Well, lucky you, because I love to hear myself talk. What threw me was that you wrote with conviction, and there was enough stuff there that was correct that I couldn't believe you didn't really know the whole thing. So here goes, and this is just off the top of my head on a very hot Amsterdam afternoon, so there's probably mistakes.
1) Consider all of the numbers that are possible between 0 and 1. Infinite right? Now, consider all of the possible integers. Also infinite. OK, now consider all of the possible numbers. That includes all of teh possible intigers (which are infinite), as well as all of the numbers in between the integers (also infinite). That means that all of the posssible numbers represent and infinity of infinities. Or that we have infinity raised to the infinity. This is larger than just plain old infinity.
I'm not really sure what you're trying to say here, but let me rephrase the example a bit. Consider the number of even positive integers -- infinitely many, right? Now the total number of positive integers, which is also infinite, and which contains all the even integers. However, the two infinities are identical, which we can prove by providing a one to one mapping of each positive integer to an even integer; e.g
f(x) = 2x
However, it is true that there the infinity of real numbers between 0 and 1 is larger, which was first proved by Cantor I think, using his famous diagonal. Yet this is the same infinity as, for example, the number of points on a Cartesian plane.
2)Ok, so in case the last example was too much like the old infinity +1 argument for you, lets look at a more rigorous treatment. Lets supose that you have a funtion f(x)=(x^2)/(x). Right? Now lets see what happens to this function as x goes to infinity. Well, we can treat this just like a normal function, so we see that (x^2)/x is hte same thing as x. So we now have f(x)=x as x goes to infinity. Well, it should be obvious that as x goes to infinity, x becomes infinity. OK, so what is the point? The point is that one infninity [(x^2) as x goes to infinity], devided by another infinity(x as x goes to infinity) was equal to infinity. This could only happen in X^2 was infinitly larger than x. That is one infinity was larger than another.
This is not true, and in fact the idea of dividing one infinity by another doesn't really make sense as you've described it here. In fact, the limit as x goes to infinity of f(x) = x is exactly the same as the limit as x goes to infinity of f(x) = x^2.
To get a large infinity, you must use it as an exponent. Call the number of integers aleph-null. Then aleph-one = 2^(aleph-null), which is the number of elements in the set of all subsets of integers, is larger, because you cannot find a one to one mapping between the two entities. However, it's not known (as far as I know), whether the number of real numbers is the same as aleph-one.
Well, yes and no. The post has gotten off topic from article somewhat, but teh monkeys on a typwritter is just an illustration. An analogy if you will. It most certainly applies. It adresses the argument that "given an infinite amount of time, X must happen."
Not really. What it says is that given an infinite series of random numbers chosen from a finite set, every possible finite sequence must be a subset. Why? Because the probability of it not being a subset goes to zero as the length of the sequence goes to infinity.
Take coin tossing. For any finite number of coin tosses, there is a non-zero probability that all of them are heads, so you could argue that the sequence is not guaranteed. But as the number of tosses goes to infinity, the probability of an infinite number of heads goes to zero.
This applies to the monkeys because there is a finite chance that a random sequence of letters and punctuation will correspond to the complete works of Shakespeare. It's very low, but it's there. For any sequence of length N, you can calculate the probability p that it contains the Shakespeare sequence, and as N -> infinity, p -> 1.
i am afraid that you are incorrect. I don't mean to be mean, but you are. Let me try to adress your post some....
You're trolling, aren't you? You're just hoping against hope that some idiot (like me) with more time than sense will read your article and launch a blistering reply refuting all the astoundingly wrong things you said. And this will make you feel -- what? Loved? Real? Like somebody who matters?
Well, I'm not going to do that. But you're wrong. You're astoundingly long-winded about it, and you have a knack for saying unreasonable things in reasonable language (are you an evangelical christian or something?), but at the end of the day, your post was less accurate than a Gulf war media briefing.
(Except about there being infinities of different sizes of course)
Well, while I'm here, I should also say that a lot of you have missed the point about the monkey illustration, which is this: it's not about monkeys. Or, indeed Shakespeare. Or even typewriters.
Oh, I agree. But that's not the biggest assumption in there: the leap from "there must be a root cause" to "and that root cause is the Judeo-Christian god" is, well, ambitious.
We get to self-existence. Since everything has a cause, there must be a root cause, and this must be God. God, as we all know, created the world, therefore that exists too. And since God is good, he wouldn't lie, therefore the senses must provide an accurate picture.
