You should still buy cds -- just not from the major labels. I've bought all my music (lately) from the artists themselves, either on-line or in person. Cut out the middle-man and everyone will benefit!
1. Moving parts suck (break first, use lots of power)
2. Labour, and thus assembly, is expensive (?)
I bet the computer of the future is very much as you describe -- why bother with any storage or data IO (other than the two obvious ones) when you've got GBs of memory on the chip and wireless. In fact, this is already happening -- I would bet that in 5 years DVD/CD drives are being phased out in favour of USB memory, or something similar. Even that will go away once wireless is omnipresent.
Indeed, the Poincare Conjecture (that every n-manifold with the homotopy groups of an n-sphere is homeomorphic to an n-sphere) has been solved in dimensions n = 1, 2, 4, 5, 6,... The only missing case is n = 3, which is the case originally conjectured (well, really "asked about") by Poincare.
The cases n = 1, 2 are not so hard and may be explained to undergraduates. n = 5 and above are not easy but not impossible to explain, either -- Smale got a Fields medal for his work in this area. It can now be covered in a single graduate level mathematics course. The idea (if I remember correctly) basically boils down to "in high enough dimensions, there is enough elbow room". To give a better analogy, generically straight lines in two dimensions meet but in three dimensions they do not. (And to really say what is going on "Two-dimensional surfaces generically do not meet each other if embedded in a five-dimensional space")
The case n = 4 was handled by Michael Freedman using very subtle techniques (at least to me!) but again relying on "having enough space to move around in".
I don't understand the n = 3 case at all, really -- no one has given a simple "These techniques should work because x, y, znd z" sort of explaination, yet. The closest they come is to mutter uncomprehensible things about the heat equation... Suffice to say -- in dimension three there is not enough room to move around in. So it is not a complete surprise that the proof for n = 3 is rather different from higher n.
Curvature is a statement on Geometry of the Universe, while being a Dougnut is a Topological Statement.Both of completely independent of each other.
It is an amazing, but true fact, that you are wrong.
That is, topology and geometry do have something to do with one another.
If you are interested you should look at a copy of
Jeff Week's book "The Shape of Space".
Long story short, if space is positively curved
or flat then the universe can only be one of finitely many
topological shapes (but it will be very difficult to tell
which one it is). On the other hand, if space is negatively
curved then space could be any one of an infinite
number of shapes, called by mathematicians "hyperbolic
manifolds". (And in this case, it should be easy to decide
which shape the universe is!)
For a readable article which explains some of this stuff read
this.
An email is so small, so easy to encode and disguise, so close to a pure meme, that she doesn't stand a chance even of identifying all the copies out there, let alone of enjoining them out of existence.
This is exactly wrong. An email is a text documnet, hence
completely binary. It's not so hard to search a database,
even one as large as the Internet, for exact matches as long
as this email. It is a linear time problem.
I believe that this
is why some experts believe that copyright enforcement is possible.
It is watermarking (embedded DRM) which is hopeless.
I freely admit that the "exact match" problem is much harder for
images, audio, and video. And perhaps also for heavily
annotated text files (such as this LawMeme piece...)
(=He may be a lawyer, but he's not a mathematician.)
As long as the average number of forwards per recipient is greater than one -- no matter by how little or how much -- the laws of probability tell us to expect a nice happy power-law curve zipping up towards infinity.
I'm almost sure that he should be saying "exponential growth" and not "power law."
Think about this: Look at the way drives work now. We (well, the OS really) reuses the space on them, and has to keep track of where all the data physically resides on the disk. What if the drive was so large, say 10 TB, that you didn't need to do that? Instead of deleting something off the drive, you simply write it to a new location and move on.
Hmm. This is an interesting idea --- never throw anything away (files, history list, web clicks), and stick time stamps on everything. The operating system becomes (or rather, includes) a revision control system. Reverting to a previous copy of the code is trivial. Resetting your life to three days ago is trivial. Changing your mind about that is easy, too.
One hopes that this sort of thing doesn't become an enforcement tool.
We do have a valid alternative -- it's called capitalism. While we're off reading "Amimal Farm" why don't you go read the article? Once you're done with that you'll realize that their main point is that most IP does not need goverment protection (i.e. patents).
It seems clear to this layperson that
the closed and open source communities rely,
at least in part, on each other. The situation
is much the same in the university vs. industry
setting.
