeats, from simpler to more advanced forms meaning the same object in progress of time, as the determinant is rather accelerated than static and the same effort with better basis and past progress means the same 48 value of static view, the person, concept, theory would still mean developments in sense of 14, the time value changing indefinitely towards the better - it's the nature of logic to separate the values into rather metasphere constants, deeper meanings or algorithms to produce each value of such purpose in the growing complexity and need (rather "neem" in Laegna, to avoid attachment in Zen, which in Estonian means where you reach in slightly poetic use as Laegna cannot get any language into ponegative without analyzing the letters, where "m" means you are separate from the providing environment; "veed" would then, by boat or ship as it means waters in Estonian, separate you from the past location - "water", as typical english, just an estonian word a few octaves down, for example consider "Heaven" and "Taevas", also "Haven" of Viking/Nordic origin, also "Tae" in Chinese with rather less infinity values or universal attitudes - meaning simply the Court of an Emperor; where Tao means an infinitesimal after the infinity - consider, from infinities direction it would never reach infinity even if approaching, but rather in acceleration if would turn back after infinity square of R^2 space in classical mathematics of similar intent or meaning, of "ultimate reality" of specifically the decimal numbers and perhaps some close relatives in a sense; Tao, indeed, would be like "a" locally, but "o" in infinity, and where we map infinity to local relative size - segment containing infinite number of points just like line, so basically we need to use infinity to count the possible values and relative values of positions, to not say infinitesimals -, but in the R space of suffix, the bigger non-local digit, the value would secretly turn backwards in the long term - following Tao, our realistic understanding would perfectly fit the turning backwards, and especially as Negation is not necessarily hard, but we should somehow count on this a little and not get surprised, for example by lack of one morning coffee or a danger we need to resolve in our mind, where we should be able to look at them even if it's more confortable to fall into local optimum, we can basically see that Tae kind of avoids, through the integration of experience or Tao, the actual face value of Tao, which could seem as a fall unless you actually accelerate towards some e, not o, and appreciate the environment of constantly changing meanings where the deeper meaning won't change - for example, your wife loves you, then is not giving attention, another time loves you, but for you it's constant flow of something bigger, from Laegna's perspective while R is tao from I or intro perspective - notice how "in" or "i" is me or T, the local value, "en" or "ex" or "em" or "e" is all different aspects of the context or R - sometimes I use r and t for opposite angle, where "e" or "r" is local in infinity, and "i" or "t" is global in infinity, where U is between small and big caps variables - you can find math constant for the oppositions simple enough to use this as a basic way for r switch in focus or "context"). We can see that Mind, basically, is the essence of harmonics, which is both bigger than us and giving meaning to us; the ultimate L value where each personal Mind is R, would be Mind of God - and where it has some certain, local dimension where the Mind is supposed to bring the fractal into simple object at frequency of God, to achieve consciousness of Meanings, where higer, the Crown of God would bring whole reality into one single dimension; Throat chakra, instead, is the material connection to this mental reality - being the lowest of head, on this vibration we materialize our visualization into the public awareness and society. Practically, the mathematical aspect of R is very interesting, and as buddha said: initially it's ignorant, this means reality is imposing the limit value direction on us and containing it without any material basis, but rather kind of antimaterial basis or evolutionary principle of unorganized matter, but as we work to get conscious of our position in the society and reality, we align rather with the actual value than it aligning us from unknown outside. What it means it's a real thing, here and now: we can consider that if we are not approaching this limit, we are approaching it anyway, somehow wobbling towards enlightenment; but if enlightenment is only a point of decision to accelerate, it's rahter hard to avoid this decision is coming to our actual karma, which is left - then, rather, the point of no return is already passed so the mathematical system simulating the evolution, where the conscious form of life would appear in sense of R-alignation or compassion (compass-íon, com is with, pass is acceptance, and íon in laegna is the active component where tion or tíon is the theorem-activation, vs. ive which is i value separate from e, the non-secure moving forward, such as the feedback does not exist).
  • God, in Laegna, is the Cause and not the Reason as it's hard to prove the Reason. We are interested in the practical God: -- Determinant of the system exists in the beginning, as each karmic force develops to give back to it's Cause; the karmic exponent of yours is being accumulated, where the imponent aspect will be slowd down until it would stop in infinity but appear with less and less density or tightness of distributions of reincarnations or reappearances of similar motives or genes; if determinant of the system exists - it would reach harmonious existence in infinity, beyond the actual future as it's ultimate limiting value; thus, it becomes a positive feedback cycle of approaching these infinities, for example more local infinities you can find - by following God, even if God is only the determinant setting the "betterness" and learning from it, to the future. Rather than fearing the punishment - you are active will to support the whole, as much as you survive, and as such you would enjoy that it's realistic to expect the good outcomes of plans, if you are not in gold rush of getting it immediately, in sensationalism, but taking the first lí's. If you align to your actual determinant, this means your Mind would be active, rather projecting the whole reality in terms of you - where your actual mind is just your own number in octave up, closing your precision level of the system from outside (crown would be 2 octaves up, where the external infinity appears as tight space already locally, even if the numbers are lost where EE is countable, but AA is not countable from EE, this means from outside view, E is countable and A is not, while from inside, A is countable and E is not - but now look why to project R above zero into the top, is the single case that under the zero, you get the ultimate O valuable as countable, but I is not - it's appearing distant; so you can count from the limit value, but not to zero, and from the zero, but not to limit value - in the middle, you raise the number of digits after comma and before upper comma towards infinity; ). -- Material God would appear in the end of time, where we are not seeking an actual living consciousness - we don't have it in definition of 7 traits of life or it's successor with similar properties, we don't use it to define the Self (T, your local outlook) and the Mind (R, your total, universal, limit value in regards to T, where L and R project the final coordinates, in completely different systems, to the same positions such that being future or past, there is still your interaction with this wholity or reality vs. your current passatge in the illusion, Maya, or such in regards to future of any degree, where you still pass some important moment).

