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They overlap like your FM stations overlap. They occupy the same band, they do not occupy the same frequencies.

Wrong, the spectral 'lines' are not actually thin lines, as you can see in the explanation here:

http://www.barrettbellamyclima...

'Lines' overlap

Pressure broadened lines or bands overlap so that over the spectral range there are no instances of 100% transmission. This is illustrated by spectra of CO2 with 100 m and 200 m path lengths respectively that show that over the spectral range there is some absorption at all wavenumbers. Please note that the spectra have been replaced with their correct titles. The previous titles were for 100 m and 200 m path lengths in error, pointed out by Brenden O'Connor.

Also: http://www-star.st-and.ac.uk/~...

No, wrong.

Um, no. You are highly misinformed.

But Von Neumann was something special.

A polymath and a polyglot, his early work with chess is not to be scoffed at.

The babylonians and God's favourite people thought that pi=3. Hey, it's good enough for government work, and probably for fighting zombies.

The decoding operation at Bletchley Park became the basis for the new decoding and intelligence work at GCHQ. With the cold war this became an important operation and Turing continued to work for GCHQ, although his Manchester colleagues were totally unaware of this. After his conviction, his security clearance was withdrawn. Worse than that, security officers were now extremely worried that someone with complete knowledge of the work going on at GCHQ was now labelled a security risk. He had many foreign colleagues, as any academic would, but the police began to investigate his foreign visitors. A holiday which Turing took in Greece in 1953 caused consternation among the security officers.

Turing died of potassium cyanide poisoning while conducting electrolysis experiments. The cyanide was found on a half eaten apple beside him. An inquest concluded that it was self-administered but his mother always maintained that it was an accident.

http://www-history.mcs.st-and.ac.uk/Biographies/Turing.html

http://www.turing.org.uk/bio/part1.html

2 minutes with Google. Rather plain, neither a beauty nor ugly (80 years old admiral photo is best, anyways).

Yes, sadly, that is all true, it is usually easier to destroy rather than create.

But, it does not change the main point about the moral and practical choices we make every day as human beings and how they can be ironic and counterproductive if we use the technologies of abundance from an assumption of scarcity.

Also, I might argue that for some people, destruction being easier than creation makes it less of a challenge and so less fun. :-)

Or to put it another way, it is in a sense "easier" as far as total time involved for people to kill themselves than to spend a lifetime involved in life -- but generally most people decide that making the effort to be engaged in life is worth it because they have things about life they value (family, friends, hobbies, children, spirituality, sensuality, community, humor, honor, singing, dancing, eating, reading, writing, whatever). In fact, for most people, there is not even a choice -- our body just keeps going and keeps us engaged (barring depression, which can often be treated in various ways ranging from vitamin D, to omega-3s, to eating more healthy food and less junk food, to a positive spiral of social-talk and self-talk, and so on).
http://slashdot.org/comments.pl?sid=1692444&cid=32644166

Our society needs to decide whether it wants to continue of the current (statistically likely) suicidal path of self-destruction or if it wants to reform. Why use the nukes, warbots, plagues and nanotech and whatever else to fight over what? Oil and slaves and racism and stuff, when we could just use the tech to make what we wanted? It remains ironic, even if it is indeed "easier" to just let the society destroy itself. Nobody ever said life was going to be easy. It is a choice.
http://knol.google.com/k/paul-d-fernhout/beyond-a-jobless-recovery#Four_long(2D)term_heterodox_alternatives

Still, a deeper philosophical issue is that we apparently can't create without destroying something else (even just a different future possibility). So, reality is always throwing us curves in simple analyses. But, be that as it may, it seems stupid for everyone to kill each other off for a "racket".
http://www.lexrex.com/enlightened/articles/warisaracket.htm

Also, on a practical basis, it is not normal for humans to kill each other without some specific heated emotional interpersonal quarrel. Soldiers in earlier wars like WWI rarely fired their weapons, and when they did, aimed to miss -- only a few soldiers way back when did most of the killing. It is only in the last 50 years or so that the US military and other militaries have refined their indoctrination techniques to be able to turn most human beings into killers of people they have no personal quarrel with. Though the military may not have given much thought about what to do with the killers after the wars are over (if the wars ever are over -- how many wars is the USA fighting now and when will they ever be over?) Now push-button drones make that even easier as soldiers in air-conditioned offices near where they live with their families are not apparently killing people -- they are just pressing a few buttons that affect fuzzy blips on a video game screen. Is that "progress"?

As Godfrey H. Hardy said in disgust:
http://www-history.mcs.st-and.ac.uk/Quotations/Hardy.html
"A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life."

