Even including all the digits doesn't get you what you want. Take the irrational number 0.123456789112233445566778899111222333444.... This contains all nine digits (with equal frequency even), but not the sequence 13. As far as changing bases, I'm not really sure what effect that has on the form of a sequence of digits. For all I know, it might be true that you can always find a base that will produce whatever distribution you want, but I've never seen anything saying so (and I don't see any particular reason to think that this is true).
True. And whether or not pi is normal is still an open question. The problem is that many posters here don't take that into account: they seem to assume that the digits of pi must contain every possible sequence of digits merely because it is infinite and doesn't repeat the same pattern over and over.
cybercuzco said: But this is already true. Given an INFINITE string of whole numbers, any noninfinite string of whole numbers is included.
It really bothers me that so many people on Slashdot seem to believe this. The statistical distribution of the digits of pi is still (to the best of my knowledge) an open problem, but the notion that any non-repeating inifinite sequence of digits must contain every possible finite sequence of digits is plainly false. For an example of an irrational number whose decimal expansion does not have this property, consider the number (in base 10) 0.10110111011110111110....
Proving that pi is irrational is not as simple as proving that sqrt(2) is irrational, but neither is it ridiculously difficult. One proof is given as exercise 7.33 in Apostol's mathematical analysis (2nd edition).
The Linux kernel is really designed specifically for gcc. Aside from using GNU extensions to C, in many places the code is designed specifically to get good object code out of gcc.
All you need is a foot pedal to type Perl code quickly and easily. I have a bunch of macros set so that I can type most "programming punctuation" without moving my fingers off the home row (or at least using a strong finger when I do). One post above said that the foot pedal was a waste of money, but I totally disagree. I have two, and as a result I have no trouble typing most punctuation, and I never have to use more than a single finger (and potentially both feet) to type a character. They also keep me sitting up straight as an ergonomic side-benefit.
You should be able to remap any key in command mode with 'map'.
For example:
map % dd
would make it so that typing % in command mode deleted the current line. You can get just about any sequence of keys that you want in there in place of 'dd'. You can even put in control characters by typing ^V before them (where ^V is actually control-V):
map % ihello there you^V
would show up in your.vimrc as
map % ihello there you^]
and would change the % so that it entered insert mode, printed "hello there you" and escaped back to command mode.
That's not quite correct. As a star collapses, it would be subject to time-dilation resulting from its own gravity. This effect, however, would only be apparent to someone close enough to the dying star to be affected by its strong gravitational field. To observers at a safe distance (say, on Earth), time flows normally and the star disappears beneath an event horizon. (An observer on the surface of the star would indeed have to wait an eternity to see the black hole form.)
In my experience, Amazon's interface and customer service are vastly superior to any competitor's. For quite a while I ordered books exclusively through them even though I was aware of lower prices elsewhere because Amazon was easy to deal with and trustworthy. I've never received spam from them (I think it's very reasonable for a company to let me know if they're offering a discount on something in which I've expressed interest), and I'm willing to believe that the people at Amazon did not (and apparently still do not) consider their patents to be "completely bogus". I want to believe that Amazon is really a "good guy" because I desperately want to be able to use their service with a clear conscience. I've spent a few months now ordering books from various other distributors, and I have been unsatisfied with all of them in one way or another. In any event, I find that I still visit amazon.com before any book purchase in order to read the customer reviews there. The only thing I've ever found distasteful about Amazon is their agressive use of the One-Click patent. Were they to drop their lawsuit against B&N, I'd be back in a heartbeat. Amazon is not playing on my interest in seeing e-commerce succeed because I really don't have that much interest in it--that's not my area.
Personally, I think it's great that these kids can gain a strong background in programming and other computer-related skills in high school. That said, the statement about making websites in English class did disturb me. When I was in high school, English class was about gaining insight into literature and learning how to express oneself clearly. Doing this can certainly involve HTML, I suppose--I just hope that important lessons aren't being skipped in favor of teaching a fairly trivial markup language.
I live in a dorm at Ohio University (I stay in the dorm partly because of the high-speed internet connection). This year, every freshman was given a computer by the University, and all year the network has been incredibly slow (I frequently couldn't tell if it was even up). Naturally, I blamed the freshmen. One day, all the speed and reliability I was used to came back. Why? Were the routers finally upgraded to handle the increased load brought on by the freshmen computers? Were the buggy DHCP servers fixed? No. I found out about a week later that the Napster metaserver's IP had been blocked. This is not in any way a free speech issue: I want to be able to read my email, and now I can.
