A more generalized uncertainty principle would be that, for two observables A and B, the product of the variances of A and B (variance -> uncertainty in general parlance) is greater than or equal to 1/4 of the magnitude squared of the commutator of the operators A and B.
Thus, any two operators whose commutator does not vanish--position and momentum, e.g., or spin operators along different axes, or energy and time--will give a non-zero result for uncertainty in the measurement of both observables.
It is true that "Heisenberg's Uncertainty Principle" usually refers to position and momentum!
Clearly you don't live in Cambridge. Bicylces are a menace and must be terminated with extreme prejudice!
I kid a bit, of course, but it seriously is a problem in places like Cambridge. Right outside of my college (in city centre, mind you!), the road narrows to one lane. Buses drive through there like madmen, and very frequently cyclists come right up on the footpath at breakneck speed. Very dangerous for all involved. I fully advocate bikes in city, because they are by far the most efficient and potentially the fastest form of transportation. But there needs to be infrastructure for it to be safe. The Netherlands, with their extensive bike lanes, is a good example.
The good thing about bikes in Cambridge is how badass you look cycling along in an academic gown whilst puffing a pipe. Badass, badass, badass.
This is utterly out of curiosity. I first saw that on "Judging Amy", and I must have cracked up for hours... is that the original source, or does it come from elsewhere?
Your figures aren't quite right. The acceleration due to gravity is only 9.8m/(*s*s) at the surface of the earth, hence V=mgh is only valid near the ground. The gravitational potential falls off as you go farther from the earth. In this case, the required energy per unit mass would be INT(GM/r, R1, R2) where R1 is the radius of the earth, R2 is the terminal point on the elevator, M is the mass of the earth, and G is the gravitational constant. Cheers!
Yeah -- that having been said, I was fairly sure the X-Prize wasn't going to be claimed, and I ended up having to eat my shirt. So I'm not going to be so quick to write this one off. But you're right; the orbital requirements are hard enough, and then the extra docking requirements... highly non-trivial, in my ignorant opinion.
If I only wanted special effects, I would stick to 64K demos, okay?
While the plot in all of the Star Wars has never been, say, Citizen Kane material, the first three were certainly not all about special effects. Okay, Carrie and Mark are not the greatest actors in the world; but the cast at least had some dynamics. Nothing like that in these new ones.
It depends on whether you favor Greek or Latin, and the two words are slightly different anyway. "Kosmos" = universe/heavens, whilst "astra" = star. I think "star sailor" has a rather romantic sound to it, but "heavens sailor" is rather grander.
There are numerous spelling and grammar errors in the letter that Merkey supposedly posted, and note the blatant CC to Maureen O'Gara. I don't know, my troll alarm is going off. Is it legit?
"Remember, if you're doing a Megapixel display, the laser is 1,000,000 times as much power as a single pixel requires."
I'm sorry, but this is just completely wrong. Assuming that the laser even has to output as much as ONE pixel (remember, that pixel is broadcasting, where as this will be focused), it would just sweep that one-pixel power over your retina. You don't "lose" the power to a spot on the retina, because the laser is continuous, or if pulsed, close enough to be continuous.
Actually, if you wrote it as exp(i*Cir) - 1 = 0, you wouldn't have to introduce 2. I don't find the addition of 2 to be very compelling. The duality you discussed can be more simply described with just 1 and 0 -- you don't need to count the elements, really. Compare this to a sphere; if you consider the SPACE the sphere is in, you need three dimensions, whereas if you consider only the sphere, you just need two. That is why GR is treated with manifolds now rather than an extension of traditional diff. geometry, which would require five (!) dimensions. That thought makes me sad.
In any case, though, I'm very down with using Cir instead of pi, but I don't think it would fly.
Your system is axiomatic. If you assume that you have numbers that add and subtract as above, then of course they will! These are the axioms you have chosen for your system.
If, on the other hand, you choose "simpler" axioms, then you might have to work very hard to get to the point of saying 1 + 1 = 2. Peano's axioms lead very quickly to this--in fact, they are about the same as the ones you stated. But you can assume any set of axioms you want. Much of mathematics is devoted to finding a "minimum set" of axioms for a particular branch, although as Godel showed, mathematics cannot be consistently axiomatic. Alas.
Granted, I'm drunk as a I post this, but I'm pretty sure I'm still a relativist...