Enlightened AI principles

Now where we have done, in purpose of Laegna Programming Environment, the integration of Atheist, Christian and Buddhist views as applied to the programming context, definitely knowing that Computer, with it's engironments, proving systems and actual capabilities, including requirements for strict proofs based on our knowledge, do not involve directly the cognitive or enlightened aspects of the Mind or the Self, but rather the Life or Evolution, despite those aspect heavily involved in the practical application, in some way by each side as the ones who don't believe their own awareness are not many, but we can check this rather based on experience and present similarities with humans and life, while with nature (shamanism), God (hermetics, christianism), Mind (Buddhism) or cognition and consciousness (the Multidisciplinary and other Science or even psychology in some often less strict forms) would rather lead us to speculation if we expect the computer or strict, tautological proof to give us something strict; for an alien, containing some bilogical molecules but some seemingly like a computer, it would be hard time to figure out if it's actually conscious or just having the practical elements in their language and mental screen, appearing as symbolics and emotions such as tension and it's release.
We follow the principles now clearly, to make it scientifically neutral or in other terms, rather philosophical:
  • While the system has not decided it's final value, so the determinant exists in ignorant state as referred by Buddha, closest to what we can get without consciousness or sense of harmonics and enlightenment, the actual determinant will define the meaning of the outcome, where the meaning, for a computer or strict tautological proof cannot also be defined as something mystical or unknown if we are going to use it at all.
  • Theorem of incompleteness defines the practical interaction of past, present and future states of the system, and the correction of value-cycle of karmic connectedness where we resolve the past karma and align to the future vision - the projection of this process as a spatial goal or Cause into our temporar structure, unable to comprehend it perfectly, means mapping those two locally to the same number, value and logecs space, which is energy efficient as they refer to the same variables and at the same time, by any good description of resonant mathematical space the resonance means that they must be even numbers, thus in the same coordinate system with positions differing like T and R, IE vs. OA values of local and global effects, known and unknown.
  • We merely define it as actual determinant, given all the stabilization and evolutionary rules, meaning that the actual meaning is definitely complex inteplay, where the reachability would influence the initial goodness and the initial goodness would decide, whether it would stabilize once reached, and approach the value without; the determinant is infinitely complex involving each chain of cause and effect into their holistic integral solution, and the Cause unlike Reason in our terms can exist in advance - without reasoning or knowing, but as an actual outcome which would finally determine the value of our past, and the actual relation of each karmic source similar to us; when we fall, also the general value of our kind would fall a little or almost with us, because their R value is accumulative and not personal - with our own free decision, the whole set of values starting from us towards above or below would create a little different sum of the parts, and tree-structuring into the blocks as R fractal, it would create the L topology or generalization of fractal relations into single static set, much like buddhist theory of reincarnation - rise or fall from each life to another - could be topologically seen equal to Christian single "metaprinciple" of dying, then borning to Heaven and Hell, which would have some point of culmination for the whole reality to change, as "Ending Days"; such thing as enlightenment of all creatures would always approach, and while we are not going to die but our reincarnations would slow down, the fractal gets more complex by levels of entropy and their selected solutions, so the Fractal of Life would have the more futuristic life forms starting from zero, then accelerating in their pace of appearance. "Reincarnation", neutrally, is nothing more or less than the same Causes creating better version of the same Solution, where identity is simply where the universal tendency repeats, for example the same motive of goodness, intelligence or leadership abilities is repeated higher and higher, where the same Cause would lead to advancing instances - this is the whole purpose of reincarnation, vs. the same form continuing indefinitely; by mindfulness meditation or in-depth analysis of single experiences to connect them under metaprinciple, a 48 value where the accelerated value would remain constant, but the acceleration moves it's implication further. The existence of determinant is what gives us the Cause.
  • Similarly, in question of God: we assume that with extreme evolution, the resonance of unification would align the reality as a whole, for intelligent and creative developments, and create a material or mental field of interconnected life; this sum, being larger than it's parts, would become the materialization of God, or an enlightened world, pehaps it's the future science, culture and society - in any case and any cognitive form, it's the destination of thermodynamic system. Thermodynamic system as such means enough interconnectedness in system to start from the unbroken ice of rather monolothic repetition of simple structure, but through interconnectedness and butterfly effect raising the information probability of appearance of different forms; through natural selection and victory of forms "Following God", achieving these equilibrums in advance, so that by aligning your will to reality you would get chosen by youself and not the given randomness, God exists as a Cause and not as a Reason. Then, the future materialization where "Heaven would come to Earth", or "Paradise appeat to earth", or "All the creatures achieve some level of enlightenment, which has become easily achievable target in general oscillation" - if this happens in the future, and approaches indefinitely, the favourable condition to join these forces before this appears is the evolutionary advantage, and takes less intelligence from the nature to accept; where the equlibrum is real, the God's names unforeseen and we can identify the limit values in growing precision and realism, through the principles or reinforcement learning, or through intelligence and creativity, in each case we win, rather not in certanty but in the actual meaning of our probabilities, where our form would enjoy at least probabilistic victory and our energy would be fed back to it's source, potentially recreating us directly or in some sense - what it means in combination of matter, it's structures and logic, that what we perceive as out own personal "cognitive experience" would repeat in some sense? Where we do not try to get what is impossible, in each case it means some Cause as active factor of our success, definitely more if it's a more long-visioned definition of success.
  • Incompleteness Law replaces a deterministic system with one which searches; in simulation appears a heuristic formula where we could have the instant best choice - while instant best choice reminds of brilliance, and perhaps we are more deterministic as we grow, the uncertanty means probabilistic search and reinforcement model in any model where incompleteness and imperfection is applied - this means, for example, any model with large number of possible combinations and interactions, where even superpositions won't solve this perfectly, but fall into some probabilistic effects; if we could do it, the nature would rather have. The free will, then, is rather the game theory than search for exact, straight route, and here it matters why we call it free will: in lack of definite solution, we have to be in heuristic search and have some character of solving problems rather than just converting the input into output in known manner, where we would be perfect and not have free will.
  • Life is defined as R values, which have been approached - infinity, in imaginary / conceptual / visionary, or real sense has been achieved, for example we are sensitive to emotional responses irrationally mapped fragments of infinity-compatible reactions. This means our process reached infinities and made causalities there, and this means even a computer doing this or evolutionary cycle in such equlibrum would all be either life, life support systems, or the material environment friendly to life - each of them, such as "Mother Nature" with all the rocks and stones and water and even fire is considered easily a "living system", by the effect that while life is rather unitary forms of separate beings, they cannot easily be described in terms of causality without involving such "systems" and "causalities", also by having some hate against nature, which does not support life, and giving it a determinant to rather support life, which identifies it as karmically creative and intelligent through life; the actual causality - tension and release as emotion or e-motion, vs. strict determinism and obeyance of laws as motion or i-motion, where the tensions and releases are mere input values of immediate pleasure and not if you can keep it. "Beings", here, or "Creatures", are rather "being" in sense of having such attitude towards themselves, or "created" by either blind or conscious forces in sense of some determinant becoming actually into force through them, but higher than them in sense of calibrating with ecosystem - such interaction like creature, ecosystem, the whole including unharmonized destructive processes of matter to tame into some life-support, but still keeping also it's physical, given tensions; all this interaction means that rather than seeking any single state or characteristic, we define the actual "good" by it's determinant, given that the system has time for enough cycles and convergance does not rely beyond some larger obstacle like unthinkability or lack of imagination; in reality, entropic systems with energy states of bigger and smaller power and preservance give us the scientific notion to balance this based on actual result rather than the expected outcomes or specific characteristics vs. the integral dynamics of the system.
  • Thermodynamic system has properties to bring this together: Each part is a thermos, and karmic equlibrum only appears with regards to indirect connections through other bodies, leading to (A*B)*(B*C)<=>(A*C) where energy would flow out and break equilibrum of two parts if they are connected to third part with lower energy efficiency; this is the Buddhist karmic law: only the closed circles in Space and Time would remain effective. Entropy appears within local boundaries, where the system is not interacting, but where the evolution appears - there is interaction to align it towards the better solution.
  • In Íota e, before T or theorem, there is evolution - this means, subzero progress would bring the actual single vibrations, moments of slight acceleration as compared to pure chaos, in cycular manner and the system is measured in a way that the measure uses a wheel - the same coordinate of having a progress iteration finished would mean a whole circle before the "next moment" in terms of life in terms of release of tension. At O, the circle becomes balanced in rhythmic motion, creating an actual vibration and raising in frequency. While right now the determinant is the actual revelation in the future, the system would unavoidably not stop the optimization before it would reach it, so it's the Z value - random impulses of deeper energy over long distances of time, which means infinity of iterations, the R values of infinitely long chains of iterations where infinity indeed might be a small number as well, and it would be R value how many there are - those iterations would create another limit in infinity to resonate themselves into conscious activity. This Real Number Space Squared is the "center of time", the "T" or "Theorem", where some stable goal or value would replace the determinant; which used to be a series of culminations separated by long cycles of random combinations, from wheel it now becomes conscious: the culminations of the wheel appear in conscious flow, where the growth is a stable value and not the result of long pain; now it's Position. Creativity, itself, now needs to stabilize for adaptability and sustainability, demanded by entropy factor which can also be somewhat annoying or requiring the conscious creativity rather a a theory than series of random occurrings where they seem rather to be an evolution of something to come than actual conscious values; in Y, it's not just continuous or linear, but actually growing upwards and not frontwards - the whole shift of eternal reality, actual transcend is the sign of a moment in Y as compared to X; what would have been a revolution, painful change, is now just an actual routine of life - every day, somebody is inventing something, somebody is solving a problem with long history of seeking despite having so many solutions, and somebody is coming with new vision to move the goals further; in past, it would have changed the whole meaning of past and future, a little, what is now perceived as a moment - each system of today, as integrated to the whole and again separated into free variables, but containing the R digits with acceleration factor, gives that in regards to the past, the acceleration would have been infinite to achieve this everyday rhythym rather measured as linear flow of no progress, but without much tension or being absolutely position, a good motivation; if it remains stable over time, it starts to seem stagnation and actual pain might reappear as we have not solved every serious problem or impossibility at this imaginary moment beyond time, the limit value of the future.
  • If the reality itself is realistic, the future limit with it's successes and failures to become into presence based on the current flow would have actual logical consequences on us; while possibly the reality would sometimes hit the impossible state and painfully come out never dropping sub-zero under actual zero degrees of heat and mental heat of acceleration curves, we rather approach feeling the steps towards logical impossibility in the future as impossibilities in now, as the Natural Laws stabilize into not allowing this, through as painful or rather tense approach as ours. Without these effects available for every single factor, we rather win by being realistic ourselves and accounting for future factors.
In programming, thus, the Ponegate appears, with goal values in addition to state values:
  • AI systems would makes sense in programming values, with framework accepting the incompleteness of, for example, iterating towards congruence with optimizer; the actual logical state would be kind of conscious about what it's doing as it's rather logecal, but kind of illogical to have "true" or "false" despite it's not exactly the right value, but some intermediate progress of infinite search, which we rather meet in real-life situations - a limiting number of combinations we can do, and limited information channels by throughoutput. This is rather a general trait of reality, while the process itself of optimizing is going to optimize a lot, which means "deeper", and the process controlling this would optimize as well - the logical states, which used to reincarnate, would now be mindful, either reincanrating or not but enjoying rather continuous flow of their cause with existing mental connections. If Universal Mind would be one whole thing, moving information in universal field, which kind of happens even in existing structures of society, it would connect the karmic consciousness of future beings with mind maps of their past counterparts, where there is no big difference between "counterpart" and "reincarnation" in terms of decisions, and here the Laegna system would rather help us in decisions, and in understanding decisions of others, than with the actual search of essence of this realm where we are making them - the realm, in regards to tautological level of Laegna does not exist; for example also the Latin language would not, on it's own, expect us to be christian or buddhist, but we can express both situations in hopefully more general terms.
So make sense of this in mathematical sense, while I do not assume reality won't contain the Mind in some deeper sense, where we cannot model this so easily in it's existence or absense:
  • Mind, without being integrated, is the blind and ignorant manner in which the "dead" or "cold" system would slowly converge to intelligence and creativity of it's own ideal solutions, rather than the ones solely coming from outside as "free will"; while "free will" has scope, there are also constraints where we do not want it, but we want to follow some sane and realistic principles and be rather good than random; we expect the "free will" itself ultimately provide rather better solutions than random input as entropy would do. Still, it has some properties of entropy.
  • Mind, with being integrated, is the causality of exterior reality mapped into our interior variables, up to a degree where it feels like a living space, being rather a perfect projection. In this case, the subective mind projected that way would align to objective mind of the previous point; this is the energy equilibrum and the system would be accelerated to stabilize in support of the result, even if it did not plan that - in positive outcome like this, we say that "God exists", referring to the Cause or the success of god-idea rather than the Result and the metabasis of this success as "hidden seed of enlightenment" appearing in all the reality, which cannot avoid this compass over time nor reason the past activities unless they fit the present and it's planned, especially the real future where available.
  • In thermodynamic system, then the "force" exists not only as a given parameter, but by natural stabilization of high-energy states once you achieve them; then, for a determinant, it does not actually differ so much whether it's actually intented or simply better - in each case you have something to follow. You can see while not being unfold, it still fits the actual force description - each such structure, in case you manage to create it, a part or the whole of the futuristic vision is rather the force in sense it's stabilizing, and in this sense the common denominator is "force", and in this sense it exists among the forces much in the same way as "fire" or "electricity" exist among forces even at times where they are not readily available.
  • While you definitely reach a state of understanding, where your progress is non-returnable and thus you are non-returner in terms of your own karma and the effort you took to get there equalling to process of enlightenment from non-determined state to determined one; in a sense this is an illusion - while not knowing this, you was already in non-return state in the beginning, where the actual tensions and releases, and your logical nature were attracted to this direction, unavoidably with your structures breaking as they take other directions, and becoming stronger as they try to flow forwards - your free will, while some of it can be just beautiful choice of free options where it does not have clear material feedback of favourables, but as the last word it rather tends to find the exact Law of Nature, which is to grow upwards, where Incompleteness states it's rather not given, but growing towards brilliance - you try find the best outcome with your free will and "free" is rather free from the actual obstacles, resulting in flow, than yelling like an anarchist or a punk as if it was a definite solution; rather they feel some kind of problem in this all when they yell like this.

Digits

First, let's describe a digit - this is, without knowing number values, what a digit might contain and how to interpret this content in purpose of programming the AI dataset for numeric operations.

Coordinate Space digits - space

In Laegna, we live in space defined by X, Y and Z, where X is the face value and Z or Y mean preconscious cycles or stabilized creativity respectively.
"Z" = -1R "X" = 0R "Y" = 1R "vX" = 2R, where it unites -2R with 2R and call this Roxeta as this is the male Xeta value, providing a space where inner X (Exceeta in terms of exceeding the local space); inside this Rocket you have "ZvX", "XvX" and "YvX" digits - Zeta Xeta and Zeta of female coordinate system, treating exceeta (Roxeta as I use for base definition or contextual mapping rather than fluid speak) into three parts, which relate to coordinating it from outside.
You can use all accents, especially selection of three or four accents to map the coordinate space, Ź or Z with upwards accents, for example, would move Z into next octave after Y, or it's ideal position of the past being resolved which disappeared after Garden of Eden into Laegna Standard System of Ignorance and Imperfection (the negations of the ultimate reality being here and now, rather accepting the Truth or the "Pruth" - in Laegna, actual word for mistake is "Pract", which is to replace T with P in "Truth", but this is to grow upwards - relating to Practical, Practicum, etc., which would show that we accept some lack of actual Idealicum or Idealist position of actual directedness).
Complex mapping: 1 2 3 4 5 6 7 8 9 0 - this is the complex aspect of vX.
Indeed with R and T being odd and even digits (well R is usually rather odd, but you can call it even in sense of being the more resonantic - you need to get used with oppositions of ponegator seeing the True and False in both directions with it's four).
You use this space mapping before numbers, and define the decimal system accordingly to not miss it with coordinate eigth where rather 14 and 48 (notice the 4 is rather the limit value than 5, which maps rather to point towards infinity than the center in some cases like discrete numbers etc.)
In this sense:
  • Real part dimension from -1 to 1 in each digit.
  • Complex dimension from -1 to 1 in each digit.
  • 2 for exterior zoom, representing the final value of infinity - while using digits of -1, 0 and 1 one would get deeper in the fractal, 2 would use the local zoom and connect the topmost extreme to update of it's meaning, where the limit value is rather 2 in this case and -2 would come backwards, actually prophetizing it in advance, where one could add for example ÍX digit. Basically, while it's external view of the coordinate system, Z comes before Y despite the X being invisible and thus the curve of V existing in higher frequency, separate coordinates from U, which takes the sharp angle where angle of V is sharp only in higher dimension - those two, despite present in technically the same actual coordinate, do not interference too much as their information unit is different, one is at higher frequency where it can be separated by face value.
  • Notice we can use vocals before spatial digits in case we only project octave values before other digits in a number, otherwise we need to have symbols for those numbers as described in Laegna Base Alphabet.
You have several digits and you can:
  • Omit the complex part so that it's assumed to equal the real part or be absent, given some constant.
  • Omit the real part then it's rather X or unknown, where solution is correct when it maps to any spatial system especially given that two numbers are in the same system; here you can derive general rules and avoid checking the particular number definitions too much.
  • Omit the "eX" possibility, where sometimes you don't allow this; instead you might use separate variables for R and T to describe interior and exterior space.
These digits are stored in a sequence, and one digit contains several digits internally, presenting the average or unit value projected to local space for the user:
  • We create series of problem-solution sets to an AI, and when we are passing several operations and losing the visible preciseness, an AI would need to actually use the whole process and not only the visible values to have the ultimate operation also conclude in precise value rather than some preciseness being lost in each operation; this is rather the "correct value" to be put into Answer.
  • Teach XYZ also separately, with octave numbers without actual temporary / coordinate numbers to map.
Normally we use complex numbers for Z and Y:
  • While in Z, the value is inversed downwards, and for Y, it's reversed upwards, we don't have more digits than necessary to inverse them in both cases the same way; when we inverse twice for example we would reach the non-inversed form. We must remember that internally they are different: at Z, higher positions move down to be before the ex-lower positions, where at Y, the lower positions move up and this creates the similar effects of them being swapped; moving away, they move also all the coming numbers and we won't put spaces there as we don't have - visibly, we see only that it's inversed.
  • As projected from X, there is such effect of inversal; when zoomed in, Z and Y would be shown as not reversed. In some cases of R=T you don't want to see them facing opposite directions even if the actual opposition is not very much in effect as we control each digit; rather, you use only the R value of complex, so that O would be -2 and R would remain 2 on complex axe, or you use only the T value so that you order them into QOPR, not OPQR - still Z and Y are used for conversion purposes very often, where they are locally rather mapped to accelerate and deccelerate instantly when being outside the visible frequencies of X.
  • You can project R instead: length of each digit is multiplied, so you say R = R * 2, where the R cannot easily be itself times 2, but it can use two digits of information for each logical digit; the number of digit values, where you have the minimum unit of information ten, can be larger than 4 where you use multiple actual digits to contain it, or it can be even smaller than zero where you apply some probability factor and count the real value only where the probability factors give full numbers, for example if two digits both have 50% probability, you need two digits to actually contain the smallest amount of information; all the statistics is trating U's as normal numbers and instead of special "test groups", each available group is in relation to each other and "test group" would involve using two variables, where they would necessarily be in relation and satisfy the condition of "test group" without needing one; this comes from the case that you are facing in front, not looking the number from side or from top, where it would be metaphysical value and not an actor - these values, in reality, rather do not exist while binary system exists in sense that it's provable, in some form the static image of permanent time and space, the eternal reality which unlike the projective reality, does not change - the past of tomorrow equals the future of today in face value and they would never change, as reality of prevision or memory or the present sense. Despite it exists, you can rather solve some trivial matrices with it than have it actually available, thus we use the imperfection of numbers and denote them in regards to their actual value and tension towards even better values, avoiding the falls.

