> -----Original Message-----
> From: owner-moq_discuss@venus.co.uk
> [mailto:owner-moq_discuss@venus.co.uk]On Behalf Of Justin Ellis
> Sent: Thursday, 28 December 2000 7:05
> To: moq_discuss@moq.org
> Subject: MD A question
>
>
>
> I got this problem from reading about interpretations
> of mathematics. It's called Conceptualism, and I think
> it poses a serious problem to the MOQ. Any help here
> or answers would be appreciated. Thanks.
>
> -As far as mathematics, Conceptualism states that we
> invent math, not discover it- it is our own modelling
> of reality in a way that we can intellectually
> understand. Math seems to fit nature so well (as per a
> Neo-Platonist claim) because we have designed it to do
> so.
>
not consciously. From a neurological perspective, a perspective that
preceeds any other, we can identify neurological states that when abstracted
map to mathematical concepts.
For example, the distinctions of objects and relationships, tasks performed
by our brains, when abstracted can point to sets of feelings directly
connected to concepts of numbers.
Thus WHOLE numbers can be categorised into objects (the prime numbers,
self-contained, indivisable except by themselves or 1) and relationships
(composite numbers reflecting the summing of prime numbers.) From these
categorisations we can create a seemingly 'infinite' number line. However,
the emphasis on OBJECT and its RELATIONSHIPS forms a 1:many distinction with
the suggestion that there is only ONE numeric concept and all else is
created from that.
When you look at the studies on autism in humans as well as studies on chick
behaviours there seems to be a lack in recognition of more than one object;
the one is held constant and difference comes from the many. In more
developed minds so there are more than one object, IOW the concept of ONE
has been generalised. Primitive tribes etc are limited to 1-2-3-many when
making numeric distinctions, IOW there is little refined feedback that
allows for going beyond these basic numeric distinctions.
Since the brain emphasises 1:many distinctions so it is in the realm of the
many that we find harmonics of the 1. When we zoom-in on the many, out pops
such distinctions as rational numbers, i.e. all of the PARTS into which we
can cut the whole. From this comes the formal mathematics concept of the
harmonic series. Note that these 'numbers' are stand-alone, it is a LIST of
single elements thus a 1/2 is a property of the series but it takes 1/2 +
1/2 to 'make' the whole.
The realisation that there are other relational properties (noting that
relational concepts stem from the MANY side of the 1:many distinctions) lead
to the identification of irrational numbers (shock and horror to pythagoras
et al). These are NOT tools for counting since counting requires an object
perspective, a 'this' from 'that' distinction. Irrational numbers deal with
invarient relationships best discovered when we use unit values (unit
right-angled triangle, unit circle etc). Thus irrational numbers sum
elements from the harmonic series as well as include 'stand alone'
irrational numbers (e.g. PI is determined by a series)
Such irrational as PI or e or sqrt(-2) assert an invarient relationship
regardless of scale, time etc. There is no dynamics in this when we compare
irrational to imaginary.
Imaginary numbers are also non-countable in that they too emphasise
RELATIONSHIPS, in particular those DYNAMIC relationships dealing with cyclic
and morphic change.
When we go further, by creating 'numbers' that get closer to capturing a
sense of reality (e.g. mathematics in quantum mechanics - the concept of the
Hamiltonian etc) we shift focus to include a point and its context. (these
types of numbers reflect COMBINATIONS of the above basic types)
Thus whole numbers are 'pure', absolute, stand-alone and so context-free.
When you get to mapping things etc so the distinction is made of a thing and
its context. In physics that context contains all of the 'rules' of the
universe and so such concepts as the wave equation used in QM is a list of
probabilities in expression of an object (aka particle) and its context (Sum
of (object+fields+probability) = wave equation).
Thus the 'purity' of whole numbers, their context-freeness, gives way to the
determination of context upon the 'particle'; the determinator of expression
shifts from the thing to it's context. (Note this same approach is reflected
in genetics etc where some argue for the gene (particle, nature, internal
relationships) whereas others argue for the context into which the gene is
placed (field, nurture, relationships to context)).
Overall the above reflects a self-contained system of measurement based on a
sort of resonance where, based on the known 'grammar' of the universe, so
all knowable expressions are listed together with a probability of
expression. The result of the act of measurement causes a 'collapse' of the
wave equation where one of the possibles becomes an actual.