I take issue with your statement that sex is necessary for life. An enormous amount of life (think bacteria) has existed on this planet without sex. If the human race really cared about God and good, decent, Puritanical morality, we'd learn to live without it too. Thank God for cloning.
I've been addicted to Civ2 for a long time, and I bought Civ:CTP as soon as it came out for Linux. I still reboot about once or twice a week to play Alpha Centauri (it's in my StartUp folder in Windows), while Civ:CTP hasn't been played in months.
Alpha Centauri is by far the best game of this sort that I've ever played. It's mostly the same game as Civ2, but it adds a few interesting twists (especially in diplomacy and government), as well as being much more automizable and having a simpler interface.
That said, it does suffer from a few obvious problems. The names of techs and units are far less intuitive than in an Earth based game (i.e., anyone who clicks on Civ2 will know what sorts of advantages can be gained from Wheel, but who would think that Industrial Economics gives you better armor). The online help is awfully good, and it goes a long way toward alleviating this problem, but maybe not far enough for some (once you've played a few hundred games, it's not really a problem anymore anyway).
I've also heard that it slows down when you have a lot of units on the board, but I've never personally experienced a problem in this area (my computer's about two years old).
I can't wait to buy the Linux version and free up an extra 1.5 gigs of hard drive space.
And maybe someday this technology will allow men in the US to replace what was taken from them at birth. One way or another, gross atrocities tend to correct themselves eventually. (Though I'd hope by the time that this line of research becomes that advanced, circumcision would be a thing of the past.) In case you're not aware, you can correct some of the damage without advanced biotech: just do a web search on "foreskin restoration" or get a book called _The_Joy_of_Uncircumcising_.
It's also fairly easy to switch keyboards on a software level if you don't want to pay $60 for a dvortyboard. Just do a web search for "Introducing the Dvorak Keyboard" and you should find a site with plenty of information. Or just go hunting around in your Windows Control Panel, or use 'loadkeys' or 'xmodmap' in Linux: there might already be a dvorak keymap in/usr/lib.
When you make statements to the effect that Darwin "proved the validity of evolution", keep in mind that he and his contemporaries knew very little about genetics and nothing of modern biochemistry. An enormous number of mutations must occur to produce a comlicated structure (such as an eye) where nothing of the sort previously existed, and none of those mutations are likely to have any inherent value on their own. The probability of actually getting an eye out of random mutations over only a few hundred million years is exceedingly small. Yes, life adapts to its environment, and species evolve into new species. This has been observed. But AFAIK nothing has ever been seen to suggest that something as complex as a cockroach could have evolved from a single-celled organism. As far as I'm concerned, evolutionism has joined religion as something that must be accepted on faith until more convincing evidence comes to light. Note: If you only intended to say that Darwin proved that species evolve into new,/slightly/ different species (an observable fact), I apologize for this post.
Actually, I believe Windows has always displayed fonts at a larger than normal size in all applications. Its creators reasoned that reading small letters would be more dificult on a screen than on paper, so they increased the average on-screen font size by about two points. It's not an evil plot; it's a relic from the days when Microsoft was genuinely concerned about ease of use.
I've never used Visual Basic, but I'd have to assume that Tk (with the scripting language of your choice) would be just as easy to use to "quickly develop a GUI application". And for a larger project, why wouldn't someone choose Qt over MFC?
I don't have a.sig--if I want to say something, I'll type it in myself.
I don't know what you mean by "math oriented stuff", but I'm a math major, and I can't remember the last time I used a calculator in a class. I keep a TI-36 around just in case but rarely use it.
If you're planning to go into a more applied field, like engineering, you'll get more use out of an expensive calculator than I have. But in this case, I would still recommend getting a cheap scientific calculator and perhaps investing in some sort of symbolic manipulation software (like Mathematica, Maple, Derive, Matlab, I don't know what else might be out there) when you head off to college. The student prices on these are fairly reasonable (only slightly more than a TI-92) and they may save you from having to trek up to the computer lab every weekend. Find out what your school/department uses before you make such a purchase of course.
Slashdot Mirror
It's not restricted to functional languages. In fact, teams using C have done quite well in past years.
