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10^120 is an estimate of the realizable positions in a game of 40 moves. The number of possible games is estimated at 10^10^50. See here for other numbers and references.

in either case, however, the spirit does not change: a google is still sufficiently big that the physical universe have trouble filling up into its large-ness.

below is slightly off-topic, but:

for ever bigger, interesting numbers (that puts the googleplex to shame, actually), try Grahams Number, Another link to Graham's Number. Please note that, interestingly (in a mathematically geeky fashion) the result Graham's Number tries to limit (it's an upper bound) is generally believed to be 6. there is also Moser's Number... i am not sure which one is bigger...

Undoubtably MathML support is there because it is in Mozilla. Between Mozilla, Netscape, and IE (with MathPlayer), all of the major browsers will support MathML. That together with support from math programs such as Mathematica, it really looks like MathML will finally become real this year.

There's a conference on MathML at the end of June this year. Leslie Lamport (LaTeX fame) and Roger Sidje (who did the MathML support in Mozilla) are among the invited speakers.

Buy it directly from Wolfram's company here.

No, Nicola Tesla did.

"The Great Radio Controversy
He (Tesla) invented Wireless radio, but Guglielmo Marconi was given the credit until June 1943,
when The U. S. Supreme Court finally settled the matter, after 16 months of investigating patent records and scientific publications,
and declared that Nikola Tesla was the true inventor of modern radio technology.
This was known as the Great Radio Controversy.
Unfortunately, most school children are still taught that it was Marconi, which shows
how simple it is for us to regurgitate uncorroborated legends, without checking on the up to date facts."

Also...along the Bell lines...

Bell Labs invented the "cellular concept"...many stations sharing common channels...

Satellite communications were another first.
(And yes, Arthur C. Clarke invented the idea of
geosynchronous orbits which the first Bell Labs Comm Satellite used.
This orbit is also known as the "Clarke Orbit")

The whole Zeosync thing's shady and doesn't quite make sense, which is of course why they've gotten flack about it.

Really, this doesn't even *sound* like a "technical BS" math explanation - it *sounds* like those people who try to explain the mysterious power of pyramids using geomery or prove the tenets of religion using "science" -- it's math definitions for about two lines, and then the proofs run around in obfuscated circles too convoluted to unravel.

I don't even agree that Zeosync gets the statement of the pigeonhole principle correct as this interpretation completely misses both the definition of a 'pigeonhole' and the reason it's important to the principle in the first place. Mostly, what bothers me is that it sounds like (I'm taking a guess - this 'technical' explanation is /really/ convoluted) their solution to add a bunch of extra dimensions to the space that dilute the data, then you compress that. In other words,

[data compressable by factor of 2]
+ [a bunch of extra unneccesary zeros]
= [new data compressable by factor of 100]

What am I missing?

is that the observable universe is defined by calculus and differential equations in very small areas: planetery motion, for example, or atomic physics.

Phenomena like life, geology and the like are very badly behaved with respect to our standard mathematical tools and we all know this.

Wolfram is suggesting that cellular automata provide a simple framework for examining the phenomena outside of the "magic circle" of the calculus: i.e. most of life and the universe.

Of course, for a long time we've confused hard science with the application of calculus, which has effected what we consider "science" to be: if it is not an equation, we don't think it's scientific.

Well,

1> go talk to some biologists

2> get used to it: equations got us this far, but after this it may be increasingly about computation.

Consider, for example, the Four Color Theorem - the only existing proof of which requires a lot of computer power to grind through cases. Is it a valid proof? Probably - but not to the standards of mathematicians who grew up in the pre-computer age, to whom an exhaustively checked list of cases does not look like mathematics at all.

We'll see how Wolfram's work fares over time, but my bet is that it will fare Quite Well.

Not to be pedantic, but what exactly is 'interpolative prediction'?

Interpolation involvels finding values b/w two known values.
I think extrapolative prediction would be a better way to phrase it :)

Hmm I wonder what the lyapunov exponent of slashdot would be ... definately positive ;) I think everyone would agree its a bit 'chaotic' around here.

Not to be pedantic, but what exactly is 'interpolative prediction'?

Interpolation involvels finding values b/w two known values.
I think extrapolative prediction would be a better way to phrase it :)

Hmm I wonder what the lyapunov exponent of slashdot would be ... definately positive ;) I think everyone would agree its a bit 'chaotic' around here.

