I write out a check to you for some amount, $X, unknown to you, and then I write out another check for $(2*X). I put each in an envelope, and put the envelopes in a hat.
You choose an envelope from the hat. After opening it, if you like, you may instead take the other envelope. Either way, you get to cash one of the checks. So - what is your best strategy?
Here are two seemingly airtight arguments, which conflict with each other.
1. You gain no information when you open the envelope, since you have no idea what X was, so switching clearly makes no difference - you are still getting one of the checks at random.
2. Call the value of the first envelope you drew Y. Now, there's a 50% chance it was the larger check, and a 50% chance it was the smaller check. Therefore, the expected value of the other check is.5 * Y/2 +.5 * 2 * Y = 1.25 * Y. Therefore, switching gets you an expected gain of 25%, so you should switch.
They can't both be right. But where is the flaw in the reasoning?
Extra credit - believe it or not, both are wrong! There is a strategy by which you can do better than just taking the envelope you drew, but strategy 2 is not it. What is this strategy?
As described, this sounds just like the singularity Vinge always writes about. I hope he gets credit. I do think there's some sort of singularity coming, but I'm less sure than Kurzweil that we can predict much of what will be on *this* side of it, let alone on the other side.
BTW, for those who (like me) had always pronounced "Vinge" to rhyme with "hinge", according to Vinge himself it rhymes with "dingy".
What the hell is that? I started reading the first chapter. OK, maybe there's something mildly interesting here; some calculations could be simpler expressed in these terms. But alarm bells went off when I read "decimal number plane" (let alone everything about how this will revolutionize mathematics).
He seems to mean real plane, but with a pejorative connotation of needing decimal numbers to do ordinary trigonometry.
Google the phrase (in quotes); you get exactly one hit - this book.
TiVo has not deigned to offer service. So those of us who moved here with TiVo boxes have had to go to extraordinary lengths to make them work.
After that effort, though - basically running a TiVo server on a home machine - we're free not only of the monthly payments, but also annoying stuff like this that TiVo adds now and then.
Still, if I were in the US, I'd rather pay than deal with the periodic configuration hassles. Similar to MythTV, I imagine. But at least we get the nice TiVo interface.:-)
The Stones sold out to the dark side...
on
Windows 95 Turns 10
·
· Score: 0, Redundant
... and that's when I threw away my Stones CDs, and started boycotting them.
I was never much of an REM fan, but to their credit, REM turned down Microsoft cold when they tried to get the rights to "It's the End of the World as We Know It".
Yeah - I'm counting the missing comma, as well as the extra comma, in "steered clear of endorsing the RSS specification hoping that Atom, would take hold".
We could be generous and just call that a misplaced comma, I suppose, but I could count more if I were really being nitpicky.
"The lightsaber being sold is not an actual functioning weapon; rather it is a silver-coloured tube with a black handle. The blade of light was added after filming by means of special effects."
ClarisWorks was developed with a four-figure startup cost, starting in 1989, and became a top-selling product with millions of users. It's true that that success was not achieved until the program was sold to Claris, and additional development resources were added.
But from the point of view of the original developers - myself and Scott Holdaway - our startup costs were very small. We bought two computers, rented a house together, and hacked. Details here:
I should add that from my personal point of view, the open source meme has made it much harder to figure out how to make a buck selling software. In the old days it was simple. OK, call me clueless. I gave up and went back to school.
Not exactly the same thing, but it is possible to build computers of a sort out of very simple physical systems: sliding-block puzzles. You know, where you have a box of wooden rectangular pieces, and you have to slide them around so as to make one reach a certain position.
The resulting computers are nondeterministic. They are computers in the sense that, given a Turing machine and a given input, you can construct a corresponding sliding-block puzzle that is solvable if and only if the Turing machine would eventually print YES. The catch is that this only works when the Turing machine is allowed to use only an amount of tape polynomial in its input size (but then, the same is effectively true of real computers). Technically, this means that sliding-block puzzles are PSPACE-complete - that's the next complexity class up from NP-complete.
Anyway, the construction does involve building logic gates out of sliding-block components, so the things are rather like actual computers. The constructions are based on the earlier result that you can build computers out of Rush Hour puzzles.
