Not necessarily. If I horribly torture Jim because Jim stepped on my toes, then I am not maximizing total happiness; the unhappiness given to Jim by the torture outwieghs the unhappiness in me that is prevented by having no-one step on my toes.
CCC
Someone who claims that faith is a good thing should not also use it as an accusation of impropriety.
I get the impression that that argument is used more to undermine claims that darwinism is a science than anything else.
Physics is a clear science; you can use the right equations and predict the motion of the Earth about the Sun, or the time a barometer will take to fall from a given height. This gives it a certain degree of credibility. The theory of evolution (and how the creationists love to remind everyone of that word, ‘theory’!) is also science; but they would deny it, on the basis that accepting it suggests that it is as credible as physics or mathematics. If they insist that darwinism is a religion, then both alternatives start from the same basis of credibility; the creationists can then point out, quite accurately, that their version is older and has been around for longer, and therefore at least claim seniority.
There’s a short story by Asimov that gives a very nice view of the whole argument.
...living on planet earth, giving you 80% of the crap you gave me seems about right.
Consider the consequences if everyone follows your rule. Assume someone gives you one unit of crap, possibly accidentally. You respond with 0.8 units. (It’s hard to measure this precisely, but for the sake of argument let’s assume that both of you manage to get it exactly right). He, in turn, responds with a further 0.64 units of crap. You respond to this with 0.512 units.
This is, of course, an infinite geometric series. The end result (over an infinite time period) is that you recieve 2 and 7⁄9 units of crap, while the other person recieves 2 and 2⁄9 units of crap. He recieves exactly 80% of the amount that you recieved, but you recieved over twice as much as you started out recieving.
If you return x% of the crap you get (for 0<x<100), and everyone else follows the same rule, then the total crap you recieve for every starting unit of crap is:
%5E2%20}%0A)This is clearly minimized at x=0.
You are correct; it is not terribly effective. However, any disproportionate response to a minor, or even an imagined, slight will reduce total unhappiness while discouraging others from hurting me.
That assumes that he is following a different rule from the rule that you are following. Does knowing that he will give you the 0.64 units prevent you from giving him the 0.8 units?
The first trick is to be able to describe how to solve a problem; and then break that description down into the smallest possible units and write it out such that there’s absolutely no possibility of a misunderstanding, no matter what conditions occur.
Once you’ve got that done, it’s fairly easy to learn how to translate it into a programming language.
If you do not hoard your ideas, and neither do I, then we can both benefit from the ideas of the other. If I can access the ideas of a hundred other people at the cost of sharing my own ideas, then I profit; no matter how smart I am, a hundred other people working the same problem are going to be able to produce at least some ideas that I did not think of. (This is a benefit of free/open source software; it has been shown experimentally to work pretty well in the right circumstances).
In the first case, starting with p such that the highest power of 2 that divides p is an integer power of 2 (2^k for some integer k); then the highest power of 2 that divides p² is 2^2k; then the highest power of 2 that divides 2q² is also 2^2k; then the highest power of 2 that divides q is 2^(2k-1); therefore q must be a multiple of 2^(k-0.5); a noninteger power of 2.
This implies that there is a number 2^(0.5). It makes no claims as to whether or not this number is rational, or integer; it merely claims that such a number must exist. (Consider: if I had started instead with the equation x²-4=0, I would have ended up showing that a number of the form 4^(0.5) must exist—that number is rational, is indeed an integer).
Now, I think I can prove that an integer q which is a multiple of 2^(k-0.5) but which is not a multiple of 2^k, for integer k, does not exist; but I can only complete that proof by knowing in advance that 2^0.5 is irrational, so I can’t use it to prove the irrationality of 2^0.5. I can easily prove that a rational number of the form 4^(k-0.5) for integer k does exist; indeed, an infinite number of such numbers exist (examples include 2, 8, 32).
No matter how forcefully that first passage conveys the irrationality of √2, it does not prove it.