Note that as we get more dynamic, as we move from 'pure' and 'eternal' whole
numbers to the use of hamiltonians etc so emphasis shifts from the 'thing'
to the 'things' context.
This is a GENERAL pattern of distinction making and is not restricted to
mathematics but is in fact a theme in ANY distinction processing that moves
from a static ONE, to a dynamic MANY.
The question is 'how' is it possible? how do our mathematical maps 'fit'
reality (as well as allow us to create other realities?)
At the level of 'pure' particle physics you find two distinctions, that of
FERMIONS and that of BOSONS.
What is interesting about these distinctions is that the general properties
of FERMIONS 'fit' to distinctions we make re all objects (i.e. they cannot
occupy the same space as other fermions - this is the Pauli Exclusion
Principle). This emphasis asserts that there are distinct, absolute objects.
BOSONs on the other hand take on general properties that we make re
relationships (i.e. we can superimpose relationships, out of relationships
come 'objects' (transformations) etc etc)
Since these distinctions form the 'fundamental' universe, so evolution from
these 'basics' should reflect the value of these distinctions; do you think
it is coincidence that our methods of making distinctions 'maps' to these
fundamentals ('out side' of us)? On the other hand, since our different
senses FORCE dichotomisation in our map making so the patterns we see are
due to our method of analysis that is 'free' of the universe context; the
universe we 'see' is all we can see due to our method of analysis 'fixed' by
the neurology.
However, if you follow the principles of evolution, adapt and adopt, so we
have adapted to our environment by internalising its characteristics.
If you look at the brain, following its development path from the top of the
spine to the frontal lobes, so you see reflected in the different behaviours
'refinements' in development.
Thus the rigid, mechanistic (if too hot/cold then MOVE), EITHER/OR of the
reptilian brain gives way to the biochemically, more choice-based structure
of the mammilian brain (you can shiver/sweat or move) which in turn gives
way to the neo-mammilian brain (we build reverse cycle air-conditioning, or
shiver/sweat, or move). Note that the latter gives us more choices in action
and so we seem to have internalised the characteristics of evolution
itself -- we practice evolution through conscious selection rather than
natural selection IOW we seem to have internalised a 'map' of 'out there'
that enables us to PREDICT things. That map is in the form of recursive
dichotomisations of object/relationships distinctions).
The development process described above for evolution is the 'same' as that
for mathematics as well as for MOQ or any other discipline.
There is a 'level' change, a transformation point, like phase transitions,
where the ONE-TO-MANY path, when it reaches the MANY, allows for
transformations to a new ONE at a 'higher' level and this includes the
emergence of properties and methods not seen before since the previous
contexts could not support them.
Furthermore, the reverse cycle is where the MANY falls back to the ONE which
in turn collapses back into the MANY of the previous level.
As for MOQ, quality is not WHITE/BLACK, quality requires COLOUR, harmonics.
It is like reflecting on the symbol '1'. To get 'meaning' out it you have to
go 'behind' it -- to the SENSE of ONENESS etc etc etc otherwise it is just
'1' as compared to '2' or '3' etc etc :-)
Quality is derived from the space in-between objects, from the expressions
of colours and sounds etc as well as from harmonic patterns 'within', either
developed or else created by chance (randomness, genetic diversity).
you can see this in mathematics where primes have an INTERNAL quality
('purity' etc) wheras fractals, for example, have an EXTERNAL quality (i.e.
the use of feedback, MIXING).
ANY system that instinctively utilises exagerations to communicate manifests
the HARD CODING of quality, of a sense of 'good' value etc
Thus feelings of beauty are not restricted to human forms but to human ideas
since behind both distinctions (human form/human idea) is the SAME method of
analysis.
best,
Chris.
------------------
Chris Lofting
websites:
http://www.eisa.net.au/~lofting
http://www.ozemail.com.au/~ddiamond
> The same could be said of Quality. The idea of Quality
> can seem like it works to us now simply because Pirsig
> has designed the MOQ to work based off reality. With
> all our analogues we have built up to reality, how can
> we ever know we are truly seeing Quality?
>
> The problem, therefore, is the possibility that
> Quality does not exist in and of itself, but only as a
> model for our experiences. Every person will have
> their own definition of Quality, even w/out the
> analogues, because it is their own modelling of what
> they perceive they see because Pirsig has said it's
> out there.
>
>
> Again, thanks for any answers.
>
>
>
>
>
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