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I stand corrected, it was Martin Gardner writing about Conway. Here's something odd.

The wikipedia version usually has much more info than the wolfram version. So I don't see how you can say they've just copied.

Take Pauli Matrices just as the first example I thought of:

http://mathworld.wolfram.com/PauliMatrices.html
http://en.wikipedia.org/wiki/Pauli_matrices

Wikipedia has lot more information

To expand on your comment, it wasn't just Galileo's pro-Copernican views which got him in trouble:

Galileo lay down the chief elements of his mechanics in Dialog on the Two Chief Systems of the World (1632), which was supposed to be an objective debate between the Copernican and Ptolemaic system. Unfortunately, Galileo put the Pope's favorite argument in the mouth of one of the characters, then proceeded to ridicule it. Galileo suddenly lost favor with the church, and was forced to recant his Copernican views and put under house arrest.

I'm not defending the church, but unless you're fireproof it's probably never a good idea to ridicule an authority that can easily have you killed for some phoney-baloney religious reason.

Oh, I completely agree that my name is very associated with my books. If you knew my name, you'd agree. My point is that any noob will screw up copy editing, layout and all the other facets of publishing, when compared with the output of someone who does only each one of these specialties for a living.

This is especially true for material that you've already written yourself. Nobody can do a good job copy editing his own work, or laying out his own book. Look at your bookshelf and I think you'll agree that it's easy to identify the books designed and laid out by the author. One needs independence from the author to do those tasks well.

I do completely and absolutely agree, however, that one must review the work of these specialists with a microscope when the proofs are returned to you, the author, for approval. I have sent text back three and four times until it is exactly the way I want, and that includes the style and substance of the index. Note that in this phase of publication the author is editing the work of the other specialists. That do-but-have-others-verify process is critial to the production of a high-quality text, but it is the author -- and only the author -- who gives the final approval for printing of the galley proofs. It is the author's responsibility to ensure that they are as he wishes them to be for, as you state, it's his name most closely tied to the book. Because he has the final approval (as well as approval at several intermediate steps, like copy editing), the author is in control over what is associated with his name.

One of the contract clauses my attorney inserted into my first contract covered the case of a published text that differed from the galley proof. That clause has never been exercised, for the books alsways have been exactly as I have approved them -- errors and all.

It has been my experience that the difference between "academic" publishers and "technical" publishers, at least as far as their treatment of authors, is zero. I've had technical publishers that were total slimes; one told me that there were many other authors he could get to write the book he wanted on his terms, so there's at least one that wasn't trying for a long-term relationship. (I haven't seen the book in print yet...) My best relationship is, in fact, with an academic publisher; they are constantly pestering me to write another book for them, contrary to your assertion. I think one's relationship with a publisher is an ergodic, independent random variable.

Regardless of whether one's publisher is considered academic or technical, however, I still say that one lives at one's peril in the publishing world without an attorney. One can think one is "cooperating on a project," but never forget that publishing is first and foremost a business.

I've written three technical books, one of which is now going into its third edition, for three different academic publishers. Points I have learned:

1. Publishers don't want you to format your book. That's their job. They want to receive double-spaced plain text, left-justified, with each figure in a separate file and a note in the text where each figure is to be inserted. (The figure captions are typically inserted at the end of the text.) Fancy things like Word cross-references, automatic footnote formating, etc. cause publishers great pain and are to be avoided.

2. MS Word works just fine for writing books. (I also wrote my Ph.D. dissertation in Word.) The only revision control I did was write each chapter as a separate file, and include a date code in the filename (so that I could go back to earlier drafts when needed). Each publisher with which I have dealt has sent me a required template; each of them was in Word. Needless to say, follow your publisher's template!

3. Figures are by far the biggest PITA in book writing and publishing. I ended up in each case sending the publisher pdf files. Get explicit instructions from your publisher about figures before you start (they will usually instruct you about their format preferences).

4. Keep your ms copies in several different media. After you've spent several hundred hours on the ms, the thought of a hard drive crash begins to weigh on your mind.