Thre's a reason everybody stops after Cogito ergo sum, and that's because the rest of the reasoning was a bit, well, dodgy.
I'm sure I've misprepresented it a bit, but Rene can always speak up if he feels slighted. No? Well, then.
The Hobbit has certainly been done
on
LOTR The Musical!
·
· Score: 1
Yours truly played Gandalf in a musical production of The Hobbit for primary school. It had its moments, though they gave most of Gandalf's action scenes to Bilbo, who also managed to kill Smaug as I recall. Busy little hobbit.
Compare these explorers with explorers of times past. Columbus lost large numbers of his crew, as did Coronado and DeSoto.
Your analogy doesn't really work. Back then, long, dangerous voyages were the only way to explore the new world. These days, we have many effective ways to explore space from Earth, and I think it's quite hard to justify sending people to "discover" things we already know about.
function Feet_To_Metres (Number_Of_Feet : Feet) return Metres is begin
return Metres (Number_Of_Feet * 0.3048); end Feet_To_Metres;
Notice that in the Ada version, it's much harder to hand out Feet to something that expects Metres. However, applying the type system to this sort of dimensional stuff has some interesting subtleties, which sadly this comment is far to short to go into.
(I'm aware that the ISO standard spelling for metre is meter, but I'm ignoring that, just as I ignore that pesky way you yanks spell sulphur)
If MySQL doesn't have it's own cache, what's this?
Uh, something very very different from a cache as one might normally use the term in the context of a database implementation.
I find it staggering that MySQL doesn't have a cache. It's not like it's a difficult thing to write -- you need to have a page in memory to look at it, so it costs almost nothing to keep it there.
Dipshit.
On the other hand, why am I bothering to tell you anything?
Checking for infinite loops is not some magical process that brings Turing's ghost down to blow your computer up. All the halting problem shows is that it's impossible to do in general. The specific is a different matter.
Your statement is unnecessarily negative, unhelpful, and a bit silly.
Ah. I have until now been unaware of the good guy implications of Bad to the Bone. Does it have to be this particular song, or will any use of some George Thorogood rockin' do the trick?
Somehow I managed to be unaware of Arnie's nature before I saw the movie (I must have been spending less time on the internet back then), so the part where he says "Get down" was brilliant.
It was strange that the marketing didn't try to keep it a secret, since the movie itself went to some trouble to make things ambiguous.
In other news, it appears that even killer she-bots from the future like to keep their modesty intact with carefully positioned hair. I think that's funny.
and then let's all laugh at the fact that this guy somehow managed to get his "case" heard by the highest court in australia. perhaps there is something wrong with the australian legal system.
From reading the transcript, I infer that he stood as a candidate for the seat of Fraser, and when he lost (because unlike the British, we don't elect nutters to parliament), he contested the results.
Contested election results are a serious matter, and I'm not altogether surprised it ended up in the High Court.
We must remember that throughout time those who make the most memorable contributions to science are usually laughed at right up until the moment they are vindicated (usually post-mortum).
And let us also remember those brave souls who were scorned for their theories, laughed at by the establishment, and died in poverty and obscurity, bitter at an ignorant and uncaring world. And yet, years later, through the application of modern science and learning, they were conclusively proved wrong on every count.
SARS has a two to seven day incubation period. If it was going to be as bad as you say, there would be an awful lot more than seven hundred odd reported cases. Flying with a respiratory mask is not only excessive, but everybody will think you're a dickhead.
As for your references to foreign 'guests', in my experience the people who fail to wash their hands are as likely to be Yanks as anything else. Which is surprising, because a quick survey of American television commercials shows a near obsession with anti-bacterial products. Or, as we like to call it, the War on Bugs.
Slashdot Mirror
Yeah, so i look forward to your reply =)
Well, lucky you, because I love to hear myself talk. What threw me was that you wrote with conviction, and there was enough stuff there that was correct that I couldn't believe you didn't really know the whole thing. So here goes, and this is just off the top of my head on a very hot Amsterdam afternoon, so there's probably mistakes.
1) Consider all of the numbers that are possible between 0 and 1. Infinite right? Now, consider all of the possible integers. Also infinite. OK, now consider all of the possible numbers. That includes all of teh possible intigers (which are infinite), as well as all of the numbers in between the integers (also infinite). That means that all of the posssible numbers represent and infinity of infinities. Or that we have infinity raised to the infinity. This is larger than just plain old infinity.
