Mathematics as a part of neuroscience

Along my search on how to deal with mathematics, I have found one paper and let me start with a quote

Materialists believe that mathematical objects exist only materially, in our brains.[3] Mathematical objects are believed to correspond to physical states of our brain and, as such, should ultimately be explicable by neuroscience in terms of biochemical laws. Stanislas Dehaene suggests that human brains come equipped at birth with an innate, wired-in ability for mathematics.[4] He postulates that, through evolution, the smallest integers (1, 2, 3 . . .) became hard-wired into the human nervous system, along with a crude ability to add and subtract. A similar position is defended by George Lakoff and Rafael Nunez, who seek to explain mathematics as a system of metaphors that ultimately derive from neural processes.[5] Penelope Maddy conjectures that our nervous system contains higher order assemblies that correspond to thoughts of particular sets.[6] She posits that our beliefs about sets and other mathematical entities come, not from Platonic ideal forms, but, rather, from certain physical events, such as the development of pathways in neural systems. Such evolutionary explanations seek to derive all our mathematical thoughts from purely physical connections between neurons.”

3. Cf. Jean-Pierre Changeux and Alain Connes, Conversations on Mind, Matter, and Mathematics (Princeton, N.J.: Princeton University Press, 1995), 13.

4. Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics (Oxford: Oxford University Press, 1997).

5. George Lakoff and Rafael Nunez, Where Mathematics Comes From (New York: Basic Books, 2000).

6. Penelope Maddy, Realism in Mathematics (Oxford: Oxford University Press, 1993).

What do you think, does it sounds plausible from a biology viewpoint?

In the paper, there are other suggestions

but I am not sure if they are really better. This is the problem with mathematics that bothers me at the moment. Any better idea?

Short discussion (see Deism and Newton):

09.04.2012 16:28:

I see some problems along this way.

Let us consider the story with Newton laws in this context. Laplace was able to create a new mathematical theory that did not exist at Newton’s time. What does it mean? That there was a gene mutation for time being between Newton and Laplace? Or that Nature has made natural neural networks in abundance already at ancient times and Newton just failed to employ full capabilities of his brain?

Also let us take my experiment with two mathematicians, I have made now a nice picture to this end, see slide 26

The theory above means that Pi exist only when mathematicians’ brains are running. Yet, it seems that a mathematical theory due to inexorable laws describes the experiment correctly even at the state when mathematicians are dead.

10.04.2012 21:55:

Finally, you are right that when living brains still exist, one have right to say that a mathematical model survives a death of a couple of mathematicians. The question is how the inexorable laws have functioned when there were no human beings. How the Universe computed itself when the mathematics has not been yet developed?


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