ABSTRACT

A fundamental tool of Science is Mathematics; so much so that to be able to mathematise something often implies that the object is 'fact' and 'objective' or at least conforming to some 'universal' law. This concept of mathematics has been paramount from Pythagoras' time in supporting our cultural understanding of 'what is Science?'; we can even distinguish the humanities from science simply due to the preferred symbolisms - words for humanities (and at times too many!) and equations for science (and at times too abstract!). We recognise that words come from 'in here' (and are subjective) but, like Pythagoras, many believe that numbers comes from 'out there' (and are objective). By considering the model of the brain as a system that processes data in the form of wholes and their aspects, and the categorisation of this data is done dichotomously (e.g. using Cartesian-like coord systems), we find that all the types of number are very much sourced 'in here', but how is it that they map 'out there' so well? Probably because 'out there' consists of wholes and their aspects...


<1>
In your comments re rationality and numbers I think it might be interesting to note that:

whole numbers --- comprise of primes or composites and reflect wholeness - fundamentalism.

rational numbers - comprise of parts of a whole and introduce text/context concepts (as well as the concept of dichotomy) (the concept of rationality is thus based on being able to make A/~A distinctions -- text/context etc.)

irrational numbers -- are not counting numbers but are more symbols for static *relationships*. They are thus never 'whole' in that when decimalised have repeating or inifinite non-repeating sequences after the decimal point.

complex numbers - are not counting numbers but are symbols for dynamic relationships (e.g. oscillations).

Add to this the concept of negation and you have the basics for any numeric representations.


<2>
These symbols emerge naturally as a result of the brain's bias to processing data as wholes and aspects -- text and context.

As we get into more complex areas so we find 'mixing' i.e. whole numbers operating in a complex number context - e.g. in quantum mechanics the 'jumps' in energy levels are controlled by integers but the overall descriptions are based on complex number equations. (Hamiltonians are very abstract 'numbers' that can combine structural and temporal data into one symbol).

In brain function, as we develop so emerge the above numbers in order -- thus we always start to teach maths with wholes and dont get into complex numbers until our teens.. and this 'goes' with mental refinement in that intense multi-context relationships are not 'everyday' events for children (or if they are the children are not too good with dealing with them in a refined way.)

We always start something in a fundamentalist way -- assertive, positive, 'the absolute'. Whole numbers. As we 'mellow' so we get into A/~A comparisons; we use dichotomy -- rational numbers.

<3>
At this point is a jump, from object analysis to relational analysis. As we start to analyse in detail so we hit on static relationships -- these consist of noting how certain parts when grouped together show an invariant aspect. (this is why PI can be expressed as a series based on the harmonic sequence; ALL irrational numbers have this simply because they 'show' the lumping of parts together; we have moved from considering a single aspect (ratio) to more complex aspects (summing different ratios).

<4>
Further analysis takes us into considering dynamic relationships where we introduce time as a factor and so emerges statistical analysis.

What is of interest is that as we develop so we bifurcate:

wholes--->rationals

wholes-->rationals
(whole+irrationals (irrationals are linked to part/whole relationships. Structurally they are inbetween whole/rationals in that they cannot be separated from the whole e.g. if I take away the diameter of a circle I have no circle!))

wholes->rationals
+irrationals+complex

complex numbers are linked to rationals in that they deal with part dynamics within a whole context.

<5>
This gives us a pattern:

A---B---C
1---2---4

A(1) -- fundamentalism
B(2) -- A + emerging text/context considerations
C(4) -- A + B + TWO types of relational considerations.


<6>
This pattern of development is 'standard' for us and C is where we get into creating complex symbols and metaphor. B is where we use analogy (I note your comments re Baars -- his method is analogous which is fundamental to 'proper' Science).

This pattern of development is in ALL disciplines and there is feedback in that once we get to C so we create symbols/metaphors that feedback into A (and are then treated as if 'real'). -- hierarchy at work. Furthermore, the more 'refined' a discipline the more symbols and metaphor as we attempt to
describe whole/aspects behaviour.

<7>
Note that a problem emerges in that ANY relational mappings can be illusion - a 'chance' pattern emerges that is given 'meaning' but is in fact just a 'chance' pattern e.g. Markov chains.

<8>
In brain structure, although the gross context for Science is left-brained the above pattern 'maps' to neocortical function -- left brain absolutes to right brain summing of aspects (and possible illusion). To switch disciplines, look at philosophy where we have:

A - objective .
B - A + categorical.
C - A + B + moral + metaphysical.

<9>
Same in the esoteric disciplines (the elements have a root source - AIR OR EARTH. Then comes AIR/EARTH and from this emerges FIRE/WATER)

Same in the models of Quantum mechanics. (see my page http://www.ozemail.com.au/~ddiamond/indexA.html)

(for a discussion on origin of maths --- see http://www.ozemail.com.au/~ddiamond/maths.html)

<10>
In the development of 'mind' so we have a gross context set by the parts of left brain and right brain. These then combine in relationships from which emerges 'novel' behaviour (novel in that the context is determined and so nothing 'new'). Thus the 1-2-4 (and feedback into 1) works like a fractal and so the left brain is 'like' A and B and the right brain adds C. As we develop so the 1-2-4 emerges WITHIN these basics. SO a left bias to objectivity as context has 1-2-4 in it in the for of numbers (as well as considering explicit relationships like categorical philosophy. But even metaphysical philosophy is 'here' simply because it can have an objective bias even when dealing with 'god').

<11>
Modern science is at the C level (statistical bias) and so touching on possible illusions and so more subjective assessments but it's initial context (and so the context that colours all that follows) is still A and it is this that 'makes' Science.

<12>
What the 1-2-4 pattern stresses is that there are FOUR ways to describe one 'thing' (and this can increase as we develop through levels). So Science is one way of describing experiences but has its focus 'out there' and it is linked to persona types we call rationals (solution seekers). The other form of left bias are sensation seekers who will describe by direct experience (thus you can see the link to Science -- its just that sensation seeking can be too fundamentalist and Science NEEDS *negation* to be able to create 'robust' maps.).

<13>
When we move into right brain areas so we enter the world of security seekers and identity seekers; these 'types' form the basic context in which the 1-2-4 pattern can work and so finer and finer analysis leads into increasing complexities but always in an overall context.

<15>
Thus the area of SUBJECTIVE analysis is linked to identity seeking and is often linked with spiritual/non-locational concepts that 'Science' cannot deal with since it is location-based.

<16>
However, if we change the traditional interpretation of Science from 'finding truth' to 'finding solutions to problems' then the context of Science shifts from a rigid one to an emphasis on formal methods and so a dynamic system that works BOTH in subjective mode as well as objective mode; we just need to recognise that subjective analysis is cultural 'truth' rather than 'universal truth' ;-)

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[Author: Christopher J Lofting
e--mail <clo@fmsc.com.au>]