dvunkannon
Posts: 1377
Joined: June 2008
|
| Quote (Reciprocating Bill @ Jan. 19 2011,11:20) | | Quote (dvunkannon @ Jan. 19 2011,09:52) | David Anderson has a post on UD, linking to an essay on his webpage, of the "Unreasonable Effectiveness" variety.
My response on his blog is in moderation, so here it is in case he quashes it.
| Quote | Hi David,
Sorry I couldn't leave this comment on your website, some problem with WordPress login.
Anyway, your essay is very reminiscent of the famous essay by Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences.
I think you are quite wrong and naive in your argument and conclusions. Ever since the invention of alternate geometries in the 19th century (by changing the parallel postulate of Euclidean geometry) mathemeticians have known that they are not discovering reality, they are inventing sets of axioms, operating on those with sets of logical operators, and seeing what results. A particular set of axioms may or may not have any relevance in the real world. (GH Hardy loved quaternions because it was elegant math that he thought would never have applicability in the real world.)
Surveyors know you can't use Euclidean geometry to map out large parts of the world, you need to use spherical geometry, in which the interior angles of a triangle add up to more than 180 degrees. We choose the most appropriate tool for the job, and invent a new tool when existing ones give too many errors to suit us.
There is nothing about mathematics that is inconsistent with evolution. Even simpler animals, such as a frog trying to catch a fly, have the circuity evolved to lead the fly in its path in order to catch it. This is modeling the real world in the interior of the brain. Marry up these skills with our abstract reasoning and you get maths.
In this sense, mathematics didn't evolve, any more than opera. We keep refining a tool that works, and throw out parts that don't work well. Do we use base 60 counting, like the Babylonians? Do we use a non-positional notation, like the Romans? No, we've discarded them. Mathematics is a tool we keep sharpening - don't be surprised it cuts so well!
As good as any tool is, it has limits. Partial differential equations really don't cut it for fluid flow, and therefore climate modeling. So we invent new tools, such as fractals and multiscale modeling.
Simple consistent mathematics works because the underlying physics of the world is simple and consistent. (The gravitational constant doesn't change randomly every two meters throughout the universe.) Therefore, our utilitarian desires have led us to develop simple and consistent sets of axioms, and simple and consistent sets of logical operators. But don't pretend other choices are not possible, or that some people find them interesting.
You write:
<i>Unless our minds are reliable, the mathematics that we do may just be after all completely abstract and an illusion.</i>
This has problems on several levels.
1 - Our minds are fallible, and we do sometimes calculate and reason wrongly.
2 - Our minds are variable, and some people are better at some kinds of math that other people.
3 - We do check each other's workings, both at the level of using math and at the level of inventing it. Many proofs of Fermat's Last Theorem had to be checked and discarded before a correct one was invented.
4 - If you applied the same resoning to our optical system, you'd be arguing that we would never see optical illusions, because evolution could evolve a perfect eye. But we do see optical illusions. Our eyes and vision are fallible, our hearing is fallible, and yes, our reasoning is also fallible.
That is what you expect from evolution. |
|
Very nice. |
Thank you. This is also my basic response to StephenB's "I'm rational, you're insane." gambit. Try getting him to answer the question of which version of the parallel postulate is in his Rules of Right Reason ™ and why. Bussel really doesn't understand the concept of different systems of axioms, and why his chosen system is not priveleged, not the only system.
--------------
I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima
|
