Disclaimer: IAAMFPHDS (I am a mathematical finance PhD student).
While quants could accurately gauge the historical covariance of different assets in a portfolio, what they failed to take into account is that there is correlation in the tails of the distribution.
An example of this is that, back in the good old days, there was a degree of correlation between the Dow and the FTSE 100. If the FTSE 100 went up, it was a decent indicator that the Dow would also be up, but by no means a sure thing. However, during the crisis, the two indices practically moved in lockstep.
The moral of the story is that in the rare event that things get bad, correlation tends to spike. The models failed to take account of this, which is part of the reason we're in this mess.
Yes, of course. You could even take the continuum hypothesis, or its negation as an axiom, since it won't contradict the other ones. It's just a really nice illustration of an undecidable problem in an axiomatic system.
What this says is that there are "different" sizes of infinity. The "smallest" is that of the integers: -1, 0 , 1, 2...
It is possible to show that one can never pair up every real number with a distinct integer. There are simply "too many" real numbers, and any attempt to pair the two sets up will result in real numbers being left over. In this sense, the set of real numbers is "bigger" than the integers.
The continuum hypothesis says there is a set bigger than the integers but smaller than the reals. This has been shown to be unproveable (given the normal axioms of set theory, aka Zermelo-frankel set theory). Since it can't be proven or disproven, you can assume it to be either true or false and get consistant, rigorous maths. In a sense, it is both true and false *at the same time*.
"Goedel, Escher, Bach" is an absolutely astonishing book about this subject, and the foundations of logic in general. Applications to AI are also discussed. Admittedly, I had to stop reading it since it rather messed my head up (Got about 3/4 through and couldn't stop dreaming about maths). Highly recommended for any self-respecting geek.
You've clearly read the book, but maybe you should look over the part about his reaction once he saw the effects of the bomb. He talks about sitting in a cafe, looking at a bridge being built, and thinking "Why are they doing that? Don't they know how pointless it is?".
The scientists who built the bomb had no idea how it would be used, and on who, so it is a little pointless to specualte how they felt about it. The point is, once they knew it was possible, they had to build it before someone else did. I should probably add here that I think its use was one of the most atrocious war crimes in history (but IANAIL, I am not an international layer. I don't know what the technical definition of a war crime is, but I know an atrocity when I see one).
Anyway, this is getting somewhat off-topic. My original point was not about scientific detachment, or anything like it. It was that scientists shouldn't be held responsible for the ill-use (or beneficial use) of their discoveries. Ideas are ideas, it's up to individuals and governments to choose how they are applied. We can build power stations, or we can build bombs.
Maybe you misunderstood my tone when I used the phrase "abstract nonsense". It's not necessarily pejorative when used in the context of maths. It originally applied to category theory, but has been extended to refer to most types of pure maths
"I'm a mathematician-in-training and I've just finished an MSc. It's so depressing to see that mathematics has been turned in the last 50 years from a way of expanding the mind and as a tool for scientific discovery to a channel for
(1) optimising wealth generation on the gambling paradise they call the stock market; and
(2) invading privacy to ensure those who have won the gamble get to keep their hardly-earnt gains."
I'm also a mathematician in training, having finished an MSc. I'm about to start a PhD working on (1). I assume (2) is a reference to the study of cryptography. Studying wealth-generation techniques does not make me power-hungry or greedy, in the same way that the people working on the Manhattan project were not monsters who wanted to extinguish life.
I'm not doing this out of personal greed, I'm doing it because the mathematics involved is elegant and interesting.
Maybe you're happy working away on your abstract nonsense, but I think I'd prefer to work on something which might actually make a difference to people's lives. Just because an application has potential for abuse doesn't make it inherently evil, as you seem to suggest.
The thing about a nine+ stone handicap is, as the number of handicap stones goes down, the difficulty increases disproportionately for the weaker player.
There's a much bigger difference moving from four stones to two than there is moving from nine to seven.
Nine stones is still a pretty enormous handicap (the maximum normally allowed), so moore's law or not, I dount we'll see a computer beat a pro in an even game anytime soon.
As far as I know, it's not possible to build up an endgame database for go. However, it is very amenable to mathematical analysis using combinatorial game theory.
In the endgame, go tends to break up into a set of smaller "subgames": Most of the fighting ends, except in a few islands dotted around the board. The standard text for mathematical go is "winning ways for your mathematical plays".
What you're missing is that in before Newton, Geocentrism was a very valid scientific theory.
Before Newton's law of Universal gravitation, scientists had no way of explaining why the planets would whizz around the sun in circles, which is what heliocentrism states. In fact, this is totally contrary to the well-established physics they had at the time. In addition to this, heliocentrism predicted parallax between the stars, which wasn't experimentally observable until long afterward.
Granted, heliocentrism explained retrograde motion of planets, but it wasn't as flawless a theory as people think. It's not a case of "geocentrism is unscientific, heliocentrism is scientific". They were both valid in their own right at the time.