Some of Scott's stuff is simply amazing. Unfortunately he was very secretive about much of his work; others later got credit for much of what he undoubtedly did first, and there's a lot that he did that is lost to time.
Here's a great collection (warning - a lot of this is just very strange sounds, not what you'd call music):
He also put a fortune into designing a "keyboard-less, automatic composition and performance machine", called the Electronium. Some of its output is on the above collection.
The Electronium is currently owned by Mike Mothersbaugh, of Devo fame.
Oh, and you know that Bugs Bunny music you always hear whenever there's a factory scene? That's "Powerhouse" - also Raymond Scott, from before his electronic music days. The Raymond Scott Quintette was very popular in the 30s.
... and chapter 34 was written by a computer program. It starts:
"Bruce walked around any more. Some people might ought to her practiced eye, at her. I am so silky and braid shoulders. At sixty-six, men with a few feet away form their languid gazes. I know I was hungry, and impelling him lying naked. She slowly made for a man could join you I know what I ought to take you probably should have. He wants it worriedly. About think what to wear? "
Re:Wait a sec, this story isn't about "dark matter
on
Dark Matter Discovered
·
· Score: 4, Interesting
Actually, it is well established that the dark matter is NOT baryonic.
The story is a bit about dark matter, because there is a dark matter presence implied by the newly discovered gas clouds. But that's no surprise - the observed structure of ordinary galaxies already implies that they as well are permeated with dark matter.
If by "from the get-go" you mean when it was still called ClarisWorks, I have to take offense (given that I wrote a lot of it). All the reviewers of the early versions, and millions of users, would disagree with you. In fact there are still lots of things you can do with AppleWorks that you can do with no other single program out there.
That said, by the time the name was changed to AppleWorks, the ball had clearly been dropped, and essentially nothing has been done for the past few years. So, dated - yes. Sucked from the get-go - I think (hope) you have a minority opinion there.
Oooohhhh... the first Eschaton book was... interesting. I can't say it really stood on its own. It required some pretty damn explanations from the other two books. Alas, it was downhill from there (sort of like the Matrix...). By the time I finished the third one, I was furious that I'd wasted my time with them at all, waiting for a payoff that never came. If that's what you mean by not quite concluded, I guess I agree.
Gateway, now, that's a classic. Required reading! But overall, IMO, the Heechee series had a downward arc (though the rest were still readable). I read a devasating review of TBWWLF the other day, and I was not surprised. Well, maybe I'll give it a chance anyway, in paperback...
Man Plus is another great Pohl book with an atrocious sequel, Mars Plus. Although to be fair, Pohl only co-wrote Mars Plus; maybe most of the blame lies with his co-author, Thomas T. Thomas (although I liked his story in Man Kzin Wars V).
I use my PC card slot all the time, to pull photos off my IBM microdrive. Yeah, I could use a USB card reader, but I don't need one. And the PC card interface is faster.
Still, if it would save cost/weight, I'd happily give it up.
As someone else has pointed out, the Stata center (which is the new building complex housing CSAIL) contains both the Gates tower and the Dreyfoos tower. However, the poster incorrecly stated that RMS will be in the Dreyfoos tower. In fact he is in the space between the two towers - known as the "warehouse" space (for reasons which escape me).
Office location in the Stata Center can be identified by letters attached to the office number. Stallman's office is 32-381, here:
(I'm right across the hall, in 32-386.) A Gates office would be, e.g., 32-G585. A Dreyfoos office would be, e.g., 32-D585. Yes, as someone else pointed out, we have a holodeck.:-)
Most of us are hoping / assuming that, like almost all other buildings at MIT, the new building(s) will be referred to by number, not by name.
IMHO MIT missed a great opportunity to influence the world for the better by publicly snubbing Gates' offer to fund (a small part of) the new building. But, I'm told, that's just not the way things work...
Well, fair enough. But you did way that the book was still being debugged when you were using it, and that the instructor didn't do a great job of teaching it.
So we need to find someone who used the book when it was finished, with a competent instructor.
Wow, I'm really disappointed to see all the negative opinion's on Keisler's book, and the infinitesimal approach to calculus.
