alexey_rom: (Default)
Фанфик про то, что могло бы случиться, если бы Гарри Поттер вырос в семье профессора, имел мозги и умел ими пользоваться: Harry Potter and the Methods of Rationality.

UPD:
И ещё одна новелла Юдковски, которая в своё время меня впечатлила, необычная вариация на тему Первого контакта: Three Worlds Collide.
alexey_rom: (Default)
Раньше слышал об этой книге, но не искал. Прочитав предисловие, уже понял, что зря.

Цитаты (взяты с reddit):

[Dedication] "To Clement V. Durell, M.A., without whom this book would not have been necessary"
[p.10] "Mathematicians always strive to confuse their audiences; where there is no confusion there is no prestige. Mathematics is prestidigitation."
He manages to pose several confusing questions about even the most basic facts. Leave alone "Question 4. Whether 1 is a number?", who can ever answer ""Question 5. Whether one should count with the same numbers he adds with, up to isomorphism?" :-)
[p.23] "This section is about addition. The fact that the reader has been told this does not necessarily mean that he knows what the section is about, at all. He still has to know what addition is, and that he may not yet know. It is the author's fond hope that he may not even know it after he has read the whole section."
[p.28] "With a few brackets it is easy enough to see that 5+4 is 9. What is not easy to see is that 5+4 is not 6."
[p.40] He defines a cancellable number x as one for which x+p = x+q never holds unless p=q. He first proves that if x and y are cancellable so is x+y, then with great care proves that 1 is cancellable, and therefore all numbers are cancellable.
[p.44–48]. In just a few pages, he gives a category-theoretic construction of the group of integers. Surely, this has never been done before.
[p.25] (On mathematical "beliefs".) "Like the world of a science-fiction story, a system of beliefs need not be highly credible—it may be as wild as you like, so long as it is not self-contradictory—and it should lead to some interesting difficulties, some of which should, in the end, be resolved."
[p.37] "unfortunately, there is a flaw in the reasoning. [..] to say that each of two numbers cannot be bigger than the other is to repeat the statement that is to be proved. It is not correct in logic to prove something by saying it over again; that only works in politics, and even there it is usually considered desirable to repeat the proposition hundreds of times before considering it as definitely established."
[Starred exercise] "Show that 17 × 17 = 289. Generalise this result."

Ссылка на DJVU версию (1.7 MB)
Ссылка на PDF версию (24.3 MB)
alexey_rom: (Default)
First of all, when I say "proved", what I will mean is "proved with the aid of
the whole of math". Now then: two plus two is four, as you well know. And,
of course, it can be proved that two plus two is four (proved, that is, with the
aid of the whole of math, as I said, though in the case of two plus two, of
course we do not need the whole of math to prove that it is four). And, as
may not be quite so clear, it can be proved that it can be proved that two plus
two is four, as well. And it can be proved that it can be proved that it can be
proved that two plus two is four. And so on. In fact, if a claim can be proved,
then it can be proved that the claim can be proved. And that too can be
proved.

Now, two plus two is not five. And it can be proved that two plus two is not
five. And it can be proved that it can be proved that two plus two is not five,
and so on.

Thus: it can be proved that two plus two is not five. Can it be proved as well
that two plus two is five? It would be a real blow to math, to say the least, if
it could. If it could be proved that two plus two is five, then it could be
proved that five is not five, and then there would be no claim that could not
be proved, and math would be a lot of bunk.

So, we now want to ask, can it be proved that it can't be proved that two plus
two is five? Here's the shock: no, it can't. Or, to hedge a bit: if it can be
proved that it can't be proved that two plus two is five, then it can be proved
as well that two plus two is five, and math is a lot of bunk. In fact, if math is
not a lot of bunk, then no claim of the form "claim X can't be proved" can be
proved.

So, if math is not a lot of bunk, then, though it can't be proved that two plus
two is five, it can't be proved that it can't be proved that two plus two is five.
By the way, in case you'd like to know: yes, it can be proved that if it can be
proved that it can't be proved that two plus two is five, then it can be proved
that two plus two is five.

George Boolos, Mind, Vol. 103, January 1994

Сомневаюсь, что по-русски можно сделать аналогичное. В частности, как обойтись без какого-нибудь слова, однокоренного "доказать"?

Ещё одно: специальная теория относительности в словах не более, чем из четырёх букв.
alexey_rom: (Default)
Жена посылает программиста в магазин: «Купи пачку масла. И ещё яиц посмотри — если есть, купи десяток.» Программист возвращается с одиннадцатью пачками масла и говорит: «Яйца есть.»

via [personal profile] maradydd 

Большая коллекция шуток на Stack Overflow: http://stackoverflow.com/questions/234075/what-is-your-best-programmer-joke

alexey_rom: (Default)



У дверей стоят три стражника. Один всегда лжёт, другой всегда говорит правду, а третий убивает людей, задающих каверзные вопросы.

(Это ловушка для сбегающих логиков. К выходу не ведёт ни одна из дверей.)

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