A neural prism is simply the mimicking by the neurology of the conversion of a whole (white light, complex sound)
into its parts (colours, harmonics). The concept of a neural prism is manifest in such areas as the auditory channels
within the brain and we can extend the concept to visual as well (Refs below).
What is noticeable is that in a prism the expression of the parts (e.g. the colour spectrum) can be interpreted
as if a sequence and this interpretation can lead to illusions regarding ordinality, cardinality, and the general
operations of the brain/mind whilst it attempts to make maps of 'out there' as well as 'in here'.
I have drawn an example of a neural prism . Please view it and use it as reference for
what follows.
One feature of the brain that is well documented is the sharing of neurons or neural networks by the senses as
well as the abstraction of networks for 'higher' duties and this includes the processing of abstract data, concepts,
ideas etc. In this article we speculate on the use of neural prisms in abstraction processing and from that the
development of a sense of 'meaning'.
There is the suggestion that neural prisms can come in two flavours, the visual biased prism that is like a light
passing through the prism to be immediately split up, and the more detailed version utilising steps (ordinality
bias), as we find in detailed binary tree derivations. (it is possible we are dealing with the same thing but that
needs to be fleshed-out more. The visual format has an aire of intuition about it, the 'instant' realisation of
something, when compared to the slightly more ordinal biased, gradually developing, binary tree emphasis).
If we use the binary tree model, one of the properties is that of pairing where the so-called sequence (see above
diagram) is in fact made-up of pairs, nodes of the binary tree
A major question here is regarding our concepts of ordinality in experimentations where prismatic processes that
are interpreted as 'from A to B' and so a 'sequence' are more a linking of qualitative differences that get 'ordered'
by the method of derivation and as such may have no sequential 'meaning'; the 'sequence' is more of a histogram
of qualities (in light expressed as colours). Thus the derivation process allows us to work 'in reverse' and so
consider such concepts as time reversal, distortions etc. etc. simply because the 'sequence' can tolerate chopping
and changing of qualities in the 'sequence' since in 'reality' it isn't a sequence! (This of course has connotations
re our concepts of causality etc. which I leave for others to ponder upon.)
Since we are an adaptive species, the refined derivation of data using prismatic processes as described above can
lead to a sense of continuity 'across' the elements of the derivation, and this sensing can serve a useful purpose
even if initially 'meaningless'; the 'deeper' the derivation so the more refined the experience of continuity and
so a development of 'consciousness' as an experience of step-after-step, moment-to-moment awareness of existence.
Note from the above binary tree diagram, btree, that each level adds a degree of 'meaning' that gets more
and more refined as we go deeper in the derivation process (recursion) and so 'links-up' the pairs in the 'sequence'
to develop a sense of continuity; IOW each level acts like a wave of differing amplitudes and as we go deeper so
these waves add-up to give the illusion of 'continuity'. (Note that in lower life forms so this degree of continuity
is limited/missing suggesting they have not developed past some threshold where all of the pairs 'link-up' to give
a degree of continuity that can build libraries to house memories etc.)
It is documented in the literature on emotions and the brain that emotion is attuned to respond to frequencies
where in particular the frequencies represent harmonics of audition and vision. This response system would benefit
from the ordering of frequency components derived from any general data that is being processed, where the emergence
of an ordinal sense can be extended into the development of language. This ordinalisation acts to take the general
data and communicate it through refined emotions. Placing the emotions in order in the form of words that then
get transmitted as a 'whole' enables a 'precise' communication ready to be broken down by other receiving parties.
This ordering of communications, whether a sentence, paragraph etc., is a histogram of the qualitative elements
of the whole message, and 'empathy', emotional resonance, is achieved when the identical histogram is created in
the brain of the receiver. We must note that feedback processes in the form of memories can act in a cardinal,
a topological, way to exaggerate/distort incoming data such that the feedback can either refine (constructive interference)
or destroy (destructive interference) the intent of the incoming message. (In the neuron the receiving areas (dendrites)
are biased to wave amplitude modulation (AM) whereas the transmission area (axon) is more single context, frequency
modulation (FM) biased. See neuron1.gif for more on this. The AM bias points to a topological
bias when compared to the more discrete, precise, 'clear' expression in FM.)
By understanding the distinctions of ordinality and cardinality, by recognising that cardinality is rooted in topology
and as such has a very 'general' emphasis on precision and so recognising the emergence from evolution processes
of a method to particularise the general and so refine the general, to be more precise, has led to the solving
of a 3000 year old 'problem' relating to a 'sequence' of symbols. We now know that this 'sequence' of symbols is
in fact the expression of a binary tree derivation process working vertically that leads to the emergence of a
pattern horizontally (you can also have visa versa -- h to v). This sequence takes on the properties of light,
where the sequence has a qualitative element, each symbol takes on a 'colour' that elicits a sense of 'meaning'.
In the sequence in question the meaning was not precise simply because there was no understanding of the method
of derivation; the intent of the originator. The assumption was that the ordering was 'primary' rather than something
derived from cardinality processes and so secondary. Once the method of derivation was identified so things fell
into place very quickly to an extant where meanings identified within the system became 'obvious'.
What is of note here is that at the neocortical level, across the frontal lobes of both hemispheres, we find the
same pattern as we do in the binary tree 'sequence' and that includes 'pairing' or as P. Goldman-Rakic calls it
'interdigitations' where we see the entanglement of left and right hemisphere connections. (see bottom diagram
of hemis.JPG ) Furthermore these
frontal lobe areas are strongly concerned with ordinality -- planning etc. and are the last areas in the brain
to develop suggesting the whole brain acts like a neural prism with data coming from posterior areas to be dispersed
to more discrete, more specialised neural networks and eventually organised, ordinalised, prior to expression.
