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I'm not sure zero has even been around for 5000+ years. I couldn't find a quick reference, but I found this long one.

Article just says it was an University of Michigan release. No author listed, so maybe De Broglie wrote it from beyond the grave.

For completeness, that guy was Karl Frederich Gauss. He also found a way to construct a regular 17-gon with straight-edge and compass (actually, an infinite class, but I forget the rule). He also did physics, mostly in magnetism.

OK, its not science literally, but what about Andrew Wiles' proof of FLT ?

I think there are still some nuggets to be found.

( crawls back into his attic )

Believe me, guys (and gals) much smarter than Nash have been defeated by the Riemann Hypothesis. They just haven't been bonkers enough to deserve a cheesy, hagiographical Hollywood movie...

Believe me, guys (and gals) much smarter than Nash have been defeated by the Riemann Hypothesis. They just haven't been bonkers enough to deserve a cheesy, hagiographical Hollywood movie...

We (the OSS community) need to make sure that we can easily and indisputably prove "prior-art"...

Done.

There is a class of geometric construction problems that are impossible with a divider (compass) and straight edge. Basically, if you can do it with a compass and straight edge, you can do it with Euclid's axioms, so this kind of construction is a sort of analog approach to symbolic proofs.

One of these problems is trisecting an angle, that is, dividing an angle into three equal angles. The picture you just posted has nothing to do with this problem.

Another is "squaring a circle", that is, constructing a square that has the same area as a given circle.

People have wasted their lives trying to do these things.

Here's a link for the curious.
Squaring the Circle

I have used a few other packages, command-line utilities, which I find useful: Recently I'm using one for my honors research project (I'm an undgergrad): GAP and another I've used which I like: PARI-GP. GAP tends to deal with group-theoretical functions, and GP tends to deal more with number theory, but both shouldn't be ignored.

I'll bite, you troll. How long have women and blacks had a chance in any of these fields? Thirty years or less? It's been three hundred or more years since the Enlightenment; I'm sure Newton wouldn't have accomplished what he did if he were born into slavery, or Einstein if he were never allowed to learn anything of substance. (And still, women were mathematicians.)

Twit. Oh hell, who am I kidding. The great early mathematicians who weren't Greek were Indian. Anyone remember Ramanujan? What about the scads of Asians in the field?

Sheesh.

Kirkcaldy is only a few miles from St.Andrews University which made all the papers in Britain about 4-5 years ago with news they'd created an image of the perfect woman and man (or something like that) ... ie those that are most attractive (on average) to members of the opposite sex. MBCook is right about the metrics involved ...

More info from a recent BBC article or from the St.A perception labs homepage - the face transformer page here is quite fun.

Kirkcaldy is only a few miles from St.Andrews University which made all the papers in Britain about 4-5 years ago with news they'd created an image of the perfect woman and man (or something like that) ... ie those that are most attractive (on average) to members of the opposite sex. MBCook is right about the metrics involved ...

More info from a recent BBC article or from the St.A perception labs homepage - the face transformer page here is quite fun.

Well, I'm not sure if you would consider Revelations "ancient greek" since it was (to the best of my knowledge) written in approximately AD 90. However, the Greeks used phonetics for their numbers. Here's some more info. Of course, this may or may not be relevant since they're talking like 1000 years prior to the text in question. I'm thinking that the language probably changed somewhat in that time.

Dr. Yorke has found the universal mechanism underlying such nonlinear phenomena.

Can someone clarify what part Mitchell Feigenbaum played compared to Yorke and a likely reason why Feigenbaum wasn't included in this prize?

See also The Feigenbaum Discovery and of course James Gleick's book Chaos.

Anyway, I think my point is that calling it a convenience number seems to trivialize it, though of course the relation you describe is one of the several true basic statements you can make about e, it's definitely not the only one.

Also, your site, autopr0n.com, rocks. I just wanted to take this brief offtopic chance to thank you and the autopr0n mods for giving the world good, fresh TGP links, and the new rating system rocks. I always refer friends to your site.

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On December 14, 1900, Max Planck presented experimental results in front of the German Physical Society and announced that they could best be explained if energy exists in discrete packets, which he called "quanta." Today is the 100th birthday of Quantum Physics. But many people who consider themselves "scientifically minded" are still baffled by the question - What does it all mean, anyway?