5. Don't worry about index generation. The publisher does that (via a contractor, usually); but feel free to edit the result.

To be honest, the most useful tool I've used writing books is a simple spreadsheet. It has three columns: a date column, counting down to the date I am contractually obligated to deliver the text; a page completed column, with the total number of pages written by the given date; and a pages per day column, which calculates, based on the date and pages written, how many pages I have to write per day in order to finish. (A rule of thumb is to have 500 manuscript pages for an academic book.) As others have commented, it's too easy not to write one day, then another, and then a week, and then you can't meet your deadline (at least with material to which you're happy seeing your name attached). The spreadsheet was my way of keeping the nose to the grindstone -- if I took time off, I had to write 2.1 pages per day to finish, then 2.2, then 3 ... but if I wrote 4 pages per day for a week or two, it would go down. It's a motivational tool.

Suff you don't know to ask about: The biggest things one should know about academic writing relate to the business of publishing:

1. GET AN ATTORNEY. The contract the publisher will send you is, of course, biased in the publisher's favor. My attorney requested changes in my first contract -- all of which were accepted by the publisher without any comment at all -- that more than paid for his fee (by several times). He also included clauses that protected me from several problems of which I hadn't thought (like, what happens if the publisher accepts your manuscript but never publishes it? Or, what do I get paid if the book is published in new media, like video or a new electronic format?) GET AN ATTORNEY.

2. Never, ever forget that your relationship with the publisher is a business relationship, not a personal one. This can be easy to forget when dealing with your editor, with whom you will have to work closely for an extended period of time. Authors have forgotten this rule at their peril: Ask Eric Weisstein. GET AN ATTORNEY.

3. Others have written about advances. I don't know anyone who gets an advance for an academic book. You get paid based on sales, after the publisher has paid everyone and everything else. Because of this, consider writing the book so that it is suitable for schools (universities, etc.). All that's required in this case is just some exercises in the back of each chap

I learned Pascal and Assembler when I was 10. You'd be amazed at what kids can pick up.

However, if you want to give them something where they can get "something going quickly", I strongly recommend languages that have an "interactive" mode, because it lets them build on a simple foundation and receive immediate feedback.

My vote goes for Mathematica. It's a trivial language to start with: "5 + 5" is a program that outputs "10". The output is visually pretty, and it can draw pictures and graphs. However, it's not a toy language, it actually allows for incredibly complex programs in several different paradigms. The advantage it has over even simple languages like Java or BASIC is that it is more abstract, and hides several details that are very difficult to explain to a beginner programmer, no matter how smart. For example, calculating "42^42" works in Mathematica ("150130937545296572356771972164254457814047970568738777235893533016064"), but will produce either an error, or an invalid result in most languages that use 32-bit integers. Even with floating point maths, the result will merely be approximate, which is yet another complex discussion to have with a beginner. The educational licenses are not too bad, I think, but may be an issue with some schools.

As an added benefit, Wolfram has gone to enormous lengths to build a huge library or tiny educational snippets of Mathematica code, including lots of fun topics like fractals, image manipulation, the game-of-life, etc... For a teacher, this saves an enormous amount of time:

http://demonstrations.wolfram.com/

Alternatively, there are dozens of languages designed for education that have interactive interpreters. Haskell comes to mind, but it has a steep learning curve.

They are copying the "computable data" initiative in Mathematica http://www.wolfram.com/products/mathematica/newin6/content/LoadOnDemandCuratedData/ and http://www.wolfram.com/products/mathematica/newin7/

They are copying the "computable data" initiative in Mathematica http://www.wolfram.com/products/mathematica/newin6/content/LoadOnDemandCuratedData/ and http://www.wolfram.com/products/mathematica/newin7/

Did you try that for boards > 76x76?
According to this : "The time needed for this algorithm grows roughly linearly with the number of squares of the chessboard, but unfortunately computer implementation show that this algorithm runs into blind alleys for chessboards bigger than 76Ã--76, despite the fact that it works well on smaller boards (Roth)"