However, I am still wondering (1) whether you read the interview with Mead about his book, or are just taking the first part of Elby's quote (about imprecise equipment) at face value; and (2) whether you are accusing Mead of being an intellectual fraud.

I did read the article, and looked at the sample pages from the book, and read another interesting speech of Mead's, and think that it might be possible that there is a lot of merit in wanting to consider some particles - particularly electrons - as manifolds with boundary in stead of as singular points.

To deal with the first question, I think that Mead's main intent was to say that the Copenhagen Interpretation went wrong in insisting upon dogmatic adherence to the point particle model. He says that they understandably did not have access to the kind of data we do now, such as being able to see a single electron, but even more importantly, they had no experimental experience with coherent systems. Since their only experience was of incoherent systems, then of necessity, statistical models were all they could talk about. Mead is saying that with mounting evidence of coherent systems such as Lasers, Masers, Bose-Einstein condensates, etc. (he lists 10 in his book), that it appears to him that this is an even more important litmus test for understanding properties of "pure particles" (my paltry words here) than something like the Heisenberg Uncertainty Criterion.

The other thing I think Mead is addressing are logical paradoxes, which like you also mention, we all know must be created by lesser minds misapplying theoretical concepts. But like you, I feel unqualified to talk about these in physics at present. My gut feeling, however, is that dogmatism has been poisoning academic physics for decades.

Finally, our thread root poster, Elby, mentioned a "growing school" of thought. The article quotes Mead as follows:

John Cramer at the University of Washington was one of the first to describe it as a transaction between two atoms. At the end of his book, Schrodinger's Kittens and the Search for Reality, John Gribbin gives a nice overview of Cramer's interpretation and says that "with any luck at all it will supercede the Copenhagen interpretation as the standard way of thinking about quantum physics for the next generation of scientists."

Well, that's my quick summary. I'd be curious to know what a "Real" scientist thought about Mead's perspective; I found it very interesting. [Disclaimer: I am not a scientist although I have a fair background in graduate mathematics and a bit as well in undergrad physics. But,] In fact, I have enough experience with math to have a certain skepticism about the wisdom of unthinkingly applying things as basic as the real number field, with its Archimedean property, or the idea of a mathematical point, with unqualified enthusiasm to great unknowns such as the elementary particles of nature. And for criticizing such an unthinking approach to matter, I would like to know if I am truly justified in applauding Mead (i.e. in the name of Real science).

In any case, I would be grateful to be educated out of any of my own misconceptions. Best of luck to you in producing Real science - I hope I get to read about the results some day!

This website is great for getting a taste of what a good science education could teach you.

[...]Which of these leaves more room for interpretation?

2+2=4

The ANSWER is equal to the SUM of the FIRST NUMBER and the SECOND NUMBER, where the FIRST NUMBER has the same value as the SECOND NUMBER. IF AND ONLY IF the SECOND NUMBER has the value of the SECOND POSITIVE INTEGER, the ANSWER will have the value of the FOURTH POSITIVE INTEGER.

Unfortunately, the use of "SECOND" and "FOURTH" here assumes that one is counting using the traditional ordering of integers. However, if one is instead using the Sarkovskii ordering of the positive integers (3 > 5 > 7 > 9 > 11 > 13 > ... > 6 > 10 > 14 > 18 > ... > 12 > 20 > ...... > 32 > 16 > 8 > 4 > 2 > 1) then that statement really means "2+2=8", which is clearly false. Therefore you don't even need be a lawyer to make people's lives complicated; merely having taken a few 300-level math courses is sufficient. Q.E.D.

• Magnus Effect
• Coriolis Effect

• Magnus Effect
• Coriolis Effect

Without it, there would be no rockets, no GPS, no advanced aircraft, no...er...Segway and of course: no bicycles!

Easy to do and beautiful to behold: : take a bicycle wheel, tie a rope to the ceiling and the other end to the nut at the axle, let the wheel hang freely from the ceiling so it sits flat like a plate, and give it a fast spin -- voila! -- it turns *upright* (on end) as it spins away! Your very own gyroscope!

For those not in the know, this is why balancing on a still bike is hard, but balancing on a moving bike is easy (look ma, no hands).

The math for you geeks :-).

There's only a limited number of positions. You can enumerate them and then 'solve' the game in the same way we generate endgame tablebases. But we lack storage and processing power for many many many years to come.

sPh

Mathematics are not "the science of numbers". It is about building a theory of axioms and theorems where nothing is unproved. You may be forgetting Godel's Incompleteness Theorem

Something that one gets used to in science is that you don't know anything in the absolute sense, but you probably do "know" things to the degree that you're willing to base your life's work off of them. On the other hand, if you spend too much time around philosophers, you might end up wondering if the world really exists, or if your senses are accurate, etc.

