One of the recent entries at Uncommon Descent is a good example. They refer to a 1980 article of Hamming entitled "The Unreasonable Effectiveness of Mathematics". It's not hard for anyone to verify that what I just wrote is the correct title of Hamming's article; indeed, the full text of the article is easily available online.
I am not going to criticize Hamming's article in much detail here. There is much that is good in it, but I feel his final conclusion is unmerited. On what rigorous basis can we measure how effective mathematics is, and on what basis are we allowed to conclude that the effectiveness we observe is "unreasonable"? It seems purely a matter of personal taste.
My own personal taste is that mathematics is remarkably ineffective, because the vast majority of events that we see in the physical world are quite difficult to model accurately. If we release a single tritium atom in a lecture hall at 10:00 AM, where will it be at 11:00 AM? No physicist in the world can tell you with very much precision.
Similarly, Hamming asks, "How can it be that simple mathematics, being after all a product of the human mind, can be so remarkably useful in so many widely different situations?" Well, lots of mathematics is not remarkably useful. Much of what I personally do has little real-life application. So how can we measure, in a precise way, when that usefulness is "remarkable" and when it is not? Hamming does not tell us. My own personal view is that humans tend to use what is effective and discard what is not. If, for example, dancing were more effective in describing the physical world, scientists would be ballerinas.
In any event, Hamming's observations are not my main point. My main point is that, at Uncommon Descent the title of Hamming's article has been altered from "The Unreasonable Effectiveness of Mathematics" to "The Unreasonable Effectiveness of Mathematics vs. Evolution". Whether this change is a matter of deliberate deception or pure incompetence, I am not certain. But it is part of a larger pattern that we see repeated.
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With scientists attempting to maintain some level of rigor/accuracy/integrity, it’s hard to see how one even combats the deliberate lies, distortions, misinformation to which the other side is willing to stoop. And now we have a compulsive liar as President drawing a devoted fanbase. The near-term future, frankly, seems bleak indeed. :(
"Whether this change is a matter of deliberate deception or pure incompetence, I am not certain."
I'm pretty sure that was a post by O'Leary. So I'm inclined to go with incompetence.
"Whether this change is a matter of deliberate deception or pure incompetence, I am not certain."
My first thought - consider the source, it's deliberate deception. But when I look at how blatant the error is
A friend draws attention to an old paper, “The Unreasonable Effectiveness of Mathematics vs. Evolution” (The American Mathematical Monthly Volume 87 Number 2 February 1980)
and then see an immediate link directly to a pdf version of the paper, it seems (to me) to be stronger: it is a deception given with the certainty that accompanies the knowledge that the people intended audience don't care that the thrust of the article has been misrepresented. Sad.
(And apparently they've back-linked this article to some problem(?) about mathematicians not yet knowing whether pi is normal.
I thought anti-vaccinationists were dense and dishonest -- these folks may surpass them).
I liked this rebuttal article by D. Abbott in an IEEE paper (PDF)
"The Reasonable Ineffectiveness of Mathematics"
http://www.eleceng.adelaide.edu.au/personal/dabbott/publications/PIE_abbott2013.pdf
Does the article by Hamming actually discuss evolution? If so, I might be willing to give them the slightest tiniest benefit of the doubt. If not, I'd go with dishonest, since they are that too.
The point about the subjectivity of the effectiveness of mathematics is further undermined by the fact that the vast majority of human beings who ever lived never learned anything more advanced than the barest of basics of arithmetic. If at all.
Most people either don't have the time to get competent at a high level of mathematics, or are incapable (or so bad at it it would take them most of their life).
One of my personal ideas is that math is thinking, thinking is math. When I have three errands to do, at different locations, and take a moment to think what is the best order to do them in, I am doing math. (There is good math and bad math - good and bad thinking - of course.)
So yes, to the extent that we understand the universe, it is math that gives us that understanding. The deeper question is, how is thinking/research/design accomplished? Another of my personal ideas is that thinking, design work, and scientific progress are done by a process of evolution (trial and error, with selection criteria and memory). If I am correct, instead of contradicting the biological theory of evolution, our mathematical accomplishments are more evidence that evolution works.
I've long been bothered by that sentiment, the unreasonable effictiveness claims. Your points about the ambiguity of both words is good, but wasn't my usual problem with it.
You mention you think we probably study the stuff that seems interesting and useful, me too, I was called a formalist once on the computational complexity blog for that sentiment I think.
But now it has me thinking about Douglas Adams' humorous criticism of the people who look at the world and think it was perfectly made for them, comparing it to a puddle that remarks on how perfectly shaped the hole it occupies is for it specifically — insisting on that perfection even as it evaporates and disappears.
The other part that bugs me is, what would a universe that wasn't amenable to mathematical modeling even look like?
Regarding the entries at "Uncommon Descent" I'm sorry but I don't have the stomach to read that kind of drivel, however, some of Hamming's papers and the Dover reprint of his " Numerical Method's ..." are things I have read.
On the back of the Dover edition a partial quote reads as follows "..the purpose of computing is insight, not merely numbers."
Your statement, "On what rigorous basis can we measure how effective mathematics is.." is like comparing Euler to Gauss, insight with invention vs. insight with invention and rigour. Or, the difference between being literal and literate: the American "rigor" vs Canadian "rigour." The context is an important qualifier.
The intent of communication is to effect a change unlike many forms of religion where the intent is to infect. To measure effect here presupposes Chomsky's "the medium is the message" where the form of the conduit enabling communication is more important than the information (or noise) passing through it.
The Borgia's, the ups and downs of Confucianism, Mormonism and Scientology are worthy of study and effectively one can be infected or not after absorbing this transmission of information (or noise). As sentient beings, if we can formulate questions then we certainly don't know everything.. or if we can't then we're ignorant.
In response to "philosopher-animal", yes, Hamming's paper does mention evolution, but only in a discussion of whether evolution has created human faculties that can accurately perceive reality (Hamming says: not entirely). But Hamming makes no assertion in his paper that mathematics does not explain evolution.
In fact, if mathematics is "unreasonably effective" when explaining evolution, that would mean that it is successful in explaining it. Something that O'Leary has never conceded.
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