Syndicate: [ot] [!nt] \n2+0\

[integer@www.god-emil.dk]

matze.schmidt zkr!bld

>... shouldn't you have the latest Hackers' technology?
>http://www.zonelabs.com/updates/za_update11.htm [18.2.2001]
>

circular + linear = recursion

Consider the following:

Cantor demonstrated transfinite numbers and in particular the clear
differences between ordinality and cardinality where ordinality is sequence
and cardinality is size. At the finite (and so local level) cardinality and
ordinality share the same symbolism but at the transfinite level the
arithmetic is noticeable different.

However, zoom-in closer to ordinality and we have cardinality in form of an
object of size X converted to cardinality in the form of duration between
'a' and 'b' where there is no size difference of a and b.

This is what we can identify in the neuron in that the AM bias of the
dendrites reflects wave amplitude and so more of a cardinality expression
(BIG, small etc) whereas the axon reflects the translation of size into
pulses and so sequence, ordinality, with variations in the TIMING (FM) of
the pulses (since the SIZE of each pulse is the same) identifying the
original cardinality.

This reflects a conversion process from BOTH/AND conditions to EITHER/OR
assertions, what COULD be to what WILL be. (we see this at the mind level
where paradox which reflects BOTH/AND is converted to dynamic EITHER/OR
states -- e,g, the Necker cube, we oscillate in sense to particularise)

The processes of particularisation move from the general/cardinal to the
particular/ordinal. Logic is an expression of ordinality and 'same size'
pulses in that "IF A then B" is not size related by more order related, to
communicate the local, to achieve precision we need EITHER/OR-ness and its
related syntax bias which means 'dot' precision is only possible at the
local, EITHER/OR level.

If you reflect on the neuroscience work you can identify how thinking about
such concepts as 'transfinite' numbers will lead to the emergence of the
ordinal/cardinal biases in that these biases reflect characteristics of
neocortical function, i.e. a more ordinals biased - single context, sequence
bias i.e. reading/writing with audition is horizontal you need INTERNAL
linkage to derive meaning, inheritance of meaning moving from raw to
refined.

This is usually identified with left hemisphere function (change scale and
it is temporal lobes bias etc etc down to a more axon-like bias in
expression)

A more cardinal bias where there is no SEQUENCE only SIZE (or more so
QUALITATIVE precision) is closer to right hemisphere characteristics in that
cardinality manifests exaggerations, distortions, relational processes
outside the simple linear format.

Pettigrew's work (with Miller etc see the hemispheres paper at
http://www.uq.edu.au/nuq/jack/jack.html ) shows that in the irregular timing
of oscillations across the neocortex, the SEQUENCE converts to a expression
of cardinality in that the QUALITY of a particular expression  that is
generated is affected by the properties of that 'side' of the brain in which
most time was spent.

IOW an identification of X is concerned with oscillations that are biased
such that a more 'right' bias in time spent leads to a more 'relational'
interpretation of X (relational emphasis, size, cardinality) than if there
was a more 'left' bias leading to a more 'object' interpretation
(discreteness emphasis, ordinality)

So, Cantor's demonstration of a local (transfinite numbers) can be linked to
neocortical biases, can be linked to the EXPRESSION of those biases.

Behind these distinctions is the object(what)/relationships(where) dichotomy
which when applied recursively allows us to demonstrate the distinctions of:

objects - whole, parts
relationships - static, dynamic

What is of interest is that we can map these distinctions to terms
reflecting FEELINGS and these feelings can be linked to fundamental types of
numbers:

whole numbers - a feeling of blending (note that within the distinction we
find the object/relationship dichotomy expressed in the form of prime
numbers/composite numbers)

Part numbers - aka rationals - a feeling of BOUNDING, to CUT literally or
metaphorically

Static relationships - aka irrationals - a feeling of BONDING, to share the
same space but keep identities unique.

Dynamic relationships - aka imaginary - a feeling of BINDING, to share the
same time (e.g. contracts).

IOW we can trace mathematical concepts, our FEELINGS of them, to having
roots in neurology. We can trace neurology to manifesting adaptations to the
environment and as such the success of mathematics is that it 'resonates'
with the environment. (When generalised it works to map 'what could be' and
that includes severe distortions of reality as we know it)

The general emphasis is an analog-to-digital/digital-to-analog conversion
process where the continuum bias, the geometric, the wave, is translated
into the discrete bias, the algebraic, the point.

Finer degrees of resolution, finer granularity, allows for the conversion of
continuum to discrete representations (all space is points) but there is a
feeling here that this process reflects what I said in the second email i.e.
there is a sense here of attempts to 'square the circle'; a concept that has
influenced many over the centuries.

With the recursion of the object/relationship dichotomy we find that at
level 3, where we have eight forms of expression, we have a set of 'raw'
expressions functional at the BRAIN level which can be manipulated,
complexified to quickly give us one out of 16 million expressions (4096 ^2 -
12 dimensions) but the general character of the 'raw' expressions can still
'shine' through.

WE here have a methodology that contains a set of meanings that is common
across the SPECIES and existed as such BEFORE we localised with language
(and I include mathematics here).

The eight distinctions are based on the identification of TEXT, foreground,
and CONTEXT, background,  and point to context having the same structure as
text, it is just spread-out, more diffuse; like a holographic film. The
METHOD is used to 'draw out' a pattern from the context, move it to
foreground but in doing so we can see the detail WITHIN the pattern but the
context, the background becomes fuzzy, is ignored.

Abstract thinking processes share the same space as concrete, sensory
biased, processes in the brain. WE think 'visual' and the visual areas
'light up'. This suggests mind as an emergent property and so has the same
structures, object/relationships identifications, but also is a context that
is robust enough to allow for 'non local' emergences -- patterns out of
'flocking' behaviours and this includes particularisation of
object/relationship identifications through the use of linguistics in
metaphors; 'mind' acts to particularise, to GROUND patterns by identifying a
particular context and associating it with a lexicon. In doing this, where
we emphasise DIFFERENCE, we can lose sight of the embodiedness of our
methods, of the species-wide SAMENESS in identifying 'objects' and
'relationships'.

If we work on the 'share the same space' model of brain/mind where what we
call 'mind' has emerged from local distinctions of neurological functions
leading to 'flocking' behaviours and so retains the FM/AM biases of the
neuron but now includes feedback processes that enable layering metaphors
upon metaphors to achieve precision (! a contradiction!) then your comments
re soma etc are valid.

We can imagine the neocortex as a huge 'eye', distorted in that fovea maps
more to 'left' and parafovea to 'right'. Overlay that with a huge ear where
in the auditory cortices and we find the same sorts of patterns with the
overall emphasis on object/relationship, particular/general,
perfect/imperfect etc)

With all of this also comes kinesthetic representations, gustatory/olfactory
representations etc all managed by abstract object/relationships distinction
processing and out of that comes mathematics. IOW mathematics as we know and
use it is part of us.

best,

Chris

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