TFA has basically stumbled upon Warnsdorff's algorithm. It's a great method, but it doesn't work for really large boards due to blind alleys. There's another method available which uses decomposition to achieve a linear running time(in # of squares), but which is quite a bit more complex to implement. There's a nice tweak to the algorithm which can get much farther than the unmodified original: in the event of a tie (where two candidates have the same number of open neighbours), break the tie by choosing the square farthest from the center. This substantially extends the maximum size of the board (to what, I don't know, because it's worked for everything up to around 450x450, which is past what was described by Arnd Roth).

Apparently, this isn't NP-complete. There is an algorithm that can solve this in O(n) time, see here: http://mathworld.wolfram.com/KnightsTour.html

This will save a LOT of time for larger boards. Try to implement this.

Honestly, tell me you could generate this with gnuplot. (Disclaimer: I've never used mathematica).

>Uhh...

"Other Recently Added Features..."

Talk it over w/Wolfram...their marketing staff is standing by :)

Run on Linux?

Yes:

http://www.wolfram.com/products/mathematica/platforms/

Yes, it does. $2495 though...ouch.

Mathematica 7 has launched, as noted in Stephen Wolfram's blog post. Among the new features are huge equation typesetting, transcendental roots, and discrete calculus. Looking back at the version 6 discussion, it's perhaps inevitable that comparisons will be made to CAR, CGsuite, GAP, Geogebra, Geometer's Sketchpad, Geometry Expressions, Geonext, LaTeX, Magma, Maple, Matlab, nauty, noneuclid, Pari, Sage, or SeifertView. In other news, the Wolfram Demonstrations project now has over 4000 interactive math demos.

Mathematica 7 has launched, as noted in Stephen Wolfram's blog post. Among the new features are huge equation typesetting, transcendental roots, and discrete calculus. Looking back at the version 6 discussion, it's perhaps inevitable that comparisons will be made to CAR, CGsuite, GAP, Geogebra, Geometer's Sketchpad, Geometry Expressions, Geonext, LaTeX, Magma, Maple, Matlab, nauty, noneuclid, Pari, Sage, or SeifertView. In other news, the Wolfram Demonstrations project now has over 4000 interactive math demos.

Mathematica 7 has launched, as noted in Stephen Wolfram's blog post. Among the new features are huge equation typesetting, transcendental roots, and discrete calculus. Looking back at the version 6 discussion, it's perhaps inevitable that comparisons will be made to CAR, CGsuite, GAP, Geogebra, Geometer's Sketchpad, Geometry Expressions, Geonext, LaTeX, Magma, Maple, Matlab, nauty, noneuclid, Pari, Sage, or SeifertView. In other news, the Wolfram Demonstrations project now has over 4000 interactive math demos.

Mathematica 7 has launched, as noted in Stephen Wolfram's blog post. Among the new features are huge equation typesetting, transcendental roots, and discrete calculus. Looking back at the version 6 discussion, it's perhaps inevitable that comparisons will be made to CAR, CGsuite, GAP, Geogebra, Geometer's Sketchpad, Geometry Expressions, Geonext, LaTeX, Magma, Maple, Matlab, nauty, noneuclid, Pari, Sage, or SeifertView. In other news, the Wolfram Demonstrations project now has over 4000 interactive math demos.

Mathematica 7 has launched, as noted in Stephen Wolfram's blog post. Among the new features are huge equation typesetting, transcendental roots, and discrete calculus. Looking back at the version 6 discussion, it's perhaps inevitable that comparisons will be made to CAR, CGsuite, GAP, Geogebra, Geometer's Sketchpad, Geometry Expressions, Geonext, LaTeX, Magma, Maple, Matlab, nauty, noneuclid, Pari, Sage, or SeifertView. In other news, the Wolfram Demonstrations project now has over 4000 interactive math demos.