That's not the case at all. Take the binary expansion of PI and interpret it as a decimal. That gives you an irrational, decimal number which doesn't use the digits two to nine.
Similarly, you can have a non-terminating, non-repeating discussion without saying "Godwin".
"Stop being an idiot and read up on it" is not helpful criticism. This is a clear example of the elitist attitude which gives techies a bad name.
If you actually know anything about the subject, why not share it, instead of using a cheap putdown. It's not like you even addressed the issue the GP brought up. His whole point was that a hidden volume doesn't show up as free space.
I'd mod you down, but you might actually learn something this way.
Personally, I believe that because the Chinese have stolen billions of dollars worth of software from the Americans since the earliest days of computers, the Americans have no moral, ethical, or legal obligation to pay for any software developed and sold by a Chinese company.
Wow, just wow. I have to say that I'm saddened and a bit dissappointed to find that anyone, anywhere thinks like that anymore. If you actually gave a little more thought to that line of reasoning, you would presumably have to concede that, for example, native americans shouldn't be obliged to pay for anything, given that their land was stolen from them several hundred years ago.
It is foolish, in the extreme, to punish anyone for the mistakes their predecessors made.
You need to be thinking in terms of general relativity, rather than special relativity here. Given that this material is falling into a black hole, we are emphatically not in the same reference frame.
The thing sbout the large severance package is that CEOs often defer any earnings they make for tax reasons. Chuck O'Neal (of Merril Lynch) wasn't paid that much purely as a severance package: it's fairly reasonable to assume he had a large amount of his assets tied up in company funds before he was ousted, and was allowed to hold on to them.
From the article: 'The project "the pain of everyday life" is a city-intervention and a digital art performance addressing public and private space within the realm of everyday constraints. It resembles an urban interface for an invisible city, an architecture which is subconsciously perceived and which constantly oscillates as resonant landscape, consisting of electromagnetic waves.'
Ugh. This reads like something from timecube. I think Hobbes (the tiger) but it best when he said "Maybe we can eventually make language a complete impediment to understanding."
Slashdot Mirror
Well, imagine what Euler or Gauss could have done with a copy of Mathematica in front of them...
Disclaimer: IAAMFPHDS (I am a mathematical finance PhD student).
While quants could accurately gauge the historical covariance of different assets in a portfolio, what they failed to take into account is that there is correlation in the tails of the distribution.
An example of this is that, back in the good old days, there was a degree of correlation between the Dow and the FTSE 100. If the FTSE 100 went up, it was a decent indicator that the Dow would also be up, but by no means a sure thing. However, during the crisis, the two indices practically moved in lockstep.
The moral of the story is that in the rare event that things get bad, correlation tends to spike. The models failed to take account of this, which is part of the reason we're in this mess.
Yes, of course. You could even take the continuum hypothesis, or its negation as an axiom, since it won't contradict the other ones. It's just a really nice illustration of an undecidable problem in an axiomatic system.
Sweet, sweet example of this: the continuum hypothesis. http://en.wikipedia.org/wiki/Continuum_hypothesis
What this says is that there are "different" sizes of infinity. The "smallest" is that of the integers: -1, 0 , 1, 2 ...
It is possible to show that one can never pair up every real number with a distinct integer. There are simply "too many" real numbers, and any attempt to pair the two sets up will result in real numbers being left over. In this sense, the set of real numbers is "bigger" than the integers.
The continuum hypothesis says there is a set bigger than the integers but smaller than the reals. This has been shown to be unproveable (given the normal axioms of set theory, aka Zermelo-frankel set theory). Since it can't be proven or disproven, you can assume it to be either true or false and get consistant, rigorous maths. In a sense, it is both true and false *at the same time*.
"Goedel, Escher, Bach" is an absolutely astonishing book about this subject, and the foundations of logic in general. Applications to AI are also discussed. Admittedly, I had to stop reading it since it rather messed my head up (Got about 3/4 through and couldn't stop dreaming about maths). Highly recommended for any self-respecting geek.
http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach
You've clearly read the book, but maybe you should look over the part about his reaction once he saw the effects of the bomb. He talks about sitting in a cafe, looking at a bridge being built, and thinking "Why are they doing that? Don't they know how pointless it is?".
The scientists who built the bomb had no idea how it would be used, and on who, so it is a little pointless to specualte how they felt about it. The point is, once they knew it was possible, they had to build it before someone else did. I should probably add here that I think its use was one of the most atrocious war crimes in history (but IANAIL, I am not an international layer. I don't know what the technical definition of a war crime is, but I know an atrocity when I see one).
Anyway, this is getting somewhat off-topic. My original point was not about scientific detachment, or anything like it. It was that scientists shouldn't be held responsible for the ill-use (or beneficial use) of their discoveries. Ideas are ideas, it's up to individuals and governments to choose how they are applied. We can build power stations, or we can build bombs.
Read "Surely you're joking Mr. Feynman" and maybe you'll see it differently.