Doubt goes hand in hand with wisdom. Once one accepts that there is room to question absolutely everything, then you just have to accept the attitude of estimating what is the most likely truth and working from there. In my (admittedly biased) estimation the laws of physics, as currently understood, are almost certainly a good approximation of truth, though certainly not the last word.

In science, careers are made by showing that the established beliefs are wrong. There are lots of people itching to overturn current theories. Sometimes there is resistance if the evidence is weak or the argument complicated, but in the long run scientists are often more likely to admit their mistaken beliefs than the public in general.

If there really is a right answer to the universe then an independant thinker should arrive at similar conclusions to the ones we already have. Unfortunately no man ever born could even learn all the science we have now, so it's nigh impossible to believe that any single person could have the capacity to independantly arrive at more than a very small part of what has already become established doctrine. On the other hand, Ramanujan did quite well, and without being shunned or killed.

If some day we do contact an intelligent alien race, that would be other best chance to study an independant notion of science. However, I doubt that they'll offer too many surprises among the areas of science that have been studied in detail.

From mathworld: "Schnirelman (1939) proved that every even number can be written as the sum of not more than 300,000 primes (Dunham 1990), which seems a rather far cry from a proof for two primes!" Still a ways to go, gents.

I'll try, but I get WAY out of my league when you talk about anything bigger than n=3.

n represents dimensions. i.e. n=1 is one dimension, n=2 is two dimensions, n=3 is three dimensions, etc.

"simply connected" just means that the boundary surrounding something is connected. For example, in n=2 space (a piece of paper for example), if you drew a line around a bunch of ants, and connected the ends, it would be simply connected. If your line was actually two lines, and weren't connected (you had two groups of ants) then you have a multiply connected boundary.

A manifold (sorry, had to use it) is just an object without a boundary. The earth is a manifold, as is any other n=3 space (3d) object that is connected to itself. In n=3 space, the only way you can have a boundary is to have two different objects, in two different locations.

Homeomorphic just means one object is like another.

They generalize the whole idea to one where all the objects are compact. That just means that the objects "surface" area is as small as it can get for a given internal volume. For example in n=3 space, you can minimize an area (like the material of a balloon) in relation to the volume inside (the helium). Circles are compact for n=2 space, and spheres are compact for n=3 space. BTW, even though I state this as if it were a fact, we don't know about all the compact spaces where n > 2. It would *seem* to make sense that a sphere is the only compact object to 3 space, but stating that as a truth, as of today, isn't possible. Maybe we can do that after they win their million bucks....

So, the whole thing boils down to showing that a compact 3d object is the same as a sphere.

Kord

Shameless plug, check out Grub!

This proof does just d=3 and it's interesting that it's essentially combinatorial. Smale's proof for d>=5 was based on differential topology, a grand and beautiful branch of pure higher math. Freedman's proof for d=4 used Yang-Mills theory developed in particle physics. d=3 looks like essentially a computer scientist's proof.

Disclaimer: I don't understand this stuff in any detail--these remarks are based on looking at the preprint and remembering stuff that I heard in math class long ago. Also, I think I'll wait to hear what the math community says, before believing the problem is really finally solved.

On the other hand, I can't...

Nickel's nothing compared to Felix Klein -- he co-wrote 4 volumes on the theory of tops, and invented the Klein bottle.

Nickel's nothing compared to Felix Klein -- he co-wrote 4 volumes on the theory of tops, and invented the Klein bottle.

Plot the Fourier transform of a file using a Hanning window.

fd file | fft -h | plot

Generate the default synthestic vowel (200 ms duration, fundamental frequency = 100 Hz and formants, F1 = 650 Hz and F2 = 950 Hz), halve the sampling rate, take the hanning-windowed Fourier transform, and plot

klatt -k | downsample 2 | fft -h | plot

Generate 2000 samples of white noise, pass it through a gamma-tone filterbank (1 channel per ERB), arrange the filtered waveforms in a cascade, such that there is no overlap between them and plot.

gaussian 2000 | fbank -e 1 | cascade -o 0.8 | plot -b

Generate 2000 samples of white noise, store a copy of the original in a file called 'noise0', then phase shift it by 90 and store the phase shifted version as 'noise90'.

gaussian 2000 | store -o noise0 | fft -p | ffilt -a 90 | ift | store noise90

Looking at it for a while, I relized that 0/0=x is the same as solving for 0=x*0 ... In other words, X can be anything (integer, real , complex...).