In a nutshell, the theory of quantum physics, first devised by Max Planck (a German scientist) about 100 years ago, states that energy can be best understood as existing in discrete packets, which he called "quanta". This can be demonstrated with a simple photoelectric effect experiment - energy from electromagnetic waves does not gradually increase but is measured out in discrete photonic packets, or "quanta".

For more information on Max Planck, visit this biographical website.

For a more in-depth, but still accessible definition of quantum physics, see this webpage part of an online encyclopedia of science.

HTH.

the eric conspiracy: You don't really believe that, do you? If this were really true, mathematics journals would publish their articles without author's names attached to them, and their would be no Fields Medal. The fact is that the method of keeping score is different, that's all.

Sorry, I should have been clearer. I wasn't talking about squables over giving/taking credit for discoveries, I was talking about the practice of trying to control the use of the discoveries as if the were the property of the discoverer. This was common in Europe at least from the time of the Pythagoreans through 1600 or so.

To my mind, the present climate of "intelectual property" in software is about as petty and counter productive as that of pre-Renaissance mathematics. Petty, for obvious reasons and counter-productive because trying to control what people can think (or what thoughts they can use), no matter what your motives, is never good for science.

This sounds to me like the traditional lament of the academic when he finds his pursuit has a practical use.

No, the lament only comes out when the practical people jumping on the band waggon that the academics built start trying to boss the academics around and impose goals and limits based on their lust for gold instead of the academics lust for knowledge.

--MarkusQ

The engineer who takes joy from building something people can use has a different view.

We need both.

*smile* That's the basis of my relationship with my wife (She's EE+MBA).

Well not exactly, I mean the clones would need to grow up on a strict diet of /. -- but that was so obvious I didn't feel it needed to be mentioned.

On the serious side, did Einstein learn his greatness from school?

How about John Carmack? After all, he just implemented everything he learned about bsp's and fps's from his college classes. Oh wait he couldn't have because he dropped out of college. I guess all his peers who stayed in college must have made much bigger contributions to the software gaming industry since they kept learning in school.

How about Srinivas Ramanujan? Self taught and dirt poor, he made substantial mathematical contributions.

All of these guys transcended their environments to achieve greatness even before the advent of /. Just think what the clones will achieve!

Secondly, just because something is not state of the art does not mean it should be dismissed out of hand. You are right about Bayes classifiers making false assumptions about the independence of features but it has been suprisingly successful in practice, even when these assumptions have been violated. This paper shows that "...the accuracy of naive Bayes is not directly correlated with the degree of feature dependencies".

While kernel machines tend to be much more accurate (and quite cool theoretically), they are nowhere near as efficient (time and space-wise) to train. You want an intelligent spam filter to go easy on available resources and for this reason I don't think KMs are the way to go.

Another nice technology for text classification is Latent Semantic Analysis but once again, probably not the best tool for this particular job.

Coastlines are fractal: the closer you look, the longer they get.

Both the ocean and the continent are made of atoms, so the fractal approximation breaks down when you look too closely, and you end up with a finite path length. For the purposes of aerial photography, you might as well take a minimal cover of the coast using discs of radius ~1km and sum their diameters. Small crinkles are completely irrelevant.

It's one of the few really fundamental mathematical discoveries of the last century.

This sounds like a troll, but there is a shred of truth hidden inside. There have been plenty of deep, fundamental mathematical discoveries in the last century, and I doubt you can find many mathematicians who would agree with your sentiments. All of the people appearing on this page have done very impressive work, and you may notice that fractals are not featured at all. Unfortunately, fractal geometry is one of the few recent advances which can be understood even superficially by people lacking a background in mathematics, and this seems to raise the public profile of the field substantially.

That was not the Nobel prize, he got the Fields medal... ;-)

There was only one mathematician, Johann Carl Friedrich Gauss. He seemed to live a fairly successful long life including having several children and making a fortune.

I'd happily pay to see De Niro playing an older Feynman. Did Feynman's role on the Challenger investigation have sufficient heroic elements? The poor guy was living with cancer during the investigation.

