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The following is from a different list I am on - but relates here to the I Ching as a universal form where I have been enquiring re the use of XOR in recursion etc and came up with this.....
(just to keep those interested up-to-date in the XOR operator use in extracting 'parts' from a hexagram etc)
---------------
Just a small update from this afternoon's readings.... thanks to prompts from those on the "Society for chaos theory in psychology" list. My focus has been on identifying the source of how the XOR operator is aiding in extracting parts information from a set of recursively-derived categories.
Val's reference to laws of form prompted me to go back and start a 're-read' - beginning with Kaufman's "Self-reference and recursive forms".
Whilst doing that I realised that Kate had asked me about feedback.
Without combining the two I would not have 'pondered' more over this casual "yeh we know that" paragraph of Kaufman's
"the concept of feedback is normally associated with a system that can be decomposed into inputs and outputs. The feedback is 'feeding back' of (a transform of) the output into the input. This results in circulatory and recursive patterns in the system. Under appropriate conditions, the recursion settles down to a steady form of interaction" p59. J. Social. Biol. Struct. 1987 10, 53-72
so what?
My original focus here has been on understanding of a discovered property of the XOR function when applied to categories derived from the recursion of a dichotomy. The REPRESENTATION of those categories has been in the form of bit patterns, where each bit reflects some 'input' from a level of recursion. e.g. 001 means 'nothing from level 1, nothing from level 2, something from level 3' OR 'integrating from level 1, integrating from level 2, differentiating from level 3'.
We could use wave forms with each level being a marker of cps measured as 2^n cps where n is the level from 1 upwards. This would use constructive/destructive interference patterns to give us a waveform representing the quality)
so what?
To **IMPLEMENT** the XOR function in the neurology required TWO neurons in that we need a feedback system to do it.
IOW the XOR function in our brains ensures, guarantees, DEMANDS, recursion to be a fundamental property of extracting information from the 'complex', simply due to the fact that to implement it we need feedback (NOT the case with AND, NOT etc)
With the recursing of an ASYMMETRIC format (axons = FM (pulse), dendrites = AM (wave), FM/AM = differentiating/integrating dynamics) that allows for the application of recursion to itself (using the XOR operator). It is this XOR methodology that (a) ensures the whole is encoded in all parts, and (b) allows for the extraction of a particular through the use of masking the bit pattern of category A with the bit pattern of category B,to bring out a description, by analogy, of the result in the form of qualities of category C.
What is indicated here is that the AM data at the dendrites is XOR-ed into parts, pulse data, by the soma and transmitted down the axon in a REVERSE ordering of general-to-particular to ensure building of data context-to-text. Given a context so more information is limited using energy conservation, we just add 'bits' to the top as needed once the bulk has been transmitted to set the 'ground'.
Zoom up to the hemispheres of the neocortex and we seem to see this same sort of FM/AM 'dynamic' but now applied to complex thoughts etc due to the increase in bandwidth as we move from neuron to whole brain.
From another source, to instigate a memory system you need at the fundamental level the XOR operator. IOW memory is fundamentally recursive in form (since XOR requires recursion and memory requires XOR it follows that memory will be mapped in a recursive manner - which is what IDM covers - the template for meaning etc)
Feedback means using the past to aid in the perception of the current and/or imagination of the future. In IDM this is mapped to the 'dimension of precision'. Here we have:
(a) NO feedback, each moment is 'unique'. representable as ...1,1,1,1,1,1,1,1
(b) feedback limited to the last moment, scale is immaterial. ADD the moments to get, ...1,2,3,4,5,6,7,8 - a beginning of 'sequence' and the AND operator - linkage.
(c) go back the last TWO moments - ...1,2,3,5,8,13,21,... the fibonacci sequence
(d) go back the last THREE to get the tribonacci sequence and so on.
(e) given a FINITE bound, as in a 'beginning', then go back to the beginning and we get ...1,2,4,8,16,32,64...
