Thursday, April 15, 2010

Does Mathematical Beauty Pose Problems for Naturalism

A redated post.

Westmont College mathematiciam Russell Howell thinks that it does. This is an interesting offshoot of the argument from reason.

5 comments:

Robert O'Brien said...

I agree, and posted as much to my blog:

http://huperborea.blogspot.com/2006/07/god-and-critical-thinking.html

stunney said...

See also this excellent piece

Edward T. Babinski said...

Mathematical equations that attempt to come nearest to reflecting our human observational studies of the cosmos are maps, not the territory itself.

Think of the cosmos as a drawing with lots of wavy lines, very complicated convoluted. The human mind tries to put a uniform grid on top of that drawing, dividing up the drawing into
lots of neat 90-degree-angled boxes of equal size, and then the human attempts to analyze one tiny box of the grid that contains a part of one tiny line of the drawing. You can use mathematics to design a theorum that equals the shape of that line, like in geometry. But that theorum may not
and usually does not hold, as more and more of the drawing and its endless intricate interweaving lines are examined, because you have to keep redefining the math and adding corrolaries as you examine each line inside each box, and in adjacent boxes.

So the difference between such equations and the cosmos itself is the difference between a map and the territory.

For us to fall in love with our own maps and say they are so beautiful they are beyond nature is perhaps a natural thing for humans to say who have worked so long and hard and over so many centuries to come up with the approximations that we have come up with thus far.

And all mathematical systems have their limitations. In base-10 we'll never know the answer to what "Pi" truly is since the decimals go on forever. Not to mention Godel and Russel's statements regarding the incompleteness of mathematics.

In any consistent theory, there must exist true but not provable statements. (Godel's Theorem)

stunney said...

It's not just mathematical and other forms of beauty that we appear to have lucked out on. It's the capacity for experiencing moral value, the capacity for religious experience, the capacity to study history, the capacity to translate Finnish into Japanese, the capacity to grow wheat for export, the capacity to not believe our species merely lucked out to become so unique across so many different dimensions of experience.

For instance, we can imagine a mathematically talented species which knew nothing of morality or aesthetics. Or a very ethical species which was hopeless at math. Or a wonderfully artistic species which was also amoral. But we got all three? Hmmm.

Anonymous said...

etb:
But that theorum may not
and usually does not hold, as more and more of the drawing and its endless intricate interweaving lines are examined, because you have to keep redefining the math and adding corrolaries as you examine each line inside each box, and in adjacent boxes.
========
But isn't something such as the inverse square law of gravity a (surprisingly) elegant and exact statement even if we can find situations where it breaks down?

Isn't your statement just a little like saying that pi is only an approximation of its reality as used in physics, due to increasing precision as we look for more significant digits?