Numbers are just human representations of memory and prediction to the
most likely outcome. In short math is probably a survival instinct.
Things precede and follow, because we seem to move through time in the
same momentary state. All math is really just addition and subtraction
of some shortcut stereotype of addition and subtraction.
We all possess the ability to cope with mathematics--if only we
recognize what's required. We all possess, if not literally a gene,
then at least an inherent ability not just for arithmetic but for real
mathematics: algebra, calculus, and the rest. A recent Darwinian
explanation for the origin of this ability, is based on the idea that
being able to handle abstract ideas and relationships confers key
evolutionary advantages.
Human infants have a rudimentary number sense, this sense is as basic
as our perception of color, and that it is wired into the brain. The
invention of symbolic systems of numerals started us on the climb to
higher mathematics. We are now approaching the crossroads where
numbers and neurons intersect. The structure of the brain shapes our
mathematical abilities, and our mathematics opens up a window on the
human mind.
It seems we have a number sense, the human mind seems to have an
innate grasp of mathematics. Place value systems (such as the Arabic
numeral system we use) arose independently in four separate
civilizations--evidence of a universal sense of number. A rudimentary
number sense is wired into our brains at birth. Experiments show that
chimps, like us, use symbols to denote numbers.
In the same mathematical reasoning that inspired Plato with visions of
eternal ideals, we find evidence for a provocative theory of
evolutionary change. The evolution of language is the surest
indication of a new kind of strictly internal brain activity, one
neither stimulated by the environment nor tied to physical activity.
Out of this "off-line thinking" emerged not only the syntax necessary
for speech, but also the symbolic logic essential to mathematics.
Enhanced symbolic abilities let early hominids think in this "off-
line" manner, while asking and answering "what if" questions about
tools, predators, habitats or prey.
Mathematics is a great artistic triumph of the race, one made possible
by an innate human ability. Language evolved in two stages and its
main purpose was not communication. The ability to think
mathematically arose out of the same symbol-manipulating ability that
was so crucial to the very first emergence of true language. Combining
a number sense with symbolic abilities, we use abstractions to
manipulate quantities, leading to arithmetic and potentially to
calculus and number theory. Abstract models describe concrete things--
from rotating clock faces to rattlesnake skins, use higher math
abilities. Mathematics is more than arithmetic. Real mathematics
involves making logical arguments about abstract objects.
Though its deepest structure shares an evolutionary origin shared with
language, math frequently calls upon a neurological number sense,
naturally strong in some, weak in others. Consequently, poets may
command powers of abstraction akin to those of mathematical geniuses,
yet still falter in doing simple algebra. But in any manipulation of
symbols, verbal or mathematical, we can easily see faculties that set
one of the earth's creatures apart from all others. Exploring the
mysterious beginnings of the mind's symbolic powers, takes us a long
way toward understanding what it means to be human.
If people are endowed with a "number instinct" similar to the
"language instinct"-as recent research suggests-then why can't
everyone do math? Why, then, can't we do math as well as we speak? The
answer is that we can and do-we just don't recognize when we're using
mathematical reasoning. Mathematics merely involves a relatively high
level of abstraction--but one we can all cope with, if we work at it.
Doing mathematics is very much like running a marathon. It does not
require any special talent, and 'finishing' is largely a matter of
wanting to succeed."
In a way similar Chomsky's theory that we are all born with "hard-
wired" linguistic ability, the mental process of making logical
connections between abstract objects and the mental process needed to
construct sentences have the identical structure. Thus, we can see
that the genetic heritage that gives us all the ability to communicate
by language also gives us the ability to do mathematics.
The Math Gene: How Mathematical Thinking Evolved & Why Numbers Are
Like Gossip
http://www.amazon.com/exec/obidos/ASIN/0465016197/
The Number Sense: How the Mind Creates Mathematics
http://www.amazon.com/exec/obidos/ASIN/0195132408/
> Numbers don't do lists, amorphous collections, sequences... look what
> happens if we think they do. Take the 'sequence' of 'natural numbers'.
> We count each number once, irrespective of its value. So we have one
> 'one', one 'two', one '65536', etc. It isn't our count of these numbers
> that arranges them, though. The numbers must magically arrange
> themselves through their own efforts, amorphously in one set, or
> sequenced, etc. But there is no method by which a number can cross the
> divide from being function-generated to being a member of an
> arrangement. In an arrangement all objects are, as far as the
> arrangement goes, identical.
>
> SPECULATION and CONCLUSION
>
> My point? My point is that we have generated myths about 'numbers';
> myths whose sources are found among school rote teaching methods. These
> methods worked only if we believed in the idea that numbers are
> independent, individual entities independent of the functions that
> create them. So, numbers possibly could, we believed then (and now),
> order themselves.
>
> We confuse arithmetical possibility with grammatical possibility. It IS
> grammatically admissable to speak of isolable numbers only because
> grammatically it is how we were taught to speak about 'numbers'. It
> started in infancy when we saw isolated 'numbers' on big coloured cubes,
> and numbers with personalities in 'Sesame Street'. The indoctrination
> continued in school through the employment of a grammatically correct,
> roted and sequenced, addition, subtraction, and times-table. Later, we
> saw numbers neatly boxed-up in logarithmic tables and - as if through
> some natural, innate ordering property - lined up on calculator screens.
>
> Numbers are not countable. They are neither isolable nor individual
> objects. The term 'numbers', 'a number', 'all' numbers, etc., are
> arithmetically inadmissable, even if they are grammatically par for the
> course.