Given a set S we say that a/b exists in S if there is a unique c in S so that a = cb. So 1/0 does not exist becaues 1 != c*0 no matter what c is. So 0/0 does not exist because 0 = 1*0 = 2*0 etc, so the c wouldn't be unique. The proper discussion for all of this is in a ring. Things can get weird. Modulo 6, 0 = 2 * 3. But I can't write 0/2 = 3 for example since 2 has no inverse modulo 6. And so on.

The moral of my story: Calculus is based on the fact that 0/0 can be anything you want, depending on how you approach it.

No it isn't. 0/0 has no meaning. Period. Calculus, is above all, based on the least upper bound property of the reals numbers and the concept of a limit.

Granted lim_{x ---> 0} x/x = 1, this does not mean that 0/0 = 1 or that you can take 0/0 to be 1. It means that the function f(x) = x/x defined for nonzero x gets as close to the value one as you like as x tends to 0.

Granted lim_{x ---> 0} (sin x)/2x = 1/2, this does not mean that 0/0 = 1/2 or that you can take 0/0 to be 1/2. It means that the function f(x) = (sin x)/2x defined for nonzero x gets as close to the value one as you like as x gets arbitraily close to zero.

It is not being precise that plagued mathematicians until the very early part of this century. Euler, Fourier and many others had some remarkable "proofs" of things that are absurdly false because they didn't properly define their notions.

Your pun, while off the mark, is however cute.

DOH! Yes, you heard right....

HMC MATHEMATICS DEPARTMENT PROUDLY PRESENTS

The Simpsons Rule: Mathematical Morsels from "The Simpsons"

next THURSDAY, March 14

6:30 PM, Galileo McAlister (HMC)

by Dr. Sarah J. Greenwald, Appalachian State University and Dr. Andrew Nestler, Santa Monica College

Now in its 13th season, "The Simpsons" is an award-winning global pop culture phenomenon. But did you know that "The Simpsons" also contains over one hundred mathematical moments, with material ranging from arithmetic to calculus to Riemannian geometry? There's even a resident mathematician/inventor, Professor Frink. Join us as we present some of our favorite mathematical excerpts from "The Simpsons," and explore the related mathematical content, accuracy and
pedagogical value.

Aftermath: Doughnuts (MMMM...Doughnuts) will be served at the end of the talk.

Cross products & scalars are from vector algebra; "Abelian" is from group theory.

-- MarkusQ

Cross products & scalars are from vector algebra; "Abelian" is from group theory.

-- MarkusQ

Eric Weinstein has a very nice web site at http://mathworld.wolfram.com/. He had huge problems with the publisher CRC Press. You can read the author's account of this at http://mathworld.wolfram.com/erics_commentary.html .

Eric Weinstein has a very nice web site at http://mathworld.wolfram.com/. He had huge problems with the publisher CRC Press. You can read the author's account of this at http://mathworld.wolfram.com/erics_commentary.html .

If you ask me GNU Applications and a few other programs are the killer apps for GNU/Linux as a CS student.

1. GCC, Binutils, Emacs/Vim (General Hacking)

2. Mesa (Graphics)

3. Bison/Flex (Compilers)

4. Linux (Operating Systems)

5. Various Packet Analyizers (Networking/Security)

5. MySQL/Postgres (Databases)

The only non opensource application I use is Mathematica, but Wolfram provides student discouts and packages such as Combinatorica are opensource.

For the second and third class, there are already working theories of how to solve most of these problems (quantum computers, zero-point energy, wormholes, etc.)

Unfortunately quantum computing cannot solve NP-complete problems in polynomial time. In fact it is uncertain whether quantum computing can solve general problems dramatically faster than classical computers. It is known that sorting and factoring can be done much more quickly, but other problems, such as parity checking and syndrome decoding (useful in error-correcting codes) cannot be sped up.

I have a feeling this is not possible to solve, but this is very difficult to prove.

Dont know what a hypercube is? click here

Binary Hypercube

the best math link

This actually argues for the statement that evolution is still in progress. (BTW, I think the article that started all this is as silly as saying "gravity doesn't apply to us now that we have rockets.")