Mathematica 7 has launched, as noted in Stephen Wolfram's blog post. Among the new features are huge equation typesetting, transcendental roots, and discrete calculus. Looking back at the version 6 discussion, it's perhaps inevitable that comparisons will be made to CAR, CGsuite, GAP, Geogebra, Geometer's Sketchpad, Geometry Expressions, Geonext, LaTeX, Magma, Maple, Matlab, nauty, noneuclid, Pari, Sage, or SeifertView. In other news, the Wolfram Demonstrations project now has over 4000 interactive math demos.

Mathematica 7 has launched, as noted in Stephen Wolfram's blog post. Among the new features are huge equation typesetting, transcendental roots, and discrete calculus. Looking back at the version 6 discussion, it's perhaps inevitable that comparisons will be made to CAR, CGsuite, GAP, Geogebra, Geometer's Sketchpad, Geometry Expressions, Geonext, LaTeX, Magma, Maple, Matlab, nauty, noneuclid, Pari, Sage, or SeifertView. In other news, the Wolfram Demonstrations project now has over 4000 interactive math demos.

He's quoting Feynman:

"There are 10^11 stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers." -- Richard Feynman

Also: Economical Number
A number n is called an economical number if the number of digits in the prime factorization of n (including powers) uses fewer digits than the number of digits in n. The first few economical numbers are 125, 128, 243, 256, 343, 512, 625, 729, ... (Sloane's A046759). Pinch shows that, under a plausible hypothesis related to the twin prime conjecture, there are arbitrarily long sequences of consecutive economical numbers, and exhibits such a sequence of length nine starting at 1034429177995381247.
http://mathworld.wolfram.com/EconomicalNumber.html

If we guess that the hull is 3 cm thick, and the hole is 10 cm in diameter (the hole is effectively a pipe), according to the ancient looking chart I found, the flow rate is 748 liters per second. (This is assuming I'm interpreting this correctly).

Yeah, it look ok. You can also go with a crude order-of-magnitude approximation (which is as accurate as we're ever gonna get for this topic) by assuming streamlined flow and applying Bernoulli's law ( http://scienceworld.wolfram.com/physics/BernoullisLaw.html so the hull thickness isn't directly relevant), with P at about 100 kilopascals, and the density of air at about 1.2 kg/m3, the velocity of air escaping is about 400 m/s, times pi*r^2 gives about 1.147 m^3/s or around 1147 liters/s. Given that there will be a helluva lot of turbulence and nonlinear transport effects due to the nitrogen in the air freezing into microscopic icicles as it nears the cold vacuum of space, the actual speed will be less than that but at the same order of magnitude, so 748 l/s sounds about right.

Actually, had I been properly caffeinated at the time I posted, I would have cited to this article instead.

Heck, just use wikipedia.

Seriously. There are enough excellent articles there to teach most of the undergrad curriculum. You can teach most of common math from http://mathworld.wolfram.com/ and so on.

And you get the added benefit that you learn to approach all of that material with a healthy dose of skepticism - after all, someone with an agenda can skew the article to their point of view.

What a concept - teaching skepticism, corroboration from multiple sources, and independent thinking.... Nah, it will never work. No money in it.

I use Mathematica for this problem. It cannot cover *all* the bases covered by {La}TeX, but it handles all of my technical document preparation needs (including equations, tables, et c.). Almost all charts/plots I generate directly (although sometimes in a separate notebook to separate implementation from result). Import of random graphics is also possible. In fact, there is TeX import/export, but since I have never used this feature I will not comment on its usefulness.

It's also kinda handy for some of that crazy computation stuff I do in preparation for document creation.

However, do not trust its PDF export. It does not embed relevant fonts in the PDF (thereby producing a potentially malformed document, depending on the font set on the recipient's/viewer's machine). Of course, I use PDFCreator for this purpose and just "print" it.

Man, I can't believe I need to argue this on Slashdot.

Turing machine is a mathematical construct. It is just like you can construct a 3D or 4D or even 160D Cartesian space in your brain, in paper, or in a computer at any time you like - but they are just mathematical constructs! Just look at Wolfram's page, it says "A Turing machine is a theoretical computing machine invented by Alan Turing (1937) to serve as an idealized model for mathematical calculation."