Read this brief summary about Alan Turing's life.

A serious, well written script documenting his incredible, tragic life would make A Beautiful Mind seem about as powerful as Pee-Wee's Big Adventure (not to knock Pee-Wee's Big Adventure - great movie, it's just no tour de force).

Try this link:
Newton

Dunno why the first added a space into the middle of the link. It wasn't there when I pasted it.

Binary computers actually arrived on the scene over 200 years after Boolean algebra was invented and refined by George Boole and first presented in a paper by him in 1854.

"Boole's system of logic is but one of many proofs of genius and patience combined." was how De Morgan commented. It is not recorded how many whiny teens said "so what".

It's first real practical use was for telephone switching.

Teenagers, practising their skills, consider their 'work' worthy of historical note. Arrogance? Youth? Ites says: easy to make drawings in the sand. Ideas are cheap. Finish the job and you will deserve to be remembered.

In 1959 Richard Feynman said that all the information accumulated in all the books in the world could theoretically fit in a cube 1/200th of an inch on a side.

You can read the transcipt of the speech from when he made that prediction.

Feynman worked on developing the atomic bomb, he won a nobel in physics and is known as much for his scientific research as for his story telling.

A little history on MC Escher here.
HTH HAND

http://wired.st-and.ac.uk/~spurdie/

In the UK.

In 1911 Ramanujan approached the founder of the Indian Mathematical Society for advice on a job. After this he was appointed to his first job, a temporary post in the Accountant General's Office in Madras. It was then suggested that he approach Ramachandra Rao who was a Collector at Nellore. Ramachandra Rao was a founder member of the Indian Mathematical Society who had helped start the mathematics library. He writes in [30]:-
A short uncouth figure, stout, unshaven, not over clean, with one conspicuous feature-shining eyes- walked in with a frayed notebook under his arm. He was miserably poor. ... He opened his book and began to explain some of his discoveries. I saw quite at once that there was something out of the way; but my knowledge did not permit me to judge whether he talked sense or nonsense. ... I asked him what he wanted. He said he wanted a pittance to live on so that he might pursue his researches.

• Gain insight into the minds of the ancients (Plato would not let anyone into his school who hadn't mastered the geometry of the Elements),
• Improve your reasoning skills (Abraham Lincoln read Euclid when he decided to supplement his education later in life), and
• Be exposed to some of the most beautiful things that mathematics - or any academic pursuit - has to offer ("Euclid alone has looked on beauty bare." --Edna St. Vincent Millay)

• Archimedes: it can be argued endlessly whether he was an physicist or a mathematician. The scientific disciplines weren't separated at all at this time.
• Newton: his main contribution to mathematics was found independedly by Leibnitz at the same time.
• Laplace was a mathematician, who was also occupied with physics.
• Same goes for Legendre.
• Dito for Maxwell.
• Einstein didn't much remarkable things for mathematics. In fact for his theory of relativity he mainly depended on Riemann's results on Riemannian Geometry. Without Riemann the theory of relativity couldn't have been formulated without severe problems.

The study will be split into two phases. In phase one, simple mobile phone tags will regularly send text messages from grey seal pups to computers at the University, allowing scientists to examine which factors affect their survival through their first year. In phase two, GPS (Global Positioning System) and depth sensors will be added, allowing, through GPRS, (General Packet Radio Service) massive volumes of detailed track and dive behaviour to be sent ashore.

(And we find 56kB/sec slow....)

check out

http://www-theory.dcs.st-and.ac.uk/IC_Group/resour ces/software/software.shtml
- for the software

and

http://www-theory.dcs.st-and.ac.uk/IC_Group/resour ces/multimedia/multimedia.shtml
for cool movies and videos of the lego robot.

Various different types of learning were played around with ; neural, reinforcement learning , handcoded algorithms....

Those pages are still to be ok'd with my local dept. though, so please email gbb@dcs.(nospam).st-and.ac.uk if you have any questions about them.

check out

http://www-theory.dcs.st-and.ac.uk/IC_Group/resour ces/software/software.shtml
- for the software

and

http://www-theory.dcs.st-and.ac.uk/IC_Group/resour ces/multimedia/multimedia.shtml
for cool movies and videos of the lego robot.