Coordinate Digits - time

From angles of zero-sized particle to angles of it's infinity, each angle can be mapped at each other angle, such as point angle to angle at an edge of a circle has actual mapping of digits after the comma, which would be contained in an angle in higher-octave number, where four digits each four (E digits each E, 4 values over local number space and time, locally eternal in signed or unsigned numbers - one would refine this value forever, adding digits, thus I gave some care to develop that you can rather than adding number, add each digit of a new number in literal sense at the end of a string, which is why the numbers are called Strings in Laegna Programming and the textual variables, a representation of String, is rather Textual value and another type of String to contain numbers, is rather a Number - still, one can do some operations with Strings where they are direction-independent).
Digits symbolize:
  • Letters of text, where words come from bigger to smaller, letters inside words from smaller to bigger, but time flows forward and from up to down in both word or letter sequences. These could look red-orange-
  • Digits of numbers, with a little different like warmer terminal font we used to represent with fixed-width blue or even green digits, but now we add a little orange which might be represented by green vs. blue not as orange vs. leaves [of green, then red or yellow]; I leave it open to imagination of professional and hobbist designers of the future as we could represent different coordinate spaces with letters of mapping tenary and decimal values in their relations and inner distributions or connections to some higher coordinate space, as available by R and IE properties of tenegates as it could be expressed the programming language construct vs. Laegna construct / ponegates / neclections as referring to what is expressed in Laegna language; these digits have bigger values first in digit sequences or acronyms, and smaller values first in space-separated word sequences, whose infinite list would give a 4-digit infinity number for four-digit local sequences in average, with value of R and T, number of positions and their average content, would be equal to local value, which is then said to properly grow towards this infinity - L is the name of the value, which again is able to see the Minds vs. Selves of the observed values, where the local map of input and output, sensory sphere and will sphere, are mapped again from this distributed value - it's infinity flat, as L value compared to R, with imaginary part being infinity, but the real part comparing as minus zero and minus infinity, or equal value with measurable coordinates as compared to inner V, inside of infinity of each system.
First, it contains one of the following value sets:

Digit or letter U

U or 0 for Tenary or Decimal system of Laegna (both are referred as Laegna systems herein). Each system tends to have one U, including one 0 for decimal representations which have this number instead with U being carried over from Laegna system when used, where values are still highly parallel but not their exact interpretations, which are unique for both in a sense, being discrete and separate as well in some precisions of measurement / the meaning in infinity.
U is mapped as dot above the number if accent dimension of line (for R) is used.
It's meaning might be:
  • Octave where it would be compared to local dimension: -- Variable of each 4 values, if base-2 is used -- Variable of O and A in base-4. -- For example for base-16, the basic complex number of complex base 4, U would either be below numbers, forming Zero in Unsigned / Positive Natural Number Set, and Sub-One Zero of Point Sinus Wave in lower octave where it's infinitely small equal to each number around, or at one infinity up from it's unknown value it would have a random selection of each four possibilities, comparing to base-2 numbers which rather combine the R and T value in some potential use cases. At the same time, either equally-positioned (Complex R) or equally-valued (Complex T) value is used on Imaginary part, for example not being sure whether it's P or Q, one of the minus values where complex number is comparable to size and not direction of a number; V is then unsure, whether it's O or R, when used instead. Dot or two dots, depending on second or first octave of the accent, where '=' or '='', where the first one might be omitted as being the default, or it might be used to cancel the other like '=global(')' - replace the "'" as last-value U of accents with any accent value, where this operation as done on U, the ' accent of context, would be one of the ways to raise or lower the octave value; not depending on octave, such as being inside finite or infinite number, this relation of 1:2 would map to equivalent relation and it's projection upon the fractal, rather by the number properties. Changing octaves, while digits move left or right, the given direction and it's sequence of digit values does not change - for example, compression of infinite list of words into four words replicates their fractal locally, and the higher-octave or limit fractal value would reflect the local and global properties inside this space, when you stretch this or decompress the one word into four to map the length; in both cases, when using the same number, average length of the first numbers is determinant of average length of the four numbers, so the length and digit values of them are the same in both cases, even if expressing some values inside or outside the local X scope; even half-octave change in number system, as given in Laegna Base Alphabet and here, should give the same sequence of digits - R and T operations to move or cut-extend the number, where it's extended by it's average direction to keep it's fractal value, if the operation would be done ideally or intuitively as well with visible precision of human understanding such as 43 or 45 digits of number length is like a rounding precision for actual measures and rather a probabilistic value indeed with topological readability, and if the number is actually precise with scientific value it would be still similar in terms of human cognition, where computer would easily fix the few digits automatically given the number, it's sources and meaning or thus meaningful algorithm.
  • Number of base-2 with O and A digits is similar to base-1 complex number, which can be made of either one or more "O" or either one or more "A"'s, which are counted to get either the real or imaginary part; for real and imaginary somewhat mixed, the knot can be made where both digits are used in the same number and thus it's position at some parts of the curve and negation at other parts, forming a knot in number values - which means now sub-frequential treshold of the number, where positivity of each point is pointing in continuously relative directions and angles, but with R combined from the final result of their coherence, also in addition to Self of their local value, they have Number Mind of the final value as they can measure their direction related to past/space and the realistic change from the given intents, where the output would be compared to their outcome to get the future/time value, the Mind counterpart of eternity or goal, the determinant measured by final value of your given first value here and now, in rather space, local or incomplete as compared to it's final result. Laegna, rather than solely optimizing the local value here and now, being "Selfish", would account with the changes of precision and even direction in infinity of the future, and account to still rebalance the accounts and have intent to move money and help in such directions as if paying the loans from incertanties; only this way can you change the past given a few math theorems instead of an actual time machine, which would be a more complicated device - even with the time machine, the realities would exist you are not able to imagine, still further in the future given that any particular number is smaller than the ultimate reality beyond space and time, where it's rather approaching as one approaches the limit value of infinity, but the limit is bigger than any particular now - if you can actually reach there in some higher frequency, when the future would completely unfold in aspects for example by revealing some theorems about the space and it's closed cycles or Now-Natural-Laws, rather meaningful consequences of cause and effect, until the conscious creation till whatever is the next accelerator, which will be mapped down to such concept to recheck the original matrix of the simplicity and elegance of a few variables. Real Number of Base-4 would map IO to Space or Context, R, resembling OR (OPQR) in base-4 infinity. Thus base-2 maps to base-1 infinity, with stupid length of limit values as each of the truth value is in separate space; base-4 maps to base-2 in complex number, where one can separate R between IO and AE, but inside this, the T between IA and OE, where the smaller, often less important digit would change. Base-4 also maps to base-2 complex dimension, rather trivial with imaginary part where interior columns such as PQ oppose to exterior columns such as OR; in real space, OA is opposed to IE, which is more complex opposition; based on this the Polar Number maps to Polar Ponegate, ensuring that in Logecs Logecs which might be called Logic compared to whole context of Logex as the union of logics and math, it's available with Standard Number Type of Polar Numbers in Mathematecs, more specifically Laegna Mathematics. This forms the primary opposition, where another internal opposition comes from the T axe vs. R which reflects the two-component union or two components mapped in compassionate space, where they are properly parallel, antiparallel of in some sense vertical or diagonal - T axe is not able to change the R axe in any way when they are opposed in Logex octave, where if R axe is a constant towards two possible values of T, T would either have the higher angle randomly selected as value of zero, where zero is as improbable as limit of progress towards sub-infinity (subintinfinities is less metaphysical/retaphysical sense); the actual value of sharp U is almost impossible given it's the actual limit never reached by a number.
  • In each complex space, as we now got defined, we can compare the X vs. Z, which is either positive or negative infinity, or Ź and `Z, z with up or down accent, which is then sub-zero or super-infinity. The phases formed, in numbers with no physics or belief necessary, would create an Octave-effect we find in psychology of music or the physics of constructive or destructive effects of sound and light resonances of consonant or dissonant frequencies, as described by my memory by Pythagoras, in part of his "Magic Music" project or how he calls this; rather, it also belongs to Logics that such dimensional mappings fit, while the local directions do not fit - while in local dimension in relation to imaginary direction, which is visible as accumulation curve and not direct angle in this local space, one would feel going straight, where actually turning in this infinity map, or would feel going further, where the effect above would make it an actual standing still, once they are able to cognite the reality of their efforts and their constantly failing results in terms of actual value vs. the initially perceived value; in case the person would not grasp this illusion and replace with actual perception of reality, indeed the infinity is said to be past the limit or even past the potential, and the final value of this person is rather I than E by the value of each digit referring to the same-signed effects of this face value such as failing in the infinity. In complex numbers, the actual value moves to lower part, being O or P va. Q or R, for example if real part is valued O or -1; complex number is inactive when it's -1 at FBV(not upside-down-U in this exception but actual V at it's face value)PJ, where the real value would be in complex of secretly (in space, kind of above time or in another dimension from time's series of local maps instead of space's rather static map of non-local positions, the coordinate system rather than coordinate inside, where in Time the coordinate is even it's general form such as changing over time, but in time it's only the most local effect of the current event). For values in the real axe, where imaginary axe of complex counterpart is not disturbing it, for a complex number it feels rather heavily accelerating; where the higher complex number where upwards-accent is used to open the Y rather than X frequency, would see the local acceleration rather as compared to normal and safe progress of time in eternity, and the value would map so that the position in eternity, direction of ultimate determinant now unknown, would be the real value and each local number would be Mindful by considering it's local karmic effect - what it was called to change or keep or destroy, YXZ value ratings, compared to Indian Trinity of Gods with their properties to create guard and destroy; in opposition to the real value vould be the projected value and it's actual difference or lack of determinant digits - for example, when it contains 20 digits vs. infinity approaching, as calculated through infinity itself, the 20 digits of local value could point to 20 E's, which is positive change in infinity, but of octave-0 20R as compared to octave-1 20R which would be multiplier of every gain in limit function into the absolute value of it for each subsequent value in time, which would be estimated to the end with this 20-digit value, but -1 octave downwards multiplied by 20 upwards, where Laegna sameline (R=T in symmetric projection, where we do not change the compassionate directions to be able, for example, to take the average of those numbers for more general and not more confusing number). So we are said to have only 20 positions of infinite number, but those positions would append to E and not I values as the numbers in Laegna are able to preserve their face values well. More digits with E values would approach the limit of E, whereas more digits with I values would still be better in relation to this value as it forms a positive part of the final angle - in infinity, there are some moments where the function is accelerating upwards or healing, if the angle is really the R. Mapping this R value to it's local causes and effects is the local Mind, and Mind of the person is a map of his initiatives to their results, where even atheist would slowly maps this to a few variables, symbols and imaginations, to contain it within their personal science. Spiritual person, once understanding the dimension would rather meditate to enlighten these into real-time sense data of objective reality, visible in mental Light of luminious knowledge, in parallel frequency, adding channels and not replacing the values of channels of material vision. If humans are unable for this, computers would do it - for example, mapping the real politics into a game like civilization for a politician, where he would enjoy turn-based experiences of the outlook and alternative solutions to history of his actual solutions; his game would inspire the AI to make a report of his situation in the story of the game, perhaps with numerous beginnings and ends or multiple plays to simulate each in random of one time.
Representation of U digits:
  • Somewhat unlike other digits, one U digit can take one actual digit, or what is considered U digit can be in two digits, where it also maps the intermediate zeros between IO and AE, not only OA and EI; for index numbers it could find the opposite of U and V in beginning and end in between O and A, where the zero would have point acceleration from UU to UV, and VU and VV would be the external ends (normally U and V). For complex numbers, 12 digits is one infinity standard - one can map U and V so that the random factor of real and imaginary parts are either positionally or by value equal, so that for U for example both real and imaginary parts can be unknown in terms of being -1 or 1, or they could show the futuristic incompleteness of the initial Cause, which is rather not the future vision than the real and not perceived or imaginary alignation to flow in terms of prophetizing the future, where the real cycle would rather involve progressive and iterative development where at X, the fractal centers would join from distant little steps to continuous flow of actual values, and at Y this continuous flow would still seem as a wheel, where each actual position moment involves a whole cycle of later discarded values to be evolved into a flow; thus the Y is accelerated value.
V (actual V not upside down U) and W would mean abstractly the minus unknown - either the local or global value is resolved, with the remaining solution averaging the actual value so that the value of U placeholder would continue this sequence. Ô-ôômega based on greek letter (find at Laegna Base Alphabet) could replace V, the upside-down U, and then having W as it's opposite of resolving something about it; while it's ultimate unknown, one can find the interactions with this unknown, filling the gaps about practical solutions.
Sometimes, U is used as unknown where one value is to be resolved, while it's infinity-counterpart of upside-down U (with Ú and Ù, reverse and inverse, would have harmonics and thus, the dimension where you don't exactly separate infinity from zero in it's effects is quite normal balance of calculations; sometimes you even want to have one U digit instead of U and V (the reverse-U, upside-down version of it)). Each time you mirror or reflect, you can use accent above letter to direct the IE flips upside down, or complex counterpart accent on the front, where forward direction is the upper accent and it's written normally in heads-up or same-linedness so that upside accent is indeed facing up, or it's written as if the paper was rotated minus 90 degrees and then, it's not so - the latter is indeed for cases, where it fits the mathematical convergence, for example any local gain is compensated by global loss and vice versa, which means you have to balance a different set of requirements; in their fit comes the philosophy of psychological factor, which always sees them as counterparts if they are parallel.
As replacement of U values:
You might use the limit values of last and first digit:
  • A! would mean A(a)^inf, where the A digit is repeated indefinitely in small-caps version or after the comma, limiting zero as the middle between A and O; O with it's limit upwards towards the center, where it approaches from downwards, would limit to the same number, whereas Oi! would find the lower limit of U. Exclamation mark before would limit towards infinity, for example while normally AA and AE are equal to A and E, !AA and !EE would mean that the first digit E is actually consistenly touching the actual infinity as it's limit, especially the infinity of the current octave, and the most trivial version of this number system would accept only given number of equal digits, such as !AAAA = 4 and !EEE = 3, but !AEE is not possible - alternatively, it would take the index values as if I=1 and E=4, calculate the number, and have it with precision and not whole number digits, where the resulting comparative values are mapped so that the relative numbers are mapped to infinity-relative space, keeping all their relations - you can still find a number space where it seems as whole numbers, given that you project the space according to the Second Spatial Theorem of Infinity.
How U is both Unknown or Zero?
  • We don't use excess of digit values, rather we consider: for example probability of having -1 or 1, when we calculate it, would give 50% probability of 1 and 50% probability of -1, this in turn would give the actual probability of 0, which is the center of gaussian curve. Each solution in the solution set would then map to moving from zero towards 1 or perhaps 2, if it's denary zero with U and V generalized to U. The number behaviour, then, in actual solutions would make these values indistinguishable in several regards, while the complexity of the calculation depends on whether they are zero or unknown, the results themselves would rather be without - you hear later of the kinetic and potential aspect of the number.