Even including all the digits doesn't get you what you want. Take the irrational number 0.123456789112233445566778899111222333444.... This contains all nine digits (with equal frequency even), but not the sequence 13. As far as changing bases, I'm not really sure what effect that has on the form of a sequence of digits. For all I know, it might be true that you can always find a base that will produce whatever distribution you want, but I've never seen anything saying so (and I don't see any particular reason to think that this is true).
True. And whether or not pi is normal is still an open question. The problem is that many posters here don't take that into account: they seem to assume that the digits of pi must contain every possible sequence of digits merely because it is infinite and doesn't repeat the same pattern over and over.
It really bothers me that so many people on Slashdot seem to believe this. The statistical distribution of the digits of pi is still (to the best of my knowledge) an open problem, but the notion that any non-repeating inifinite sequence of digits must contain every possible finite sequence of digits is plainly false. For an example of an irrational number whose decimal expansion does not have this property, consider the number (in base 10) 0.10110111011110111110....
Proving that pi is irrational is not as simple as proving that sqrt(2) is irrational, but neither is it ridiculously difficult. One proof is given as exercise 7.33 in Apostol's mathematical analysis (2nd edition).
The Linux kernel is really designed specifically for gcc. Aside from using GNU extensions to C, in many places the code is designed specifically to get good object code out of gcc.
All you need is a foot pedal to type Perl code quickly and easily. I have a bunch of macros set so that I can type most "programming punctuation" without moving my fingers off the home row (or at least using a strong finger when I do). One post above said that the foot pedal was a waste of money, but I totally disagree. I have two, and as a result I have no trouble typing most punctuation, and I never have to use more than a single finger (and potentially both feet) to type a character. They also keep me sitting up straight as an ergonomic side-benefit.
Oops. Should be an escape after the ^V.
You should be able to remap any key in command mode with 'map'. .vimrc as
For example:
map % dd
would make it so that typing % in command mode deleted the current line. You can get just about any sequence of keys that you want in there in place of 'dd'. You can even put in control characters by typing ^V before them (where ^V is actually control-V):
map % ihello there you^V
would show up in your
map % ihello there you^]
and would change the % so that it entered insert mode, printed "hello there you" and escaped back to command mode.
How about:
Do you know what DMCA stands for?
That's not quite correct. As a star collapses, it would be subject to time-dilation resulting from its own gravity. This effect, however, would only be apparent to someone close enough to the dying star to be affected by its strong gravitational field. To observers at a safe distance (say, on Earth), time flows normally and the star disappears beneath an event horizon. (An observer on the surface of the star would indeed have to wait an eternity to see the black hole form.)
In my experience, Amazon's interface and customer service are vastly superior to any competitor's. For quite a while I ordered books exclusively through them even though I was aware of lower prices elsewhere because Amazon was easy to deal with and trustworthy. I've never received spam from them (I think it's very reasonable for a company to let me know if they're offering a discount on something in which I've expressed interest), and I'm willing to believe that the people at Amazon did not (and apparently still do not) consider their patents to be "completely bogus".
I want to believe that Amazon is really a "good guy" because I desperately want to be able to use their service with a clear conscience. I've spent a few months now ordering books from various other distributors, and I have been unsatisfied with all of them in one way or another. In any event, I find that I still visit amazon.com before any book purchase in order to read the customer reviews there.
The only thing I've ever found distasteful about Amazon is their agressive use of the One-Click patent. Were they to drop their lawsuit against B&N, I'd be back in a heartbeat. Amazon is not playing on my interest in seeing e-commerce succeed because I really don't have that much interest in it--that's not my area.
Personally, I think it's great that these kids can gain a strong background in programming and other computer-related skills in high school.
That said, the statement about making websites in English class did disturb me. When I was in high school, English class was about gaining insight into literature and learning how to express oneself clearly. Doing this can certainly involve HTML, I suppose--I just hope that important lessons aren't being skipped in favor of teaching a fairly trivial markup language.
I live in a dorm at Ohio University (I stay in the dorm partly because of the high-speed internet connection). This year, every freshman was given a computer by the University, and all year the network has been incredibly slow (I frequently couldn't tell if it was even up). Naturally, I blamed the freshmen. One day, all the speed and reliability I was used to came back. Why? Were the routers finally upgraded to handle the increased load brought on by the freshmen computers? Were the buggy DHCP servers fixed? No. I found out about a week later that the Napster metaserver's IP had been blocked. This is not in any way a free speech issue: I want to be able to read my email, and now I can.