Various different types of learning were played around with ; neural, reinforcement learning , handcoded algorithms....

Those pages are still to be ok'd with my local dept. though, so please email gbb@dcs.(nospam).st-and.ac.uk if you have any questions about them.

Fermat's Last Theorem

If that were the case--that it's learned from parent to kitten--then you'd expect cat cultures to evolve, where different communities of cats would have different vocabularies. This is seen in chimps right in the same neighborhood. With cats being so widespread, it wouldn't be hard to demonstrate that cats in Albania have developed a different culture of vocalizations than their cousins in Brazil. (Has anyone done this? I couldn't find any evidence.)

Also, just because it isn't Darwinian evolution, depending on differential reproduction to pass traits, doesn't mean it's not evolution. Long before Darwin, there was Lamark, who recognized evolution and gave his own theory as to the mechanism. After a century of ridicule by Darwin advocates (not including Darwin, who seems to have thought highly of Lamark's work), a large number of findings in cellular biology beginning in the 1970s show support for both natural selection and environmental influence in passing new traits to offspring.

What does that have to do with cats? I dunno. But there's more to this evolution thing than they're arguing in southern courts. Don't discount new ideas just because they show up in the media (though it's not any sort of endorsement, for sure).

There's a lot of theories about alternatives to the big bang besides the one mentioned in the Yahoo article. The main one that is getting a lot of interest in scientific circles isn't this new one in the Yahoo article. Instead, it's the so called Ekpyrotic theory, with the name coming for the Greek word for fire. It is so intresting because it brings together two disparate areas of physics: inflation and M branes. Inflation is a weird concept that says the universe expanded from the diameter or an atom to the size of a grapefruit almost instantly - required to explain the way galaxies are clumped and clustered in the sky we see today and first postulated by a guy named Alan Guth. M branes are an offshoot of string theory postulated by Ed Whitten. There's tons of stuff on these topics on the web; all of it is facinating, enter any of these terms in a search engine and keep reading. Next stop, Google...

There's an error in that algorithm. Can you spot it?

It's Fibonacci, not "Fibinacci"

Interesting point..
According to the article, Switzerland didn't have patent laws until 1907.
According to A.E.s biography he worked at the patent office from 1902 to 1909..
Any swiss IP historians around who can elucidate?

A missionary is not just someone on a mission, it is someone who is sent on a mission

Merriam webster disgrees. Missionary: a person undertaking a mission and especially a religious mission.

You should be able to see the parallel between religion and the feelings that drive people to write Free Software. Think of all the times you've read the phrase "linux zealot" in this forum.

Anyway, I wasn't trying to say that "missionary" was the perfect word to describe Free Software developers. I admit it's not. It's a damn sight better than "hobbyist" though.

You're right, they do it for something much more serious than that: fun

"Fun" can be interpreted in many different ways. Some people do they're paying dayjob for "fun" (Bill G doesn't have to work any more, does he?). Saying that you are doing something for fun is not the same as saying you are a "hobbyist".

until you make your living from it, you're a hobbyist

So Einstein was a hobbyist. And so's Bill Gates. Yes, he gets paid, no it's not his "living", he already has that.

That letter indicated a low level of seriousness relative to a shrink-wrapped closed-source software shop, too.

You've never read an EULA, then, or attempted to get support for shrink-wrapped software.

Einstein did science for a living, therefore he was a professional scientist.

Please, at least get your facts right. Einstein was a patent clerk. He did his science in his "spare time".

If missionaries never gave up, the Spanish Inquisition would still be going on

As I've said, I know the word "missionary" is not perfect. The word "amateur" is in fact the correct word, but thanks to the sustained badmouthing by "professionals", the word now has the same connotations as your "hobbyist". So I still think "missionary" is the more fitting title.

Ok, so this is out of context...

correct me if I'm wrong

Gladly...