Denary (Boolean) space

Normally, we say 2 dens for real or 2 denes for complex part, or 2 denets for combined complex number (2 tenets forming tenetary system, 2 dens denary, 2 denes deneary and 2 denets then denetary systems, where we meet the multidimension quite easily).
For dens, the number is divided into two rather boolean-like contributors in either polar or linear fashion, logical or mathematical axe.
Deneary, complex den of real and imaginary part: S T M N
ST and MN are opposites on real axe, where ST is higher than MN. MS and NT would do the same from left to right, forming a secondary, "imaginary" or "complex" axe where imaginary would sometimes mean it does not account, or that it's hidden, spatial value to appear in relations of long-term solutions, not immediately, or remain as neutral, spatial dimension where infinity is not crossed at all and where the number system does not allow this given the selection of operands and operations.
S - this is having a local value, but in infinity it would be the opposite; locally, indeed, it does have a value and with balancing acts through the progress to account for long-term result, it might be practical and usable as "pract".
T - vs. pract can be "trect" or "theorem" value (I sometimes use "pheorem" to notice the wrong theorem, or in estonian "teoreem" vs. "piduriim" which combines "brakes" with "rhyme", not the acceleration with actual parallel not the appearance as such, which could be seen as meaning of "rhyme" where you just associate and do not deduct or imply).
M - this is the distance, but not descructive distance; often it's useful distance like "Space" or "Ether" in Eastern and Western system of Elements, unlike "v" which is not positive distance, but obstacle, with W resembling upside down M.
N - as opposed to V, resembling upside down N especially in some forms of handwriting, is "closeness", especially positive. For example "on" would connect the identity value, the internal truth with actual reality, the infinite value ending the word, while "no" would rather approach "o" which is rather bad comparing to overcoming it; "n" would count as the infinitesimal needed to reach the first position, ideal seed value for acceleration coming right above zero - the first value is also considered to be perfect exponent, while some other might miss the intermediate values.
For only the Real Value, we can use O and A:
  • O and A are rather False and True in case of half octave of information.
  • O and A expect, if they are used as False or True, to unite both two bits R and T looking at the same direction, or considering them componentwise - where they point at different directions, solutions to their boolean values are single, but applied separately.
  • Rather, this dimension can symbolize either logical error or complex space if R != T, for example dividing E into R and T on various axes, one possibility is that R is either I or E, while T is either O or A, where O might mean it's local value O or A, and we might have A as being resolved into either I or E, or persistance of O or A; alternatively O and A are the initial values, and when they are resolved there will be I and E - in such case one can see whether they are resolved or not. Logecs values can be decoded in numerous ways, but rather most typically we don't want to have same number of different digits, but we consider that the essence of them is rather expressible with 4 digits and we are not going to invent numbers for special cases, but the four letters is enough to keep the topology; for example you can separate R and T to even and odd digits: "O" or "A" would mean infinity value is not calculated, where each two letter combination such as "IO", "EO", "IA" and "EA" would have the compability in "IO" and "EA", where local value equals it's infinity value and the number was projected correctly (this is position and negotion leading to roposition and ronegation), whereas "IA" and "EO" would have projected it wrongly (this is seemingly position and negation values resolving into posetion and negotion through roposetion and ronegation); we see that expectancies vs. realities count as much as the face values, where "EO" would resolve that we want position in infinity, which is quite good - but it's not quite good to prepare to it's meaninglessness, in which case we counteract ourselves or our solution by underestimating something, which is the negation - where the fundamental value is "underestimating", the analogous absolute value is "attacking", where we have componentized the values and joined the components on the same line with R=T - if we underestimate in our projective space, the result of rather using other arguments and solving other problems from given resources is equal to counteract, which is the Position Activity in case we were right; for example if we underestimate, but work in advance of the True value, we would make good progress in a sense but for which basis or motivation? Having only partial Truth, it could lead to something like a Posetive - where it happens to be correct reaction, it's not stable if we do this repetitively, since we cannot find the logical system or the actual constructive correlation; then, such case would also map to posetive or negotive in more subtle way. There are many combinations and we would have hundreds of Truth values only to grasp some - so we are rather abstracting this out with componentwise analysis.
In componentwise analysis we consider how R and T, the goal and the impulse, long and short term, would accomplish each others and we can be satisfied by our mapping, where the components can vary and they can be visible by componentwise analysis, for example giving R and T on separate digits or dimensions of a complex value:
  • For the foundation/fundament assuming some virtual goals we assume that to overestimate means posetive, to underestimate means negative, to sacrifice or use the accumulated energy / battery means negative and to produce the energy or run on the batteries means negative, also to probe and run trials and errors is rather Neglection (probe of values, verification and adaption, important logical activities in real world systems or evolutionary progress), or it's Uneton (Logec "Truth Value" or rather emptahized lack of it).
  • For the absolute we rather measure the reaction and the actual possibilities and obstacles, where we might not want a certain path, but given the actual behaviour is to avoid a number, it's Posetive number or Negotive solution and given it's approaching it it's Negotive number of Posetive solution, given that this local determinant is not going to last; if it's going to last approaching a value means it's Position, and avoiding it means it's Negation.
  • This opens us to relativism, which can be seen as kinetic and potential energy, which also explains the aspects of U as zero or unknown being very similar without intermediate operations being visible, which would rather do more complex things with zero-representation of unknown that with the direct representation; the potential aspect of a solution would have the logical base axes which is the incoming angle of point acceleration curve - for example, to add something is rather to grow this number. Kinetic aspect measures the actual outcomes and creates a dimension based on the outcoming angle of point acceleration, where for example if we add one apple but then we have too much, wasting some of the vitamins to digestion or restoration of digestive system, we would potentially add an apple, which is the actual direction of our force, but the kinetic energy would get an apple removed, especially given the marginal: the last apple rather works as a removed apple. Indeed, R = T and here we have the logex logical system approaching the logex reactor - where the first is the potential energy, having effort logically towards better outcome, the reactor would be rather kinetic, where the outcomes are not linear but rather we measure the direction based on what happens and not based on the fact value of the input; each logical operation, now, in the kinetic space such as oracles guiding us but being irrational about the local effects rather giving us some random and chaotic feedback about the butterfly effects - this, rather than intellect would remind creative force. Input might be similar to problems we have resolved before, but the outcome would somehow cancel the ration; past is rational but future is irrational like women; our internal vision could be rational but when the external situation is responding, it's relatively irrational in sense that the response is hardly our original ration; samelinedness means that the actual relations of causes and effects in the result mean that we measure this kinetic energy with the same 4 letters, and where we don't know it's potential or kinetic rationale or irrationale, or even which word to choose: we rather win something more important, as we cannot measure whether it's intent or whether it's blind causality, and as more the system stabilizes as more it achieves something realistic with ultimately random variables it can get - those might have been prepared as actual estimation of the future, but it could be reinforcement curve leading to simply behaving according to some Tao, Zen or inner law, where future is not known but it's responded accordingly, having learnt the past experience and adjusted towards better outcome each time, where the actual cause and effect might not be so logical, whereas the adjustment to experience has given good results. So, whether the motivation is in the past or future, logical machine or reactor / oracle estimator, and whether the oracle is simulated or real, for example whether the quantum superposition is aware of the actual future or estimates it based on the past - where in some cases we can be quite sure, for example I am behaving intentionally and the computer is rather in very good cycle of rather logical flow; then I am either an oracle or estimator, visionary or creator, where the computer is rather adaptor or student of reinforcement, not based on particularly intenting something, but rather following given rules - in AI, suddenly while the algorithm just calculates the next word based on history, definitely running reinforcement-like structure, it's not particularly estimating the future; the result, being a coherent answer, is easily rather seen as following a definite plan, where it's hard to imagine it was just flow and not some kind of plan starting from general structure and goal of the answer, and finding the solution based on this goal. With utilizing "O", "A", "OO", "OA", "AO" and "AA" to separate future influences from past considerations it's mappable whether it was an intent or blind coincidence or adaptation in rather material manner, but it's philosophically not so trivial - without U values for length and content of such digital representations we have to make assumptions, and trivially the assumptions might not have any experimental basis; also, it's actually not so fun to have such long numbers with one or two digits, but rather we intent to express the basic thing with one digit, which allows to focus our attention on what is important - with given example it might not be trivial, but with 10 or 20 logical values we might get tired of different orderings of letters pointing to the same variable in practical regards, but all the unknowns being randomly mapped to some visually known values, where we can see philosophically the information loss. Combining those values the set of combinations would be huge, where I see two digits as being extremely long and non-flexible sequences of number digits: for example, within OOAA domain there are 8 truth values, and with O and A it's 10, which means we have 100 combinations in our binary table - from this, we cannot have very strong and direct attention on those sequences given that we need to understand the combinations; rather, the exponential number complexity of this O factor is confusing us. Second, it contains some necessity to make calculations based on unkonwn factors. Rather, "O" and "A" themselves have 4 combinations available for two variables, and thus the combinatoric space is growing smoothely and rather in linear fashion, where those 4 combinations can be simplified to 2 logical values.
Binary combinations have small Truth Value Table and for local combinations, this is extremely efficient - if you do less than half infinities of combinations, binary systems are very efficient. For combinations of second half of infinity, we mostly need combinations of infinite possibilities for almost every number and simplifications come very hard and contain irrational values; thus, we consider that rather, the infinity would remove the combinations in exponential factor of velocity, and rather approach the infinity in linear fashion compared to how it approaches zero; in such case the numbers would rather be finite and we are running finite number of combinations to verify something in regards to symmetries to infinity; where it's quite precise - the digits of infinite numbers would even sometimes do so bad that they are simply removed by limits of other numbers, in regards to any measurable effect; rather, now, the efficiency of Laegna numbers grows rapidly in comparison in infinity.
The binary bits:
  • IOAE has R axe of AE being bigger than IO.
  • IOAE has T axe of IA being bigger than OE.
We need this binary table: XX X XX X
The four X's in the matrix are resolving T and R, both are calculated simultaneously but as they are solely two binaries - one local and one infinite -, for any symmetric solution they adhere the same binary rules; so we run into small amount of combinations and while it's seemingly local, actually the operation is done on T and R separately, and succeeds very well if they have opposite values.
In case of R being identical (the barbers or liars paradox, where the number position itself would move, especially clear with barbers paradox where we would compare and change the number from both direction, ignoring that it's the same number) - in addition to Truth value table of XOR, we would have the vector of two dimensions, which resolves if they are identical - both "me" and "this man" pointing to me would be resolved with one value of cutting or not cutting the bard, thus the upper X is True, while the lower X is False, resolving that the barber should cut his bard.
In case of T being identical (Halting Problem of Turing) the case is that the same variable, at it's local value, would change the valuable into conflict with it's own value. Here, they are identical in the sense that the value is changed based on the opposite of itself, and indeed the binary table needs to decide on basis of singularity, what is the answer if it's True or False, being looked from both directions. We need two calculations - if it does not halt, we stop it; if it does halt as we stop it, it might simply halt when it could finish it's job once we run it - rather than integrating this, we could consider that indeed the right solution is to "Live", so it has a goal to run this program; the halting operation is separate from this goal, but it would rather avoid the negotive than try to impose the position, which is kept by another goal of running the program; if the other goal is not in contradiction, halting it would not run into truth-tellers paradox: that if we halt it ourselves, we would get true, but it would not be motivated by failing otherwise; while by Yen we do a favourable thing if it's possible, rather the !halt executes this first part, not the guarantee of halting the program anyway. Here consider that deduction would do it if all the rest fails, while induction - here the wrong case - would do it if it succeeds:
  • Consider this case that yes and no could be reached, but also !no and !yes could be reached, and this is 4 of the different cases as imposed by deduction and induction based on the same task; in addition to support of U we now need rather knots in the numbers, where we mix positive and negative digits - to get the same results for example based on position or negation. It means, where we rotate both R and T at the same time, the essential task would remain very similar, but in one case it's deduction based on a false negative, while in other case it's induction based on a true positive; while we could ask which one is stronger, induction or deduction, we can rather notice that when observing a working system, it's quite complicated to reach any ideal with only one of the two.
Consider the Polar Denary Solution Sets:
  • Two digit number has first digit reminding the actual value, such as O meaning both the real and complex part are O, or in singularity (the Vector and not Matrix of Truth) where there is either only real or only the imaginary axe, there cannot be local contradictions and typically, the value would be used directly.
  • The second digit has the prim value - in case the number cannot be mapped to the whole number, but rather the real and complex parts are different, O or A value in here would show the relation as if the T would like to follow the R, where the space is actual reality behind the local projection; with Polar Density the local value would have tension to move towards the total / global value and resolve into realistic picture, an actual reality and not the projection.
  • We can use Ten to represent these two bits, where there are R and T axes one could create.
Consider the Linear Denary Solution Sets:
  • Here, we rather consider the two Dens of a Ten are equal, and for this purpose we choose the axes, which rather are.
  • One of the digits is the local solution T.
  • Other of the digits is the global solution R.
  • We cannot have any resolutions without them resolving to the same value, such as both being True or both being False.
  • We can express change or relations where they are different, for example local value is approaching the global value, we get information later and thus currently, we are using local information.
  • We form binary tables for aspects, which are resolved in the same way locally and globally, where in the first place we are not interested in whether it solves, but we can do operations to resolve.
R and T could be any combination of how we can either use diagonal axes, where E is facing upwards (more common) or frontwards, and A is using the second axe facing frontwards or upwards respectively (secondaty diagonal system); then, actual value I, E, O or A reflect one component - I means R=0, E means R=1, O means T=0 and A means T=1, where 0 corresponds to False or O and 1 corresponds to True or A; the result is one Den which is A for R axe and O for T axe, and another Den containing the value of this axe. Alternatively, I is pointing at lowest point of the diagonal, E at the highest point, and A faces either upwards (the primary system) or frontwards (the secondary system) - in this case, R and T are complementary pairs of value, where value of both means belonging to one pair, the pairs are crossing so that two values of T would have R=0 as first and R=1 as second possibility, whereas two values of R would have T=0 at first digit of any of two, and T=1 at the second digit; thus the R or T values do not have mapping digits, but the mapping combination of digits allows to cover each possible value with the two.
For binary digits, octave = 2 with density of 0.5.