I'm not really sure what you're trying to say here, but let me rephrase the example a bit. Consider the number of even positive integers -- infinitely many, right? Now the total number of positive integers, which is also infinite, and which contains all the even integers. However, the two infinities are identical, which we can prove by providing a one to one mapping of each positive integer to an even integer; e.g
f(x) = 2x
However, it is true that there the infinity of real numbers between 0 and 1 is larger, which was first proved by Cantor I think, using his famous diagonal. Yet this is the same infinity as, for example, the number of points on a Cartesian plane.
2)Ok, so in case the last example was too much like the old infinity +1 argument for you, lets look at a more rigorous treatment. Lets supose that you have a funtion f(x)=(x^2)/(x). Right? Now lets see what happens to this function as x goes to infinity. Well, we can treat this just like a normal function, so we see that (x^2)/x is hte same thing as x. So we now have f(x)=x as x goes to infinity. Well, it should be obvious that as x goes to infinity, x becomes infinity. OK, so what is the point? The point is that one infninity [(x^2) as x goes to infinity], devided by another infinity(x as x goes to infinity) was equal to infinity. This could only happen in X^2 was infinitly larger than x. That is one infinity was larger than another.
This is not true, and in fact the idea of dividing one infinity by another doesn't really make sense as you've described it here. In fact, the limit as x goes to infinity of f(x) = x is exactly the same as the limit as x goes to infinity of f(x) = x^2.
To get a large infinity, you must use it as an exponent. Call the number of integers aleph-null. Then aleph-one = 2^(aleph-null), which is the number of elements in the set of all subsets of integers, is larger, because you cannot find a one to one mapping between the two entities. However, it's not known (as far as I know), whether the number of real numbers is the same as aleph-one.
Well, yes and no. The post has gotten off topic from article somewhat, but teh monkeys on a typwritter is just an illustration. An analogy if you will. It most certainly applies. It adresses the argument that "given an infinite amount of time, X must happen."
Not really. What it says is that given an infinite series of random numbers chosen from a finite set, every possible finite sequence must be a subset. Why? Because the probability of it not being a subset goes to zero as the length of the sequence goes to infinity.
Take coin tossing. For any finite number of coin tosses, there is a non-zero probability that all of them are heads, so you could argue that the sequence is not guaranteed. But as the number of tosses goes to infinity, the probability of an infinite number of heads goes to zero.
This applies to the monkeys because there is a finite chance that a random sequence of letters and punctuation will correspond to the complete works of Shakespeare. It's very low, but it's there. For any sequence of length N, you can calculate the probability p that it contains the Shakespeare sequence, and as N -> infinity, p -> 1.
i am afraid that you are incorrect. I don't mean to be mean, but you are. Let me try to adress your post some....
You're trolling, aren't you? You're just hoping against hope that some idiot (like me) with more time than sense will read your article and launch a blistering reply refuting all the astoundingly wrong things you said. And this will make you feel -- what? Loved? Real? Like somebody who matters?
Well, I'm not going to do that. But you're wrong. You're astoundingly long-winded about it, and you have a knack for saying unreasonable things in reasonable language (are you an evangelical christian or something?), but at the end of the day, your post was less accurate than a Gulf war media briefing.
(Except about there being infinities of different sizes of course)
Well, while I'm here, I should also say that a lot of you have missed the point about the monkey illustration, which is this: it's not about monkeys. Or, indeed Shakespeare. Or even typewriters.
Oh, I agree. But that's not the biggest assumption in there: the leap from "there must be a root cause" to "and that root cause is the Judeo-Christian god" is, well, ambitious.
Descartes tried to answer the first question.
Descartes tried to answer all three.
We get to self-existence. Since everything has a cause, there must be a root cause, and this must be God. God, as we all know, created the world, therefore that exists too. And since God is good, he wouldn't lie, therefore the senses must provide an accurate picture.
Thre's a reason everybody stops after Cogito ergo sum, and that's because the rest of the reasoning was a bit, well, dodgy.
I'm sure I've misprepresented it a bit, but Rene can always speak up if he feels slighted. No? Well, then.
Yours truly played Gandalf in a musical production of The Hobbit for primary school. It had its moments, though they gave most of Gandalf's action scenes to Bilbo, who also managed to kill Smaug as I recall. Busy little hobbit.
Should I have put a spoiler warning there?
I will admit that I don't know what versioning Linux uses.
Oh, you really don't want to go there.