To prove the computer you're using to post thing to Slashdot is not a Turing machine - just ask yourself - Can you computer fit in a program that is infinite in length? Can you computer run a program that requires an infinite amount of memory? If you answer "no" to any of my questions, you are not using a Turing machine.

Maybe the ISS is best where it is but maybe, iff a lunar orbit station would be usefull as a step towards the future lunar base this might be a good method for getting it there. Build a space station that is better designed for lunar orbit in earth orbit, use this method to get it to lunar orbit after completion. Leave the ISS where it is. That is, if a lunar orbit station is even usefull and if the lumpy gravity issue that another postor mentioend isn't a total deal breaker.

Yeah! And I always liked Tupper's self-referential formula: http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html

Perhaps this is an example of how Google is limiting critical thinking.

A pound is equal to a certain number of grams in Earth gravity. That does not change that pound is a not a (scientific) unit for mass.

To see examples of pound as force, see: http://scienceworld.wolfram.com/physics/Slug.html (unit of mass is foot-pound-second) or http://en.wikipedia.org/wiki/Slug_(mass) (unit of mass that accelerates by 1 ft/s2 when a force of one pound-force is exerted on it.)

To minimize confusion, pound-force and pound-mass are sometimes used to avoid the (somewhat archaic) slug. This fits with the common usage of the kilogram (which is a mass unit) to also be used as a force unit. The more formal force unit in SI is the newton as I think was mentioned previously.

None of these differences matter if you are talking about objects in the same Earth gravity. If you are talking about a different level of gravity, the distinction between mass (as pound-mass, slug, or kg) and force (as pound, pound-force, or newton)

What is the point of trying to compete when you lose your edge as soon as you release your product/application?

This is a problem with competition in general. Without free software, the competition is less intense, so that short-term niches can appear. Perhaps there is an argument for competition to be less intense, so that the marketplace has an opportunity to anneal.

However, free software still provides competition; that the competition is perhaps too effective doesn't contradict that basic fact.

As competition, free software is interesting in that its wage is non-monetary, this leads many who don't realy grok supply and demand, and the roots of money in barter to consider such non-monetary wages as being somehow against the spirit of capitalism. Such distortion is then used to link volentarism with oppressive regimes, so as to present the exercise of freedom as anti-freedom.

Pretty bizarre, if you ask me...

Not quite. A set of measure zero is not necessarily empty. For example, the set of rational numbers is measure zero inside the reals. See here. Also, 'place' is a technical term. See here for a definition.

The puzzle isn't as simple as this. For a start one needs to understand analytic continuation as the usual formula for Zeta does not hold for arbitrary complex numbers.

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

Uh... you are comparing "Zero is a number" etc to "God exists"... axioms in Math and Science are "small". How does God exist? What are the scope of his powers? What is the density, length and colour of his beard? Does he have noodly appendages? Probably the most "controversial" axioms in Math (in the sense that they may not be self evident) are:
1. The parallel postulate (f a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.)
2. The axiom of choice (Let C be a collection of nonempty sets. Then we can choose a member from each set in that collection. In other words, there exists a function f defined on C with the property that, for each set S in the collection, f(S) is a member of S.)

In both cases, both axioms have been assumed both true and false to create their own sets of theorems (E.g. Euclidean geometry, which everyone knows (well..) vs. Non-euclidean geometry which is used in relativity etc... these differ on wether or not the parallel postulate is accepted)

Calling God an axiom is a losing argument.

Also, as any fool knows, you can tile a floor with pentagons.

I wouldn't buy a book from CRC personally: CRC Lawsuit Frequently Asked Questions

For tomography reconstructions one typically needs SVD (Singular Value Decomposition) which are of n^2 sizes. E.g. consider a reconstructable image of 128 x 128 = 16384 pixels total, this needs (temporary) processing matrices of size 16384 x 16384, which, as you can see, grows rather fast with even moderate reconstruction grids.