I happened to run across the book on Keisler's site a couple of months ago, and... I read the whole pdf through virtually non-stop. All 913 pages. This is by far the best introduction to calculus I've ever seen - very intuitive and clean.
Those of you arguing for the conventional, limits-based approach vs. the "nonstandard", infinitesimal-based approach are missing the point that the very notation in standard use for calculus (dy/dx etc.) really makes no sense without a notion of infinitesimal. Originally Newton developed calculus in terms of limits, while Leibniz used infinitesimals. Leibniz's notation won out over Newton's, because it accords with the way mathematicians intuitively think about calculus. Neither approach was on a sound mathematical footing until the limits-based approach was formalized in the 1870's. The infinitesimal-based approach was only formalized in 1960, by Robinson - the mathematical tools needed to do so were not available in the 19th century. Due to an historical accident Robinson's approach is called "nonstandard analysis", but the implication that there is anything deficient or deviant about it does not follow. (BTW, in addition to infinitesimals, the hyperreals (or "nonstandard numbers") also include infinite numbers.)
With this approach, developed in Keisler's book, not only is the notation in accord with the model, but many results are much more straightforward to understand and to prove. No more long, tedious epsilon-delta arguments. Really, the only thing complicated about using nonstandard numbers for calculus is the formal development of the hyperreals - and in this book that is relegated to a brief treatment in an appendix. It's easy enough to state and use the properties of the hyperreals without having to go through their formal mathematical construction.
I find it disheartening that the book was allowed to go out of print, and that there are now no (as far as I'm aware) current popular calculus texts using the infinitesimal-based approach. I, like the original poster, and like most students learning today, was always confused by what you could and couldn't do with dy and dx. How I wish I'd had this book 20 years ago.
The upside is that the book is now freely available on the author's site! Go get it!
Slashdot Mirror
I write out a check to you for some amount, $X, unknown to you, and then I write out another check for $(2*X). I put each in an envelope, and put the envelopes in a hat.
.5 * Y/2 + .5 * 2 * Y = 1.25 * Y. Therefore, switching gets you an expected gain of 25%, so you should switch.
You choose an envelope from the hat. After opening it, if you like, you may instead take the other envelope. Either way, you get to cash one of the checks. So - what is your best strategy?
Here are two seemingly airtight arguments, which conflict with each other.
1. You gain no information when you open the envelope, since you have no idea what X was, so switching clearly makes no difference - you are still getting one of the checks at random.
2. Call the value of the first envelope you drew Y. Now, there's a 50% chance it was the larger check, and a 50% chance it was the smaller check. Therefore, the expected value of the other check is
They can't both be right. But where is the flaw in the reasoning?
Extra credit - believe it or not, both are wrong! There is a strategy by which you can do better than just taking the envelope you drew, but strategy 2 is not it. What is this strategy?
informative, insightful
Din-jee. Good ol' dingy Vinge...
As described, this sounds just like the singularity Vinge always writes about. I hope he gets credit. I do think there's some sort of singularity coming, but I'm less sure than Kurzweil that we can predict much of what will be on *this* side of it, let alone on the other side.
BTW, for those who (like me) had always pronounced "Vinge" to rhyme with "hinge", according to Vinge himself it rhymes with "dingy".
What the hell is that? I started reading the first chapter. OK, maybe there's something mildly interesting here; some calculations could be simpler expressed in these terms. But alarm bells went off when I read "decimal number plane" (let alone everything about how this will revolutionize mathematics).
He seems to mean real plane, but with a pejorative connotation of needing decimal numbers to do ordinary trigonometry.
Google the phrase (in quotes); you get exactly one hit - this book.
TiVo has not deigned to offer service. So those of us who moved here with TiVo boxes have had to go to extraordinary lengths to make them work.
:-)
After that effort, though - basically running a TiVo server on a home machine - we're free not only of the monthly payments, but also annoying stuff like this that TiVo adds now and then.
Still, if I were in the US, I'd rather pay than deal with the periodic configuration hassles. Similar to MythTV, I imagine. But at least we get the nice TiVo interface.
... and that's when I threw away my Stones CDs, and started boycotting them.
