Chad, inspired by Mark's contradictions, asks for peoples' favourite dubious proofs.
Dave contributes some classics, but
Astronomers excel at dubious proofs.
Mathematicians despair of "physics proofs".
They lack rigour, shall we say. Often such trivia as uniqueness, or even existence are omitted, and we proceed with "whatever works".
My favourite, which I recently used in class, is a variation on the Ansatz (dumb things always sound better in foreign languages).
I derived a a set of evolution equations to first order, noted that by inspection they were formally an insoluble set of coupled partial differential equations, and then offered a "solution by inspection" - a dispersive wave equation, natch.
It works, so why not use it.
But, that is moderation compared to what people do to actual data.
There my recent favourite is the proof by "what else could it be"...
Some recent nice claims in the literature, which are almost certainly correct, but arguably overstated, note the presence of significant statistical variation in spectral features, and then note that this "must be due to X" where "X" is the claimed detection.
The problem is that the data is not actually good enough to demonstrate that, it merely demonstrates that there is some absorption/emission there, somewhere in a fairly broad spectral region, at some marginally significant level.
The proof is "well, what else could it be"?
What else indeed.
Actually, physically it could be other things, but that'd be so astounding it'd be interesting.
On the other hand, on a recent paper I co-authored, the referee gave us a hard time because we had not logically excluded all other possible theoretical explanations in our work.
I was tempted to invoke Fermat.
But, instead suggested that this was an overbroad expectation, and that we might defer to the more usual approach, and let subsequent actual data test the different theories.
The editor liked that.
Feel free to include your favourite "A mathematician, physicist and Xologist...", joke, but only so long as it includes sheep or equivalent.
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More like this
A mathematician, a physicist, an engineer, and a blogger have left from the Waverley Station near Princes Street, and are riding a train through Scotland from Edinburgh to Glasgow.
The engineer looks out the window, sees a black sheep, and exclaims, "Hey! They've got black sheep in Scotland!"
The physicist looks out the window and corrects the engineer, "Strictly speaking, all we know is that there's at least one black sheep in Scotland."
The mathematician looks out the window and corrects the physicist, "Strictly speaking, all we know is that is that at least one side of one sheep is black in Scotland."
The blogger frantically types the above anecdote into his WiFi laptop. "Hey, don't you guys realize that we're in an anecdote, quite similar to many that you have no doubt already heard?"
After some observations and rough calculations, the engineer understands the situation and starts laughing.
A few minutes later the physicist understands too, and chuckles to himself happily, as he now has enough experimental evidence to publish a paper.
This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humor (or humour in Scotland) from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.
The blogger has been watching the others come to these realizations, and posts this comment. He smiles to himself with satisfaction. Another evening well spent.
Oh. Right. I forgot the reference.
"The Physicist, the Mathematician and the Engineer: Scientists and the Professional Slur"
Carolyn F. Gilkey
Western Folklore, Vol. 49, No. 2 (Apr., 1990), pp. 215-220
doi:10.2307/1499408
There. Now it's publishable.
You might want to re-write the first paragraph something more like:
"A mathematician, a physicist, an engineer, and a blogger are travelling by train from Edinburgh to Glasgow. The train passes out of the city and into the countryside, passing fields and woods."
guthrie: I might. But, first, the mathematician, physicist, engineer, and blogger would seriously disagree about the meaning of the word "field."
Second, I should have said "Waverley Station" rather than "the Waverley Station" if I wanted to give the correct impression that I'm intimately familar with Scottish rail stations, though not, I should add, intimately familar with sheep.
The Carolyn F. Gilkey paper is actually quite interesting.
Caltech's massive Interhouse party happened last night, technically until around 2:00 a.m. this morning, for those intimately familar with Caltech culture.