In the inertial reference frame of the object, decelerate and accelerate do indeed have separate meanings... one creates a positive delta-V, the other negative... I'm quite sure of the difference between the two in my own reference frame. Just because velocity is not an absolute doesn't mean that is has no meaning.
Slashdot Mirror
Thus, any two operators whose commutator does not vanish--position and momentum, e.g., or spin operators along different axes, or energy and time--will give a non-zero result for uncertainty in the measurement of both observables.
It is true that "Heisenberg's Uncertainty Principle" usually refers to position and momentum!
I kid a bit, of course, but it seriously is a problem in places like Cambridge. Right outside of my college (in city centre, mind you!), the road narrows to one lane. Buses drive through there like madmen, and very frequently cyclists come right up on the footpath at breakneck speed. Very dangerous for all involved. I fully advocate bikes in city, because they are by far the most efficient and potentially the fastest form of transportation. But there needs to be infrastructure for it to be safe. The Netherlands, with their extensive bike lanes, is a good example.
The good thing about bikes in Cambridge is how badass you look cycling along in an academic gown whilst puffing a pipe. Badass, badass, badass.
Danke!
This is utterly out of curiosity. I first saw that on "Judging Amy", and I must have cracked up for hours... is that the original source, or does it come from elsewhere?
Good God, a recursive acronym embedded in a Slashcronym! TGIF.
Your figures aren't quite right. The acceleration due to gravity is only 9.8m/(*s*s) at the surface of the earth, hence V=mgh is only valid near the ground. The gravitational potential falls off as you go farther from the earth. In this case, the required energy per unit mass would be INT(GM/r, R1, R2) where R1 is the radius of the earth, R2 is the terminal point on the elevator, M is the mass of the earth, and G is the gravitational constant. Cheers!
Newspapers in New England were calling 1816 the year without a summer. Damn Darkfriends...
Yeah -- that having been said, I was fairly sure the X-Prize wasn't going to be claimed, and I ended up having to eat my shirt. So I'm not going to be so quick to write this one off. But you're right; the orbital requirements are hard enough, and then the extra docking requirements... highly non-trivial, in my ignorant opinion.
Yeah, I deserve that ;) My excuse is that it was early morning... but here's hoping my professor doesn't read this!
Well, I thought it was funny!
While the plot in all of the Star Wars has never been, say, Citizen Kane material, the first three were certainly not all about special effects. Okay, Carrie and Mark are not the greatest actors in the world; but the cast at least had some dynamics. Nothing like that in these new ones.
It depends on whether you favor Greek or Latin, and the two words are slightly different anyway. "Kosmos" = universe/heavens, whilst "astra" = star. I think "star sailor" has a rather romantic sound to it, but "heavens sailor" is rather grander.
There are numerous spelling and grammar errors in the letter that Merkey supposedly posted, and note the blatant CC to Maureen O'Gara. I don't know, my troll alarm is going off. Is it legit?
I'm sorry, but this is just completely wrong. Assuming that the laser even has to output as much as ONE pixel (remember, that pixel is broadcasting, where as this will be focused), it would just sweep that one-pixel power over your retina. You don't "lose" the power to a spot on the retina, because the laser is continuous, or if pulsed, close enough to be continuous.
Fucking. Nerds. Brilliant. Commentary.
Grad school cracked you too, eh?
Right right. I should have been more clear on that. Thanks for the correction! :)
Best of all in relativistic tensor notation -- only 1! (Well, up to your choice of gauge, anyway...) Cheers!
E^2 = P^2 + M^2
I love that sig, by the way :)
In any case, though, I'm very down with using Cir instead of pi, but I don't think it would fly.
If, on the other hand, you choose "simpler" axioms, then you might have to work very hard to get to the point of saying 1 + 1 = 2. Peano's axioms lead very quickly to this--in fact, they are about the same as the ones you stated. But you can assume any set of axioms you want. Much of mathematics is devoted to finding a "minimum set" of axioms for a particular branch, although as Godel showed, mathematics cannot be consistently axiomatic. Alas.
Jebus, I should read the subject lines... oh well. Cheers.
NEC, make your time.
You see, generally things get announced shortly before they happen so that people remember them. And Stargate rocks out, okay?
In the inertial reference frame of the object, decelerate and accelerate do indeed have separate meanings... one creates a positive delta-V, the other negative... I'm quite sure of the difference between the two in my own reference frame. Just because velocity is not an absolute doesn't mean that is has no meaning.