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I sincerely hope that soon small-to-medium enterprises can own supercomputers. With all the low budget physics stuff going on at Universities around the world, cheap supercomputing can only be a good thing.

Actually they can with software like that from Dauger Research, Project Appleseed and Wolfram Research with gridMathematica

The cool thing here is that this code can be run on all of the desktop computers that already occupy companies and universities world wide allowing for easy access to supercomputer level computational speed (for those problems that can be attacked using parallel computation of course) using the same computers normally used for productivity.

Very cool.

The output is fed through a low-power Schottkey diode to clamp the waveform and lock onto the desired frequency. I'm sure you can tell what I'm getting at: in order to receive frequency RF, one must generate frequency IF via local oscillations (LO), and IF directly corresponds to RF. Stephen Wolfram points out the relationship V[IF] = V[RF] + V[LO] for increasing and V[IF] = V[RF] - V[LO] for decreasing. Armed with this formula and decent knowledge of the radio's tank circuit, it is trivial to pick up the LO and IF frequencies your car radio transmits, albiet inadvertedly, and customize the billboard contents accordingly. Quite simple really.

I'm neither a mathematician nor a physicist, but I study mathematics, and I can tell you that "compactified" is a real math word, that real mathematicians use.

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I'm neither a mathematician nor a physicist, but I study mathematics, and I can tell you that "compactified" is a real math word, that real mathematicians use.

Search

The

Fucking

Web

I'm neither a mathematician nor a physicist, but I study mathematics, and I can tell you that "compactified" is a real math word, that real mathematicians use.

Search

The

Fucking

Web

I'm neither a mathematician nor a physicist, but I study mathematics, and I can tell you that "compactified" is a real math word, that real mathematicians use.

Search

The

Fucking

Web

I'm neither a mathematician nor a physicist, but I study mathematics, and I can tell you that "compactified" is a real math word, that real mathematicians use.

Search

The

Fucking

Web

I keep a bunch of "classic" bookmarks around. Some are undisputed gems, others are, well, to my taste. Bytes being cheap here's a batch.

• Ars Technica: The PC enthusiast's resource
• AmbySoft Inc. White Papers: Scott Ambler's Online Writings
• windows.oreilly.com -- Deep Inside C#: An Interview with Microsoft Chief Architect Anders Hejlsberg
• TQ
• The Rise of ``Worse is Better''
  
• A Whirlwind Tutorial on Creating Really Teensy ELF Executables for Linux
  
• Theist Hall of Shame
• Internetworking Technology Overview
  
• Software Technology Review
  Eric Weisstein's World of Mathematics
• P.S.: More Than Just Words
• Welcome to the On-Line Encyclopedia of Integer Sequences
• John McCarthy
  
• Slashdot | Net Translations of Dead-Tree IT Classics
  
• advICE
  
• 0xdeadbeef archives
  

That's exactly the oposite from what Stephen Wolfram is saying: that everything in nature has an underlying ALGORITHM, not a mathematical formula. Check out this light news.com article, or just read his wonderful book: A new kind of science.

There is a reason they are charging you only $130 for the student version. It's like a drug: after you have spent many hours getting familiar with Mathematica, you will then buy the full version for $1880 rather than spend more time learning another system. Matlab is even worse: last I checked, the full version costs upwards of $3000 in any reasonable configuration. And you'll end up paying that every time you change jobs. Matlab and Mathematica packaging may be convenient, but they are not technically that much better than the free alternatives to justify that kind of hassle and expense (in fact, I would argue that they are technically worse than the free alternatives, but that's a different argument).

Do yourself a favor and don't invest much time in "student versions". View the use of Mathematica and Matlab in the classroom for what it is: a carefully orchestrated marketing program designed to get students hooked. Spend your time learning something that is open and that you can add to your personal toolbox without having to pay some company large amounts of money again and again.

• Windows 95/98/Me/NT/2000/XP
• Mac OS X
• Mac OS 8.1 or later
• Linux (Redhat 7.1 or equivalent) or later
• PowerPC Linux (Yellow Dog 2.1 equivalent or later)
• AlphaLinux (Redhat 6.2 or equivalent) or later
• Solaris 8 or later
• Compaq Tru64 Unix 5.1 or later
• HP-RISC HP-UX 11.00 or later
• IBM RS/6000 AIX 5.1 or later
• SGI IRIX 6.2 or later

woof.

• Support for multiprocessor machines, heterogeneous networks, LAN, and WAN
• Support for scheduling of virtual processes or explicit distribution to available processors
• Support for virtual shared memory
• Support for synchronization, locking, and latency hiding

woof.

