* Tony Hoare, 1980 "I was eventually persuaded of the need to design programming notations so as to maximize the number of errors which cannot be made, or if made, can be reliably detected at compile time. Perhaps this would make the text of programs longer. Never mind! Wouldn’t you be delighted if your Fairy Godmother offered to wave her wand over your program to remove all its errors and only made the condition that you should write out and key in your whole program three times!" Why ("in the bowels of Christ" - Oliver Cromwell 1650) is this so difficult to understand? All programming notations eventually come to resemble TECO: that is to say, line-noise. Another one: "Never to this very day has the full truth of this story been told: That one fine morning, when the Emperor felt hot and bored, he extricated himself carefully from under his mountain of clothes and is now living happily as a swineherd in another story." From his Turing Award paper CACM 1981, "The Emperor's Old Clothes". He can be an exquisitely stylish writer. Both Hoare and I worked for computer companies (he in a much grander capacity than me), and with both married technical authors we met there. We both entered academia sometime after. We were both much concerned with type-theories (me almost exclusively). * Martyn Thomas, 06 Aug 2009 The excuses that people come up with to justify their unwillingness to learn and use some simple mathematics should be collected in a book and studied by psychiatrists. * Bo Diddley (1928-2008) "A dude with a pencil is worse than a cat with a machine-gun." Seemingly, he was paid no royalties till about 1962. * Giovanni Sambin (Frauenworth, 2006) "The structure here is very shy. It will not come out if we are too noisy." I like the idea of investigating mathematics like David Attenborough hidden in the bushes (with a TV crew). Mathematicians as natural historians. Also that one has to be quiet to listen to the shy voice of the things themselves, or the gorillas, and take care not to scare them off with mental noise. * Leslie Lamport: (concurrency mailing list, 1988-1990: Flame re distributed processes and granularity) http://www-i2.informatik.rwth-aachen.de/Forschung/MCS/Mailing_List_archive/con_hyperarchive_1988-1990/0077.html: I admire philosophers. They have so much to teach us. From Aristotle I learned that heavier bodies fall faster than lighter ones; Kant showed me that nonEuclidean geometry is impossible; and Spinoza proved that there can be at most seven planets. And now, the philosophers on the concurrency mailing list have told me all the things I can't do because I use a logic based on an interleaving model. The only foreign language for which I am at all equipped to appreciate fancy literary style is American. There are not many American or European computer scientists who can compete with Lamport's writing style. (Style aside, I'm very persuaded of the importance of many issues he's identified in the foundations of programming, in about half of which I'm on his side of the argument he inevitably provokes.) An important trait in Lamport's style is fulmination against philosophy. For someone so down on philosophers, he talks about how things are in reality and language an awful lot. Being down on philosophy and street-wise is of course impeccably philosophical Socratic and Wittgensteinian style. I particularly like Lamport's answer to questions as to whether the 35'th infinite cardinal equals the ASCII code for 'c': "I don't know, and I don't care." If that's not interesting philosophy, what is? [About the planets, wasn't it Hegel?] [Actually I think among decent philosophers one could propose Descartes, from whom he learnt algebraic geometry; Frege, from whom he learnt the predicate calculus; Turing, from whom he learnt that termination is undecidable; and the more recent Lamport, who has given us ways of describing sequential behaviour, based on an interleaving model of concurrency.] Other Lamport quotables: * from a footnote of a letter to the editor CACM Nov 1979 In the interests of restoring meaning to our language I will call programs "programs". I urge the ACM to do the same. * from a paper on software specification: "One wants a different map of Texas for driving from Amarillo to Houston than for finding new deposits of helium." This could (almost!) be the first line of a(n obscure) Bob Dylan song. * "I don't know and I don't care!". This is (was?) Leslie's usual retort to a question like "So, Mr. type-unbeliever, what's 1/0, huh?". I once asked him whether it could be aleph_{53}, and I think he said "Why not? How could it matter?". Michael Rathjen once replied to a similar question by comparing it to the question of whether Hamlet preferred Marmite to Strawberry jam. I admire this sort of thing: it makes me think of passing through a point at infinity, and coming up the other side. * Howard Aiken (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aiken.html) Don't worry about people stealing your ideas. If your ideas are any good, you'll have to ram them down people's throats. Sadly, having to ram your ideas down people's throats, or having someone else's rammed down yours, is only a necessary condition for them to be any good. * Napier, John b. 1550, Merchiston Castle, near Edinburgh, Scot. d. April 4, 1617, Merchiston Castle From the preface to "Plaine Discovery of the Whole Revelation of St. John" (1593). dedicated to whoever was "your Majesty" in Scotland in 1593. "Let it be your Majesty's continuall study to reforme the universall enormities of your country, and first to begin at your Majesty's owne house, familie and court, and purge the same of all suspicion of Papists and Atheists and Newtrals, whereof this Revelation forthtelleth that the number shall greatly increase in these latter daies." It is difficult to imagine this in any other voice than Ian Paisley's, but Napier lived in Merchiston and may have sounded more like Stanley Baxter. See also the beautiful http://www-groups.dcs.st-and.ac.uk/~history/Bookpages/Napier10.jpeg * Charles Babbage: "Propose to an Englishman any principle, or any instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, a defect, or an impossibility in it. If you speak to him of a machine for peeling a potato, he will pronounce it impossible; if you peel a potato with it before his eyes, he will declare it useless, because it will not slice a pineapple." - (I saw this in a newsgroup signature, and have not checked it. It appeals to me partly because I regard myself as 1% more Scottish than English.) According to wikipedia, Babbage had an intense hatred of street music. In retort, he was tormented with an unending parade, outside his house, of "fiddlers, Punch-and-Judys, stilt-walkers, fanatic psalmists, and tub-thumpers". He once baked himself in an oven for "5 or 6" minutes, at 265 deg C, to see what would happen. * David Hilbert, {\em Bull AMS}. {\bf 8}. 