First: complex numbers, explained. You may have heard the question asked, "what is the square root of minus one?" Well, maths has an answer and we call it i. i*i = -1. If the real number line...-4, -3, -2, -1, 0, 1, 2, 3, 4... is represented as a horizontal line, then the numbers...-4i, -3i, -2i, -i, 0, i, 2i, 3i, 4i... can be thought of as the *vertical* axis on this diagram. The whole plane taken together is then called the complex plane. This is a two-dimensional set of numbers. Every number can be represented in the form a+bi. For real numbers, b=0.
Right. Now the Riemann Zeta Function is a function/map (like f(x)=x^2 is a function) on the complex plane. For any number a+bi, zeta(a+bi)will be another complex number, c+di.
Now, a zero of a function is (pretty obviously) a point a+bi where f(a+bi)=0. If f(x)=x^2 then the only zero is obviously at 0, where f(0)=0. For the Riemann Zeta Function this is more complicated. It basically has two types of zeros: the "trivial" zeroes, that occur at all negative even integers, that is, -2, -4, -6, -8... and the "nontrivial" zeroes, which are all the OTHER ones.
As far as we know, *all* the nontrivial zeroes occur at 1/2 + bi for some b. No others have been found in a lot of looking... but are they ALL like that? The Riemann Hypothesis suggests that they are... but until today nobody has been able to prove it.
Re:Replace it with a key labelled [help]
on
Is Caps Lock Dead?
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· Score: 1
I bought a Logitech keyboard recently which has about a dozen additional keys on it. These are all marked with helpful things like "webcam" and "shopping". It also had one marked "iTouch", a button whose sole purpose was to open your browser and take you to the iTouch website - iTouch being the software that was bundled with the keyboard. WOW, SO USEFUL.
Fortunately you could use the software to customise these. You also had an "F-Lock" key which could switch your 12 function keys between 12 other (also programmable) functions. I spent a while programming all these for more useful things, but it was a week later when I realised that the F-Lock key always defaulted to "on" when I turned my computer on. Always. Numlock, Capslock and Scroll Lock all remembered their previous state, but I had to turn off F-Lock every time I powered on because I use function key shortcuts so often. This became so annoying that I eventually uninstalled the software.
In conclusion, the Logitech Cordless Desktop MX ain't worth the cash overall, but the MX700 mouse is worth every last penny.
Re:Caps Lock? Who cares about Caps Lock?
on
Is Caps Lock Dead?
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· Score: 1
I'm kind of embarrassed to actually ask this, but... what does Scroll Lock do, anyway?
you can't get online afterwards and post about it in forums
Then what do you call GameFAQs? There are thousands of console videogame forums.
And flexibility is a weakness too. PC games manufacturers have to take into account a billion possible hardware configurations when they make their games - lengthening production time, and introducing bugs and the need for patches.
Perhaps more to the point, Cartoon Network deserves Futurama. It's the only American TV network I've yet to hear anything bad about. Man, if CN got the Simpsons too, you'd never have to change channel.
I found that Winamp takes an age to load a 1000-file directory of MP3s, but that was because of one of my options settings, the one that makes it read all the metadata at the same time. Changing that from "read on load" to "read on display" or "read on play" solves the problem.
Unfortunately you seem to have the same problem with M3U files, which is a puzzler. It should save the metadata along with the M3U...
"Sufficiently advanced technology is indistinguishable from magic." ~ Arthur C. Clarke. Of course, even the quadratic formula or a simple integral looks like magic to most people...
I'd like to see a similar movie that was in a more scenic part of the world, Europe maybe. America may rock and all, but the west coast sure looks to be a big, yellow space...
On an unrelated note, what is the music he used? It sounded pretty good.
Note also that if pi terminated (i.e. the rest was zeroes) then that still counts as repetition and that would make it rational. Since pi has been proven irrational, it cannot terminate. Therefore, there is no "last digit" of pi.
Maths. Although, as a mathematics student, I got lost at "natural generating function is the Dirichlet series", mainly because as far as I know I haven't been taught the meanings of "natural generating function" or "Dirichlet series".
Interesting that this game should come out around now, because Tetris: The Movie (starring Al Pacino as "L") was always supposed to come out in Summer 2004.
Shame I wasn't on Slashdot yesterday, when I could have legitimately said "The Day After Tomorrow comes out the day after tomorrow". Oh well... never get to use that line again...
Slashdot Mirror
First: complex numbers, explained. You may have heard the question asked, "what is the square root of minus one?" Well, maths has an answer and we call it i. i*i = -1. If the real number line ...-4, -3, -2, -1, 0, 1, 2, 3, 4... is represented as a horizontal line, then the numbers ...-4i, -3i, -2i, -i, 0, i, 2i, 3i, 4i... can be thought of as the *vertical* axis on this diagram. The whole plane taken together is then called the complex plane. This is a two-dimensional set of numbers. Every number can be represented in the form a+bi. For real numbers, b=0.
Right. Now the Riemann Zeta Function is a function/map (like f(x)=x^2 is a function) on the complex plane. For any number a+bi, zeta(a+bi)will be another complex number, c+di.
