The blinkered mathematician principle
Mathematicians are good at mathematics; they are often quite good at
intellectual matters unrelated to mathematics; but they are often quite bad at
matters slightly related to mathematics.
"Blinkered" in the sense of narrow vision.
Here are some typical examples (involving chance) of resulting statements which are
ridiculous outside that narrow vision.
- There is no element of chance in chess.
Your opponent might make a mistake; or you might make a brilliant move without realising it.
- Spending an evening gambling in a casino is foolish because you are likely to lose money.
No more foolish than any other evening's entertainment that costs money.
- The birthday problem shows that amazing-seeming real-life coincidences are "just chance".
No. No. No. This is like saying "understanding the dynamics of a pendulum proves the Universe is deterministic".
It may well be (as I believe) that real-life coincidences do indeed happen no more frequently than
"just chance" predicts, but proving this would require an
honest argument detailing the kind of coincidence under discussion.
- Littlewood's law seeks to debunk non-rational explanations
of 1-in-a-million chance events
by pointing out that, if there are a million such events possible in one month, then
such "miraculous' events will occur on average once a month.
But how exactly does the invocation of 999,999 unspecified hypothetical events (that didn't happen)
differ from superstition? As in the previous item, you need an honest argument.
- (Edited from a Nobel Prize winning author). An insurance company can guarantee it will always
profit by basing its calculations on the law of large numbers.
Write 100 times: AIG, AIG, AIG, .....