> -----Original Message-----
> [mailto:[EMAIL PROTECTED]]On Behalf Of elephant
> Sent: Tuesday, 27 February 2001 10:42
> Subject: Re: MD On materialism....
> Chris, if apes can count then they are language users.
> > From: "Chris Lofting" <[EMAIL PROTECTED]>
> > Date: Tue, 27 Feb 2001 21:52:53 +1100
> > Subject: RE: MD On materialism....
> >
> > These distinctions are mapped in the above paper to NON-linguistic
> > representations (even apes can count :-))
> And as to your claim:
> > There are TWO expressions of number, one (!) is exact and the other
> > approximate
> - this I find to be gibberish.  Can you explain what you mean here without
> citations?
> Thanks
> Elephant

Dear Pachyderm, perhaps we need to define what we mean by language. I think
term is usually used to represent a system we use to communicate BETWEEN
individuals. This distinction does little to flesh out 'language' WITHIN the
individual where affective processes exist pre external expressions (sounds,
symbols) where we communicate with our selves (or without making that
distinction, we can 'resonate' with the environment, thus a sense of
is felt 'all over'). IOW we can establish internal communication that is not
based explicitly on tonal or symbolic manipulations but on emotions or their
reifned form expressed by the term 'feelings'.

I can thus 'feel' magnitude (bigger/smaller, longer/shorter) with a
tuned to distortions, exagerations and so relational processes (this gets
topology etc as a fundamental).

I can feel sequence (before/after) with a mechanism tuned to ordering and so

Magnitude does not require sequence to function and as such both of these
systems can operate more or less independent of the other.

When you COMBINE these distinctions, and external language enables this to
done precisely, so we introduce such concepts as what COULD be vs what IS in
that a sense of SEQUENCE allows you to reflect on a magnitude that *gets*
bigger/smaller over time. Note that the emphasis on precision forces an
on the LOCAL, the PARTICULAR, whereas in magnitude this emphasis need not be

Reasearch  (as in the reference I supplied) has validated the above
in that there ARE pre-linguistic mechanisms that allow for a sort of
proto-numeracy to occur. These systems become refined when we humans link
by using external language and so even more particularisation.

To go a little further, the distinction of objects and relationships by our
brains (as well as the brains of chimps, chicks, zebra fish, bees...) allows
the creation of affective processes that go to identifying what WE call
integers, rationals, irrationals, and imaginary numbers. (and from them
more abstract concepts as complex numbers, quaternions (hamiltonians) etc)

The humble (!) bee has a brain structure abstractly similar to ours in that
bee's brain makes the distinction of domain-specific data from
data. Domain-specific means context-specific and in humans this is managed
by a
hemisphere bias where a hemisphere (usually the left) specialises as a sort
interpreter based on setting a specific context from which to interpret. It
happens (and I dont think it is coincidence) that the other hemisphere in
has demonstrated a bias to VALUE processing other than the syntactic
emphasis on
'correct/incorrect' associated with the interpreter.

The difference between human and bee is that in humans we can cycle between
possible interpretations whereas the bee is more hard-coded with sets of
domain-specific neural systems with a vertical format, and linking these is
horizontal 'value' connector.

The 'interpreter' seems to work on SAMENESS/DIFFERENCE mappings in both
and bee and as such there is an emphasis on KNOWN/UNKNOWN. (as in where past
identifications become 'known' and novel ones 'unknown' that get labelled in
some way. Bees seem to use pictorial mappings, colour coding etc Note that
colour is a HARMONIC of light and it so happens that that part of the human
brain that is better at processing colour is also linked to processing
in general. Thus the domain-specific/value-specific distinctions we find in
are also reflected in more refined, more flexible, formats in humans.)

This known/unknown distinction has also been discovered in the brain of the
zebra fish, a left bias to KNOWN and a right bias to UNKNOWN so we are
to see a common neurology across seemingly very different lifeforms; but
the fundamentals of the neuron are common to all and the left/right
are in fact mappable down to the neuron level and the axon/dendrite

To get back to numeracy, The 'primitive' feelings mentioned above are best
expressed as those of:

A feeling of Blending - wholeness, to become 'ONE'. Symbolised by whole
(primes/composites distinction reflects the object/relationship pattern even
WITHIN whole numbers)

>From a feelings context there are two forms, of blending expressed in (a)
internal linkage, to develop a sense of 'one' within, and (b) external
to develop a sense of 'one' between IOW a social 'oneness'. Note how this
a 'twoness' emphasis where 'one' is expressed as a group membership and so
least two are needed to form this 'oneness' experience.

A feeling of Bounding - parts, symbolised by what we call rational numbers;
many ways can we 'cut' the whole.

A feeling of Bonding - static relationships, symbolised by what we call
irrational numbers, sharing the same space (magnitude) with something else
without loss of unique identity.

A feeling of Binding - dynamic relationships, symbolised by what we call
imaginary numbers, sharing the same time (sequence) with somethingelse
potentially without loss of unique identity but exposed to
transformations/transitions; cyclic/morphic changes.

These simple affective expressions are part of any system that utilises
object/relationship distinctions and the diversity is across mammals,
fish etc etc  Thus a fish can emulate imaginary numbers by rotation!  The
feeling of rotation, the expression, is a behaviour that in our minds is
abstracted and symbolised by imaginary numbers.

The advantage we have had is in being able to ENTANGLE these sorts of
in the spoken/written form and as such make precise mappings of reality and
importantly store that information to be passed on to the next generation
without any internal 'modifications'. This storage process creates 'idiot
savants' in the form of disciplines e.g. Mathematics which contains within
object/relationship mappings as we have but in one specific format, only one
manner of expression.

It is from these primitive affective processes that through refinements
(even if
illusions) we can create a spiritual sense of 'one-ness' either within
sense of one) or between (group sense of one).

Note that this sense of oneness correlates with the feeling of BLENDING that
linkable to feelings associated with WHOLE numbers and that includes PRIME
numbers and so a sense of primacy (and many mathematicians have experienced
beauty of mathematics and sense of connectivity with 'god' or what/whomever

For MOQ, you get quality from feeling, affective processes. These processes
structure based on recursive dichotomisations of the object/relationship
distinctions (or more so the FEELINGS from which these distinctions are
made --
note that the amygdala, one of the prime areas in the brain for emotional
processing works on what is called the 'fight/flight' dichotomy (synonymous
the advance/retreat dichotomy) IOW feelings stem from extreme emotions --
was some work on this using Catastrophe Theory to show the different
formats derivable from this simple dichotomy)

With all of this we can equate the characteristics of such concepts as
Platonism, Taoism, Zen Buddhism, 'traditional' Buddhism, Christianity etc
all of these are value expressions linked to particular domains -- can bees
a sense of spiritual? perhaps...:-) but it would be 'total', no distinction
making, no monkey 'mind'... bees know Tao without knowing *of* Tao...

best regards,

Chris Lofting
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