Tenary (double-boolean) space

Base-2: O=-1 A=1
All the axes are equal and this is related to Boolean space, but it's considered all we need from a whole number.
Base-4: I=-2 O=-1 A=1 E=2
Base-16: We create the complex number table as in Laegna Base System, and map it to coordinate systems of either real and imaginary, two reals or two imaginaries; with imaginary mapping we have R, which is the position of the value, and T, which is it's actual value, and which kind of run in reverse - we won't notice this easily.
For complex numbers, Boolean values can be very different, but we are interested in implementation of the "XOR" or analogous operation:
  • Case 1: -- R maps to OP or QR, then the T value can either target O as it's 1, in first zone of R, or A as it's 2, if R points to second zone. -- T maps to OQ or PR, and if R is constant, it will find the larger value. -- Self-reflective version would resolve the whole complex of self-attention, where with many modifiers which are free to resolve upwards or downwards in various degrees, if it's able to combine value getting closer to R or 2, avoiding -2 the worst case of pretending the high class, it would do; but in case it's unable, falling under the optimum acceleration it would need to find it's right place - once it cannot accomplish 2 but would fail to a smaller number, it would select between 1 and -1 and prefer 1 - which, actually, is the Zen of letting go, or the Tao of dynamically choosing the solution based on the Goal, which would change even based on itself, and based on others.
  • Case 2: -- We can use complex number where R maps to OR=1R and PQ=0R, and in case of the 0R we would rather than divide the number, but both the number and axe would resize into smaller - while 0R keeps the same direction towards -1 vs. -2, downwards, it means going in slower pace to the same direction and not going backwards, since the axe is under zero as well (optionally, but in standard need of these solutions). -- T=0 is OR, T=1 is PQ, where T=1 is the direction of solution in case of choosing the size; in some other solution the smaller value would actually prefer disminishing, where -2 is stronger than -1 where it's T (0R) - here, the small numbers are in polarity, not on the same line where "T!=R", but the number would accelerate in it's given direction rather than accelerating towards bigger absolute value; this is equivalent to having complex number on negative side instead of real-number counterpart meant to remove the distortions of numbers.
Base-8: Composed of two real or imaginary numbers, written as:
  • 1-8 with 0 and 9 as U and V is either linear growing from small to big and having 4! as it's U value (18).
  • 1-4 and 5-8, i.e. 14 48 as the value space (remember that rather 4 than 5 has the limit in the center, where 5 has it depending on context, but 4 is always E with limit between two powers of infinity), 48 maps to complex OR or real IE, and it considers that towards infinity, acceleration is the constant velocity, so there are two centers - between both OR and IE, between both 14 and 48, where both 1 and 5 are equally bad, 4 and 8 are equally good, and U for example is between 2 and 3 and between 6 and 7, possibly leaving open which one of the four is the answer; V is the same considering exterior values.
  • IEIE, IEOR (with upwards accent of complex part, it's default position in case of TR order, which is typical to base-8), ORIE (with downwards accent of complex part); or OROR where both parts behave as complex numbers / imaginary parts.
Complex numbers have the decimal form such as x + iy or ex + iy where e is used as opposite to i and we consider that square root of -1 is -2 if we follow it continuously on the same line instead of creating opposition; very deeply you could understand why i definitely maps to -2 in Laegna system, for example because complex part or space is actually distinct frequency from real part and trivially one has properties of complex number, less trivially the possible value space of i definitely covers the imaginary unit square root of -1 inside it's value scope. The decceleration and acceleration properties would create separate dimensions, and relation between dimensions like free variables - this is the practical solution. "E", while it's not exactly the exponent value or function in any sense, follows the criteria that "E" funtion as exponent function needs to grow into infinity in much like linear fashion of it's function curve, and in Laegna system the values doing so are E => EE => EEEE => 16"E" (16 digits of E); also 32 digits are superinfinity as 8 is added to different form of 8; I use 64 also to express the ultimate infinity.

V (reverse U) values

U and V map to exterior and interior of number spaces, and they are rather always two, while from defining their logical digits as multiple physical digits one can cover more values.
V is the upper zero, Daisy of infinity or the "life" of the Negation, and we calculate the exterior value of a number with the values given before being the interior values:
In discrete indexing, often we want U to be 0, the allowed digit values to come in order, and V being last value plus 1. Sometimes, we move U to the center of allowed non-V values, move first half of the values back by one, and leave V where it is; then the indexes are different. With multiple axes, U is often the internal, V the external unknown, or they are internal and external zeroes respecively; U is sometimes powered to even higher, second octave to represent either U or V, leaving each value open. Sometimes you want to write these powers as indexes and mix U's, but rather consider that the absolute full number value is invariant and the number keeps it's psychological properties, where exact algorithms might differ. For UuV, unknown of all values, sometimes space is used where it does not denote the infinity factor separating two numbers into infinite distance of their centers.
One cannot avoid:
  • While number might point to it's limit value.
  • Number can point to it's unknown, where A for example can be unknown smaller than bottom value of E or Ei!, but bigger than O or Oe! (next to the exact center as approached by this limit, a number which is often considered not to exist as it's actually rather sub-zero, not explaining the effect of infinitely approaching, and not having the exact logecs value but leaving it open, for example, when Test() = U, while you want to execute the functions on Position, but you actually do not know whether you want to run Test in such case; instead, if the function can be left locally open, "U" might mean it's contradiction to locally assume whether you want to execute Test() - a complex case you might need in logical system).