Regarding Babbage - first off, the concepts underlying the Difference Engine came to Babbage in 1812 (and, since Babbage was born in 1792 - that would make him 19 or 20 years old at the time!), as he was thinking on logarithms and the inacuracies that could occur during their calculation. He didn't follow up on his ideas until 1819, at which point he began building a small Difference Engine, finishing it in 1822. In 1823 he applied for and got a grant to build a larger engine (which was not completed). The Difference Engine, however, was more a calculator, and not a computer. The later Analytical Engine (began in 1833 - also not completed) was a true programmable device. More information can be found here and here...

Ada Lovelace, however - didn't invent the loom you refer to - that goes to Joseph Marie Jacquard, who invented the Jacquard Loom in 1802 - which utilised a series of punched cards to control warp threads on each pass of the weft thread. Ada obviously knew quite a bit about these looms (as did Babbage, who conceived of using punch cards for the control of Analytical Engine, presumably after seeing such a loom in action - indeed, the names he settled upon for what we today call the CPU (Mill) and memory (the Store), happen to be derived from terms used in the weaving industry at the time!), and so wrote in her Sketch of the Analytical Engine in 1842:

The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs. It is in this that the distinction between the two engines lies. Nothing of the sort exists in the Difference Engine. We may say most aptly, that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.

Indeed - even she understood the value of the Analytical Engine over that of the Difference Engine - its programmability (weavability?)!

I could indeed go on - you neglect to mention Konrad Zuse, as well as the contribution of Atanasoff and Berry (the ABC) for the first electronic stored program computer.

But I will stop here...

Worldcom - Generation Duh!

http://www.charlesworth.com/isr/issues/isr231/1379 _18/

Those of you familiar with German can also have a look at a short overview of Adam Ries' "Rechnen auff der Linihen" from 1518, which describes how to calculate the multiplication on the Abacus and is considered as the first mathematical book for the common people: Rechnen auff der Linihen

After "Rechnen auff der Linihen", he wrote "Rechnen auff der Linihen und der Federn" which also is considered as the introduction of the Arabic numbers to Central Europe.

(see Adam Ries - German)

The Arabic numbers had been introduced to Europe in 1202 by Leonardo Fibonacci (who also found the famous "fibonacci numbers", now a standard algorithm for describing recursion).

And last but not least, also an article in English: Adam Ries.

Sebastian

Umm....maybe. After this "direct detection" was announced, another group, with BETTER detection capability, failed to find the claimed signal.

The original group then admitted that the supposedly directly detected planet was not so bright

Why all the controversy?

the signal was 20000 times fainter than the noise

Repeat:

the signal was 20000 times fainter than the noise

More than you ever wanted to know about this star

----
cliamer: IAAPA

To implement the Turing machine's infinite tape in a cereal, of course, you wouldn't use Life cereal, you'd use Aleph-Nought-Bits...

the concept of Algebra was made famous by the work of Abu Ja'far Muhammad ibn Musa Al-Khwarizmi His work was brought to Europe in the 12th Century. At that time -- although the words were translated from the (right-to-left) Persian to (left-to-right) Latin, the (right-to-left) numbers in the book were copied verbatim.

This mistake has been perpetuated for the last 900 or so years. Ever wondered why you do most simple math operations (addition, subtraction, multiplication) from right to left?? It's because The European number system is written backwards.

If the original translators of Al-Khwarizmi's works had thought to write the numbers the way that european words are written, We would be little-endian too. As it is, I'm sure that there are many persian/arab immigrants who wonder why we switch from european left-to-right to the arab right-to-left whenever we deal with numbers.

As for those people who think that bits in a little-endian byte are stored backwards, they're not. In a 32 bit word, they're stored 0,1,2,3....31. we just WRITE them in big-endian nibble format because to do otherwise might confuse our already warped notion of how numbers work.

If you think about it, it makes complete sense to store data in little-endian format. You start work with the bits where the pointer points to; Truncating from fullword to byte requires simply ignoring the extra bytes; Arbitrary-precision math doesn't require you to skip to the end and count back... You simply do your operation until you run out of bytes. Data can be stored as [max-len] [used-len] [data] [sparebytes]; extending precision simply requires using more bytes.. No need to change pointers or copy data to make space for the extra digits.

If computers had been developed in Persia, where modern Algebra developed, there wouldn't be any big-endian/little-endian fight to speak of. Ditto if the original translators had their shit together.
`ø,,ø`ø,,ø!