Archives - Mathematics: Page 30
Author: amparo enriquez (Fri Jul 22, 2005 5:13 pm)
Title: The Essence of Mathematics
THE ESSENCE OF MATHEMATICS
To some mathematicians math constructs although real are not physical. They are intelligible and captured by the human mind; one can think about them and even perceive them, but only through intellectual intuition. However, one cannot think of math entities as equal to ideas or to the mental images that we have of them, because while ideas and images might vary, mathematical entities are the same for everyone.
The statement that math constructs "although real are not physical" doesn't in itself bother me. What bothers me is the word "real". That is, how do we explain the reality of such constructs purely on the basis of the brain? I'm not attempting to call in spirituality here, but the definition and explantion of "real" is difficult when we're limited to explaining our mental life in terms only of the physical brain. I mean, without any more defining "real" any more than it has been, I'll make the statement that the mind "although real is not physical".
It might be good to equate physicalism with materialism. Most scientists avoid dualism at all cost, in general they seem to have a consensus in favor of materialism to the point that reality and materialism go together, hand by hand. However an absolute proof ruling out dualism has not been demonstrated.
From a materialistic point of view the images that mathematicians capture in their mind are most probably images or mathematical concepts a product of neural networks.
I would like to think that “real” or “physical” are both material and that the mind is material too, in spite of its emergent characteristics, of course one can always say that is after all a matter of opinion since we depend on consensus (based on scientific evidence) and not on an absolute proof.
The interaction of the physical brain with our surrounding physical world, including the cues and psychological messages we receive from others, helps build mind’s constructs (representations). The mechanism involved in this complex task appear to be biological and learned in nature.