Freeman Dyson talks about that here:
http://books.googl

The author attacks Einstein for

abandon[ing] the hypothesis of an ether without furnishing a satisfactory substitute for this hypothesis. As has been previously stated, the very experiment which the relativity theory seeks to explain depends on interference phenomena which are only satisfactorily accounted for on the the hypothesis of an ether

source

For a different perspective, try Ether and the Theory of Relativity

1 ton = 1000kg, welcome to the metric system.

Not so fast. Do you mean a British ton, US ton, or metric ton(ne)? And, for more confusion, see that there is also a French ton.

Okay. I should stop being facetious and get my 7 hours of sleep (relative to current Earth's rotation period - has to be said, because it is slowing down).

During the first year of my Phd (1996?) I worked on the networking stack of a Persisent Operating System called Grasshopper.

They throw up a lot of interesting problems from a research point of view, but I'm not sure they're ready for prime time... (and yes I realise the intervening years have started to add up!)

Pushing boundaries is good in research of course, and lots of things do end up appearing in real products even if not the in the form originally imagined.

--Q

Aristotle had a great theory on gravitation. He even *invented* the word "gravitation". His theory stood undisputed for two thousand years. It was considered absolute truth. There was only one problem: it was a WRONG theory.

It was only after Galileo invented a method to measure the speed and acceleration of falling bodies that the foundations were laid for Newton's theory of gravitation. And it was Michelson's experiments showing small discrepancies in measuring the speed of light that allowed Einstein to develop his corrections to Newton's theory.

In my opinion, a truly intelligent mini-brain with no more than a few tens of thousands of neurons would surprise us with its clever abilities

This was done nearly twenty years ago with a simulated cockroach brain.

The big problem with human-level intelligence is that it appears to need a human-brain sized neural network. Consider how successful intelligence is from an evolutionary point of view. Humans have totally dominated the biosphere, no other animal within the same range of body size is as numerous as humans, except for those animals we raise for food.

If it were possible to evolve human-level intelligence with smaller brains, it would probably have happened by now. Looking from the biological evolution side, we see in the fossil record a steady increase in brain size in our ancestors. I seriously doubt human-level intelligence is possible with less than about a hundred billion neurons.

Clearly this is an emotional issue for you, which is why you refuse to perceive reality. There's no more point to trying to convince you, you are impervious to reason.

I guess your mind was already made up. Anyone else following this thread may be interested to pick up e.g. The (Complete|New) Dictionary of Scientific Biography or read the St Andrews History of Mathematics archive to learn the lifespans of the people I listed in my previous post and obtain a few pointers to more detail about the individuals' lives.

None of them had access to flying machines, open heart surgery or a hundred thousand porn sites from the comfort of their own bedroom, but to translate that into hopeless, wretched filth ("abject squalor") requires a pietistic leap of reason.

Well the Old Testament was written by backward Taliban types in the dark ages. What do you expect?

Something I didn't realise about the Old Testament until recently is that when they talk of the the Philistines binding Samson in 'chains of iron' it's because the Philistines had managed to master the technology to use iron but the Israelites hadn't.

http://en.wikipedia.org/wiki/Philistines#History
The Philistines long held a monopoly on iron smithing (a skill they possibly acquired during conquests in Anatolia), and the biblical description of Goliath's armor is consistent with this iron-smithing technology.

So 'God's chosen people' hadn't enterered the Iron Age at that point. There's lots of other signs that they were not exactly academically inclined either, like the biblical value of 3 for Pi which was less accurate than the value the competing civilisations knew.

The Qu'ran is just a bad mashup of the same primitive ramblings that inspired the Old Testament with some self serving editing by Mohammed. Or more likely early Muslims, since Mohammed was not particularly literate and had more important things to do with his time, like capture slaves and booty from more settled neighbouring tribes.

Thank the ancient Babylonians, who used a base 60 number system. They came up with the concept of 60 seconds to a minute, 60 minutes to an hour, 24 hours to a day.

The work is dated and I've seen nothing else since, but the idea of providing presentations as videos or audio recordings for review by students who can select, speed up, and extract what they need should have merit.

Here's a quote I picked up a few years back's:

"Apparently, American Psychological Association research has shown that while listening to a speaker, people do the following things:

*18% are really listening to the speaker

*25% are having erotic thoughts

*57% are thinking about something else

(Note: I say "apparently" because I read this in a handout I got at the CPSI conference, and haven't been able to find any actual confirmation of this research on the APA site.)

