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It is a mix of Hexagonal and Penatagonal shapes, more commonly seen as a C60 (carbon60) or Bucky-Ball.

Icosahedra and dodecahedra are strongly related, so that's why a soccer ball looks a bit dodecahedral (having, as it does, 12 pentagons). In fact, if you keep on truncating a icosahedron's corners more and more deeply, you end up with a dodecahedron. Duality is very cool!

2*b || !(2*b) is actually a tautology :P

According to Google, "2*b || !(2*b)" is most likely a generalized incomplete beta function

(As seen on Wolfram's functions

Yea, right - find a person who has no clue about anything, and ask her "a question of cosmic proportions", to cite Prof. Preobrazhensky... I bet she also has a fully formed opinion about usefulness of synchrotrons, and is ready to advise humanity on how useless tensors are (since she can't buy them at Wal-Mart.)

These people are flatlanders - always were, and always will be. People that can't lift their eyes off the ground and look into the sky. People who think inside the box and are proud of that. People who want to stop you from looking up.

This is a well known flaw of democracy. It breeds mediocrity, because every social innovation tends to be suppressed if it does not serve the most immediate needs of the society, since the society in its voting average is stupid.

One truly may wish to have a Space Tyrant as a ruler; maybe ruthless sometimes, but smart and with a vision - not that circus of politicians who don't even know what a vision is, and who bury the society deeper and deeper every year.

It's called positronium, and it lasts 10^-10 seconds.

True. However it's likely, but unproven, that pi is a normal number.

Yes.

Ok so I'm nitpicky, it's tebibyte not tibibyte.

Kibi, Mebi, etc. were created to represent 2**(10*n) (1024, 1048576, 1073741824, etc..). Because in the past there have been problems between one group using SI kilo and others using the made up kilo. When you have things that mean something different, even if they only mean something different in different contexts you'll have problems when people need to communicate.

10Mbps != 10485760 bps .. at least not usually. heh.

Even MathWorld lists what a Mebibyte is.

You said: This is absolute rubbish, a different system of quantification should be used when referring to binary powers, as the borrowing of those from SI is clearly misleading.

There is a system that isn't used by many people. For example, it uses kibibyte for 2^10 bytes and mebibyte for 2^20 bytes (and so on).

You said: This is absolute rubbish, a different system of quantification should be used when referring to binary powers, as the borrowing of those from SI is clearly misleading.

There is a system that isn't used by many people. For example, it uses kibibyte for 2^10 bytes and mebibyte for 2^20 bytes (and so on).

Links:
Newton
Liebniz

Links:
Newton
Liebniz

There is at this point no theory or observation that doesn't validate relativity.

Its a wild and wacky world out there.

rather than trying to build arguments on some superstition or some science-fiction belief.

All scientific theories were once wacky out-there beliefs. Instead of saying "What are you an idiot thinking you can break some well accepted theory! Conform, damn you!", perhaps you should explain why they are wrong.

Everthing is a theory until is proven wrong.

The Metropolis algorithm, first described in a 1953 paper by Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and Edward Teller, was cited in Computing in Science and Engineering as being among the top 10 algorithms having the "greatest influence on the development and practice of science and engineering in the 20th century."

They probably should mention the Jahn Teller Effect

There are some toll-systems in place now that give speeding citations if you cover the distance between two toll-booths in too short a time

Who would have thought that the Mean-Value Theorem would someday be used to give fines. They don't know WHERE you were speeding, but the theorem is clear, there exists such a point "c". Damn.

I would imagine that the creator is playing on every state in quantum mechanics being a superposition of eigenstates of observables.

Or he is attempting to make some play on eigenvectors, but I don't think that this music is composed by some sort of linear transform in the space of the musical components. I'm not sure. Go check out Mathworld's writeup on Eigenvectors if you want to pursue that path of marketing madness. Maybe it would make more sense if the stream wasn't completely slashdotted.

Actually, 2^128 possibilities dictates that you can expect to try 2^127 different files (assuming pure brute force and the law of averages). This would take *signifigantly* longer than 2^64...in particular, about 2^63 times longer.

Oh, and there is no "law of averages".

But then of course no Computer science courses above programing 1 uses windows machines.