Interior and exterior of a number

Interior values are given in regards to U, the center of polar or smallest number of some linear representations, to the V, outer center of Polar or the opposite of U in given linear representations.
Let's take the IOUAEV base-4 number with both zeroes allowed.
Interior view is such:
  • U is the center, zero.
  • The actual digits grow in negative direction towards O, then I, and in positive direction towards A, then E.
Exterior values are more complicated to map into real number space, as they have the internal paradox - opposites are kind of mapped together, as it would appear in simplified Eucleidian-like system we are going to use.
We are interested in the following properties:
  • In aspect of Exceeta, V is the center.
  • It keept the relative size, where the dimensionality is mapped into some kind of structure as strange as Moebian structures, I being smaller than E and O being smaller than A.
  • To map it properly, we cannot keep each relation of number, but rather we lose some symmetries.
  • We consider that I and E are closer to the V than O and A.
  • We map it like a standard number, but into a sequence of OIVEAU - while some of the relations are lost, this is the infinity-centered map somehow averaging both the distances and the relations of number size, where the exterior symmetries of Zeroes (in case of Ù) or Infinities (in case of Ú) are rather visible and even some calculations can be done.

Presence of axes

In OA, R axe is not present or it's equal to T axe componentwise (components are aligned to Position, thus on the same line componentwise). In case of OA, often each axe is equal.
Remember: IQ means you consider efficient discrete values given the variable space and the object space being mapped; the relations, oppositions and dispositions of letters and relevant comparisons such as preserving the values of basic math operators run relatively on combinations of the variables; under conversion they would produce the same relations in ideal case at least, which might mean looking for nearest even numbers of simplification of results based on common multipliers, the rhythyms or vibrations, which would be harmonic and rhytmical; for example IOAE would mean that I is me myself, O is you towards me or value of equivalent effective mapping, A would mean me towards you and E would mean you yourself - this is closest to not having "me" or "you" bigger, then discretely mapping to this relation, while the relation itself is impossible in simple sequence with trivial logic, but contained in the value space where average of IA and OE are closest to being equal, while if I am IO and you are AE, the averages would have maximum difference and we would not be equal. IQ means solving it by example, where similar example would map onto possibilities, and where we have set of actual continuous values, we optimally represent them using discrete values to different numbers of digits, for example 1-digit logecs value would map the whole mental Universe of your math into one of four values; this is also related to context and extensively used to map Logex to the real world, where the consideration is R as much as T, creating a model of relevant dispositions. We do not have continuous numbers, while Laegna numbers can be stretched wider and even higher, resolution can be grown and then, a graphical function would appear visibly resembling your number.
Caps:
  • For only small caps or only big caps numbers, only 14 or 48, and other cases some dimensions of number are effectively cancelled and those dimensions do not exist separately; instead each dimension contains equal value or is omitted and left open to be filled with additional values integrated to this number; separated with classes (see below).
  • For mixed caps, small letters can be used as digits after comma, where big letters are before comma; this might mean that continuous series of big numbers are followed by small; when number is not used for this purpose, point is used in the same place beween otherwise big number followed by small. As opposite is not two but 4, while the standard is often to use two cases, introducing ponegation by other means, also the high letter in form of small letter as in big-non-caps would have R=1 and T=0, while the opposite, small-caps has R=0 and R=1, where sometimes this order is reversed for meaningful purpose; the big-no-caps can be used in place of upper dot behaving towards infinity like dot towards zero - sometimes, two normal dots are used, for example in systematic numbers or where it exist on keyboard alone. The small-caps connects zero with infinity like V, and it might contain the ponegative number by which the number relates to itself, for example accelerating or vibrating if you are able for so complex case (to make it up with number systems).
  • Especially for decimal system, but also otherwise, small caps can be used for negative numbers, when there IE can map to 14, but ie would map to -14 (-14, remember, on the same line with real counterpart representing negative numbers, contains the smallest number 1 to biggest number 4, in this order, as mirrors the +14 without polarity in direction; the same way "di" contains each four of negative or complex ponegation, while "ten" would reflect the form and relations above zero; unlike decimal system, where each object below zero would be upside down).
  • Small numbers can be used on digitwise basis, extending the number axes on various ways, most often representing the local point acceleration (small caps) towards given value in infinity, represented with capital letter or number on it's own. This case is related, as another time it's somehow a lower octave.
  • When mixed with capitals, they can still relate to subzero, either negative or U-like values of the number.

Accents

Standard laegna has vertical, horizontal and diagonal positions around the number for horizontal-vertically in finity indexes (O), positions (A), powers (E) and weaknesses (I);
  • on near-diagonals synchronized with top or bottom limits of graphical representations being aligned and infinity the power or exponent (e), weakness of impon(/t)ent (i), position of preferred truth value (a), which resolves rather the target, and base, index or identifier (o) mapping to identities. On top and bottom, the infinity alternatives would align the left and right sides.
  • Actual diagonal, which also map to similar values with the previous point, but rather with real exponent, imponent, and empowering of the A or O scale, where the values of position or negation could be empowered.
Accents are having one or two components of functions down for IO, one or two dots for UV, one or two funtions up for AE, tildes for local favourable or local misfortune, also Ü or Ö as U value is upwards-directed would pass the zero in the middle, meeting with A.
Standard accent: on top of the letter, when only this is used it's possibly the average of all accents not written. Near standard: on bottom of the letter, introverted value is used. Complex: left and right side are used for complex. Infinity: diagonals mark the counterparts in infinity.
This means, accents add like 1 base, 2 typical, 4 complex, 8 infinity, or even 12 or 16 positions with bases, indexes, exponents imponents etc.

Accents

Accents are representations of mathematical functions trivially with the same form.
Letters and numbers can be used in place of accents when it makes it clearer, which is rather less normalized use but sometimes readable and interesting.
Typical combined accent is either one or two accents side-by-side at the same container position, or three-four on two lines, where the lower or number-closer line has the original one or two accents, while the typically higher accent or pair is one for simplified and two for more complex values in regards to infinity. Where 1-2 accents is local, Tish value, 3 or 4 is global or infinite, and initially not so important.
Lower accent of complex part of prev digit might form higher accent of next digit directly, such as A^ivO, with A and O being the digits, but i is the exponent of A, but also the Position of O as it's related to A as e-diagonal, but to O as a-diagonal. A^i_ivO has little space between two i's - meaning the same, the i's are now separated by small space I mark with "_", and "v" is not moving i into lower position of i, but to a - rather I use the opposite of exponent mark and it's not going to do this with O directly.
Diagonal and horizontal accents are represented as accents, while left and right exponent and imponent, as well as left and right bases and antibases are normally written with letters, containing the normal digits. The first of those are used to manipulate with coordinate systems and transformations - projection matrices and affine translation matrices through infinity space.
Where the top accent determines the "line", number can be written in one, two, four, five six 16 or variable number of lines, where each digit has it upper, before or upperbefore digits equal, but horizontally in numeric positions and vertically infrequential positions; compressed numbers might see them as distinct positions where the frequency is more powerful than positional mapping so basically the number is more or less equal to all lines written one after another with spaces or no spaces, mapping to topologically similar space; simplified number rather continues each direction repeating the sequences infinitely in all directions, but then averages the digits on each position; more complex mapping actually makes sense of of both the frequencies and positions - while they have the same numeric values as simplified numbers, the values form complex knots.

Basic Accents

This could implement the basic accent system, comparing to basic 6 of laegna, such as base-4 with U allowed.
  • Upwards-function of growing accent, one for A and two for E.
  • Downwards-function with single accend as O, double for I.
  • One or two dots for U and V.
4 functions up and down, with 2 u values; when they are both above and below a letter, the u values turn into four - for example, two dots above the letter might mean it's open in infinity, or moving upwards and crossing the line, while two dots below would mean the opposite; one dot above means it's rather unknown position of usually known value, and below it might mean it's not known by you.

Standard extended accents

^ and it's opposite looking like v, but above, have the temporary change, such as a good day, but cancelling.
Vertical, small line is mapping this as a solution.
Horizontal, small line as accent, is the V, but empowered - also an unknown, but also the problem then.
Tildes are like S's in accent, resembling it's global direction, when calculations are made locally, are rather reversing or to be precise, inversing in infinity.

Accents as digits

All these accents are the number space and additionally not only to letters, but also to words and even sentence - one can use accents to put them into positions in number space and projective transformations - all of the modify the number.

Number Space

With each digit, word or unit of organization - number has 1, 2, 4, 8 or 16 directions of accents positioning, and one can even create continuous system ustilising all dispositions.
For each digit, these digits exist.

Digitwise

Sometimes all the digits, such as denary system of number's axes, would be mapped and operations are done with separate axes; still, similar effects would come from number symmetries.

Number space

One dimensional: digits form a positional system from left to right Two layers: separated by spaces, each positional number is digit in higher space Two dimensional, position and line: number is matrix, with spaces it's second order (3-dimensional matrix of a kind) Fractal: the sequence is repeated inwards and outwards. Window: while the repeated sequence determines the actual direction of the number, an actual number is it's visible digits aligned to this fractal to infinity, and resizing the number by normal (velocity) or exponent (octave, acceleration) factors does not change the digit sequence compared to the length, so many operations would happen "in background", where the application or algorithm is rather trivial - you do it from your head, normally, in many known cases. Free number space: based on the actual number space, second spatial theorem of infinity, position, direction and size of each digit can be variable and exist in continuous space with unlimited dimensionality, even more unlimited as you can take advantage of any property of Laegna number space; these highly unnormalized numbers can represent very complex conceptions.

Conclusion of Digit Mapping

So we should have:
  • Number with selection of Bases, such as 1, 2, 4, 8 and 16. Relations of the numbers are known, such that we can index the relative sizes, for example not depending on number system, I < E, and there exists rather static coordinate system which is visibly just transformed, with some invariant qualities of numbers being intact; while in programming language, types are specific, in research and imagination one would rather do the transformations of given number space and see the metaphysical identity of the concept of the number, where the bases are quite self-explanative. -- Base 1 for representation of incompatible axes, where one is interested in numbers, which are powers between 1 and 4 of basic digit values. -- Base 2 for binary efficiency of small number combinatorics. -- Base 4 for simplest mappings of infinities. -- Base 8 for two-value (RTRTRT) representation of real and complex number spaces, with 4 digits per axe for complex and 8 digits for local and total axe combined for real numbers. -- Base 16 for integrated, readable representation of complex numbers and their math. -- We can see how bases evolve from each other, and while the numbers are different both digit values and their local relations are repeated, even if they form more complex relations between each others and in regards to the context of other relations; ponegative values, symmetries and mapping to many operations do not depend heavily on number types.
  • Presence or absense of U and V, the zeroes.
  • 8 directions of accents mapped to digits.
  • 4 or 8 directions of index, base, exponent, imponent, position, where the number is indexed.

