The blog *Uncommon Descent* is, of course, one of the two main propaganda arms of the intelligent design movement — the other one being “Evolution News”. Since the ID movement is essentially based on religious dogma and deception, it’s no surprise that these blogs have a large amount of fake content. But I am always surprised at how *shamelessly* they mislead.

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.

stevewatson says

At the risk of being overly charitable, I’d guess that Denyse just copied her post title into the body as the paper title. Not malicious, but typically careless. But she does raise another deep mathematical question that I’m sure you could answer: what’s a “celeb number”? 😉

As for the Hamming article: it seems obvious that the universe must contain some kind and level of regularity in order to support the existence of beings like ourselves, and for any kind of regularity, there exists (by definition?) a mathematical description. What’s the big mystery?

cubist says

The tite of this blogpost is one word too long.

heddle says

I didn’t even know Uncommon Descent was still active.

I agree with Hamming, although I also agree you could quibble with his title. Wigner put it better, I think, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” which doesn’t imply that all mathematics is effective, just that math we need for physics. (I understand that

unreasonablemay not be the best word. MaybeSurprisingis better.)I teach a honors course called

The Evolution of Physicsand one thing I ask the students to ponder is this: what would have happened to the development of science if Newton’s 2nd law turned out to be anonlineardifferential equation?”Perhaps yet another way to put it is: “The surprising linearity of everyday physics.”

shallit says

Prof. Heddle, why exactly do you find it surprising?

heddle says

Because I know no a priori reason why the universe should be so linear. Newton got to calculus because he could compute the gravitational field of one piece of mass dm as if all the other dm’s weren’t present, then sum (integrate) all the independent calculations. But what if the gravitational field of dm was altered by the fields of the other masses i.e., what if its contribution was different from when it is the only mass present? (That is not an unreasonable scenario.) It would have been game over man.

I am not suggesting anything theological by this, I am only suggested that the mathematics of everyday physics could have been way, way harder. I do find it surprising that it is so simple. (And of course I’m not alone, I’m in good company, giants like Wigner and Feynman.)

shallit says

Well, there’s no reason (as far as I can see) that the universe should be

any particular wayat all! Should we be surprised, for example, that there are 3 spatial dimensions and not 2 or 4? Or that tritium has a half-life of 12.5 years, and not 12.7? Or that the fine-structure constant is very close to 1/137, and not 1/139? Or that there are 8 (or 9) planets in the solar system, and not 7 or 10? I just want some reasonably objective way to measure how much we should be surprised byanyphysical description.As for physics being “simple”, I think if you ask undergraduates if they think it is, they will say it is not. Look how long it took relativity to be discovered by humans.

When it comes to philosophy like this, I am completely

unimpressedby the opinions of great physicists — even Wigner and Feynman.heddle says

Hmm. Seems like a lack of curiosity on your part, but to each his own.

shallit says

My curiosity is about why you think it is surprising, but you didn’t explain why. Of course I’m interested in why the universe is the way it is, but it seems we don’t have the slightest idea at the moment, and I doubt I would have any special insight into the question.

Reginald Selkirk says

Someone would have realized that it didn’t apply very well, someone else would have come up with the correct formula, and Newton would consequently be somewhat less famous.

colnago80 says

Actually, there was an article with the same title written some 20 years previously by the physicist Eugene Wigner.

http://homepages.physik.uni-muenchen.de/~vondelft/Lehre/14t0/Wigner-Unreasonable-Effectiveness-of-Mathematics.pdf

shallit says

Yes, Wigner’s article is quite famous and it is cited in the Hamming article.

cubist says

Mathematics can be thought of as a “language” which can describe… pretty much anything that’s internally consistent, and some things that aren’t. In this light, why

shouldn’tmath be applicable to the universe we live in?