I see your CS geek and raise you a math geek

Where any of the answers "acute triangle"?

Or are you making some kind of joke I don't get?

There are different types of dimension. Topological, Lesbesgue, Fractal, Basic.

However, if you're referring to "unit dimensions" in physics specifically, there's a simple reason for that. And it doesn't have to do with the structure of the world. Quite simply, the fact follows from our use of integer derivatives to study change, as opposed to fractional derivatives. Units are syntactically variables, and must be treated as such during computation. Of course, this is why 3m x 5m is 15m^2. But it is also why the 3/4th derivative of position in time would end up with whacky unit exponents.

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

The relations derived using the fractional calculus are just as true as the standard treatment. The integral formulation is merely computationally simpler.

But on the same note, challenges to established scientific principles must themselves be scientific, and that is the problem here.

Almost. You have to distinguish between the scientific principles that are theories, laws, hypotheses, and conjectures which must be thus challenged as you note, from the scientific principles that are the underlying methodology and philosophy of science. The ID-iots are taking advantage of a slightly sloppy demarcation between what is "science" and what isn't, and argue when you question whether or not what they're trying to do is "really" science, and bring up questions like experimental repeatability.

Of late, I've found you can get a nicely formal definition useful for bludgeoning them senseless is to use as your underlying philosophical assumptions the Robbins Axioms, ZF set theory, and the Strong Church-Turing Universe Thesis. From there, via Wallace & Dowe's "Minimum Message Length and Kolmogorov Complexity" and Vitányi & Li's "Minimum Description Length Induction, Bayesianism and Kolmogorov Complexity", we get something that looks a lot like the scientific method of testing hypotheses against each other.

The downside is that that doesn't care whether you got your theory by watching an apple fall or it came handed to you on Golden Tablets by a choir of Seraphim. On the other hand, most journals don't really care about that either, as long as you attribute the co-authorship.

But on the same note, challenges to established scientific principles must themselves be scientific, and that is the problem here.

Almost. You have to distinguish between the scientific principles that are theories, laws, hypotheses, and conjectures which must be thus challenged as you note, from the scientific principles that are the underlying methodology and philosophy of science. The ID-iots are taking advantage of a slightly sloppy demarcation between what is "science" and what isn't, and argue when you question whether or not what they're trying to do is "really" science, and bring up questions like experimental repeatability.

Of late, I've found you can get a nicely formal definition useful for bludgeoning them senseless is to use as your underlying philosophical assumptions the Robbins Axioms, ZF set theory, and the Strong Church-Turing Universe Thesis. From there, via Wallace & Dowe's "Minimum Message Length and Kolmogorov Complexity" and Vitányi & Li's "Minimum Description Length Induction, Bayesianism and Kolmogorov Complexity", we get something that looks a lot like the scientific method of testing hypotheses against each other.

The downside is that that doesn't care whether you got your theory by watching an apple fall or it came handed to you on Golden Tablets by a choir of Seraphim. On the other hand, most journals don't really care about that either, as long as you attribute the co-authorship.

IT means that the energy stored as a magnetic field is 725 MJ

See http://scienceworld.wolfram.com/physics/MagneticFieldEnergyDensity.html

In fact, it is pretty likely every cube can be solved in as few as 21 moves (or less),
as someone (Dik Winter) has already written a program that does just that.
Source: http://mathworld.wolfram.com/RubiksCube.html

Ever thought that by just throwing needles, you could figure out Pi? Check out this Pi by probability site. http://mathworld.wolfram.com/BuffonsNeedleProblem.html

According to this guy, we find "contemporary writers opting for vocal chords instead of vocal cords 49% of the time". That's pretty big, and it may end up being another accepted spelling.

Circles also have chords.

Try MathWorld instead. Okay, some of it's still pretty hard to understand (it IS mathematics, after all), but at least it's authoritative.

Demonstrations

Mathematica is a much better hammer for that type of nail.