Processing information with motifs

The axiom of identity states that For any "thing" (A = A) & (!A ! = A), which means that a thing is itself and not what its not. this is ubiquitous about nature and as we will see also expresses itself among the distribution of natural things as patterns. it is important for us in the field of AI because it introduces a complement to the hebbian factor which is that that things seemingly not related actually correlate. if A = A represents the hebbian factor (a thing is coincident with itself) then the other part would be !A != A (a thing is not coincident with what its not). But we see some more information than that last present in the complement. It fully contains all those elements found in A=A within its structure, i.e there are two A's in its expression as well as an equal sign. This should lead us to need to express it more appropriately as "a thing is coincident with those things that are not coincident with itself" . but that does not make full sense ,so we have to add a separating principle. This we call a set of dimensions.In the universe we have as these dimensions the dimensions of space and time. so in it we have "different rocks" separated by space for example. Note that there are two words there . "Different" which is clearly (A !=!A) and "rocks", an umbrella term which implies sameness or A=A. If we zoom into that sameness i.e. we take an individual rock, we notice that it has some "different textures"...those two words again and each texture has "different location" on the rock.....this analysis goes on forever. in nature , a the same species occupies the same niche, and "different species" occupy "different niches", We could zoom into both of those sameness's, i.e. the species and the niche, to point out that each animal eats "different instances of the same food" and each niche has "different constituents". In the weather, two places with the same weather will have "different wind dynamics", and each gust of wind will have "different direction"...this goes on for ever. We may ask what use may we make of this. Well if you look in nature , this distribution of sameness and difference seems randomly placed, but is not, its just in "different places" in "different ways"., What this means is that we may build a kind of causal model. The reason some places are rocky, is BECAUSE other places are sandy. If the rocky formations were not there , neither would the sandy regardless of whether they exist in the nearby locations or not. This is a bizarre consequence of this rule, just as the reason you can read this text is because it and the background have "different colors". Humans have picked up on this "different sameness" principle , and it is understandably ubiquitous in everything we do. including the very thoughts we think. In music and art the practice of developing motifs is fundamental to it. A motif is a different instrument playing the same rhythm. Or the same progression at a different scale....this is where creativity is defined. In how much you can change (differ) the same thing. The structure of mathematics also follows this rule. duality has been observed in many branches of mathematics where we have "different branches" exhibiting "the same principles".. If we are to go back to music we realize that the circle of 5ths is a result of this rule. Were we given a particular way to create notes, and we chose a 12 note based scale , then the 2-5-1 progression would be the one that maximizes both difference and sameness within the scale. The 2 is at one end of the progression. The 5 is furthest away from it, i.e. most different. (because an 8 will actually be modular closer to 2 than a 5) and then the 1 is again very different from the 5, but in a different way from the way the 2 was. It is NOT a coincident that this is the most pleasing progression in music. note that were we to choose a 17 note scale we would define pleasing as another type of progression that maximizes difference and sameness within the context of that scale.And we would not necessarily choose the middle of the scale and its "edge" because we would need a holistic approach that considers the maximum divergence between each note that forms a circle (i.e gets back to where it started) , and that might ultimately mean something else. Now we take this to Artificial intelligence. We know we have the hebbian principle which is equivalent to A=A, but how could we represent the alter ego A !=!A? well to start of with, we know that what we must do is represent the same thing differently, and it must be different in the same way. so here is an example algorithm. for creating music.with just a piano for a start. given a scale and a piano. 1.Pick a note at random. 2. pick another note at random and play it 1 beat after the first. 3.copy and paste these two notes all across the whole song. { the first note represents A=A and the second represent the same piano at a different tone, A != !A} this is the lowest resolution. 4. move one resolution up and consider the first two notes of the song.and group them together. 5. take the same time length a step wise across from those two, i.e. the second set of similar two notes in the song and change them by making them oppose (differ from )the second two. { so if the two notes went up from c to g we get two notes from g to c in the next half bar.} 6.do this across the song for every second half of a bar. 7. take the top two notes of both halves of the bars in the song , i.e. the top notes here are g, and move them the same distance apart in different directions. So we may have one half now being c to a and the other f to c. 8. perform 5 to 7 for the bottom notes. 9. copy this bar to all the other bars. { then we move to a higher resolution} 9. group the first bar together.replace the second bar with its different sameness. This will entail grouping those notes that are equivalent and separating them by an equal amount from each other modular within the scale. this may introduce too much difference so we only change exactly half of the material, whichever half. Then we do this for the whole song, i.e. all the bars. To do this with more instruments we simply do the same process within the space of frequency ranges, and to make this more expressive we may choose to be dynamic in which symmetries we want to create and remove, but it is important that the distribution of resolutions of symmetries is also symmetric across the song. Note even the individual frequencies in the piano can be arranged this way. Given a frequency range the algorithm should come up with the best way to populate it , given the different sameness principle. One might then ask what type of music would this generic algorithm make. the answer depends on the scale and distribution of different sameness's. That is what "A" training regime would optimize. But how would we train it. Music has a type of quality and that is a consequence of the circle of 5ths. The circle of fiths as i explained is a function of the axiom of identity in its fullness. it also has a mathematical duality. The particular chromatic scale we have ,was chosen to have just enough notes that the separation of two individual consecutive notes is as close to a number with an integer denominator that is smallest as possible. That happens to be pleasing to the ear.what it also means is that the progressions where chords differ by a number closest to a number with an integer denominator that is smallest as possible is also the most pleasing.And when those two clash we preffer the chords ordering over the individual note ordering. And ultimately the song whose elements differe the least from a that number is optimal even when that means its elements dont follow the rule. That is another way of deriving the circle of fiths. Were we to create a scale for NLP so to speak, where each word was a note.. We choose a basis for preffering a particular next word after a first..that extends and depends on the prefference for one sentence after the next. just as you may choose two notes that differe the least but will change so that the prfference of chords that differe the least is met given the closest note separation under that condition, so you have to change the particular notes for the chords to optimise this, we train the system with the goal of optimising a certain separation of the notes/words which are represented by a the closest rational with an integer denominator.We will learn the actual numbers through training, but moving from chord to chord (sentence to sentence )needs to happen by moving towards the smallest divergence from a rational with a small integer denominator. This will set up a type of circle despite the fact that the notes may not be evenly spaced. So when given a set of utterances/chords we use the "circle" of the scale to select the best response. To do this we need to be able to train for its setup by modulating the actual denominators needed,and the order of the words. If this is clear i will explain how to do this.