Courses above the introductory level shouldn't care what you're running. Your code should run the same, no matter where you run it...toward the end, we had a mix of Linux, Win2K, NetBSD (which replaced SunOS on some ancient SPARCstation 1s), IRIX, and some other stuff I can't remember...it was usually recommended that you make sure your code would build on whatever the TA would use for testing, but properly-written code should build on anything. I usually did most of my coding/debugging on Linux on one of my machines and only did a quick compile/test on the grading machine to make sure I didn't do anything non-portable (which rarely happened). Hell, as late as 1997 I even ported one project (finding a knight's tour from a given starting position) from C to BASIC on an Apple II so that I could add graphics to it to plot the tour (not knowing at the time anything about graphics under X11 or Win32). I dumped a few of those to an Imagewriter and turned that in along with the C and BASIC programs.

0.999... = 0.9+0.09+0.009+...

This is a geometric series with initial term 0.9 and common ratio 0.1.

The infinite sum is:
initial term/(1-common ratio)
= 0.9/(1-0.1)
= 0.9/0.9
= 1

See MathWorld.

Alright. So, say that x is 0.99999... with an infinite number of nines. You claim that x is a number distinct from 1 (since you claim 1 - x is nonzero). Since the the rationals and irrationals are both dense in the reals, we know that if we pick any two distinct reals, we'll always have numbers between them. That is, it's impossible to pick a number and the "next" real number without skipping over any. Yet that is essentially what you've done by positing that the gap between these numbers is infinitely small.

Put in other terms,

1 - x = limit(n->infinity, 1 - sum(9*10^(-i), i=1..n)) = limit(n->infinity, 10^(-n))

So let y equal 1 - x. We can show that if y != 0, then 1 - x < y even with a finite number of digits. Just pick n to be the least integer which is at least -log(y)+1 and then 10^n < y just considering a finite number of digits, n.

That is, if you tell me what the nonzero gap between the numbers that you expect to see, one can show that the gap is less than that. Since the gap is a nonnegative number that is less than all nonzero (ie, positive) choices, it is zero.

Therefore, 0.9999999..... = 1.

On an even more off-topic note, has anyone else started to think that trolls that bring up controversial mathematical statements are probably the best way to get responses nowadays? Not to say that the OP was a troll, but if it was, congratulations on all the responses. Also, congratulations to the Monty Hall problem poster some days back that was a troll.

Except when y = infinite (more precisely aleph-0). Who said the sum is a finite sum?

However, try and think about what this problem really is mathematically, rather than in terms of chess or magic squares. A knight's tour requires the knight to visit every square on the board exactly once. Replace "squares" with "nodes," and "board" with "graph," and what we have here is the problem of finding a Hamiltonian path with some interesting constraints.

And that's where this problem gets interesting- finding a Hamiltonian path on a graph is known to be NP-complete, a designation which carries with it all sorts of baggage, including some of the million-dollar sort. The fact that the question of whether magic knight's tours exist on an standard 8x8 board required 60+ CPU-days to answer speaks volumes about the complexity of the problem, and demands answers as to how this complexity comes about, and why there is no solution with the given constraints. Far from being just a silly mathematical curiosity, this is a problem that presents a lot of potential applications with regards to algorithms, complexity, and computability. Also, if you can find an algorithm that finds Hamiltonian paths in polynomial time, you get the aforementioned free money.

So yes, the problem of finding a magic tour seems worthless if you only consider the problem literally in terms of a chessboard and magic squares, instead of as a model for other complex problems in mathematics, science, and engineering. But by the same token, how interesting and useful would the Traveling Salesman Problem be if it were only applied to traveling salesmen?

If you're mystified by spin and quantum physics in general, This entry on ElectronOrbitals is a good place to start.

This is a new part of (or companion to?) Eric Weisstein's Mathworld. It's expanded now into Science World. Some of the references to electrons and spin are not yet complete, but there's enough here to get started.

If you're mystified by spin and quantum physics in general, This entry on ElectronOrbitals is a good place to start.

This is a new part of (or companion to?) Eric Weisstein's Mathworld. It's expanded now into Science World. Some of the references to electrons and spin are not yet complete, but there's enough here to get started.

If you're mystified by spin and quantum physics in general, This entry on ElectronOrbitals is a good place to start.

