Posts Tagged ‘life’
Procrastinators seldom do absolutely nothing; they do marginally useful things, like gardening or sharpening pencils or making a diagram of how they will reorganize their files when they get around to it. Why does the procrastinator do these things? Because they are a way of not doing something more important. If all the procrastinator had left to do was to sharpen some pencils, no force on earth could get him do it.
— John Perry, in his brilliant essay Structured Procrastination
Am I the only one who finds the last sentence above not a joke at all? Who has tried for months to send a single email?
(Prof. Perry’s short humorous essay is a true classic of our times, and one I have found much insight from. The trick of being able to do X simply by thinking of a more important Y has helped me many times, whenever I have remembered to apply it, and the essay helps one avoid the wrong tack of minimising commitments. Still, sometimes, there are things X to be done for which no more important Y comes to mind, and it is not clear what to do in that case.)
Fermat’s last theorem has a long and exciting history. Which everyone knows, so I’ll not mention it here.1 What I suddenly find to be remarkable though, is the very first event. The fact that Fermat scribbled it in a margin of Diophantus’s Arithmetica. That Pierre de Fermat, in France in 1637, was reading an ancient book written by a Greek in the 3rd century. That he was reading it in such a manner that the book’s asking how to split a square into two squares should impel him to not only investigate the question of how to split a nth power into two nth powers, for all n, but to also do it until he believed he had a truly marvelous proof.
When was the last time you made margin notes in a book?
Off topic: The book only answers the question for 16(=4²). Wikipedia has pictures of the relevant page for a 1621 edition, and the 1670 edition that contains Fermat’s notes. (Fermat died in 1665.) I’m not sure I’ve deciphered the Latin correctly (the Greek is right out), but what it says is the following.
[BTW, in case you have been thinking so far and have the objection that 16 cannot be written as the sum of two squares, I should point that for Diophantus, “number” apparently meant “positive rational number”, there were no other kinds of numbers. Negative and irrational numbers were “useless”, “meaningless”, and “absurd”.]
Suppose one of the two squares that add up to 16 is Q=N². [“Q” because it is a square, “quadratum”.] The other square is 16-Q. If the other square is (2N-4)²=4Q+16-16N, [um, why should it be?] then we get 16-Q=4Q+16-16N so 5Q=16N, or N=16/5 and Q=N²=256/25 (which is misprinted as 256/52 in the 1670 edition), and the other square is 144/25, which add up to 400/25=16. So the (an) answer is that 16 = (16/5)² + (12/5)².
You might notice this is not really an answer; all that Diophantus has done is take 3²+4²=5² and multiplied it appropriately to make two “squares” add up to 16. We could do the same for any square, e.g. for 49=7², we could write (7×3)²+(7×4)²=(7×5)², then divide out by 5² to say (21/5)²+(28/5)²=49. For any x, we could take any a and b such that a²+b²=1 (e.g. 3/5 and 4/5) and write x²=(ax)²+(bx)².
↑1. I found today (2008-11-27) an anecdote. The setting is this: it was April 1994. Andrew Wiles had first announced his proof in June the previous year, and sent it off to a journal, but a hole had been found. It seemed at first it would take only a few hours, then weeks, to fix it, but months had dragged on without success. And on April 3 1994, Gian-Carlo Rota sent out an email announcing that Noam Elkies had found a counterexample to Fermat’s last theorem! So it seemed that the hole was unfixable after all. There was some disappointment all around before it was realised that the email was an April Fool’s joke, that had somehow got incorrectly dated :-) I found it on Wikibooks, but see Lance Fortnow’s blog post for the email.
Here is a very interesting article called Quitting the Paint Factory by Mark Slouka. Although, of course, I’m the one who needs it the least.
Reading Aaron Swartz’s essay today, I learnt that rewards and punishments do not work.
There are a lot of myths about productivity — that time is fungible, that focusing is good, that bribing yourself is effective…
He also quotes Alfie Kohn, who has written books and articles on related ideas, and especially quotes one particular article. Others agree: Wanting to do the tasks is most important. Even David Allen thinks so. There’s also Paul Graham’s essay, in which he points out that having a to-do list and doing the things on it — the minor, unimportant “errands” — is also actually a form of procrastination that avoids doing the really important things, and that most of us use the errands as an excuse, and make sure we don’t have time to do the important things.
Ubuntu/Debian have a nice small useful package called gtimelog.
, but I think I’ll check them out some other day and actually do something useful now, for a change. There is also org-mode; screenshots in the tutorial and manual here. Orgmode homepage, another howto, debian package?, and Sacha Chua’s unbiased comparison with Planner.el.