I take issue with your statement that sex is necessary for life. An enormous amount of life (think bacteria) has existed on this planet without sex. If the human race really cared about God and good, decent, Puritanical morality, we'd learn to live without it too. Thank God for cloning.
or Mistaa Supaakuru depending on how you want to translate the japanese characters on the box
I've been addicted to Civ2 for a long time, and I bought Civ:CTP as soon as it came out for Linux. I still reboot about once or twice a week to play Alpha Centauri (it's in my StartUp folder in Windows), while Civ:CTP hasn't been played in months.
Alpha Centauri is by far the best game of this sort that I've ever played. It's mostly the same game as Civ2, but it adds a few interesting twists (especially in diplomacy and government), as well as being much more automizable and having a simpler interface.
That said, it does suffer from a few obvious problems. The names of techs and units are far less intuitive than in an Earth based game (i.e., anyone who clicks on Civ2 will know what sorts of advantages can be gained from Wheel, but who would think that Industrial Economics gives you better armor). The online help is awfully good, and it goes a long way toward alleviating this problem, but maybe not far enough for some (once you've played a few hundred games, it's not really a problem anymore anyway).
I've also heard that it slows down when you have a lot of units on the board, but I've never personally experienced a problem in this area (my computer's about two years old).
I can't wait to buy the Linux version and free up an extra 1.5 gigs of hard drive space.
And maybe someday this technology will allow men in the US to replace what was taken from them at birth. One way or another, gross atrocities tend to correct themselves eventually. (Though I'd hope by the time that this line of research becomes that advanced, circumcision would be a thing of the past.)
In case you're not aware, you can correct some of the damage without advanced biotech: just do a web search on "foreskin restoration" or get a book called _The_Joy_of_Uncircumcising_.
It's also fairly easy to switch keyboards on a software level if you don't want to pay $60 for a dvortyboard. /usr/lib.
Just do a web search for "Introducing the Dvorak Keyboard" and you should find a site with plenty of information. Or just go hunting around in your Windows Control Panel, or use 'loadkeys' or 'xmodmap' in Linux: there might already be a dvorak keymap in
When you make statements to the effect that Darwin "proved the validity of evolution", keep in mind that he and his contemporaries knew very little about genetics and nothing of modern biochemistry. An enormous number of mutations must occur to produce a comlicated structure (such as an eye) where nothing of the sort previously existed, and none of those mutations are likely to have any inherent value on their own. The probability of actually getting an eye out of random mutations over only a few hundred million years is exceedingly small. /slightly/ different species (an observable fact), I apologize for this post.
Yes, life adapts to its environment, and species evolve into new species. This has been observed. But AFAIK nothing has ever been seen to suggest that something as complex as a cockroach could have evolved from a single-celled organism. As far as I'm concerned, evolutionism has joined religion as something that must be accepted on faith until more convincing evidence comes to light.
Note: If you only intended to say that Darwin proved that species evolve into new,
Whoever cracked Microsoft's router, play nice and put it back the way it was.
Actually, I believe Windows has always displayed fonts at a larger than normal size in all applications. Its creators reasoned that reading small letters would be more dificult on a screen than on paper, so they increased the average on-screen font size by about two points. It's not an evil plot; it's a relic from the days when Microsoft was genuinely concerned about ease of use.
I've never used Visual Basic, but I'd have to assume that Tk (with the scripting language of your choice) would be just as easy to use to "quickly develop a GUI application". And for a larger project, why wouldn't someone choose Qt over MFC?
.sig--if I want to say something, I'll type it in myself.
I don't have a
I don't know what you mean by "math oriented stuff", but I'm a math major, and I can't remember the last time I used a calculator in a class. I keep a TI-36 around just in case but rarely use it.
If you're planning to go into a more applied field, like engineering, you'll get more use out of an expensive calculator than I have. But in this case, I would still recommend getting a cheap scientific calculator and perhaps investing in some sort of symbolic manipulation software (like Mathematica, Maple, Derive, Matlab, I don't know what else might be out there) when you head off to college. The student prices on these are fairly reasonable (only slightly more than a TI-92) and they may save you from having to trek up to the computer lab every weekend. Find out what your school/department uses before you make such a purchase of course.