I was never much of an REM fan, but to their credit, REM turned down Microsoft cold when they tried to get the rights to "It's the End of the World as We Know It".
Yeah - I'm counting the missing comma, as well as the extra comma, in "steered clear of endorsing the RSS specification hoping that Atom, would take hold".
We could be generous and just call that a misplaced comma, I suppose, but I could count more if I were really being nitpicky.
Actually there are no less than five comma errors in that one summary. That's quite an accomplishment, but it's extremely painful to read!
"The lightsaber being sold is not an actual functioning weapon; rather it is a silver-coloured tube with a black handle. The blade of light was added after filming by means of special effects."
Well, what's the fun in that?
gigananotube?
ClarisWorks was developed with a four-figure startup cost, starting in 1989, and became a top-selling product with millions of users. It's true that that success was not achieved until the program was sold to Claris, and additional development resources were added.
But from the point of view of the original developers - myself and Scott Holdaway - our startup costs were very small. We bought two computers, rented a house together, and hacked. Details here:
http://www.swiss.ai.mit.edu/~bob/clarisworks.php
I should add that from my personal point of view, the open source meme has made it much harder to figure out how to make a buck selling software. In the old days it was simple. OK, call me clueless. I gave up and went back to school.
The resulting computers are nondeterministic. They are computers in the sense that, given a Turing machine and a given input, you can construct a corresponding sliding-block puzzle that is solvable if and only if the Turing machine would eventually print YES. The catch is that this only works when the Turing machine is allowed to use only an amount of tape polynomial in its input size (but then, the same is effectively true of real computers). Technically, this means that sliding-block puzzles are PSPACE-complete - that's the next complexity class up from NP-complete.
Anyway, the construction does involve building logic gates out of sliding-block components, so the things are rather like actual computers. The constructions are based on the earlier result that you can build computers out of Rush Hour puzzles.
More info here:
Ditto. I missed just the first episode (33). Spent some time looking for a bittorrent, without success.
:-(
I'm in Canada, so we don't get the BSG marathon that evidently aired on Sci-Fi.
Some of Scott's stuff is simply amazing. Unfortunately he was very secretive about much of his work; others later got credit for much of what he undoubtedly did first, and there's a lot that he did that is lost to time.
Here's a great collection (warning - a lot of this is just very strange sounds, not what you'd call music):
Manhattan Research, Inc.
He also put a fortune into designing a "keyboard-less, automatic composition and performance machine", called the Electronium. Some of its output is on the above collection.
The Electronium is currently owned by Mike Mothersbaugh, of Devo fame.
Oh, and you know that Bugs Bunny music you always hear whenever there's a factory scene? That's "Powerhouse" - also Raymond Scott, from before his electronic music days. The Raymond Scott Quintette was very popular in the 30s.
... and chapter 34 was written by a computer program. It starts:
"Bruce walked around any more. Some people might ought to her practiced eye, at her. I am so silky and braid shoulders. At sixty-six, men with a few feet away form their languid gazes. I know I was hungry, and impelling him lying naked. She slowly made for a man could join you I know what I ought to take you probably should have. He wants it worriedly. About think what to wear? "
Now can anyone tell us who the SF authors are?
Actually, it is well established that the dark matter is NOT baryonic.
The story is a bit about dark matter, because there is a dark matter presence implied by the newly discovered gas clouds. But that's no surprise - the observed structure of ordinary galaxies already implies that they as well are permeated with dark matter.
If by "from the get-go" you mean when it was still called ClarisWorks, I have to take offense (given that I wrote a lot of it). All the reviewers of the early versions, and millions of users, would disagree with you. In fact there are still lots of things you can do with AppleWorks that you can do with no other single program out there.
That said, by the time the name was changed to AppleWorks, the ball had clearly been dropped, and essentially nothing has been done for the past few years. So, dated - yes. Sucked from the get-go - I think (hope) you have a minority opinion there.