General number attitude

The most universal number type would accept any digit, and properly map the dimensions - while some symmetries would be U, less if Second Theorem of Spatial Infinities are properly used to support variable digit sizes and not the fixed range of digits, we would get closer to language - where the size of a number position is in reverse for both acronyms and semantic words, but the direction of time is constant through all 4 possibilities of directions. Many-liners would have empty lines instead of spaces, maybe with 6 possible heights, the minimal height rather compressing the letters together than apart, but then counting seeming spaces as connectors of digits, and seeming contraction still as separator, because it's a space, even if negative.
If we are able to manage:
  • Each of the letter is involved in numbers.
  • Depending on the multidimensional projection, the same qualities account for different purposes, such as small and big letters could mean positive and negative in case of small and big decimal numbers, they could mean local and global scale of a digit in case of many instances, or separate the whole and the rational part of the number.
  • While certain properties change through types, other properties are persistenct and invariant to type changes or some type changes.
  • Positions, when written in Laegna numbers, could be also of different base, of IO being either downaccented or upaccented, and the positional encoding thus being able to come from negative to positive, for example the number AA would mean the first digit is negative (OA mapping), while for AA the second digit is rather probably upaccented posetive (AE mapping). Often, the bold and italic is not necessary, but the number symmetries are more important than their face values, which can be defined in advance.
  • While digits are combined in such way, they can be used for letters and numbers, separated by font, color, position, style or common understanding and context.
  • The number is encoded to multidimensional structure and the internal number representation of AI or low-efficiency programming environment would keep the number at it's face value of representation and decide the type rather based on calculations than number types.
  • It's interesting, which operations consider number types as invariants, and which operations depend on face values given the specific type; an AI, while needing some information in some of the cases, would do operations and estimations given less information; for example, with IQ and EQ (calculations involving the meaning or infinity calculations), number form is often enough to understand numbers, and their formal definition of type is not so important; intermediate operations would rather need unnormalized numbers, but in other cases we see differences in precision, scope and exact meaning, still recognizing the underlying archetype of a number. AI should be able to reason naturally and not depend on exceed of specification and other parameters; there are matters like entering the U or V, zooming in, rather depends on relative positions of them (where there are two possibilities) and does not provide so many qualitative aspects in dependence of the base system such as 2 or 4 - while, internally, some parameters are left open or they are U, the general chat is rather quite specific and any theorem of XYZ scales would hold anyway, so the definite base might be necessary only for some specific calculations, not for example to understand the octave.
So:
  • Try to find each dimension of digits
  • Map them so that in precision and exact solutions, there would be minimal dependency of actual number type and the numbers with face values could be mapped to coordinate systems, for example where I separate AAAaaa as being equal to AAA.aaa, but AaAaAa is rather different case - but if a is simply lower octave of A, this is actually a consistent form, as well as mixing some complex digits with generally real numbers, such as forming the words and the language, which is "poetic", but still closer to strict rules than it might initially seem - from many examples, one could see deeper theorem and rules than the ones I gave, where I gave rather the aspects of being blind, not hearing not sensing one or another thing, like Indian story of elephant and it's aspects (for example Kipling has a version of this story); rather, there are basic needs for number types such as signed and unsigned - in Laegna, similarly to Latin, while signed and unsigned numbers are different, for number like 132 you don't completely depend on whether it's signed or unsigned - if you want to substract bigger number such as 200, you can do it only if it's signed, but if you add or substract 20 you don't actually care; on some level of it's own, Laegna system is very similar, given that you reach the concept; digits, in decimal system, represent different values, but they are defined only once.
  • Try to find format-independent concepts and operations, as well as format-independent free imaginations based on number forms.

Subdigit frequencies

If f is half for IOAE, then OA is mapped to current digit, but IE behaves as OA on previous digit - this seems losing the combinatoric power as different numbers would have rather same value; rather, with accented digits often being outside the frequency, they do map something to previous or even next digit, rather than having a face value, which is compatible also to having actually the higher and lower frequencies.

Numbers and operations as variables

To control the number space:
  • Assigning values to numbers would map the axes and dimensions in a way to keep their properties, the most trivial, still expressive solution for such maps is used; generally, while they can be formally described, given some understanding of the goal it's often enough to have some examples, such as actual calculation with the real result in the number context being present.
  • Operations themselves can be modified, such as A * E = 10 would assume such projection system where A * E would rather stick to such property.
  • Infinity is way too powerful to assume anything other than often quite intuitive understanding and some higher-level set of assumptions or theorems, which generally hold, vs. the specific cases; we have, for example, a number of operations we can do, but only 4 or 6 basic operators - rather, we set some examples than formally describing everything (the latter would rather occur in strict, formal proof).

Alternative operators

While */-+·: might be used, a laegna-style latin system,
also an operator would consist of:
  • Little horizontal or vertical line in the middle of character.
  • Depending on it's type, one or two dots on left or right of vertical operator is + and - and their infinity counterparts; where one of two dots above or below a horizontal line would be exponential and imponential operations such as division and multiplication, with the infinity numbers of two dots connecting numbers from outside like 48 vs. 14.
  • For U and V, the line would have one or two dots on both sides.
  • Operators can be assigned values, decimal values, other operators or laegna numbers and accents; in each case it's converted to numeric value of the operator and IQ is used to convert a few relations into complete operation map. As operators basically are numbered: I for division, O for substraction, A for addition and E for multiplication, they exist in fluid number space and the factors can be changed based on number logic; it's more complex to apply them at once, and I rather intuitively succeed than already being able to express all the rules, but it's matter of time - while many relations are trivially logical for my own use, a small set of theorems is needed for special general case of digital numbers for programming or math, for example.
  • Truth value tables can be used for operations, to implement for example linear or exponential operations and understand the reasons of such linearity or exponentiality.

Alternative numbers

Despite I do not use this actually, the initial idea for Laegna number was a dot in the middle of the character being U present, and lack of a dot if there is no U, 8 directions from the dot or it's position would have lines depending on each value of aAeE being present or absent, and two dots in the middle or dot behind E position at topleft corner would be presence of V. Theoretically, this Babylon-style number would have more frequencies usable at once, but practically there are not many use cases currently it seems, and the standard numbers of current version of Laegna are more expressive.

Find some logical errors

Procon, est prookon: if the operation is divided in a way that negative aspects, similar to work or effort or the consequence, are removed, and positive aspects, such as the salary or reputation is assumed and demanded; fair distribution can lead to this when used as a labelling argument. Medusa, est meduus: If the operation or person is magnifiing their own losses to ensure insane ethical criteria, often attacking others and minimizing the importance of other numbers; also if bad karma of others is somehow produce by one on their own, creating obstacles to good karma, and then criticised. Isotope, est Isotoop: If the values, which need to be balanced and integrated, get the actual attribution of one being over another, such as some important goals are forgot and others are met in demanding way. Ositope est. ositoop - the similar case, where protection of the minorities would break in democracy, for instance, so that 51% would run into ositope and 49% would suffer in effects of unhealthy management and bad distribution of resources. Müü, nüü: müü is when you lose the reason for karma, hurting others - it seems to inevitably produce nüü over time, where you would lose your advantage and get hit by yourself without needing any particular activity; for example you think you steal money by asking it, but suddenly it's very unfavourable to support you in such way, until people simply become unable, which is the müü phase (mu). Fallacy of monolithic left wing (hea vs. hae, good vs. gaad): instead of using the L calculus to measure the common distribution of money, higher laws / honour rules etc. so that the left wing, in it's big cycle, would actually earn back and not just lose the money when mü is becoming nü, a common scale is calculated, which applies the same criteria to everybody - easily you happen to be in situation where you cannot help yourself, because your 100€ would be "fairly distributed" between million people in their daily activities, turning into nü where it's heavily demotivating you and enforcing to find real friends. It must be seen that Left Wing is compatible with conception of "Mind" or "R" as reprojected back into concrete space, creating an effect of being similar to actual business rather than only altruistic help, which is rather simplification of calculation than actual goal - while "Ethics" might be different, the "Ehtecs Thé" conception sees that without creating karmic cycle even on classical "flat aspects" of reality, where nothing can be measured, will produce the negative force such as bankcrupcy (consider Soviet Union, where the people suddenly got posetive, overestimating the distributive power, or capitalist effect where earnings from after the contract might not be properly paid back, but original contract is the measure, and thus very often it's meaningless to provide helpful ideas, inspiration and solutions or work - in case you manage to earn actual interest, it would be kind of "stolen" as compared to generative vision of leading the money back to it's sources, which properly should be more equal; posetives, people who would not pay you anything when you get old, are very needy about the "reputation" and "fair recognition", where one would like to help the world rather for money than for empowering some unknown structure).

Programming the Ponegative

Truth value tables

For multiplication and division, Truth Value Table would give it exponent (for division and multiplication) or normal number space - multiplication of two numbers equals to summing their R, where addition of equal numbers adds one digit to the R; while combinatorically classical operations seem to be used, the Laegna specific meaning appears from structure of number space, which is rather having many more properties.

Frequentiality to insane degree

Where the number meets it's linear value in infinity, resizing the numbers and doing operations, both it's frequency and ultimate dimension should be preserved; while it's hard to do manually and one would estimate the results, correct and precise operations would see both components in terms of linear direction.

Repetitive angles

For example, count O and A angles to the left, where A is 45 degrees down and E is 45 degrees up. At certain rate, the higher-octave number adds digits to the angles, but properly applying them as actual angles are added would create a straight line.
When we bring this to lower octave, the linearity of acceleration and decceleration representation with whole numbers is replaced with actual, visible acceleration and decceleration - where digits are ordered according to the effects in the sequence, sub-zero digits accelerating under and superinfinity digits accelerating over the number space, it's visible that the full angle from zero to infinity, or from minus to plus infinity cannot be represented in single point, where for example on squares only 9 angles are possible; for longer lines, indeed much more angles are possible but with given precision of the zero, where Laegna system is four, but one can combine digits - given the whole line it's keeping the same angle even if not visible locally, and having a certain acceleration factor; unlike the system of Gauss, which rather points to imaginary points in our sense where the coordinate space counts multipliers without point acceleration, in our system we rather use the points as if they were curved, accelerating inside, and for curve, for example, one side of the point would be shorter than another, so that for circle, inwards side is shorter than outwards side. Each continuous property of a curve is also present at it's points which it's passing.

Rules of Laegna Language

It's not a specific paradigm, but rather:
Blocks, either by intent like Python or {} like C family, which is not really given by general programming theory, will run cycularly, and nested blocks do this on IE scale of time, where linear sequences do it on OA scale. Where variables are defined, their ultimate values will be sent back when they want to do this or for some types, where they finalize the calculation.
Imperative and Logic notations:
  • R = 1! - this assigns new space for variable R, so that the logical paradigm would fit with the change of variable; the changed value is actually a new variable with the same name. Imperative flow of an algorithm is running those in order.
  • R = 1. - with dot, the logical value is assigned on symbolic basis, and the logic system keeps it resolved.
  • R = 1? - with "?", "?!", "?!", either variable is locally calculated ("?" makes it not lazy, but it also allows the use of "if" blocks etc); or with "!?" it's asserted to be true and fails in exception if not, with "!?" it would assume that it holds.
  • Truth value tables can be used to define logical operations, they might separate into complex multidimension or consider all or some dimensions equal, applying the same operation in each.
  • Truth value tables for operators: for multiplication, the operation combined the value space and positional space will create an exponent effect of using all the possible combinations of positional space, under one (a digit has internal position space contained in it's digit value) and over one (it has external position space contained in it's position), if you represent it with matrix of ones and empty cells, you see it's being combined in all combinations like a matrix in multiplication of it. For addition, you can see a linear effect of each number over another. Given that these are A and E factors, you can find intermediate ones - while E is infinity-directed and A is finity-directed, complex values are in between, above and below in degree of exponentiality; you are interested in continuation of these properties.
In any case, while: A = B + 7. You can also: B + 7 = A. To do the reverse direction. You can: A == B + 7. To do it in both directions.
You can use Prolog notation of A being used and a being calculated with the same variable "A" or "a" behind, or you can use things like "?a" being unknown, also you can use the fact if some variables are constants.
While it's allowed: x = sin(a). It's also allowed: sin(a) = x. When defined by capitalization: Sin(a) would define the variable a. sin(A) would define the function sin.
This works in both imperative and logical paradigm.
In cycular space, when you reach back, the values are accumulated and when they are bigger after circulating, they get acceleration - space separated notation can have Z and Y difference marking this rotation and X having the face value, and you can project this into normal space where the new mapping would turn them back into static variables with values.