• Support for multiprocessor machines, heterogeneous networks, LAN, and WAN
• Support for scheduling of virtual processes or explicit distribution to available processors
• Support for virtual shared memory
• Support for synchronization, locking, and latency hiding

woof.

Has anyone else heard about the research into people balancing sticks on their fingertips, and how this has to do with random neuro-muscular noise, but generated by the body instead?

Has anyone else heard about the research into people balancing sticks on their fingertips, and how this has to do with random neuro-muscular noise, but generated by the body instead?

Sorry, but I refuse to put a source of radiation powerful enough to run my laptop or cell phone that close to my brain or testicles. I can't think clearly without all of the above, and don't want to mess them up for myself. (Note that cell phone antennas help place the radiation away from the head, when you get a cell phone with a decent external antenna, so they're of lesser risk, and only affect my brain, not my reproductive organs.)

Electromagnetic radiation is NOT THE SAME THING as beta radiation. One is a particle (an electron to be exact, of which there are already plenty of in your current batteries) and the other is a magnetic field.

...I'm definitely going to take advantage of F !=ma. I'm going to give my car a good shove tomorrow morning and ride it all the way to work.

I just hope that we don't spin out of orbit while F != G(m1m2)/d2. I guess, though, that if we start to spin out of orbit, somebody on the far side of the planet can just give it a shove and we'll be back in place.

Unfortunately, I've already noticed my CPU getting hotter. And I stood on this really tall guy's shoulders but I couldn't see very far...

Sheesh, especially for displaying geographic data about the folding clients, Equirectangular would be a much better choice, since the calculation for point placement is perfectly linear.

Can't help you much on packages, but can on a definition.

NURBS - Non-Uniform Rational B-Spline

Essentially, a NURBS surface is a mesh of B-Splines, and B-Splines are a way to represent a curve using knots and points (sometimes called control points or de Boor points). A B-Spline is similar to a Bezier curve (try it in Photoshop). The only difference is you add "knots" which force the curve to go through some fixed points. The first point and first knot are always the same, as are the last point and last knot (these are the "edges" of the mesh), so you need at least 3 points and two knots to make a B-Spline curve and 4 knots and 5 points to represent a mesh (if the B-splines share point between their curves, which not normal - 6 is normal - you end up with an hourglass shape).

The mesh itself is called non-uniform because the knots don't need to be equally spaced from one another. Rational means simply using real numbers not Imaginary.

here's a picture of a B-spline

There are numerous problems with NURBS surfaces, most of which you'll never worry about (us developer types do). There's a pretty good article on this by Intel

On the other hand, NURBS have the advantage of being able to remove knots and control points and scale performance for processors (sacrificing quality).

Interestingly (to me, at least), the points aren't called weighted control points anywhere (at least not from most google results I looked at), as they were in most texts when I took computer graphics in college. All weighted control points means is describing the points of the NURBS curve as a unit vector (vhat, v with the carat symbol on top) and a multiple (weight) of that vector, rather than the actual x,y,z of the point. The point formula was thus w*vhat, where vhat=v/Norm(v). That's probably technobabble to most people, so I'll shut up now :)

http://mathworld.wolfram.com/EllipticCurve.html

It was also use by Anrew Wiles in 1993 to prove Fermat's famous last thereom.

http://mathworld.wolfram.com/FermatsLastTheorem.ht ml

Enjoy!

http://mathworld.wolfram.com/EllipticCurve.html

It was also use by Anrew Wiles in 1993 to prove Fermat's famous last thereom.

http://mathworld.wolfram.com/FermatsLastTheorem.ht ml

Enjoy!

US> 30 -> 60, you will be hard pressed to notice the difference (but it IS possible)
U>I would disagree with this assertion, though it does depend on the application.

For people who have been trained to look for it, yes, they will be able to notice it. I was talking about the general populous. ;-)

U> I'm particularly aware of this because the PS2 game I'm working on tends to run at 30 fps in the game shell, but occasionally hits 60. There's such a profound qualitative change that we might have to clamp the rate at 30 to prevent the bursts of 60 from making 30 look bad. :)

Yeap, as a fellow PS2 developer I fully agree. I first noticed the 30 vs 60 difference back on the PS1.

Sounds like you've also discovered that it's better to minimize the difference between the lowest and highest frame rate as it will appear smoother. I believe Carmack mentioned that was his findings as well in one of his Quake plans. i.e. minimize the frame rate drops.

