Math as an Experimental Science

On Wed, 30 Aug 2006, BuddhaThu wrote:

I am an empirical/intuitionist in my approach to math.

To me, symbols on a chalkboard are sensed by way of the eyes. They are
empirical.

There are two sorts of mathematicians, those who think symbolically and
those who think visually. I tend to be a symbolic thinker. Perhaps you
also.

But rules governing the symbol manipulation are invisible to the naked
eye.

To name a number is not the same as the governing rules of the numbers.
It is like calling someone 'President of the USA,' without giving
him policy rules and procedures to be President. He has yet to play the
game.

I am not into mysticism. I just believe that is how the brain works.

Rules are beyond the five senses, but they are neurological.

Thinking about how the brain works, clogs the brain.

Rules governing math manipulation can never be stated or written while
you are doing math. You will never be able to resolve your problem!!!

It will become a paradox of meta-mathematics. It will result in
infinite regress. Infinite regress is not the same as infinite
recursion.

It will be inconvenient and cumbersome while working out your numbers.
You should just know how to do it.

You do not write out the rules when you calculate 2+2=4. You just do
it. There is a how, but no why. There is only description, but no
explanation. Explanations belong to physical things that can cause
things to happen. Symbol abstractions can only describe them.

So in a way, math is experimental, but in a way it is not. It is
'not' because symbol abstractions do not have the same level of
independence, or 'a hands off' attitude during a scientific
experiment.

I believe mathematics to be a free creation of the human mind. There is
a level of freedom that is lacking in scientific experiments. I am not
Platonic. Math is not an objective enterprise.

Here, 'to experiment' has a difference in grammatical context.

'Experiment' is fact because the opposite can be true. This is due
to change and contingency.

Quaterions were an experiment that disproved a theory.

Math is experimenting where the facts are dependent upon us. We make
the rules and the symbols. The numbers do not manipulate themselves.

Science is experimenting where the facts are dependent upon the world.
The math just helps us to describe them. But only nature can causally
explain.

They are truly two different things. Yet, they are equally empirical on
two distinct levels.

'Experiment' is a word that simultaneously deploys imitation and
creativity.

It used to be during the Renaissance, artists like Da Vinci would try
to learn about nature by copying it to its exact detail on canvas.

Science does the same, except it gives the paintbrush over to nature.

This does not in anyway deny creativity.

In an experiment, we let nature recreate itself. But how we set it up
is up to the creative ingenuity of the scientist.

In a mathematical experiment, numbers are imitated and combinations of
rule are deployed, but how they are used in those combinations are up
to the ingenuity of the mathematician.

I have to quit now. I am feeling a bit foggy. It is time for a cup of
tea. :-)

Indeed, as I commented, thinking about how the brain works clogs the
brain as surely as meditation on not thinking continues thinking.

.

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