Triangles And Sequences

Any sequence can be represented by 3 numbers. Therefore Triangles Are Best At Representing Sequences. In fact, Triangles are the “Essence” of A Sequence. Notice in Face-Recognition Technology and Topology in General, the Extensive Use of Triangles. An Origin for the Triangle is Needed to Define the Beginning Of the Sequence.

triangle

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On Numbers

In my previous post On the Alphabet I discussed the inextricable relationship between the alphabet we see around us and numbers on a sub-conscious level.  In fact, it is my belief, that all of human experience through our senses can be translated into numbers on a sub-conscious level.

Sound

The simplest example of sound being converted into numbers is music.  I thank my friend Shaw Han Liem (a.k.a I am Robot and Proud) for this insight.  Music exists on an alphabetical scale, A=1, B=2, C=3 and so forth.  Each note therefore, can be mapped to a letter, with small variations introduced by flats and sharps.  You can therefore translate a melody into a series or string of numbers, B-C-D would become 234 and it could exist in a key, like C major.  Interestingly, C major which is tied to the number 3, has always been a special number in holy books (ex holy trinity) and numerologically (the favourite number of Pythagoras and the triads).  Perhaps this is one of the reasons that C major is the first key music students learn and also a very popular key to compose and listen to music in.

Another aspect of music is rhythm.  Most music is rhythmic, which introduces a subconscious numbering that “shapes” the overall flow of numerical information in the notes.  It makes music “digestable”, but why?  It is my feeling that the subconscious processing system as I described in my last post operates on a synchronous clock, determined by the music.  Much like a processor, asynchronous information is processed at the pace of the clock, determined by the beat of the music.  We all have an internal clock, some people have a stronger sense of the passage of time than others, but for the most part all people have a sense of the pace of time.  This clock syncs with the music’s rhythm or beat to process information or “instructions” in digestable chunks.  Interestingly, 4/4 time happens to be the most popular rhythm which is based on the human heart beat.

The “subconscious clock” I speak about is deeply rooted in our nervous system, there is the sympathetic and parasympathetic nervous systems that together regulate our overall mode of operation.  One is synchronous and the other is asynchronous.  Music stimulates and works with both systems.  This is why in human speech, what you say is as important as how you say it.  Tone and the pace at which you speak in Western languages can convey emotion, different states of mind and so forth.  Interestingly, in Chinese and some African languages, the tone changes the meaning of the entire word all together.

When we listen to a song, which combines music and lyrics, we are receiving all kinds of numerical information in our subconscious through the tone, rhythm, meaning of the lyrics and spelling of the lyrics.  This is processed by our subconscious processing system and the “output” is insight and feelings.

But nature also has a rhythm, determined the day and night.  Perhaps this is why we refer to it as a circadian rhythm.  All living creatures live by this rhythm, behaving in a asynchronous musical way, which is where the root of Taoism comes from.  Next time you walk into a forest or even the park, contemplate the sound of the birds, the playful sound of happy children, all chiming away to the rhythm of day and night that guide our lives existence.

Vision

It has only been recently since we’ve been able to ascribe numbers to colours.  Nowadays, a colour can be described from a limited palette in RGB terms or similar numerical systems.  Lightspace descriptions as pioneered by Steve Mann offer a much more “real” representation through a larger number space to describe a given colour, however even these representations are limited by computing power or available memory.  The fact remains, that colour in terms of numerical experience of the world are infinite.  There is no one blue, there are an infinite number of shades or hues of blue.  When it comes with most colours and numbers, colours represent the concept of infinity in the numerical subconscious processing system.

However, that does not mean that colour lacks symbology, quite the opposite, colours are incredibly symbolic as I have discussed before.  Blue can represent the sky or ocean, and all the vastness and imagination that is with in it.  People sometimes say they are “feeling blue”.  Feeling red implies anger, love, passion and so forth.  In fact one of the most popular colours in the last few years has been wine red, which is a combination of purple and red.  Purple represents royalty and red represents humanity.  Arguably such a symbol may represent the idea of “Royal Humanity” or if you are religious, “Royal Jesus”.  I would argue that the output of the numerical subconscious processing system is in fact a colour denoting a feeling.