> Incidentally, I can tell the difference between a 60Hz refresh rate and a 70Hz refresh rate, 60Hz seems to flicker for me, especially in my peripheral vision.
For CRTs, I also concur. 60 Hz flickers way too much! I don't have your visual perception quality (lucky b@$tard ;-) so I had to crank my CRT up to 100 Hz before I stopped noticing the flicker. Interestingly enough my LCD is only at 60 Hz and is rock solid (especially for text.)

Cheers

--
Mathematics is queen of the sciences, but
Number Theory is the queen of mathematics
- Gauss - "Prince of Mathematics"

Ok, so now I'm completely and utterly confused about whether a "pound" is a unit of mass or a unit of force. This link convincingly points out that we should abolish this bizarro Imperial system. Use the metric system when discussing physics, please...

...remember that Wolfram.com the site on which the story resied == Mathematica. The company whose product Mathematica is. So, do not expect to see something unprejudiced. It's an interesting story anyway :)

...remember that Wolfram.com the site on which the story resied == Mathematica. The company whose product Mathematica is. So, do not expect to see something unprejudiced. It's an interesting story anyway :)

Maybe you should do a little research before spouting off about how there are no useful distributed computing projects out there.

You could take a magical rubber band and stretch it around a sphere and then slide the rubber band along the surface. As you work your way around, you'd find that the length of the rubber band varied along the surface. The important thing is that you can slide the rubber band so its length is essentially zero--a.k.a. a single point.

Poincare (Poincaré really but thanks a lot Slashdot for not letting me ...) speculated that if you had any simply connected closed 3-manifold is homeomorphic to the 3-sphere (which I'm just parroting back from the Mathworld site at Wolfram.) The theory was later expanded to include the equivalent in N dimensions. In other words, if you take something that only has an "outside" and no holes, you could mash it into the shape of a sphere, or slide the rubber band right off it no matter what.

The other side of the story is things like a torus, or for a tastier example, donut. It's not "simply connected closed 3-manifold" because if you put a rubber band around the "meat" of the donut through the hollow middle and never be able to get the rubber band off without breaking the donut or the rubber band. Yum.

The thing that hasn't yet been proven is whether this is true for 3-dimensions as originally speculated. The Mathworld site at Wolfram says that it's been proven for N=1, 2, 4, 5, 6, and >=7, but not for 3. I don't know why ... I mean, can't you just define a point that is in the center of a given manifold then make a sphere that is the average distance from all points on the surface and define a new surface that is half-way between the two surfaces, and repeat forever to show that you really get a sphere ... for a torus, for instance, you'd get a point, but for a cube you'd get a finite sized sphere ... same for a Dixie cup, except it'd be really small.

You could take a magical rubber band and stretch it around a sphere and then slide the rubber band along the surface. As you work your way around, you'd find that the length of the rubber band varied along the surface. The important thing is that you can slide the rubber band so its length is essentially zero--a.k.a. a single point.

Poincare (Poincaré really but thanks a lot Slashdot for not letting me ...) speculated that if you had any simply connected closed 3-manifold is homeomorphic to the 3-sphere (which I'm just parroting back from the Mathworld site at Wolfram.) The theory was later expanded to include the equivalent in N dimensions. In other words, if you take something that only has an "outside" and no holes, you could mash it into the shape of a sphere, or slide the rubber band right off it no matter what.

The other side of the story is things like a torus, or for a tastier example, donut. It's not "simply connected closed 3-manifold" because if you put a rubber band around the "meat" of the donut through the hollow middle and never be able to get the rubber band off without breaking the donut or the rubber band. Yum.

The thing that hasn't yet been proven is whether this is true for 3-dimensions as originally speculated. The Mathworld site at Wolfram says that it's been proven for N=1, 2, 4, 5, 6, and >=7, but not for 3. I don't know why ... I mean, can't you just define a point that is in the center of a given manifold then make a sphere that is the average distance from all points on the surface and define a new surface that is half-way between the two surfaces, and repeat forever to show that you really get a sphere ... for a torus, for instance, you'd get a point, but for a cube you'd get a finite sized sphere ... same for a Dixie cup, except it'd be really small.

For super-geeks, here is is a more thorough discussion of the Poincaré Conjecture.

http://mathworld.wolfram.com/PoincareConjecture.ht ml

Here is an example with all sorts of definitions you can read.

http://mathworld.wolfram.com/PoincareConjecture.ht ml

If there's many cards on a network, and you want to know how many total you can add before two of them will end up with the same card, the answer's far smaller -- 2^24, which is still pretty huge(it's a bit more than 16 million). It's a different problem because each time you add a new card, the card after has one more it can possibly match with. This is known as the birthday paradox, so named because this precise logic means that given 23 people in a room, there's a +50% chance that two people have the same birthday. Each new person is one more to match with.