Only an ideologue (RMS, Bill Gates?) would
think that only half of the equation makes sense.
Slashdot Mirror
You should still buy cds -- just not from the major labels. I've bought all my music (lately) from the artists themselves, either on-line or in person. Cut out the middle-man and everyone will benefit!
Oh, and billy at billyband.com rocks.
Huh. Kinda like HIV.
1. Find out what tests the goverment wants run on "secure" software,
2. figure out which of these tests are interesting and new, and
3. perform them on Linux, etc.
"create an entire system on a chip"
This will surely happen. Why?
1. Moving parts suck (break first, use lots of power)
2. Labour, and thus assembly, is expensive (?)
I bet the computer of the future is very much as you describe -- why bother with any storage or data IO (other than the two obvious ones) when you've got GBs of memory on the chip and wireless. In fact, this is already happening -- I would bet that in 5 years DVD/CD drives are being phased out in favour of USB memory, or something similar. Even that will go away once wireless is omnipresent.
You might be interested in the book "Missionary Position" by Christoper Hitchens.
Indeed, the Poincare Conjecture (that every n-manifold with the homotopy groups of an n-sphere is homeomorphic to an n-sphere) has been solved in dimensions n = 1, 2, 4, 5, 6, ... The only missing case is n = 3, which is the case originally conjectured (well, really "asked about") by Poincare.
The cases n = 1, 2 are not so hard and may be explained to undergraduates. n = 5 and above are not easy but not impossible to explain, either -- Smale got a Fields medal for his work in this area. It can now be covered in a single graduate level mathematics course. The idea (if I remember correctly) basically boils down to "in high enough dimensions, there is enough elbow room". To give a better analogy, generically straight lines in two dimensions meet but in three dimensions they do not. (And to really say what is going on "Two-dimensional surfaces generically do not meet each other if embedded in a five-dimensional space")
The case n = 4 was handled by Michael Freedman using very subtle techniques (at least to me!) but again relying on "having enough space to move around in".
I don't understand the n = 3 case at all, really -- no one has given a simple "These techniques should work because x, y, znd z" sort of explaination, yet. The closest they come is to mutter uncomprehensible things about the heat equation... Suffice to say -- in dimension three there is not enough room to move around in. So it is not a complete surprise that the proof for n = 3 is rather different from higher n.
It is an amazing, but true fact, that you are wrong. That is, topology and geometry do have something to do with one another. If you are interested you should look at a copy of Jeff Week's book "The Shape of Space".
Long story short, if space is positively curved or flat then the universe can only be one of finitely many topological shapes (but it will be very difficult to tell which one it is). On the other hand, if space is negatively curved then space could be any one of an infinite number of shapes, called by mathematicians "hyperbolic manifolds". (And in this case, it should be easy to decide which shape the universe is!)
For a readable article which explains some of this stuff read this.
This is exactly wrong. An email is a text documnet, hence completely binary. It's not so hard to search a database, even one as large as the Internet, for exact matches as long as this email. It is a linear time problem.
I believe that this is why some experts believe that copyright enforcement is possible. It is watermarking (embedded DRM) which is hopeless. I freely admit that the "exact match" problem is much harder for images, audio, and video. And perhaps also for heavily annotated text files (such as this LawMeme piece...)
As long as the average number of forwards per recipient is greater than one -- no matter by how little or how much -- the laws of probability tell us to expect a nice happy power-law curve zipping up towards infinity.
I'm almost sure that he should be saying "exponential growth" and not "power law."
Hmm. This is an interesting idea --- never throw anything away (files, history list, web clicks), and stick time stamps on everything. The operating system becomes (or rather, includes) a revision control system. Reverting to a previous copy of the code is trivial. Resetting your life to three days ago is trivial. Changing your mind about that is easy, too.
One hopes that this sort of thing doesn't become an enforcement tool.
We do have a valid alternative -- it's called capitalism. While we're off reading "Amimal Farm" why don't you go read the article? Once you're done with that you'll realize that their main point is that most IP does not need goverment protection (i.e. patents).
Dude, you've got to get out more. :)
It seems clear to this layperson that the closed and open source communities rely, at least in part, on each other. The situation is much the same in the university vs. industry setting. Only an ideologue (RMS, Bill Gates?) would think that only half of the equation makes sense.