It's just cool (though maybe unrealistic)!
on
Tying Knots With Light
·
· Score: 5, Informative
The (slashdot) summary really does miss some of the key points, and emphasize the "fusion containment" aspect, which I doubt anyone takes seriously as a use of this. One of the points that I think is key is the whole subject of homotopy groups (which I've really just learned about).
Maxwell's equations (and the wave equation, the Helmholtz equation in momentum space, etc.) have a family of solutions characterized by various parameter values. When you first start learning physics, you typically only allow real-valued wavevectors, which leads to only propagating waves and so on. Later on, you start to realize (as did George Green around 150 years ago, and Newton realized experimentally) that allowing for complex wavenumbers is more appealing mathematically (because it allows for more complete solutions), and actually leads to physically realizable solutions that propagating waves just don't give you. The effect of passing from real to complex wavenumbers is, on the face of it, crazy, but easily understandable once the analysis is carried out, and simple to visualize on an Argand diagram.
However, homotopy groups (if I understand it correctly) say that there may be other solutions to such equations (in nonlinear/dispersive media) which one can't get to from just simple replacements of real with complex numbers, and so forth---these divisions are the "families" of solutions. There just isn't a simple projection from one family of solutions to another, and the solutions of from one may bear no resemblance to the solutions from other famililes. This means that there may, in sufficiently complicated systems, be physically realizable behaviors which a system may fall in to, which aren't describable by the "usual" solutions of the equations. Of course, Maxwell's equations work wonderfully in all situations I've ever heard of (no concession to the "Electric Universe" wackos!), so perhaps nature, for some reason, won't allow other families of solutions to make themselves known on any scale I know of.
So far as I know, as long as you don't have to *transcode* the data (for example, to fit a double-layer DVD onto a typical 4.1GB recordable DVD), there's no problem with copying bit-for-bit, and then burning that onto whatever medium you want, whether or not there's copy protection on there.
Discworld MUD, because so much of its content is engineered by *players*, rather than DMs, seems to be pretty damned natural. One gets a sense of amazing engineering, but it's also as if the whole world has escaped just a little from its designers, and become something a bit... more.
Allow these water bears to reproduce, and take them back up. Rinse lather repeat, and we will have creatures capable of surviving long durations in space.
Perhaps the moderation as "troll" is because you state that the "mom forced her child to have three abortions in the span of six months" (the article only says that the first one was forced by the mother), but what of the man having sex with his 14-year-old "girlfriend" and the girl who got pregnant three times? Bravo for selective outrage.
Of the 13 listed on my gparted setup, 4 cannot currently be shrunk using that tool. 13 - 4 = 9. Perhaps installing other tools (for example, reiser4progs) will change the availability of the different gparted utilities.
My fastest way of checking what operations can be supported on filesystems at the present is by checking what gparted can do. Of the filesystems it works with right now, only four (jfs, reiser4, ufs, xfs) can't be shrunk using gparted.
Bravo! Someone who actually understands---and is able to cogently research and explain---some of the tricks that many algorithms use to trick people into thinking the programs are worth the ruled paper they're printed on! Nice.
Slashdot Mirror
The (slashdot) summary really does miss some of the key points, and emphasize the "fusion containment" aspect, which I doubt anyone takes seriously as a use of this. One of the points that I think is key is the whole subject of homotopy groups (which I've really just learned about).
Maxwell's equations (and the wave equation, the Helmholtz equation in momentum space, etc.) have a family of solutions characterized by various parameter values. When you first start learning physics, you typically only allow real-valued wavevectors, which leads to only propagating waves and so on. Later on, you start to realize (as did George Green around 150 years ago, and Newton realized experimentally) that allowing for complex wavenumbers is more appealing mathematically (because it allows for more complete solutions), and actually leads to physically realizable solutions that propagating waves just don't give you. The effect of passing from real to complex wavenumbers is, on the face of it, crazy, but easily understandable once the analysis is carried out, and simple to visualize on an Argand diagram.
However, homotopy groups (if I understand it correctly) say that there may be other solutions to such equations (in nonlinear/dispersive media) which one can't get to from just simple replacements of real with complex numbers, and so forth---these divisions are the "families" of solutions. There just isn't a simple projection from one family of solutions to another, and the solutions of from one may bear no resemblance to the solutions from other famililes. This means that there may, in sufficiently complicated systems, be physically realizable behaviors which a system may fall in to, which aren't describable by the "usual" solutions of the equations. Of course, Maxwell's equations work wonderfully in all situations I've ever heard of (no concession to the "Electric Universe" wackos!), so perhaps nature, for some reason, won't allow other families of solutions to make themselves known on any scale I know of.
Now, if only we could get greeting cards to sing that for us...
Can't be worse than the colorscheme on SlashMail, right?
You're disappointed by 39-foot-long crocodiles? I guess I have to raise my standards somehow. (Not directed at you, honey)
Only the cool ones died out, leaving us with the current underwhelming descendants and pretenders.
But... but... Bono wears sunglasses all the time, man! All the freaking time!
Man, I watch porn just to get cookies flashed at me!
I started to google it, but then got sidetracked by -- Ooh! Shiny!
So far as I know, as long as you don't have to *transcode* the data (for example, to fit a double-layer DVD onto a typical 4.1GB recordable DVD), there's no problem with copying bit-for-bit, and then burning that onto whatever medium you want, whether or not there's copy protection on there.
Who is actually the OWNER of the system?
Hell, they don't even know who the pwnerer is yet.
Oh, good point. Now the onus is on him to explain what he meant.
I would almost risk having them hate science, as long as they also can't stand rap music.
Discworld MUD, because so much of its content is engineered by *players*, rather than DMs, seems to be pretty damned natural. One gets a sense of amazing engineering, but it's also as if the whole world has escaped just a little from its designers, and become something a bit... more.
Allow these water bears to reproduce, and take them back up. Rinse lather repeat, and we will have creatures capable of surviving long durations in space.
Oh.... Good. Just what we (and they) need.
Those're STDs.
Plan 9 from User Space.
Yeah, that was quite preciousssssss.
Even gargoyles gargle!
Interesting.
Perhaps the moderation as "troll" is because you state that the "mom forced her child to have three abortions in the span of six months" (the article only says that the first one was forced by the mother), but what of the man having sex with his 14-year-old "girlfriend" and the girl who got pregnant three times? Bravo for selective outrage.
And it will likely be ignored for many of the same reasons. http://www.conservapedia.com/Conservapedia_challenge
Mac fans start to whine after a while.
Their cooling systems get noisier, too.
Of the 13 listed on my gparted setup, 4 cannot currently be shrunk using that tool. 13 - 4 = 9. Perhaps installing other tools (for example, reiser4progs) will change the availability of the different gparted utilities.
My fastest way of checking what operations can be supported on filesystems at the present is by checking what gparted can do. Of the filesystems it works with right now, only four (jfs, reiser4, ufs, xfs) can't be shrunk using gparted.
Bravo! Someone who actually understands---and is able to cogently research and explain---some of the tricks that many algorithms use to trick people into thinking the programs are worth the ruled paper they're printed on! Nice.
Ah, but I only RTFComments.
Pfft. That nebula smells of orange-sounding elderberries, anyway. You'll know it when you get there.