I’ve heard it said that “Trivial” is a mathematics professor’s proof by intimidation.
I can see a genie taking a shortcut here.
“In any story worth the tellin’, that knows about the way of the world, the third wish is the one that undoes the harm the first two wishes caused.”
— Granny Weatherwax, A Hat Full of Sky.
In short, the genie may well conclude that every m’th wish, for some m (Granny Weatherwax suggests here that ‘m’ is three) your wish would be to have never met the genie in the first place. At this point, if you’re lucky, the genie will use a value of n that’s a multiple of m. If you’re unlucky, the genie will use a value of n that’s km-1 for some integer k...
Alternatively, you’ll end up with a genie who can’t handle the math and does not understand what you’re asking for.
I can’t be certain, but it’s possible that the post which led to shminux’ inclusion on that list was this one—in which shminux quoted gwerm’s conclusion that a gifted conversationalist is at least as likely to be a psychopath as a genius.
Looking over my post again, after a good night’s sleep, I see that it wasn’t as coherent as it appeared to me yesterday. Let me see if I can put my point a little more clearly.
The paragraph centers its claim of the irrationality of √2 on the idea that p² contains exactly twice as many powers of 2 as p does. But that is only true because √2 is irrational, making the demonstration a circular proof.
Consider. If √2 were rational, in the form of z/y for some coprime integers z and y, then it would be easy to find an integer that is not itself an integer power of 2, but whose square is an integer power of 2; z would be such a number.
Text-to-speech device provided. It reads from the scroll with perfect accuracy and low speed. It will take a few hundred years to complete this task.
You will need to change the batteries once an hour; it you forget, it starts reading from the start of the scroll again. (And where do you get a large supply of size Q batteries, in any case?)
Does he have any suitable raw materials?
If √2 is rational, then √2 can be written as z/y for some integers z and y, where z and y are coprime. Then, 2=z²/y².
Consider the hypothetical integer z. It is equal to √2*y. Since y and z are coprime, y cannot contain a factor of √2. Thus, z does not contain a factor of 2; the highest integer power of 2 that is a factor of z is 2^0.
On the other hand, z² does have a factor of 2; it is equal to 2*y² (since y has no factor of √2, y² therefore has no factor of 2).
Therefore, to claim that p² contains exactly twice as many powers of 2 as p is exactly equivalent to claiming that √2 is irrational.
In poor societies that permit slavery, a man might be willing to sell himself into slavery. He gets food and lodging, possibly for his family as well as himself; his new purchaser gets a whole lot of labour. There’s a certain loss of status, but a person might well be willing to live with that in order to avoid starvation.
Didn’t the Jews have that back in the years BC? It’s sort of cultural, but it’s been around for a while in some cultures...
We do, however, approve of people not getting married until age 25 or 30 or so, but sleeping with whoever they like before that.
You might. I don’t. This is most probably a cultural difference. There are people in the world to day who see nothing wrong with having multiple wives, given the ability to support them (example: Jacob Zuma)
The only relevant difference that I can see is that, in the first paragraph, the solutions are explicitly limited to the rational numbers; in the second case, the solutions are not explicitly limited to the reals.
A question.
The possible mind, that assumes that things are more likely to work if they have never worked before, can in all honesty continue to use this prior if it has never worked before. But this is only a self-sustaining method if it continues not to work.
Let us introduce our hypothetical poor-prior, rationalist observer to a rigged game of chance; let us say, a roulette wheel. (For simplicity, let’s call him Jim). We allow Jim to inspect an (unrigged) roulette wheel beforehand. We ask him to place a bet, on any number of his choice; once he places his bet, we use our rigged roulette wheel to ensure that he wins and continues to win, for any number of future guesses.
Now, from Jim’s point of view, whatever line of reasoning he is using to find the correct number to bet on, it is working. He’ll presumably select a different number every time; it continues to work. Thus, the idea that a theory that work now is less likely to work in the future is working… and thus is less likely to work in the future. Wouldn’t this success cause him to eventually reject his prior?