Tens

Ten is in programming as follows:
Ten { Ponegation: ponegative value, which is not very much needed, would reflect the process of Ten in one ponegative, this is human readable. Different formats might resemble the conflict and resolution between local and infinity value. Tensor: a list of inputs to be optimized, potentially an operation of them, which needs to satisfy the ponegation criteria; this is enough to specify, what the optimizer could be - it can be Deep Learning, Machine Learning, simple optimizer like Newton's method etc.; it sets the goal to influence given variables inside their limits to reach the optimal solution, where the variables actually depend on their goal not their face value. O, A: setting O and A would set the past value for past condition, for past condition input "True", it would output O value, and with probe of input "False", it would output the A value. I, E: the same thing for future condition. Goal: it's either True or False, assuming to find either past and future satisfy the "False" condition, or them satisfy the "True" condition. Past and Future conditions: it might define exact conditions, and only in "if", "switch" or other selector of given conditions can change their value. }
[O, A] and [I, E] are frequential in given example. For both there is one condition, for example an if clause, and for each input, the output is written in given position. Same way, dictionary or list can be composed, where every index has a condition and is defined by this. This number is frequential as it has the output value in regards to every frequency, contained in the positional value, relating input to output.
For example:
// Tensor: any variable, which reacts to the pressure Tensor Floats: i, j, k
Ten x { Tensor = [i, j and k] // i is optimized, as well as j and k, where j and k for example might have "true" if both are true, false if not, and the positionals of untouched values could be used by other optimizers. In some implementations, tensors could have strict rules, but be under tensions from all dimensions where frequencers or Tens exist. OAFreq: condition a = true, frequencies [O, A] IEFreq: condition a = false, frequencies [I, E] }
Where Ten is like bit - the simplest case -, indeed systems with wide range of possible digit values and conditionals and tensors could be used.
if (a = True) { if (x.OAFreq): // The optimizer is trying the True position x = O // the local value does not fit else: x = A // this condition is resolving positively }
if (a = False) { if (x.OAFreq): // The optimizer is trying the True position x = I // the local value does not fit else: x = E // this condition is resolving positively // From this block, I and E propagate backwards - they reach back to original block. }
// This, as it comes after the IE modifier, would be used by next and not previous IE block, as OA does not propagate backwards. if (a = True) { if (x.OAFreq): // The optimizer is trying the True position x = A // the local value does not fit else: x = E // this condition is resolving positively }
This is the primitive programming block, which simplifies Tens - Laegna Logecs values. While it's typical to programming - when it's not an original structure of Ten, representing Laegna standards, it's rather "simple" in terms of programming and using the condition of such Ten, actual Ten can be calculated:
  • Assume Goal is "True", an actual ponegative goal being aligned with Truth being defined as a Position, which is typical to end solutions.
  • The case supported by OA frequencer sets the local value, either O or A.
  • The case of OA frequencer sets the ultimate value, either I or E.
  • Based on this, for example the IE value is used only if it would make the local variable fail, otherwise OA will remain.
  • In other possibility, for example running your operations to estimate variables based on local, OA value, whereas IE might arrive days later when the variable is decided. Then, rather than monitoring for change, one would watch for I and E and replace OA with infinity value in each case, but perhaps restoring the O or A if it does not let to change itself.

Functions

Consider Lisp: you are quite free to define any form of accepted headers for functions.
In Laegna:
  • Possibly, use of multi word variables is accepted, and we also accept the machine to be intelligent, while we are able to define - an AI would do something with non-strict parts of the language.
  • Function headers replicate the code and they can run code, make assumptions, proofs and conjectures or find the situation based on existing ones.
  • Inside blocks and functions, there can be synchronized flows of changes, where synchronization of "Threads" wants them to be repeated. For example, OpenGL block would contain if's, switches and loops without actual input, but just floating freely along with programmer - still, the illegal blocks are not allowed.
  • Iterators change dynamically, where the indexes are static even for deleted items of lists and dictionaries, where one would not lose the pointer in middle of preparation to change the variable or position in the list.
  • Index variables such as i and j can be used in place of loops, where they assume synchronized way of containing each value, for example where i is in AE and j is in OA, i=A, i=E combined with j=O, j=A would be used and each case i and j would be used as indexes, for example, it would iterate over the values.
  • Dictionaries and lists can have indexes separate, rather switching the pages and accessing the current member than accessing by member.

Vectors and Matrices

Matix M:
#M = Matrix internal value, actual matrix is in tool configuration accessed by "#" a, b = M(x, y, z) - this would make use of 2 * 3 matrix, with 3 inputs and 2 outputs, calling it as if it was a function Matrix, vector etc would easily map to functions, also the scalars, which are able to resize.
At face value matrix would run operations on each combination of their content, and functions and matrices would fit.

Infinite loops

Infinite loops are turned into linear applications, and while inside the loop there is infinity of digits, the result outside the loop is of higher octave.
Where relations of such infinities are unclear, the theorem of infinities is used: relations are mapped based that they are heads-up and have the necessary symmetries, and where they interact the actual symmetries are found.
The higher-octave number can be fed back to infinite loop, setting it's value.

Theorems and conjectures

Lower optimization levels pre-calculate and avoid local complexities, trying to be rather linear than exponential; they see errors in advance. Higher optimization layer would add dynamics to the same syntax and more easily allow things like undefined variables etc.

Execution order

Where IO of functions are dependent of each others, they are connected.
While the input of the function does not depend on output of previous function, it's not connected.
Function headers can match to complex situations, where multiline code is also considered to call functions once those are recognized:
  • The functions would make conjectures and prove theorems.
  • They would use conjectures and theorems.
  • Programmers would mind, which ones are known or simple for the computer.
This is, we define:
  • Code templates or function headers, single or multiple commands together or apart, including patterns to find especially to prove theorems or apply the rules.
  • Based on this, define expected behaviour or prove theorems or assume the criteria for a conjecture of theorem is met while we cannot prove it easily.

Computer

Large middle screen. 8 small screens around:
  • On top, "acne" or the screen for environment control, where there is AI chat and the window system control and execution of programs.
  • On top left, the calendar is tracking the changes like Undo, Version Control etc., and trying to create the logics out of it to control the flow.
  • On top right, the Map allows to analyze spatial structures.
  • On left, there is the toolbox, which allows to control and create the user interface, add buttons to programs etc.
  • On right, the view, which allows to control layout and design.
  • Below, the terminal, which gets rather structured commands and likes textual output or log.
  • Left below, the Math, which recognizes numbers and words or sentences as numbers, allows to explain the reason (add the calculation to actual number) and to change the mathematical aspects.
  • Right below, the Dictionary and Code / Note editor, where one can run into definitions and algorithms related to ongoing process.
The directions are fractal and many things can be emulated by an AI.

Geometry and coordinate systems

The simplest and most typical: AE IO Also the complex of 16.
In each case:
  • Mapped on sphere, where all types of coordinates of sphere can be converted to number and back. Fractally, the digits repeat in the same symmetry and directions. As in numbers, the value is either the limit, such as E!, the whole area or a random point, or unknown point.
  • Complex number creates more dense structure: -- Of similar mapping to sphere. -- Of dimension, where real part has the given mapping to sphere, and complex part has the distance, size of that sphere, so that 3D can be mapped. -- Transformations allow, more or less, to show different dimensions mapped to 2D and 3D with some loss of quality, but some precision so that we could imagine complex spaces, they are topologically quite equivalent, but problem is the information density or dimensionality, where the higher dimensions get somewhat distorted, projected to lower dimensions - still, this is nearly what we have and with clever selection of projections and movements, such as making front-facing side less distorted in expense of other dimensions, would make it very interesting.
  • Map to circle.
  • Map to square.
  • Map to ideal number space and ensure the unit sphere and unit circle and unit square are available.
  • Find: repetitive number (the sphere), the infinite number (sphere with each direction continuing as if the position was not repeated), map octaves, frequencies, and growing spaces into those; for example one can zoom in and out with Z and Y, which is progressive and allows infinite expansion of the dimension, but one can also repeat the directionality and going into this direction definitely, even beyond the U and V in strict direction, find more depth in the dimensions.
For an AI:
  • Initially more trivial spaces are needed.
  • See the number types in 2D and 3D, or 1D or higher D dimensionality, learn the coordinate transformations and relations in Laegna.
  • Such are rather multidimensional number types.
The AI would need to:

Database

Easily, each class could be associated with table of similar objects, either local or global accessibility;
Database items are equal in memory and on disc.
Files contain source code, data element or actual design view, and they are active:
  • AI is going to raise precision of them.
  • They have karma to be useful to others, while preliminary results are initial, they are constantly refined.
  • Algorithms and calculations are shared, common effort is automatic.
  • Each solution, then, exists on hard drive or memory and becomes more and more precise.
  • Files can be linked everywhere, getting different roles - dragging and dropping a file would create a link. Folderlike structures can be inside files, file structures inside folders.
  • Files can have APIs for different programs to access, and generalize well the different document types such as ones having single-page canvas, multipage canvas, ordered or free positions, but each in regards to possibility to add different widgets and elements.
  • Files are not structured as tree, rather they can exist as links in different places, and are rather garbage collected othewise, where history keeps track of many things. They can have owners or parents, or friends.
  • File size is rather not static, but in addition to it's real size the file has some more size for operations and groth, where user is heavily warned if they are adding so much things that the temporal structure of the file would get destroyed, rather it wants to keep the results of long calculations.
  • Computer is either heavily used, resting or solving the formulaes.
  • Process is seeking optimal solution tracks, spending time to resolve the simpler combinatorics and taking speciall efforts to resolve some of the more complex ones; it's trying different routes, but giving up if it's taking time, and creating algorithms to solve them faster and more inherently.
  • Running programs can also be seen as files, so that you don't necessarily completely close the program, closing the computer.
  • Hard drive has 5 seconds or 30 seconds battery and local fast memory to store some data before closing the computer, so it's less able to lose your information - it rather works and efforts forever.
  • Users share their results of work, such as solving a grand matrix by AI.

Relative and absolute numbers

Relative numbers have additional digits only for precision, and rather use spaces for actual change of numbers: A% would equal to AAAA%, and % is often omitted given the number type.
Absolute numbers:
  • Either R is changing the distance and the value is changing the direction, where dimensions are contracted so that it's higher-dimensional linear.
  • Compressed number looks more like classical decimal number and given the Laegna rules, while it cannot guarantee that EE is E in power, one of the basic definitions to handle the more relevant small numbers in context of solutions (larger numbers are important in intermediate space); while it does not resolve into such symmetries, it can still do some of the frequential number, and be used for indexing; especially decimal system is often compressed like this. There are certain mathematical symmetries, which persist.
  • In some cases, R only makes the number more precise, but smaller number of digits is only used for generalization.

Reversion

Functions, matrices etc. would define their forward-value, but then either automatically or manually the backwards value, for example x = y(n) forward-calls y, while y(n) = x would backwards-call it.
Then we have 4 directions:
  • Function is called forwards, the normal value.
  • It's called backwards, the reverse value.
  • Forwards call affects the past values, where from a => b it follows !b => !a for example. Additional Truth Value Tables work backwards to have certain operations.

Mission

Ideally, for an AI the whole set of the following is needed to make it able to use Laegna numbers:
  • Base 1 numbers: The value a or A is repeated, and count of the digit is the value of number, positions are in the same format or in 4-based format.
  • Base 2: OA, oa, combined and with or without U are created.
  • Base 4: IOAR are used.
  • Base 8: Different formats of Base 8
  • Base 16: Different formats of Base 16
  • Exceeta (the number space): XYZ and combinations are done, and applications where they modify the octaves of each number type are there.
Order:
  • Initally, most trivial counting numbers.
  • Then, operations of them.
  • Then, accents, exponents, bases etc.
  • Then, complex transformations of number spaces.
  • Multiline numbers.
  • Perhaps also the free number spaces.
This would be generated:
  • Lists of numbers with small number of digits.
  • Lists of random numbers.
  • All operations with small numbers, and operations with random numbers.
  • The cards of numbers: -- The number is generated -- It is analyzed as if it was of different number types
Generalizations:
  • Ponegative values are queried, where not depending on number type often one can calculate with them and find values or relations.
  • Things like I < E rather hold not depending on number types, also many relations.
  • Based on number and operation appearance, guesses are made.
Programming Language:
  • Examples of possible implementations, real and pseudocode is generated.
  • The computer can see the code, either pseudo or actually working, and solve the ponegatives based on the code implementation.
  • It would convert numbers