In image formats - at the level of the fibonacci sequence we have a cicular spiral pattern. At the level of the binary sequence we have a square spiral pattern - inbetween are all of the 'variations on a theme'.
BEYOND (e) and we move into complexity/chaos dynamics (Verhulst, Mandelbrot et al)
The focus on PRECISION means that each of the above sequences serve as positions for interpretation of reality -some will do it through patterns of the fibonacci, most of us do it through patterns of the binary (or 'beyond' - i.e. use of imagination where we put in 'extra' energy that destablises, allows for 'emergence' etc)
The RECURSION of a dichotomy is covered in the binary - what about the others? Their recursion is of fractal dimension. The range is 1.6^n to 2.0^n (less than the fibonacci sequence and there is little or no 'growth'. Beyond 2.0 and we get into complexity etc) For high precision we have to use the realm of the binary, the exclusive OR. The tightness of the spirals is determined by what number PAIRS are used out the sequence to create the spiral. (using the fib pattern as an example - 5/8 is wide, 13/21 tighter)
I still have not reached the EXACT, formal, description of what is going on but it looks like this:
Given:
000, 001, 010, 011, 100, 101, 110, 111
where these are recursed from the 0/1 dichotomy, if I then apply recursion to EACH I will get the same patterns I get when I XOR the whole set of qualities with each. I apply recursion to each by 'bit flipping' - we step through each quality's representation using binary number patterns. Thus to 'flip' through 000 left-to-right we have:
000, 100, 010, 110, 001, 101, 011, 111
IOW the link of recursion to XOR means I will get the same patterns be it applying recursion to each quality or just XOR-ing all against one. The DIFFERENCE here is that the use of recursion just gives me a 'parts list' ordered by analogy (an AND format), whereas the XOR gives me the X-ness of the particular property A expressed through context B in the form of an analogy to property C (since the language for a row is finite and it is supposed to describe 'all there is', so analogy/metaphor is the 'preferred' form of description).
I have used 'bit flipping' before to describe things but did not equate the need for recursion to create the XOR operator in our brains and so the association of 'bit flipping' (recursion) with XOR-ing.
Chris.
(just to keep those interested up-to-date in the XOR operator use in extracting 'parts' from a hexagram etc)
---------------
Just a small update from this afternoon's readings.... thanks to prompts from those on the "Society for chaos theory in psychology" list. My focus has been on identifying the source of how the XOR operator is aiding in extracting parts information from a set of recursively-derived categories.
Val's reference to laws of form prompted me to go back and start a 're-read' - beginning with Kaufman's "Self-reference and recursive forms".
Whilst doing that I realised that Kate had asked me about feedback.
Without combining the two I would not have 'pondered' more over this casual "yeh we know that" paragraph of Kaufman's
"the concept of feedback is normally associated with a system that can be decomposed into inputs and outputs. The feedback is 'feeding back' of (a transform of) the output into the input. This results in circulatory and recursive patterns in the system. Under appropriate conditions, the recursion settles down to a steady form of interaction" p59. J. Social. Biol. Struct. 1987 10, 53-72
so what?
My original focus here has been on understanding of a discovered property of the XOR function when applied to categories derived from the recursion of a dichotomy. The REPRESENTATION of those categories has been in the form of bit patterns, where each bit reflects some 'input' from a level of recursion. e.g. 001 means 'nothing from level 1, nothing from level 2, something from level 3' OR 'integrating from level 1, integrating from level 2, differentiating from level 3'.
We could use wave forms with each level being a marker of cps measured as 2^n cps where n is the level from 1 upwards. This would use constructive/destructive interference patterns to give us a waveform representing the quality)
so what?
To **IMPLEMENT** the XOR function in the neurology required TWO neurons in that we need a feedback system to do it.