Maybe you misunderstood my tone when I used the phrase "abstract nonsense". It's not necessarily pejorative when used in the context of maths. It originally applied to category theory, but has been extended to refer to most types of pure maths
http://en.wikipedia.org/wiki/Abstract_nonsense
"I'm a mathematician-in-training and I've just finished an MSc. It's so depressing to see that mathematics has been turned in the last 50 years from a way of expanding the mind and as a tool for scientific discovery to a channel for
(1) optimising wealth generation on the gambling paradise they call the stock market; and
(2) invading privacy to ensure those who have won the gamble get to keep their hardly-earnt gains."
I'm also a mathematician in training, having finished an MSc. I'm about to start a PhD working on (1). I assume (2) is a reference to the study of cryptography. Studying wealth-generation techniques does not make me power-hungry or greedy, in the same way that the people working on the Manhattan project were not monsters who wanted to extinguish life.
I'm not doing this out of personal greed, I'm doing it because the mathematics involved is elegant and interesting.
Maybe you're happy working away on your abstract nonsense, but I think I'd prefer to work on something which might actually make a difference to people's lives. Just because an application has potential for abuse doesn't make it inherently evil, as you seem to suggest.
Yes they are: Computer science is a branch of discrete mathematics. It's just that software engineering isn't computer science.
Pff. Real mathematicians just picture N dimensions, then set N = 4.
The obvious solution to this problem is to develop an un-decryptable cypher.
Behold:
AME33u899##d8909iksalel!
Well, given that the RIAA have attempted to sue people who don't own a computer, I'd be inclined to disagree...
You're confusing an oxymoron with a tautology.
The thing about a nine+ stone handicap is, as the number of handicap stones goes down, the difficulty increases disproportionately for the weaker player.
There's a much bigger difference moving from four stones to two than there is moving from nine to seven.
Nine stones is still a pretty enormous handicap (the maximum normally allowed), so moore's law or not, I dount we'll see a computer beat a pro in an even game anytime soon.
As far as I know, it's not possible to build up an endgame database for go. However, it is very amenable to mathematical analysis using combinatorial game theory.
In the endgame, go tends to break up into a set of smaller "subgames": Most of the fighting ends, except in a few islands dotted around the board. The standard text for mathematical go is "winning ways for your mathematical plays".
Here's a link to a short article expanding on mathematical go, and some other game theory:
http://math.berkeley.edu/~berlek/cgt/cgt-info.html
Sorry to reply to my own post, but I carelessly forgot to add that you can learn more from a Preimiter Institute lecture on the subject, available here:
http://www.perimeterinstitute.ca/index.php?option=com_content&task=view&id=551&Itemid=568&lecture_id=3503
What you're missing is that in before Newton, Geocentrism was a very valid scientific theory.
Before Newton's law of Universal gravitation, scientists had no way of explaining why the planets would whizz around the sun in circles, which is what heliocentrism states. In fact, this is totally contrary to the well-established physics they had at the time. In addition to this, heliocentrism predicted parallax between the stars, which wasn't experimentally observable until long afterward.
Granted, heliocentrism explained retrograde motion of planets, but it wasn't as flawless a theory as people think. It's not a case of "geocentrism is unscientific, heliocentrism is scientific". They were both valid in their own right at the time.
That's not the case at all. Take the binary expansion of PI and interpret it as a decimal. That gives you an irrational, decimal number which doesn't use the digits two to nine.
Similarly, you can have a non-terminating, non-repeating discussion without saying "Godwin".
"Stop being an idiot and read up on it" is not helpful criticism. This is a clear example of the elitist attitude which gives techies a bad name.
If you actually know anything about the subject, why not share it, instead of using a cheap putdown. It's not like you even addressed the issue the GP brought up. His whole point was that a hidden volume doesn't show up as free space.
I'd mod you down, but you might actually learn something this way.
Wow, just wow. I have to say that I'm saddened and a bit dissappointed to find that anyone, anywhere thinks like that anymore. If you actually gave a little more thought to that line of reasoning, you would presumably have to concede that, for example, native americans shouldn't be obliged to pay for anything, given that their land was stolen from them several hundred years ago.
It is foolish, in the extreme, to punish anyone for the mistakes their predecessors made.
You need to be thinking in terms of general relativity, rather than special relativity here. Given that this material is falling into a black hole, we are emphatically not in the same reference frame.
The thing sbout the large severance package is that CEOs often defer any earnings they make for tax reasons. Chuck O'Neal (of Merril Lynch) wasn't paid that much purely as a severance package: it's fairly reasonable to assume he had a large amount of his assets tied up in company funds before he was ousted, and was allowed to hold on to them.
From the article:
'The project "the pain of everyday life" is a city-intervention and a digital art performance addressing public and private space within the realm of everyday constraints. It resembles an urban interface for an invisible city, an architecture which is subconsciously perceived and which constantly oscillates as resonant landscape, consisting of electromagnetic waves.'
Ugh. This reads like something from timecube. I think Hobbes (the tiger) but it best when he said "Maybe we can eventually make language a complete impediment to understanding."
Interestingly enough, man himself fits that description pretty neatly