This is a new part of (or companion to?) Eric Weisstein's Mathworld. It's expanded now into Science World. Some of the references to electrons and spin are not yet complete, but there's enough here to get started.

hey this is easy! October price: the leviathan number!

So this analyses binaries and will find all issues where the code will halt and will exceed its resource requests, thus eliminating the need for testing...

I call Snake Oil.

For those who don't know about the Halting Problem or Busy Beaver Problem then you should really know about what computers can or cannot do.

I dare say these people have some basic pattern matching, but this is NOT a reason to stop testing.

If you were to take a large chunk of anti-matter and compress it to the point where it became a black hole it would be indistinguishable from a black hole made out of positive matter. The only information you can get from a black hole is it's mass, rotation and electrical charge, every other bit of information about the particles that go into it is destroyed (which gets you into some interesting speculations on black hole entropy that I don't even understand). This is known as the "Black Hole No Hair Theorem". If you were to take two black holes, one of them the aforementioned anti-matter black hole (which is a contradiction in terms because once you've created the black hole you've lost all of the information about what made it) and the positive matter black hole and run them into each other you would end up with a bigger black hole.
Kip Thorne's book on Black holes Black Holes and Time Warps: Einstein's Outrageous Legacy is a good place to start if you want to learn everything about black holes you can learn without having to be as smart as Thorne or Stephen Hawking. Timothy Ferris'sbooks The Whole Shebang: A State of the Universe Report" and Coming of Age in the Milky Way also have some good stuff on black holes.
Now, since dropping two black holes into each other isn't going to do anything more interesting than creating a bigger black hole (which is interesting in and of itself but is not particularly spectacular in an explosive sort of way what you want to do is take two neutron stars, one made of neutrons and the other made of anti-neutrons and run them into each other. That would provide a rather impressive explosion, or you could take a neutron star and pile matter on top of it until it's gravitational attraction is greater than the degeneracy pressure. At this point, according to theory, a black hole will be formed and a huge amount of energy will be released as the neutron star collapses into the black hole.

There are anti-neutrons - the parameter that changes is spin, IIRC.

No - neutrons have a half unit of spin, and the spin of a neutron can be "up" or "down", just as with other half-spin particles such as electrons and protons. The same is true of anti-neutrons, so a neutron and an anti-neutron can have the same spin (both "up" or both "down") or can have opposite spins (one "up", one "down").

It's other charge-like quantum numbers, such as baryon number and isospin (unrelated to spin), that change in the neutron. (They also change in any other particle, e.g. both anti-protons and anti-neutrons have a baryon number of -1, rather than the +1 that the proton and neutron have.)

There are anti-neutrons - the parameter that changes is spin, IIRC.

No - neutrons have a half unit of spin, and the spin of a neutron can be "up" or "down", just as with other half-spin particles such as electrons and protons. The same is true of anti-neutrons, so a neutron and an anti-neutron can have the same spin (both "up" or both "down") or can have opposite spins (one "up", one "down").

It's other charge-like quantum numbers, such as baryon number and isospin (unrelated to spin), that change in the neutron. (They also change in any other particle, e.g. both anti-protons and anti-neutrons have a baryon number of -1, rather than the +1 that the proton and neutron have.)

I was wondering if a West-East measurement of Kansas was a valid approach. The assumption is that Kansas is a very small part of a very large spheroid (where two of the axis have the same radius). This is true because Kansas is a part of Earth, and the Earth is most closely approximated by an oblate spheroid (called the reference ellipsoid). But like I said, the assumption is that Kansas is like the rest of the world, where it could be dramatically different (assuming there were an anti-Kansas that was equally different in the opposite direction so that the two would average out to the reference ellipsoid). Even their own results betray this assumption, the flatness of the earth is 0.00335, but the flatness of Kansas is 0.997.

I have a great .sig but I'm not going to give it to you.

see: powers of ten

Googol

What if you had a web page and gave a publisher rights to print an edition of the web page. Would you then be able to keep up your web page? Don't bet on it.

Granted its version 4.2 but it can be done.

Link to the list of available platforms.

If these do well I see no reason for Wolfram to ignore it or treat it like a second class system. The fact that it exists shows there was enough demand already for it. Plus IBM will undoubtedly port a good chunk of their software titles to it.

gridMathematica also runs in parallel for those who need to process extremely complicated mathematical forms.