1 - (d! / ((d-n)!d^n)) > 50%
where d is the number of possible options (i.e. 365 for birthdays), and n is the number of selected values (i.e. people).

So for the MAC address case if MAC addresses where randomly allocated (which they're not) you be looking for the smallest n where:

1 - ((2^48)! / ((2^48-n)! (2^48)^n)) > 50%

n will be considerably less than 2^24.

However, all of this is irrelevant as MAC addresses are not randomly picked by manufacturers and won't be randomly picked by people changing them.

It's a logarithmic scale. The volume of the sound goes up ten times for every ten decibels. Here's some math and a comparison chart.

There's actually about 10^81 atoms in the universe. There are about 10^120 possible boards of chess (including mirror images etc) see Chess -- from Mathworld and Atoms in the Universe.

Since a physical singularity (as opposed to a coordinate singularity) by definition does not follow the laws of physics, a "Cosmic Censorship" principle was proposed stating singularities can only occur inside a black hole, where they cannot interact with the rest of the universe.

Kip Thorne and John Preskill, however, believed that a "naked singularity", devoid of an event horizon, could exist. Steven Hawking made a bet with Thorne and Preskill in 1991 that naked singularities could not exist, but conceded when supercomputer simulations by M. Choptuik showed naked singularities were indeed possible.

--Adam

Note, I wrote that is the limit for electron degeneracy to prop up the star. I didn't mean to imply a star past the Chandrasekhar limit will collapse to a white dwarf.

Science World says ~1.2 solar masses, in agreement with the figure I posted.

It happens that University of California, Davis physics department has a good cosmology group, and I'm a graduate student here. The last seminar I went to about this topic indicated that the Hubble redshift evidence pretty strongly correlated to an exponential inflation due to the cosmological constant, for what that's worth.

As far as singularities go, Roger Penrose proved the Singularity Theorem back in 1965; therefore, all black holes have singularities.

There is a difference between a coordinate singularity and a "physical singularity", although General Relativity (which equates space curvature with gravity) can make it hard to sort out (the proper techniques involve conformal mapping, again pioneered by Penrose) and of course, path integrals and complex analysis. But to simplify the picture, you don't die by going to the North Pole, even though that is a coordinate singularity in a spherical coordinate system. You will die, however, from encountering an object of unknowable physical properties.

Charged and/or spinning black holes have two event horizons; an inner and outer. The outer event horizon is the one dictated by light rays neither spiralling in nor escaping. The inner event horizon is dictated by a worldline unavoidably encountering the singularity.

Physicists actually have no problem with time travel; see the Novikov Conjecture, which basically dictates that closed timelike curves are self-consistent (e.g., you cannot kill your grandfather once you are able to travel back in time; you are now in a closed timelike loop, and past and future are subjective). Any FTL travel == time travel, and there are several interesting possibilities. Robert Forward wrote in his "Dragon's egg" books about using a Kerr black hole to travel back in time, and in "Timemaster" about using negative matter to do likewise (negative matter != antimatter; negative matter has negative mass).

Fascinating stuff. The math is actually extremely interesting; one of the perks of studying physics ;-) (There aren't many). --Adam

Note, I wrote that is the limit for electron degeneracy to prop up the star. I didn't mean to imply a star past the Chandrasekhar limit will collapse to a white dwarf.

Science World says ~1.2 solar masses, in agreement with the figure I posted.

It happens that University of California, Davis physics department has a good cosmology group, and I'm a graduate student here. The last seminar I went to about this topic indicated that the Hubble redshift evidence pretty strongly correlated to an exponential inflation due to the cosmological constant, for what that's worth.

As far as singularities go, Roger Penrose proved the Singularity Theorem back in 1965; therefore, all black holes have singularities.

There is a difference between a coordinate singularity and a "physical singularity", although General Relativity (which equates space curvature with gravity) can make it hard to sort out (the proper techniques involve conformal mapping, again pioneered by Penrose) and of course, path integrals and complex analysis. But to simplify the picture, you don't die by going to the North Pole, even though that is a coordinate singularity in a spherical coordinate system. You will die, however, from encountering an object of unknowable physical properties.

Charged and/or spinning black holes have two event horizons; an inner and outer. The outer event horizon is the one dictated by light rays neither spiralling in nor escaping. The inner event horizon is dictated by a worldline unavoidably encountering the singularity.

