Tuesday, December 28, 2010

Facts More Important than Theory

Most people think facts are easy and theory is difficult. It is often the other way around. As Charles Darwin wrote:
False facts are highly injurious to the progress of science, for they often long endure; but false views, if supported by some evidence, do little harm, as every one takes a salutary pleasure in proving their falseness.

So I got a lot of pleasure reading the insane amount of commentary on Steven Landsburg's puzzle about the percentage of boys in a population where they stop on the first boy (answer: with 1 family 30.685...%, approaching 50% as the number of families goes to infinity). The disagreement between many very smart people gets into semantics (is it really 50%, or just beneath it?), but in any case, if you put out a logic puzzle and make a mistake, it won't last long if its important. Not many people redo empirical analysis, however, because it's not something you can just figure out in your head: you have to gather data, understand it, clean it, etc., and then apply statistics.


michael webster said...

The only interesting fact about the discussion is that people are arguing over whether to translate the original question; as, commentator at mathoverflow.net, put it:

"The issue is how one works out an "average proportion"---is it "average # boys" / "average # girls" or is it "average of #boys/#girls". These are visibly going to be different."

How can people argue over what the "right" translation of the english language problem to a formal calculus without specifying what counts as a correct translation?

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Michael Meyers said...

Agreed... I thought the whole argument was stupid as it was not about math per se, but about meaning of an English sentence.

Anonymous said...

"Not many people redo empirical analysis"

... partly because academics are loathe to publish the data underlying their analyses.

Anonymous said...

One must also consider that collecting data is not the glory work. The real "genius" is in manipulating data until you get the desired answer. Data collection and all the painstaking effort that goes into doing it the right way is regarded as mere grunt work.

At least that's what climate scientists think. They use the same reheated data time and time and time again to publish new papers.

Steven E. Landsburg said...

Michael Meyers wrote:

Agreed... I thought the whole argument was stupid as it was not about math per se, but about meaning of an English sentence.

Would that this were true. Some of the argument is along these lines, but a lot of it is still coming from people who want to argue that E(G)=E(B) and *therefore* E(G/G+B)=1/2. That's not a semantic difference; it's just flat out wrong.

Drewfus said...

Looks like getting good data just got a whole lot harder.