The thing to note is that optimal reproduction is having as many offspring as you can afford to rear into your ecological niche. Flies can lay lots of eggs, because raising a baby fly is very, very cheap. Lions have orders of magnitude fewer cubs because raising baby lions (who must be defended, fed, taught to hunt, etc.) is a prolonged and time consuming enterprise. (Just try it some time if you doubt this.)

So the observed birth ratios are perfectly consistent with the notion that there is a lot more competition to be "wealthy" and "successful" than there is to be "poor"--and as a consequence, it takes disproportionately more effort to raise a successful child that to raise a luser.

Not only have we not "escaped evolution" we haven't even escaped this simple definition of "optimal" family size; Bill Gates could certainly afford to follow the "fly" strategy produce an army of tens of thousands ill educated brats that would assure his success in the gene pool, but instead (as we all do, on average) he follows the logic of optimal family size and chooses the "lion" strategy. Likewise, I had my first child at 40. I could have started at eighteen at had dozens of "I can count to twenty 'cause I ain't go no shoes!" kids, but I preferred to raise one that will be more likely to someday explain the zeta function.

-- MarkusQ

No, Copyright is not exclusive. Several people can share the copyright on one work and you can grant copyright to other people without invalidating your own copyright. So much about theory. In practice many publishers want you to grant (transfer) them exclusive copyright for unlimited future (so that you lose you right to copy your own work!). See e.g. the case of Eric Weisstein vs. CRC Press LLC, esp. point 5 in the Author Agreement. Some suggestions how to deal with publishers with respect to copyright can be obtained from the Mathematical Copyright page.

No, Copyright is not exclusive. Several people can share the copyright on one work and you can grant copyright to other people without invalidating your own copyright. So much about theory. In practice many publishers want you to grant (transfer) them exclusive copyright for unlimited future (so that you lose you right to copy your own work!). See e.g. the case of Eric Weisstein vs. CRC Press LLC, esp. point 5 in the Author Agreement. Some suggestions how to deal with publishers with respect to copyright can be obtained from the Mathematical Copyright page.

• Structure and Interpretation of Computer Programs
• Common Lisp HyperSpec
• Common Lisp the Language, 2. ed
• Common Lisp - A gentle Introduction to symbolic computation
• The Scheme Programming language, 2. ed
• Reflections on trusting trust
• Lisp: Good News, Bad News. How to Win Big
• John McCarthy's homepage
• Dennis Ritchie's homepage
• Various classic papers it's a shame ACM never bothered to continue adding to
• Another list of classic papers (this time related mostly to programming language design)
• GTK-Gnome Application Development (not a classic, though, as the field is too young)
• KDE 2.0 Development (not a classic though, as the field is too young)
• Eric Weissteins Mathworld
• Compilers and compiler generators - an introduction with C++ (although I'm not too sure if it deserves being called a classic...)
• Parsing techniques - A practical guide
• Art of assembly language programming (never was a dead tree, but good anyway)
• Paul Carters 386 assembly book (same comment as above)
• An Introduction to Scheme and its Implementation (see comment above)
• How to design programs - An introduction to programming and computing (not a classic, yet!)
• The Gutenberg archives contains much non-copyrighted classic fiction in ASCII format
• Sacred texts has copies of or links to many religious text for various major (or minor) religions

You have to be careful when dealing with many paper book publishers when discussing publishing something developed from the Internet. This territory is unfamiliar, and will often lead to dire consequences if all parties involved don't understand what's going on. Take the case of Eric Weisstein, author of the CRC Concise Encyclopedia of Mathematics. His book was based off of years of his own work on his website, Eric Weisstein's World of Mathematics, and some collaboration from outside sources. After CRC published the book, they demanded that the website be taken down, effectively ending all collaborative work on the project. You can read more about the incident here. One calendar year and lots of litigation later, the website is back online. Don't let this happen to you.

You have to be careful when dealing with many paper book publishers when discussing publishing something developed from the Internet. This territory is unfamiliar, and will often lead to dire consequences if all parties involved don't understand what's going on. Take the case of Eric Weisstein, author of the CRC Concise Encyclopedia of Mathematics. His book was based off of years of his own work on his website, Eric Weisstein's World of Mathematics, and some collaboration from outside sources. After CRC published the book, they demanded that the website be taken down, effectively ending all collaborative work on the project. You can read more about the incident here. One calendar year and lots of litigation later, the website is back online. Don't let this happen to you.

It was at Bell Labs ... but the guy who developed the Uniform Sampling Theorem was Nyquist, not Shannon.

Actually, going by entropic laws, it would seem that the Universe is better described in say, 700 constants, than say, 6 constants.