IOW the XOR function in our brains ensures, guarantees, DEMANDS, recursion to be a fundamental property of extracting information from the 'complex', simply due to the fact that to implement it we need feedback (NOT the case with AND, NOT etc)
With the recursing of an ASYMMETRIC format (axons = FM (pulse), dendrites = AM (wave), FM/AM = differentiating/integrating dynamics) that allows for the application of recursion to itself (using the XOR operator). It is this XOR methodology that (a) ensures the whole is encoded in all parts, and (b) allows for the extraction of a particular through the use of masking the bit pattern of category A with the bit pattern of category B,to bring out a description, by analogy, of the result in the form of qualities of category C.
What is indicated here is that the AM data at the dendrites is XOR-ed into parts, pulse data, by the soma and transmitted down the axon in a REVERSE ordering of general-to-particular to ensure building of data context-to-text. Given a context so more information is limited using energy conservation, we just add 'bits' to the top as needed once the bulk has been transmitted to set the 'ground'.
Zoom up to the hemispheres of the neocortex and we seem to see this same sort of FM/AM 'dynamic' but now applied to complex thoughts etc due to the increase in bandwidth as we move from neuron to whole brain.
From another source, to instigate a memory system you need at the fundamental level the XOR operator. IOW memory is fundamentally recursive in form (since XOR requires recursion and memory requires XOR it follows that memory will be mapped in a recursive manner - which is what IDM covers - the template for meaning etc)
Feedback means using the past to aid in the perception of the current and/or imagination of the future. In IDM this is mapped to the 'dimension of precision'. Here we have:
(a) NO feedback, each moment is 'unique'. representable as ...1,1,1,1,1,1,1,1
(b) feedback limited to the last moment, scale is immaterial. ADD the moments to get, ...1,2,3,4,5,6,7,8 - a beginning of 'sequence' and the AND operator - linkage.
(c) go back the last TWO moments - ...1,2,3,5,8,13,21,... the fibonacci sequence
(d) go back the last THREE to get the tribonacci sequence and so on.
(e) given a FINITE bound, as in a 'beginning', then go back to the beginning and we get ...1,2,4,8,16,32,64...
In image formats - at the level of the fibonacci sequence we have a cicular spiral pattern. At the level of the binary sequence we have a square spiral pattern - inbetween are all of the 'variations on a theme'.
BEYOND (e) and we move into complexity/chaos dynamics (Verhulst, Mandelbrot et al)
The focus on PRECISION means that each of the above sequences serve as positions for interpretation of reality -some will do it through patterns of the fibonacci, most of us do it through patterns of the binary (or 'beyond' - i.e. use of imagination where we put in 'extra' energy that destablises, allows for 'emergence' etc)
The RECURSION of a dichotomy is covered in the binary - what about the others? Their recursion is of fractal dimension. The range is 1.6^n to 2.0^n (less than the fibonacci sequence and there is little or no 'growth'. Beyond 2.0 and we get into complexity etc) For high precision we have to use the realm of the binary, the exclusive OR. The tightness of the spirals is determined by what number PAIRS are used out the sequence to create the spiral. (using the fib pattern as an example - 5/8 is wide, 13/21 tighter)
I still have not reached the EXACT, formal, description of what is going on but it looks like this:
Given:
000, 001, 010, 011, 100, 101, 110, 111
where these are recursed from the 0/1 dichotomy, if I then apply recursion to EACH I will get the same patterns I get when I XOR the whole set of qualities with each. I apply recursion to each by 'bit flipping' - we step through each quality's representation using binary number patterns. Thus to 'flip' through 000 left-to-right we have:
000, 100, 010, 110, 001, 101, 011, 111
IOW the link of recursion to XOR means I will get the same patterns be it applying recursion to each quality or just XOR-ing all against one. The DIFFERENCE here is that the use of recursion just gives me a 'parts list' ordered by analogy (an AND format), whereas the XOR gives me the X-ness of the particular property A expressed through context B in the form of an analogy to property C (since the language for a row is finite and it is supposed to describe 'all there is', so analogy/metaphor is the 'preferred' form of description).
I have used 'bit flipping' before to describe things but did not equate the need for recursion to create the XOR operator in our brains and so the association of 'bit flipping' (recursion) with XOR-ing.
Chris.