Details on ClarisWorks/AppleWorks history here:
http://www-swiss.ai.mit.edu/~bob/clarisworks.php/
Bob Hearn
Oooohhhh... the first Eschaton book was... interesting. I can't say it really stood on its own. It required some pretty damn explanations from the other two books. Alas, it was downhill from there (sort of like the Matrix...). By the time I finished the third one, I was furious that I'd wasted my time with them at all, waiting for a payoff that never came. If that's what you mean by not quite concluded, I guess I agree.
Gateway, now, that's a classic. Required reading! But overall, IMO, the Heechee series had a downward arc (though the rest were still readable). I read a devasating review of TBWWLF the other day, and I was not surprised. Well, maybe I'll give it a chance anyway, in paperback...
Man Plus is another great Pohl book with an atrocious sequel, Mars Plus. Although to be fair, Pohl only co-wrote Mars Plus; maybe most of the blame lies with his co-author, Thomas T. Thomas (although I liked his story in Man Kzin Wars V).
So, from this perspective, what use is not fair use? How is copyright law not always in conflict with the first amendment?
I use my PC card slot all the time, to pull photos off my IBM microdrive. Yeah, I could use a USB card reader, but I don't need one. And the PC card interface is faster.
Still, if it would save cost/weight, I'd happily give it up.
As someone else has pointed out, the Stata center (which is the new building complex housing CSAIL) contains both the Gates tower and the Dreyfoos tower. However, the poster incorrecly stated that RMS will be in the Dreyfoos tower. In fact he is in the space between the two towers - known as the "warehouse" space (for reasons which escape me).
:-)
Office location in the Stata Center can be identified by letters attached to the office number. Stallman's office is 32-381, here:
http://www.csail.mit.edu/resources/maps/3/381.gif
(I'm right across the hall, in 32-386.) A Gates office would be, e.g., 32-G585. A Dreyfoos office would be, e.g., 32-D585. Yes, as someone else pointed out, we have a holodeck.
Most of us are hoping / assuming that, like almost all other buildings at MIT, the new building(s) will be referred to by number, not by name.
IMHO MIT missed a great opportunity to influence the world for the better by publicly snubbing Gates' offer to fund (a small part of) the new building. But, I'm told, that's just not the way things work...
Well, fair enough. But you did way that the book was still being debugged when you were using it, and that the instructor didn't do a great job of teaching it.
So we need to find someone who used the book when it was finished, with a competent instructor.
Anybody??
Wow, I'm really disappointed to see all the negative opinion's on Keisler's book, and the infinitesimal approach to calculus.
I happened to run across the book on Keisler's site a couple of months ago, and... I read the whole pdf through virtually non-stop. All 913 pages. This is by far the best introduction to calculus I've ever seen - very intuitive and clean.
Those of you arguing for the conventional, limits-based approach vs. the "nonstandard", infinitesimal-based approach are missing the point that the very notation in standard use for calculus (dy/dx etc.) really makes no sense without a notion of infinitesimal. Originally Newton developed calculus in terms of limits, while Leibniz used infinitesimals. Leibniz's notation won out over Newton's, because it accords with the way mathematicians intuitively think about calculus. Neither approach was on a sound mathematical footing until the limits-based approach was formalized in the 1870's. The infinitesimal-based approach was only formalized in 1960, by Robinson - the mathematical tools needed to do so were not available in the 19th century. Due to an historical accident Robinson's approach is called "nonstandard analysis", but the implication that there is anything deficient or deviant about it does not follow. (BTW, in addition to infinitesimals, the hyperreals (or "nonstandard numbers") also include infinite numbers.)
With this approach, developed in Keisler's book, not only is the notation in accord with the model, but many results are much more straightforward to understand and to prove. No more long, tedious epsilon-delta arguments. Really, the only thing complicated about using nonstandard numbers for calculus is the formal development of the hyperreals - and in this book that is relegated to a brief treatment in an appendix. It's easy enough to state and use the properties of the hyperreals without having to go through their formal mathematical construction.
I find it disheartening that the book was allowed to go out of print, and that there are now no (as far as I'm aware) current popular calculus texts using the infinitesimal-based approach. I, like the original poster, and like most students learning today, was always confused by what you could and couldn't do with dy and dx. How I wish I'd had this book 20 years ago.
The upside is that the book is now freely available on the author's site! Go get it!
Bob Hearn