There is one unique case, which I think has some significance, where a colour is linked to a number and that is the colour green.  Green in Chinese (綠), in both Cantonese and Mandarin, has the same exact pronunciation (including the tone), as the number 6 (六).  In Cantonese it is pronounced “look”, which is interesting because we are most sensitive to the colour green in our vision from our early ancestral days in the forest and jungle.  It was important to distinguish between poisonous plants and predators.  Subconsciously, on a collective conscious level as Jung would describe it, we associate green with the number 6 in the numerical subconscious processing system.

Taste and Smell

Taste and smell are similar to vision in that they contain the concept of infinity for the subconscious processing system.  However, even still, when you taste or smell food it contains the summation of all kinds of numerical information determined by the amount of time cooking and the various amounts of ingredients used in the food.  Just like vision and colour, it is a result of a summation of various amounts that vary over an infinite range.

On the Alphabet

The alphabet is more than a string of letters.  When the alphabet as the phoenicians used to write it, each character mimicked an ideogram that was in turn was based off hieroglyphic symbols from the Egyptians.  The subconscious mind of readers and writers of this ancient alphabet would therefore have all kinds of symbolic associations with each letter in a typical word, sentence, or paragraph they read.

But, there is another aspect to the alphabet and alphabets in general which make them interesting.  More particularly, most alphabets have a specific order to them.  The ABC song which children are forced to memorize at a young age contain the order of all of these symbols, A is the number 1, B is the number 2, C is the number 3 and so forth.  Therefore any string of text can be converted into a series of numbers.  In modern terms, the alphabet is a mapping for the subconscious mind between letters and numbers.  Next time you stand at a busy street corner, with flashing signs and store fronts, as well as ads, consider that your subconscious is really digesting numbers in addition to all the symbolism associated with the letter itself.  I first stumbled upon this idea when I heard that the Hell’s Angels refer to themselves as the 81, H being the 8th letter in the alphabet and A being the first, 1.

Fundamentally, all of us on a subconscious level translate between letters and numbers and vice versa all the time, along with all the other translation of symbols around us into numbers which I have explained previously.  Our subconscious minds crunch this information and give us insights, or intuition, on what to do next based on the number crunching.  Once symbols have been converted to numbers, they can be represented in binary, the lowest base in mathematics.  It is from this insight that I believe the subconscious mind works in binary terms and the conscious mind works in ternary terms (yes, no, maybe).

One must remember that when humans existed in nature, in the forest or jungle, there were less numbers or symbols to crunch.  The artificial environment that has been created around us, is I suspect, a result of people who consciously “set the rules” which everyone agreed upon.  Take the symbol theta for example, it represents an angle in mathematics, who decided this?  And does it have to do with the position of theta in the greek alphabet?  When you see an equation in mathematics, it is rich in symbolism and perhaps even numerology, based on the transcription of letters to numbers.

Another aspect becomes interesting with using the Alphabet as a basic general “cypher” that decodes letters into numbers, the same can be done by sharing a different cypher one which is based on simply shifting the order of the characters or introducing a different ordering to the standard alphabet.  Sharing such a secret cypher amongst a group of people allows for even more private, secure, communication.

Perhaps companies like Alphabet have the answer.  😉

 

N Value Based Logic and Neural Networks.

I had a discussion with my friend David Ha who is a Google Brain Resident at Google and he suggested that beyond Ternary logic and computing systems, N-Based logic and computing is being developed matched to the corresponding data set and application for neural networks and machine learning.  He believes strongly that neural networks and machine learning will function optimally with “non-binary codes”, by going N-valued.

Here’s some further reading:

https://arxiv.org/abs/1609.00222

Also from the ICLR, a well known conference for Machine Learning:

https://openreview.net/pdf?id=ByOK0rwlx

The great thing about N value based logic is that because of turning completeness, we can implement these systems on binary computers.  However, my feeling is if the hardware is based on ternary systems this would be optimal.

Ideally, it is possible to implement ternary computing through photonics.  The two polarizations of light representing binary and darkness for the unknown.  If we could do this, we would have neural networks computers operating at the speed of light.  I have presented this idea to my class mate and talented Prof at U of T, Joyce Poon (j o y c e . p o o n @ u t o r o n t o . c a).