Compare these explorers with explorers of times past. Columbus lost large numbers of his crew, as did Coronado and DeSoto.
Your analogy doesn't really work. Back then, long, dangerous voyages were the only way to explore the new world. These days, we have many effective ways to explore space from Earth, and I think it's quite hard to justify sending people to "discover" things we already know about.
I mean, that's not really exploration, is it?
Close! But why use the temporary?
type Feet is new Float;
type Metres is new Float;
function Feet_To_Metres (Number_Of_Feet : Feet) return Metres is
begin
return Metres (Number_Of_Feet * 0.3048);
end Feet_To_Metres;
Notice that in the Ada version, it's much harder to hand out Feet to something that expects Metres. However, applying the type system to this sort of dimensional stuff has some interesting subtleties, which sadly this comment is far to short to go into.
(I'm aware that the ISO standard spelling for metre is meter, but I'm ignoring that, just as I ignore that pesky way you yanks spell sulphur)
If MySQL doesn't have it's own cache, what's this?
Uh, something very very different from a cache as one might normally use the term in the context of a database implementation.
I find it staggering that MySQL doesn't have a cache. It's not like it's a difficult thing to write -- you need to have a page in memory to look at it, so it costs almost nothing to keep it there.
Dipshit.
On the other hand, why am I bothering to tell you anything?
And you know, if they were announced one at a time, somebody would be whining because there was no box-set-with-a-discount.
Let's make another 3.11 joke, shall we?
...
Man, it's still too soon to be making jokes about that. We lost a lot of good people, and
Oh, sorry, I thought you said 9.11
Checking for infinite loops is not some magical process that brings Turing's ghost down to blow your computer up. All the halting problem shows is that it's impossible to do in general. The specific is a different matter.
Your statement is unnecessarily negative, unhelpful, and a bit silly.
I'm so sick of people posting exactly what they think mods want to see just to get a few Karma points.
Hey, you got modded insightful, you big karma whore you!
Sometimes I think it's because our American friends aren't ready for naked women yet
So how do they make new Americans then?
Ah. I have until now been unaware of the good guy implications of Bad to the Bone. Does it have to be this particular song, or will any use of some George Thorogood rockin' do the trick?
I guess "You Talk Too Much" wouldn't work though.
Somehow I managed to be unaware of Arnie's nature before I saw the movie (I must have been spending less time on the internet back then), so the part where he says "Get down" was brilliant.
It was strange that the marketing didn't try to keep it a secret, since the movie itself went to some trouble to make things ambiguous.
In other news, it appears that even killer she-bots from the future like to keep their modesty intact with carefully positioned hair. I think that's funny.
BTW, a Palmtop with 128MB RAM should be quite fast - like say, aLinux desktop with 1GB RAM..
Yes, there should be a significant speed boost, just like when you paint a red stripe on your car.
and then let's all laugh at the fact that this guy somehow managed to get his "case" heard by the highest court in australia. perhaps there is something wrong with the australian legal system.
From reading the transcript, I infer that he stood as a candidate for the seat of Fraser, and when he lost (because unlike the British, we don't elect nutters to parliament), he contested the results.
Contested election results are a serious matter, and I'm not altogether surprised it ended up in the High Court.
We must remember that throughout time those who make the most memorable contributions to science are usually laughed at right up until the moment they are vindicated (usually post-mortum).
And let us also remember those brave souls who were scorned for their theories, laughed at by the establishment, and died in poverty and obscurity, bitter at an ignorant and uncaring world. And yet, years later, through the application of modern science and learning, they were conclusively proved wrong on every count.
There's a lot more of these guys.
Yes, especially the ones in the coma ward, because they can't say no.
This is an ongoing April Fool about posting excessive amounts of April Fools?
Annual, actually.
You realize, don't you, by actually saying that something will never happen, you have practically assured that it will happen at some point.
I will never have sex with Hugh Jackman.
So security is bloat now? My, we've come a long way.
SARS has a two to seven day incubation period. If it was going to be as bad as you say, there would be an awful lot more than seven hundred odd reported cases. Flying with a respiratory mask is not only excessive, but everybody will think you're a dickhead.
As for your references to foreign 'guests', in my experience the people who fail to wash their hands are as likely to be Yanks as anything else. Which is surprising, because a quick survey of American television commercials shows a near obsession with anti-bacterial products. Or, as we like to call it, the War on Bugs.
I mean you don't see any text based adventures anymore except with MUDs.
I respectfully beg to differ.