102, 437--479. "The deep significance of certain problems for the advance of mathematical science in general and the important role which they play in the work of the individual investigator are not to be denied. As long as a branch of science offers an abundance of problems, so long it is alive; a lack of problems foreshadows extinction or the cessation of independent development. Just as every human undertaking pursues certain objects, so also mathematical research requires its problems. It is by the solution of problems that the investigator tests the temper of his steel; he finds new methods and new outlooks, and gains a wider and freer horizon." I don't know what Hilbert meant by a problem, but I suspect he meant something with a perfectly clear meaning, that evades showing true or false. Problems that evade precise formulation, and problems of clarification are also necessary for the health of any branch of science. * Georg Cantor, Doctoral thesis (1867) In mathematics the art of proposing a question must be held of higher value than solving it. I think meaningfulness (as in asking questions) is as interesting as questions of truth (as in settling a question), and more problematic. * J. von Neumann (1943. ``The Mathematician.'' In Works of the Mind. Chicago, IL: University of Chicago.) "As mathematics travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from ``reality,'' it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely {\em l'art pour l'art}. .... In other words, at a great distance from its empirical source, or after much ``abstract'' inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up.". So von Neumann thought the basis of mathematical meaning is empirical application. * George Berkeley (Principles of Human Knowledge, 119): "Arithmetic has been thought to have for its object abstract ideas of Number; of which to understand the properties and mutual habitudes, is supposed no mean part of speculative knowledge. The opinion of the pure and intellectual nature of numbers in abstract has made them in esteem with those philosophers who seem to have affected an uncommon fineness and elevation of thought. It hath set a price on the most trifling numerical speculations which in practice are of no use, but serve only for amusement; and hath therefore so far infected the minds of some, that they have dreamed of mighty mysteries involved in numbers, and attempted the explication of natural things by them. But, if we inquire into our own thoughts, and consider what has been premised, we may perhaps entertain a low opinion of those high flights and abstractions, and look on all inquiries about numbers only as so many difficiles nugae, so far as they are not subservient to practice, and promote the benefit of life" I imagine this spoken in a Leeds or Yorkshire accent; but ISTR he was from Dublin, and probably sounded more like Shane MacGowan. I like this because I am precisely one who dreams of "mighty mysteries" involved in certain kinds of arithmetic. * Gottlob Frege: Grundgesetze der Arithmetik (1903) "A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press." I had a much less dramatic version of such an experience in 1978. My nemesis was Peter Aczel rather than the by then late Mr. Bertrand Russell. In response, I abandoned what I was doing (which was exploring the underpinnings of dependent type theories, about which I had anyway many doubts) and instead made a living happily as a programmer, in another fable. * Schopenhauer: Anus obit, onus abit -- The old woman dies, the burden departs. Schopenhauer once assaulted a steamstress who refused to leave his apartment. He was obliged to make substantial annual payments to her for the rest of her life. This is what he said when at last she died. It is a 4 word poem. * Alan Perlis: Simplicity does not precede complexity, but follows it. It can be really hard to recognise simplicity. * James Brown: Hair is the first thing. And teeth the second. Hair and teeth. A man got those two things he’s got it all. You don't know what you've got till it's gone. (Joni Mitchell, I think.) * The bible: "When I was a child I spoke as a child I understood as a child. I thought as a child; but when I became a man I put away childish things." At school, I had to learn several passages in the (King James VIth/Ist) Bible "by heart". This was among the better parts of my education, besides learning Geometry and Latin. Passages like these were very definitive for me of beautiful ideas expressed in beautiful English. * Albert Einstein: "The difference between stupidity and genius is that genius has limits" The word "genius" has never meant anything to me, but I've known several remarkable people. The words they've brung to mind are "focus", "serious", (all-too-)"human" and "sweat". * John Major, British Tory PM 1990 -> 1970, about Labour leader Neil Kinnock, a notorious windbag: "The reason he never stops talking is because he's got nothing to say and so he doesn't know when he's said it." * I forget where I saw this: "God grant you the courage to change what you cannot accept, the serenity to accept what you cannot change, and the common decency to shut the fuck up about it." * Lou Reed. "One chord is fine; two chords is pushing it; three chords and you're playing jazz."