Sierpinski gasket, Pascal's triangle, and IC

[lightofreason]

This is a 'transfer' of discussion in another thread regarding not having to learn Chinese to understand the IC in that the IC is a metaphor for something 'deeper' - namely the method used by our species to derive meaning by encapsulating noise to generate an ordering of categories used to describe 'all there is'.

Our brains, your brain, our disciplines, your personality etc etc etc are all containers that capture noise. In that capturing an order emerges that allows us to share meaning etc through all languages having the same underlying meanings. There is hierarchy involed as well in the form of containers in containers - and so a movement from general to particular and so increases in specialisations.

To see the pattern than comes out of capturing noise, google "chaos game".

To see the relationship of the IC to this pattern (the sierpinski gasket) search Pascal's triangle.

If we colour the odd vs even numbers in that triangle you get the sierpinski gasket. The I Ching is derived from self-referencing of a dichotomy and as such the yin/yang line representations reflect the binomial theorem (aka pascal's triangle) where A=1. B=1, n=6 in the equation (A + B)^n = this gives us 2^6 and so the 64 categories of hexagrams.

Since ANY containment of noise will elicit the same generic structure, and local context will then 'customise' things (unique labels etc) - the generic IC reflects the order that comes out of encapsulating noise. As such the IC is applicable to ANY such encapsulation as a source of analogy/metaphor in describing the content/dynamics of what has been contained.

The encapsulation and 'bouncing around' of noise inside the container reflects self-referencing of a dichotomy, it feeds back onto itself. Our nature is such that we are not symmetric but more asymmetric (X <= Y) and so cover symmetric and anti-symmetric.

Of note is that our brains are focused on processing frequencies and the best form of arial to pick up frequencies is in the form of the sierpinksi gasket!

 

[martin]

Site software confused? I try to post something but it ends up before my earlier post ...

 

[martin]

drop down levels in the hierarchy and we see lots of dynamics going on - consider the dynamics that make up what you are seeing - the massive number of distinctions made to give you a moment of sight; the tens of thousands, millions of neurons involved in by the milli second so I dont agree with your concerns.

Sure, a massive number of distinctions, but it is not at all clear which role recursion plays in visual perception. Is recursion essential? How important is it? There is a lot of debate about that.
Same with other tasks, such as learning a language or understanding language. One thing seems to be clear and that is that humans can't handle deep recursion very well in understanding language. They soon get stuck. Perhaps because of limits on the capacity of our working memory.
With so much uncertainty about the role of recursion, how much recursive depth the brain is able to deal with (probably task and level dependent), etcetera, etcetera, we cannot be very sure about the fractal nature of it all, I would think.
I wonder, btw, if deep recursion, beyond say level 2 or 3, has any survival value. Do we need hexagrams to survive?

(This post ends up in the wrong place for some reason. Retrograde mercury?!)

 

[martin]

Hmm, all very interesting but ... there are only 5 recursions/iterations in a hexagram and that is by far not enough to create anything that even begins to look like a Sierpinski gasket or any other fractal whatever.

You need big numbers for some order to emerge, many iterations, structures with hundreds or more lines instead of hexagrams.
Who is going to write that I Ching? GigaConfucius?

 

[lightofreason]

Hmm, all very interesting but ... there are only 5 recursions/iterations in a hexagram and that is by far not enough to create anything that even begins to look like a Sierpinski gasket or any other fractal whatever.

You need big numbers for some order to emerge, many iterations, structures with hundreds or more lines instead of hexagrams.
Who is going to write that I Ching? GigaConfucius?

look at Pascal's triangle - colour in odd/even (yang/yin) and out pops the triangle. Basic (A + B) ^n (also note that the IC covers 2^12 and is easily extended - as I have emphasised in the context of compression of meaning - IOW we flesh it all out and then compress - which is what RNA/DNA dynamics do - curl it all up.)

Each level of compression is usable in its own right to communicate - and so we can communicate using representations from 2^12 as we can from 2^1.

drop down levels in the hierarchy and we see lots of dynamics going on - consider the dynamics that make up what you are seeing - the massive number of distinctions made to give you a moment of sight; the tens of thousands, millions of neurons involved in by the milli second so I dont agree with your concerns.

If we review the nature of 'thingness' and so an object, concept, notion etc the nature reflects positive feedback emerging form negative (yang from yin). If we review the information processing 'up' the neurology to the brain we see levels of frequencies serving as constructors of patterns at the next level but each level is slower than the previous, reflecting delay in gratification, in making the 'point', the 'thing' identifiable.

This dynamic reflects oscillations across the positive/negative feedback dichotomy where from the negative comes the positive that in turn, when related with some other forms the negative etc etc (yin-yang-yin-yang...)

Libet has shown a consistant 0.5 second difference between working with consciousness vs working from instincts indicating there is LOTS of time used to get a word/symbol formed and recognised by consciousness.

Finally note that the general-to-particular dynamic means we move from a 'vague' form to a 'crisp' form when using fractals with each level of precision usable to communicate meaning - thus level 1 is A/NOT-A, level 2 is digrams, level 3 is trigrams and so on -- all usable to reflect meaning.

Your focus on numbers is too precise, we are dealing with qualities, the language of the vague and there is enough to allow the gasket dynamic to function - as we can be the binomial theorem out of the gasket and the IC out of the theorem, as we can emotions etc I see no issues re the gasket influence.

This also covers containers in containters, we move from the general to the particular. The 'fractal' is in the form of the dichotomy self-referenced to elicit qualities usable to communicate in general.

The general neurology operates at 40-80 HZ. - we can react faster than we can think. Move up the brain and things slow, we move from 80/40 to 20, 10, 5, 2, 1 etc - we use gearing to slow things down and so increase delay to benefit decision making etc, being discerning.

For the full set of categories we have POTENTIALS that then get actualised in an ad-hoc manner and so not all is available - we see here the patterns of EPR at work - keep firing distinctions (A/NOT-A) and over time a pattern emerges linking all of the dots ;-)

Chris.