But the reason these constants _are_ of prime importance is because as a solution to certain tensor calculus equations in relativity, and these constants have been observed to be unattainable, but have been observed. Ofcourse, it is entirely possible like how we once thought that the speed of sound could not be exceeded, we may still be wrong about the speed of light and absolute zero, but that is a remote possibility because no particle in the world has been observed to have c nor have absolute zero (now don't get me started on photons.... as I read somewhere, your guess is as good as mine on what they are).

...but no one has given any reason in the last 30 years as to why we should accept the current BH theory other than it looks good on paper and the "problems" will be solved one day.

Good point. But you are forgetting one important point - there has been _some_ evidence showcasing possible black hole like behaviour, which cannot be explained by gravistar theory, atleast not yet. Example - Event horizon, dense areas which are surrounded by matter with an invisible core, and so on. In fact, Chandra has observed the existence of an Event Horizon in M82.

If you have done any amount of tensor calculus & quantum physics related mathematics (which I'm assuming you have), you'll know that Black Holes can be described with considerable ease in a Riemann plane, than gravistars.

Think of the implications these guys are suggesting --

1. You have submanifolds which would overlap as more matter gets in, and so the relativistic frame would in itself be a function carrying many frames. Assuming a standard rate of expansion for each of these frames, you can imagine the number of frames which would be in existence by now.

2. The gravitational effects caused by a tending mass are described in general relativity. These use a mere 16 coupled hyperbolic-elliptic nonlinear partial differential equations, called the Einstein field equations. Now, you have a solution for these called Bertotti-Robinson Solution, and when these are applied to a Black Hole, they work out just fine. This, despite assuming a uniform magnetic field.

However, you will realise owing to the submanifolds, you may not be able to apply the same to a gravistar. It'd be way too complex. And Bertotti-Robinson have been proved

3. Despite what the say about the Schwarzschild Black Hole, the exterior solution for such a black holes _has_ been proved, and it conforms to the field equations proposed by Einstein.

Now these are independent results to the same set of equations. I think I'd rather trust Einstein than these guys :-)

Anyways, it would be interesting to watch how this would get on. I'm not against this theory, just that there _seem to be_ far too many unanswered questions.

David Hilbert originally proposed 10 questions, not 11. The final list included 23 questions. See here for more details and the specific questions.

a high speed network and a google of different communications devices.

I think you mean a googol, not a google. See also Google's explanation. Please keep you're words straight. ;-)

(Oh, it's also available at MathWorld - great to have it back!)

Either this is a troll, or you're just very, very... underinformed. To address your first point, that the odds of a positive mutation occuring are very small, I'll refer you to the Law of Truly Large Numbers. Essentially, if you have a population (sample size) so large, unlikely things are bound to happen. With six billion humans on this planet, something that happens to only one in every million people, you end up with 6,000 very unlikely things happening. Now think of how many microscopic organisms there were when all this preliminary evolution was going on. I don't know, but I'd say it didn't take them long to surpass six billion samples. To address your second point, I'm fairly sure that whatever plant-like life first managed to live on land was asexual, thus having to have the same mutation in two different specimens that are close enough to end up mating is irrelevant.

Yah, I just bought a student copy of Mathematica for about $200 CAN. The pro version (exactly the same) is about 5 times the price of the student version. If it wasnt for the student version, I wouldnt have bought it at all. What would the makers prefer? $130 USD (minus media price) or dick squat?. And yes, I had to provide proof that I was a student (my student ID) by fax to the company.

The only problem I have with the software product is that you have to "activate" it first. I tried to register with them last Friday, but I guess it was too late and now christmas break is taking place. I said "funk dat" and downloaded a key generator. It was the only way I could use the software that I payed for. Also, it isnt illegal because I payed for the damn thing and it is considered fair use.

All I can say is that it was worth the 200 dollars I payed. If it cost any more than that, I would seriously reconsider the purchase.

1) the various quantum tunneling experiments, where the Mozart 40th Symphony was transmitted through solid metal at several times the speed of light. There is a good link here. There was even a NOVA special or something on that (see that transcript here, - info about 2/3rds into the material)

2) maybe something involving the research of Steven Wolfram (developer of Mathematica), as seen in his forth coming book A New Kind of Science, which is very geeky, very bizarre, and right up this alley, and is supposed to be a rethinking of the very fundamentals of how science works. My head hurts already. This book is due for publication in January 2002, and is well worth pre-ordering.

So, you're saying that Mathematica isn't helpful?