This is yet another reason that LaTeX is Good.

If you're doing anything at all with computer algebra (rather common in applied math and engineering science anyway) you'll find you can get maple or mathematica to output your equations at any stage of processing in TeX. They even have little TeX-rendering front ends now.

This is really really nifty, because it means that you can play with the algebraic form of an equation (or a whole table of related equations) and see what form of the same equation typesets the most clearly and readably -- with a far lower probability of making typographic errors!

I did a lot of the equations for my thesis like this, in the late 80's -- using cut-and-paste between different virtual terminals under X windows to get the TeX output from command-line maple and mathematica into my vi session where I was writing my thesis--in plain TeX.

Great reproducibility and easier to keep stuff organised too. It means you can save the maple or mathematica workbook in the same directory as that section of your thesis (and the bibtex file associated with it, and the fortran/C source you also had maple/mathematic spit out to test numerical approaches to solving the same problem).

Someone mentioned FrameMaker -- that was originally just a SunWindows WYSIWYG front-end to TeX. A long long time ago. It was too expensive, and there were several open source alternatives to preview your DVI output, some of which survive to this day.

If you play music with other people lilypond makes the most beautifully typeset music I've ever seen -- in LaTeX --and automates the transcription process for you as well. From the command line. Which means you can set it up as a web service for your muso buddies, who might be blowing a B-flat instrument, while you keep the master transcription in C for the piano. While there are lots of pointy-clicky windows apps that will do this, the typesetting quality is not nearly as good, and because they require someone pointing and clicking, it's much harder to use them as processing back ends to some other thing you might want to do. e.g. a transcription service that you and your friends need in order to play stuff together. But a way to get rehearsal copies to them quickly without a lot of fiddling around in Windows.

If you view gravity as nothing more than the curvature of space-time (as opposed to a "force") caused by the presence of mass, then there's no way to obtain an "inverse curvature" at a given point in space. Hence, there can be no anti-gravity.

However, if they find that there is indeed a mediating particle (graviton) for the gravitational force, and one could lessen the effects of those particles or even block them, the gravitational force would thus be lessened or blocked.

Perhaps something analagous to a Faraday cage for gravitational effects.

There's a whole class of problems which can take a tremendously long time to solve, but for which the solution, once found, can be verified very quickly.

The distributed.net key-cracking contest was like this -- you don't have to double check every piece of work because once you've found the key, it is trivial to test it to make sure it's right. The OGR project works the same way, and I suspect that SETI uses a similar model.

If it was true that you had to double-check everything then there would be absolutely no benefit to distributed computing. You'd be better off just building a supercomputer and doing everything just once.

benhaha says: Light is red-shifted climbing out of the gravity well.

Can you expand on this? I've never heard of this, and I can't think of anything in my 40+ years of layman's reading on physics that could be expressed this way.

Here's a few links. Google for "gravitational redshift" and you'll get lots more.

Link.
Link.

To summarize, the gravitational redshift (or blueshift, for light falling into a gravitational potential well) is a real effect. It was demonstrated by Pound and Rebka at Harvard University in 1960. They used essentially monochromatic gamma ray photon sources at the top and bottom of an elevator shaft, and measured the shift in frequency for photons traversing the shaft each direction. Kudos to Einstein--General Relativity gets another check mark.

Hardly a poor analogy at all, my friend.

Not all new work in mathematics is inaccessible. Matter of fact, some of the most beautiful creations of the past century or so not the complex, inscrutably hard-to-read proofs like Wiles' proof of Fermat's Last Theorem.

Consider Godel's proof. The basic idea behind it is so simple that even a kid could understand it. Yet it turned the mathematical world on its head.

You can also look at Ramsey Thoery. While there are some incredibly arcane and impenetrable areas that a hardcore mathematician can go into, the basic idea is simple enough in English: The Party Problem.

As for utility-- well, I'm sure you realize that for a long time, nobody DID pay mathematicians to do their work. Fermat was a lawyer and a political figure who did math as a (very serious) hobby. Archimedes was paid for creating war machines and weapons-- not math. Gauss was employed in astronomy, which served as an impetus to creating some of his mathematics. Ferro was a paper maker.