Physicists actually have no problem with time travel; see the Novikov Conjecture, which basically dictates that closed timelike curves are self-consistent (e.g., you cannot kill your grandfather once you are able to travel back in time; you are now in a closed timelike loop, and past and future are subjective). Any FTL travel == time travel, and there are several interesting possibilities. Robert Forward wrote in his "Dragon's egg" books about using a Kerr black hole to travel back in time, and in "Timemaster" about using negative matter to do likewise (negative matter != antimatter; negative matter has negative mass).

Fascinating stuff. The math is actually extremely interesting; one of the perks of studying physics ;-) (There aren't many). --Adam

our understanding of physics breaks down at the edge

Now the singularity is a different matter. No coordinate change can fix things up there.

... but close ... it's actually r = 2GM / c^2, where G is the Gravitation constant and M the mass for the main contributor to the gravitational field, the black hole. For a more detailed explanation, see here.

it's often used to help those in the drill units under the earth to communicate with those above)
- I'm not even bothering with this one...

The benefit of higher frequencies is that they travel in straight lines
- This is apposed to, say, those low frequency waves that like to travel at right angles, right?

This is why 2.4Ghz wireless has become popular. 2.4Ghz was chosen for wireless networking because the frequency is the same as the resonance of trees and bricks,
- Lovely thought. So you're saying all our forests are going to turn into the Tacoma Narrows Bridge? After all, that is what happens when you hit an objects resonate frequency.

antenna at the drill cage is secure, and then point a high powered (say 1MW) transmitter down towards the ground, and et voila..
- Hrmmm, metallic cages... hmmm, Faraday Cages. Yup, that'll help signal reception!
- 1 mw is high power you say? Damn, my old brick cellphone should be able to reach Istanbul!

I'm surprised a big networking company like Novell or nVidia hasn't jumped on to this and started to produce expensive proprietary gear for the rich oil companies to buy
- nVidia is doing networks now? Won't they be surprised! Man, ATI will be ticked.

Either way, wireless (radio) is the way to go when sending a signal through an electrically busy area. This is why wireless networking is popular in power stations, since fiber optics tend to suck up too much interference.
- Hahhaa, I'm just laughing to hard at this one.

You know, if you are going to troll, at least make it plausible.

Qusars were discovered by Anthony Hewish NOT Geoffrey Hewish, and Jocelyn Bell. See a short bioghraphy from Eric Weisstein's World of Scientific Biography.

The National Energy Research Scientific Computing Center maintains a web page in which binary-encoded words (with a = 1, ..., z = 26) can be looked up in the first 4 billion digits of pi.

The National Energy Research Scientific Computing Center maintains a web page in which binary-encoded words (with a = 1, ..., z = 26) can be looked up in the first 4 billion digits of pi.

The National Energy Research Scientific Computing Center maintains a web page in which binary-encoded words (with a = 1, ..., z = 26) can be looked up in the first 4 billion digits of pi.

Regarding phase velocity vs. group velocity, both phase velocity and group velocity can exceed c - see Superluminal, second paragraph. Group velocities exceeding c have been done for decades - for a bit of a history, see No thing goes faster than light.

The innovation in this case seems to be that it's doable with cheap equipment, and over fairly long distances.

http://scienceworld.wolfram.com/physics/Superlumin al.html
http://www.weburbia.com/physics/FTL.html
http://physicsweb.org/article/world/13/9/3

The thing that really seems interesting about this is that they're doing this with cheap equipment, which will make experimenting with this a lot easier.

Can anyone explain how this would be used to increase subluminal transmission of electrical signals, as mentioned in the article? This whole group velocity thing has always seemed like a bit of an illusion to me, and none of the explanations I've seen has really clarified how it's anything more than that.

I hope this is not repeat:

http://scienceworld.wolfram.com/physics/

It is not a book you can read but a very good reference to look up formulae etc.

For physical insight, the standard reference would be "Feynman lectures on physics". You cannot beat that. For fun stuff "Mr. Tompkins in paperback", try to find the original edition though. It won't make you think tigers are worthless, don't worry.

things (He has mathworld and the physics one is up and looks like he is still adding things but it is ok). Wolfram's Physics World

You are probably thinking of a Casimir Operator.

If so they are not related.

There are more kinds, circular for example. It means the electric field is rotating, either clockwise or counterclockwise. Eric Weisstein's World of Physics also mentions elliptic polarization.

Lord Kelvin (William Thomson) created an older pitch experiment: one which had a variety of objects lying on a tray of pitch that are slowly sinking in.

Its usually on show in either the Hunterian Museum or the Department of Physics and Astronomy at Glasgow University.

As I recall, this is considered the oldest continuously running scientific experiment, with the exception only of a wheat-breeding experiment in England? (I can't find references on that, just remember it from back in the mists of time)

BTW: it is more fun to watch paint dry - its faster...