Since the individual neuron contains these prism properties, where in the brain the axon connection is to many
dendrite regions of other neurons, so we see a 'fractal' like formation of a prism in the whole brain. The emphasis
on neural prisms favours the emphasis on adaptation to light as well as sound enabling the development of refined
communication skills using abstractions of the original adaptations of our senses to our environment.
Identifying the 'illusion' of ordinality points to properties of the method of derivation 'shining through' the
ordinal biases that develop when we start to talk; from a cardinal perspective communication is more the processing
of spectrums that elicit patterns of emotion. These processes are 'hidden' by the emphasis on the spoken word and
so ordinal processing.
We know that in most individuals the 'right' brain is more biased to topological issues and in infants is more
developed, pointing to early development being an exercise in topology where the genetics twists and turns, squeezes
and pulls as it adapts to the local environment. A sense of the ordinal develops later especially with the development
of speech such that the cardinal gets 'pushed aside' becoming specialised in context processing and *general* relational
issues including identifications through metaphors and implications -- all processes that require distortions/exaggerations
-- as well as 'colouring' communications using emotions.
The developed bias to ordinality due to speech can force us to overlook patterns in information that are not ordinal
but are in fact sourced in the cardinal. This includes such 'simple' concepts as 'odd/even' which in our number
system comes as a pair, reflecting the underlying methodology used to process cardinality and over which we impose
ordinality. There is the suggestion in this that the making of a distinction, which always leads to the identification
of a dichotomy, forces the creation in our minds of a 'meaning' space and that space is created using recursion
and so the emergence of binary tree formats and pairings. The 'meaning' space now becomes a 'sequence' space that
is more a histogram of meanings encoded in the distinction we have made. (BTW - Note Prof J Pettigrew's comment
on a 'left' brain sensitivity to the horizontal
(http://www.uq.edu.au/nuq/jack/jack.html - papers on hemisphere
switching)
The sequence space has properties that allow us to interpret the content 'in reverse' or to chop and change the
content around; the structure of the space allows us to suspend thermodynamic issues and in doing so use the space
to build our maps of reality. This ability to distort/exaggerate and so allow for 'novel' concepts reflects the
topological roots of the space. The success of this is in the rich creative processes that can be performed but
the illusion of the ordinal also allows for the creation of illusions since the space lacks ordinality itself;
the space has a more spectral format that can be interpreted as if ordinal (left-to-right) but is more 'vertical'.
The illusions of ordinality are identifiable when we notice the space contain pairs in that the identification
of pairs reflects properties of the unconscious method of data processing, the taking of an expression, something
cardinal, and zooming-in for details using recursive dichotomisation (IOW discretisation which is akin to cutting,
something the topologically biased 'right' brain has a problem with since for it 'all is linked together' - and
so coffee-cups are the 'same' as doughnuts). The illusion of the ordinal comes when we 'connect' the pairs into
a 'meaningful' sequence. If the meaning remains 'hazy' then there is the suggestion of illusion (or else a need
to 'go deeper').
All of the above touches on the very foundations of our thinking, on our reflections on consciousness as well as
the structures of our maps including the encoding of illusions based on misconceptions regarding ordinality and
cardinality. The illusion of the ordinal is the root of our concepts of time, of causality etc and as such there
is the suggestion that the emergence of consciousness in the form of awareness of moment-to-moment in self and
in others was a chance event, a product of an adaption in deriving precision; those life forms that instinctively
'drilled-down' further when processing information developed an edge in the form of weak senses of connectivity
that became extremely refined in 'us' and in doing so introduced us to the ability to make maps and from those
make predictions.
In conclusion I would like to point out how the process described, of moving from cardinal to ordinal and so from
diffuse to detail, from general to particular, from approximation to precision, reflects the functionality we identify
in DNA/RNA processes where mRNA favours an ordinal bias, a precise gene coded in EXACT order, when compare to the
more cardinal, the more topologically sensitive DNA where a 'gene' is spread-out requiring distortions, exaggerations,
re-combinations, cutting and pasting to extract the 'pure' gene.
That said, if mRNA 'space' is like the discussed 'sequence' space then the ordinal bias 'hides' cardinal processes
encoded in the sequence; the 'sequence' is interpretable more as a histogram of qualitative expressions within
the 'gene'; thus 'start' and 'end' markers in the codes serve as identifiers of the boundary that contains the
gene's spectrum where communication is by spectrum exchange.
The 'fact' that in the helixes we can clearly identify pairings in the codes points to topological roots, suggests
that the mRNA 'sequence' isnt just that; there are relational issues within that add complexity to the 'simple'
mRNA strand and to analyse those strands from an ordinal perspective can lead to confusion; all of the 'sequences'
identified in the HGP, all of the surprisingly 'few' genes present point to possible mis-interpretations where
ordinality hides properties that are cardinal and due to the ordinal bias in perspective these properties have
as yet not been clearly identified. By understand HOW we perceive so we can be more precise in our perceptions
and easily deal with confusions due to ordinal/cardinal entanglements.
Chris Lofting.
Further reading/refs:
General neurology/cognitive science refs see http://www.ozemail.com.au/~ddiamond/brefs.html
for more 'heavy' going:
For modeling see:
Koch, C., and Segev, I., (1998)"Methods in Neural Modeling" MITP
For neural prisms see:
Cirrincione, G., Cirrinocione, M., & Van Huffel, S., (1999)"Neural Geometry for Constrained Optimization"
(copy of the paper is on my website --
http://www.eisa.net.au/~lofting/neuralprism.pdf )
and
Hoppensteadt, F.C., (1997)"An Introduction to the Mathematics of Neurons 2nd Ed" Cambridge UP
For solving a 3000 year old 'problem' see http://www.ozemail.com.au/~ddiamond/cracked.html