The idea here is that it really doesn't MATTER if the public pays for the work of mathematicians. We'll do it anyway, because we love it.

RSA turned out to be a combination of different parts of number theory that turned out to change our world. Who would have thought that this and this would turn into something this amazing. Don't let anyone dismiss pure math...

RSA turned out to be a combination of different parts of number theory that turned out to change our world. Who would have thought that this and this would turn into something this amazing. Don't let anyone dismiss pure math...

Nichts gegen Bremsstrahlung, aber...

Z backscatter seems to base on the Compton effect. (At least that's what the specs from AS&E say.)

There are three major effects ionisating radiation has on matter. Photoeffect, Compton-effect and pair emission. The last one appears only with very high energies, the first one need elements with high mass.

This leaves the Compton effect that mainly takes place with medium energies and affects rather light elements, as used in organic matter. Briefly, the photon splits into a less-powerful photon and an electron. The new photon might (or might not) come back to you. This (back-)scattered light can be detected with special sensors.

For medical purposes this scattered light is a PITA since you only get some gray blurred edges. But it seems to me that now there exists a new technique to get some good information out of this scattered light.

Just my two cents...

X-ray backscattering has been studied on an experimental level pretty extensively for quite a while. Perform a Google search on bremsstrahlung. Bremsstrahlung means "braking radiation." Electron bremsstrahlung is the most common. When an electron is deflected by the electron cloud of an atom, that acceleration produces an X-ray at an angle that is oblique to the original direction of the electron's path.

My Bachelor's degree is in Physics, and my junior/senior research back in 1987-1989 was on bremsstrahlung. You can find more on the subject at:

http://scienceworld.wolfram.com/physics/Bremsstrah lung.html

Some nice non-game applets I found recently: here and here.

Mean-Time Between Failures is usually assumed to fbe a Poisson Process. Given that assumption, one can take N hard drives and run them for three or four months. Based upon how many of those N die in the first three to four months, one can make a pretty good stab as to the average time it takes one of their drives to fail.

You know, it's almost a shame to screw up the amusing notions /.ers come up with by adding actual information, but I can't help it, all those years of teaching I guess.

Okay, first of all: "mean time between failures" is obviously a statistical measure -- it is an average over a large number of individual items. In most electronic components (including light bulbs!) the statistical distribution of the time between failures is the exponential distribution, which has the odd property that it's "memory-less" -- it doesn't matter how long since the last failure it's been, the mean time to the next failure will still be the same. A consequence of this is that if the MTBF is 10,000 hours, the probability of failure in any particular hour would be 1/10,000th. So, if you set up 10,000 components, all running simultaneously, you'd expect one of them to fail within the first hour; conversely, if you ran them for 1000 hours, and 998 of them failed, you could be fairly certain that the MTBF would be around 10,000 hours.

Note, by the way, that this is only true when the failure time distribution is exponential -- so it works for electronic components, but not for, say, bicycles and cars and roller skates, which are more likely to fail the older they get.

This has an obvious problem, of course: if the MTBF is high, it can take forever to test. Consider, for example, something I worked on for NASA some years ago: trying to prove that a fly-by-wire system will have a mean time between failures of 1e10 hours. (This is about the same failure rte as the airframe, which is how they came up with the number.) 1e10 hours is about 1.141 million years, by the way.

(Pop quiz: if MTBF is a million years, how do you explain the occasional airframe failure, say, eg TWA 800? Hint: It doesn't require any foul play.)

At that point, you've got a couple of choices: first, you can make a lot of copies and run them simultaneously. Relatively easy for $50 disks, hard for billion dollar 747s.

Second, you can make the estimate by computation and modeling which is what you do for web systems. Conceptually, it's pretty simple to do this, although it can be a kind of pain in the ass.

The third way, which is new and cool, is by Bayesian estimation of failure rates. This method lets you make increasingly accurate estimates of the failure rate based on short experiments. I don't have time to go into it, but there are some good sources available on the web.

Mathematica's programming language is like that too... you can code a problem in many ways, and you can code it concisely and tersely or verbosely with lots of LongFunctionNames.

quotes

page from the tour

It's an awesome language but hardly anybody uses it to the full potential (of course since it only comes with $hundreds software package that might have something to do with it....)