Now, a zero of a function is (pretty obviously) a point a+bi where f(a+bi)=0. If f(x)=x^2 then the only zero is obviously at 0, where f(0)=0. For the Riemann Zeta Function this is more complicated. It basically has two types of zeros: the "trivial" zeroes, that occur at all negative even integers, that is, -2, -4, -6, -8... and the "nontrivial" zeroes, which are all the OTHER ones.
As far as we know, *all* the nontrivial zeroes occur at 1/2 + bi for some b. No others have been found in a lot of looking... but are they ALL like that? The Riemann Hypothesis suggests that they are... but until today nobody has been able to prove it.
No, trust me, they are definitely four consecutive digits of pi even so. Somewhere in the first 99849 digits, in fact.
Maths is so cool.
I bought a Logitech keyboard recently which has about a dozen additional keys on it. These are all marked with helpful things like "webcam" and "shopping". It also had one marked "iTouch", a button whose sole purpose was to open your browser and take you to the iTouch website - iTouch being the software that was bundled with the keyboard. WOW, SO USEFUL.
Fortunately you could use the software to customise these. You also had an "F-Lock" key which could switch your 12 function keys between 12 other (also programmable) functions. I spent a while programming all these for more useful things, but it was a week later when I realised that the F-Lock key always defaulted to "on" when I turned my computer on. Always. Numlock, Capslock and Scroll Lock all remembered their previous state, but I had to turn off F-Lock every time I powered on because I use function key shortcuts so often. This became so annoying that I eventually uninstalled the software.
In conclusion, the Logitech Cordless Desktop MX ain't worth the cash overall, but the MX700 mouse is worth every last penny.
I'm kind of embarrassed to actually ask this, but... what does Scroll Lock do, anyway?
you can't get online afterwards and post about it in forums
Then what do you call GameFAQs? There are thousands of console videogame forums.
And flexibility is a weakness too. PC games manufacturers have to take into account a billion possible hardware configurations when they make their games - lengthening production time, and introducing bugs and the need for patches.
Well, that's our ultimate intention.
IANwhoeverthehellwouldknowthisstuff but I'm guessing that the solar panel would probably have to be at least the size of an umbrella. Pretty awkward.
On the plus side, it'll almost certainly receive five out of a possible five stars from the other, identical AI who reviews it.
You mean $RECENT_FORMULAIC_MOVIE ?*
*Best I could come up with was I, Robot, which additionally stars robots
Personally I'm more partial to that Old Fortran liquor.
Perhaps more to the point, Cartoon Network deserves Futurama. It's the only American TV network I've yet to hear anything bad about. Man, if CN got the Simpsons too, you'd never have to change channel.
Best is in that haunted house, when he sees that someone has written a number in blood on the wall.
"01011100101? What does it mean, Bender?""Nothing, it's gibberish. [catches sight of the mirror image and screams] 1010011010?! Ahhhhhh!"
1010011010 being 666 in binary. I also seem to recall him being pursued by a flying toaster and the Windows logo as he flees in terror.
I found that Winamp takes an age to load a 1000-file directory of MP3s, but that was because of one of my options settings, the one that makes it read all the metadata at the same time. Changing that from "read on load" to "read on display" or "read on play" solves the problem.
Unfortunately you seem to have the same problem with M3U files, which is a puzzler. It should save the metadata along with the M3U...
Erm, neither 13, 123, 93 or 103 are cubes. What you mean is 1729 = 1000 + 729 = 1728 + 1, or 1729 = 10^3 + 9^3 = 12^3 + 1^3.
"Sufficiently advanced technology is indistinguishable from magic." ~ Arthur C. Clarke. Of course, even the quadratic formula or a simple integral looks like magic to most people...
I'd like to see a similar movie that was in a more scenic part of the world, Europe maybe. America may rock and all, but the west coast sure looks to be a big, yellow space...
On an unrelated note, what is the music he used? It sounded pretty good.
Wouldn't that be the Spinning Cube of Impending Doom II?
I'm curious: has anyone who played NG also played Super Monkey Ball? How do they compare, difficulty-wise?
Controller breakage stories? Man, I could tell you stories...
*GEEK* chicks. Grrrrr.
I consider it an extremely good way to attempt to impress chicks, since chicks who are impressed by this kind of thing are more likely to be chicks.
Let's see, it wants a password, twenty billion possible combinations... "JEFF"... Hey! It works!
"How did you know?"
"Ah, well, the programmer left a back door. And his name was Jeff Jeffty Jeff. And he was born on the 19th of Jeff, nineteen-jeffty-jeff."
Note also that if pi terminated (i.e. the rest was zeroes) then that still counts as repetition and that would make it rational. Since pi has been proven irrational, it cannot terminate. Therefore, there is no "last digit" of pi.
Maths. Although, as a mathematics student, I got lost at "natural generating function is the Dirichlet series", mainly because as far as I know I haven't been taught the meanings of "natural generating function" or "Dirichlet series".
Interesting that this game should come out around now, because Tetris: The Movie (starring Al Pacino as "L") was always supposed to come out in Summer 2004.
Shame I wasn't on Slashdot yesterday, when I could have legitimately said "The Day After Tomorrow comes out the day after tomorrow". Oh well... never get to use that line again...