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Hi Philip, this is all fascinating stuff.
I can't help think though that the reasoning of this kind of mathematical enterprise is backwards.
Surely numbers like the golden ratio and the plastic number have no meaning as numbers. For example it is just evolutionary chance that we use the decimal system to represent them, because we have 10 (thumbs & fingers)?
Our brains have extracted perceptual principles that 'work' in the world because they work, i.e. you can fit two A4 sheets together to make an A3 sheet. Biology probably does something similar to form the architecture of the structures it needs to produce.
Surely the number comes after this? It is only as humans that we can then use this number in meaningful ways as a short cut when implementing architectural design?
So, in PCT terms, do our input functions reorganise in order to extract relationships between perceptions that 'work' when we choose to act on them, and these can then be represented as numbers later through our particular skill at manipulating symbols?
Warren
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On 19 Sep 2014, at 00:15, PHILIP JERAIR YERANOSIAN <pyeranos@ucla.edu> wrote:
<plastic number.pdf>
Good points, Warren. Needless to say, the word, “number”, is a strange word. But the fact that we use the decimal system to represent numbers is inconsequential, as the concept of decimal or hexademical or binary, etc, has nothing to do with a “number system”. A number system is composed of such properties which allow “ordinary” algebra to occur: concepts such as reflexivity, transitivity, and associativity.
i.e.
a = b means b = a,
a = b = c means a = c, and
a(bc) = (ab)c
I don’t think that we use the decimal system because we have 10 fingers. Other cultures used other systems but all humans had 10 fingers. The golden number and the plastic number simply have special properties. The ultimate goal, I believe, would be to understand the importance of these properties in the context of certain systems of equations. In PCT terms, I think these numbers have as much to do with controlling non-living systems as with our perceptions.
Rick asked me, earlier, to discover exactly what perceptions “pure” mathematicians are controlling. I have dutifully sought these variables out. There are, in fact, only a few universal methods of proof, all of which are easily enunciated in PCT terms. I will organize a presentation and report back to you soon.
Fascinating, please do!
···
On Sat, Sep 20, 2014 at 1:34 AM, PHILIP JERAIR YERANOSIAN pyeranos@ucla.edu wrote:
Good points, Warren. Needless to say, the word, “number”, is a strange word. But the fact that we use the decimal system to represent numbers is inconsequential, as the concept of decimal or hexademical or binary, etc, has nothing to do with a “number system”. A number system is composed of such properties which allow “ordinary” algebra to occur: concepts such as reflexivity, transitivity, and associativity.
i.e.
a = b means b = a,
a = b = c means a = c, and
a(bc) = (ab)c
I don’t think that we use the decimal system because we have 10 fingers. Other cultures used other systems but all humans had 10 fingers. The golden number and the plastic number simply have special properties. The ultimate goal, I believe, would be to understand the importance of these properties in the context of certain systems of equations. In PCT terms, I think these numbers have as much to do with controlling non-living systems as with our perceptions.
Rick asked me, earlier, to discover exactly what perceptions “pure” mathematicians are controlling. I have dutifully sought these variables out. There are, in fact, only a few universal methods of proof, all of which are easily enunciated in PCT terms. I will organize a presentation and report back to you soon.
–
Dr Warren Mansell
Reader in Clinical Psychology
School of Psychological Sciences
2nd Floor Zochonis Building
University of Manchester
Oxford Road
Manchester M13 9PL
Email: warren.mansell@manchester.ac.uk
Tel: +44 (0) 161 275 8589
Website: http://www.psych-sci.manchester.ac.uk/staff/131406
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