Almost anything can be attacked as a failure, but almost anything can be defended as not a significant failure. Politicians do not appreciate the significance of ‘significant’.
-- Sir Humphrey Appleby
Almost anything can be attacked as a failure, but almost anything can be defended as not a significant failure. Politicians do not appreciate the significance of ‘significant’.
-- Sir Humphrey Appleby
(Great delicacy and tact are needed in presenting this idea, if the aim is, as it should be, to bewilder and frighted the opponent. …)
-- Carl Linderholm, Mathematics Made Difficult
Let me explain why it’s not easy to see that 5+4 is not 6.
Earlier, the numbers were defined as
2 = 1+1
3 = 1+2
4 = 1+3
5 = 1+4
6 = 1+5
7 = 1+6
8 = 1+7
9 = 1+8.
Where + is associative.
Consider a “clock” with 3 numbers, 1, 2, 3. x+y means “Start at x and advance y hours”.
3
2 → 1
Then 1+1 = 2 and 2+1 = 3, as per our definitions. Also, 3+1 = 1 (since if you start at the 3 and advance 1 hour, you end up at 1). Thus 4 = 1, 5 = 4+1 so 5 = 1+1 = 2.
So 6 = 5+1 = 5 + 4.
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.
Carl Linderholm, Mathematics Made Difficult.
These are the languages I know. While Clojure is interesting, I haven’t had the chance to learn it, and I would feel guilty offering tutoring services in a language I don’t actually know how to program in.
That said, if you want to learn Clojure and take advantage of my tutoring services, the closest equivalent is scheme.
It has the advantage of being more well defined though ;)
Leonard, if you were about to burn or drown or starve I would panic. It would be the least I could do. That’s what’s happening to people now, and I don’t think my duty to panic disappears just because they’re not in the room!
-- Raymond Terrific
On some other subjects people do wish to be deceived. They dislike the operation of correcting the hypothetical data which they have taken as basis. Therefore, when they begin to see looming ahead some such ridiculous result as 2 + 3 = 7, they shrink into themselves and try to find some process of twisting the logic, and tinkering the equation, which will make the answer come out a truism instead of an absurdity; and then they say, “Our hypothetical premiss is most likely true because the conclusion to which it brings us is obviously and indisputably true.” If anyone points out that there seems to be a flaw in the argument, they say, “You cannot expect to get mathematical certainty in this world,” or “You must not push logic too far,” or “Everything is more or less compromise,” and so on.
-- Mary Everest Boole
I believe that no discovery of fact, however trivial, can be wholly useless to the race, and that no trumpeting of falsehood, however virtuous in intent, can be anything but vicious.
-- HL Mencken
P(A) = 2^-K(A).
As for ~A, see: http://lesswrong.com/lw/vs/selling_nonapples/ (The negation of a complex proposition is much vaguer, and hence more probable (and useless))
The number of possible probability distributions is far larger than the two induced by the belief that P, and the belief that ~P.
I’m not sure why you’d assume that the MML of a random proposition is only one bit...
Three more words then, reductio ad absurdum.
“Bayesian Bob: … I meant that in a vacuum we should believe it with 50% certainty...”
No we shouldn’t: http://lesswrong.com/lw/jp/occams_razor/
As for proving a negative, I’ve got two words: Modus Tollens.
Bob does need to go back to math class! ;)
If things are nice there is probably a good reason why they are nice: and if you do not know at least one reason for this good fortune, then you still have work to do.
Richard Askey
I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.
Bruce Lee
If a process is potentially good, but 90+% of the time smart and well-intentioned people screw it up, then it’s a bad process. So they can only say it’s the team’s fault so many times before it’s not really the team’s fault.
I didn’t do the engineering, and I didn’t do the math, because I thought I understood what was going on and I thought I made a good rig. But I was wrong. I should have done it.
Jamie Hyneman
Voted up for the maths and clear exposition.