Most people can speak about 150 words per minute, but can hear and comprehend 900-950 words per minute. So after the first 20 seconds or so of a presentation, the audience will fade in and out and think about other things. So, we were told, you can make this work in your favor by drawing a line down the center of your notepaper and recording "in" thoughts on one side, and the "out" thoughts on the other side. This is supposed to free you from trying to remember "out" thoughts, and encourage you to generate ideas without losing track of the presentation. http://www.corante.com/ideaflow/ 20030201.shtml#21117"

Others have noted some web sites of possible value. Here are several more:

http://www.hardscience.info/

http://library.advanced.org/10170/menuw.htm

http://webphysics.iupui.edu/

http://www.aip.org/education/

http://www.falstad.com/mathphysics.html

http://www.vias.org/feee/index.html

http://www-groups.dcs.st-and.ac.uk/~history/Indexe s/HistoryTopics.html

http://www.mhs.ox.ac.uk/geometry/content.htm

http://acept.la.asu.edu/courses/phs110/expmts/toc. html

http://nsac.ca/eng/courses/math1000/index.asp

Hope there's something of value there. Jim

Djikstra, or Goedel?

"Gödel proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system."

http://www-history.mcs.st-and.ac.uk/Mathematicians /Godel.html

Thanks, but we're both wrong. Me, moreso than you. :-)

In Ancient Greek, Digamma is the sixth letter/number. It, along with Koppa and San (after Omega), are obsolete and no longer used in Greek.

http://www-groups.dcs.st-and.ac.uk/~history/HistTo pics/Greek_numbers.html

In studying the science and maths in the Vedas, it's important to distinguish truth from hype.

Truth:

The Rig Veda has geometry and elementary trigonometry , used in the construction of Vedic Altars.

Most mathematics in the Vedas are in the Shulba Sutras (appendices to the Vedas) . The most notable mathematical achievements in the Shulba Sutras was a series expansion for calculating the square root of 2. The Sutra calculated it to 1.4142156 (accurate to the 5th place of decimal). Keep in mind that Vedic Rishis did not actually know what an irrational number was. Neither did the Greeks, papart from the fact that they existed (they did not have a way to express them).

With the Greeks, mathematics was developed with a rigorous standard of formalism. However, they did not know how to express irrational numbers. They thought that all numbers that could be well-defined were ratios of integers and, since sqrt(2) was not one, they thought it did not exist. the Vedic rishis were more pragmatic and cared more for results than theory so they simply treated it as a sort of "approximate rational number"and managed to calculate it with a high degree of accuracy (much like computer today, which can't understand irrational numbers but express them as truncated rational numbers). The series in the Shulba Sutras was:

sqrt(2) = 1 + 1/3 + 1/(3X4) + 1/(3X4X34) + ...

which we can derive today using modern maths by Taylor expanding :

sqrt(a^2 + r) with a = (4/3) & r = (2/9)

In addition, the three Shulba Sutras have a statement of the Pythagorean theorem in terms of the sides of a rectangle

So, the early Vedic mathematicians probably did not understand irrational numbers, an instance in which the Greek insistence on logical correctness was a hindrance. The Greek did not regard sqrt{2} as a number since they could not express it exactly as a ratio and they knew that they could not (i.e. after Euclid's proof that sqrt{2} is irrational). The Vedic Rishis needed rational expression for it but, undeterred by the incompleteness of their knowledge, they proceeded to make what use they could of this number.

The same attitude led them to discover infinity, zero and -ve numbers as well, since their usefullnes outweighed the difficulties in understanding them within the framework of ancient mathematical models.

Also, the Satapatha Brahmanas in the Vedas contain complex geometrical constructs that predates Greek geometry.

The Hype:

All that pseudoscientific nonsense about spaceships and what not. Please read the Vedas carefully. There is no mention of "spaceships" though legends do point to flying chariots in the Puranas, they are parables, not to be taken literally.

More Indian Maths (just a small sample):

Also, we must not let obsessions with the maths of the Vedic period cloud the much more groundbreaking discoveries in Maths in India in later periods (Aryabhatta and the Zero, Bhaskaracharya and algebra in the leelevati), and, of course the grammatical rules of Panini, which have been imbibed into the Panini-Backus form

http://en.wikipedia.org/wiki/Panini-Backus_form

OR the mathematics of the Jains, such as the first beezganit samikaran (algebraic expressions), and other similar achievements of the classical and medeival periods such as the Bakhshali approximation for computing square roots:
http://en.wikipedia.org/wiki/Methods_of_computing_ square_roots#Bakhshali_approximation
and, of course,

Aryabhatta:
http://en.wikipedia.org/wiki/Aryabhata

Varahamihira:
http://www-gap.dcs.st-and.ac.uk/~history/Mathemati cians/Varahamihira.html

Bhaskara:

And so he did. But he did it 500 years later.

Your argument was that Muslim architecture was in most part due to their policy of leaving societal elites in place, including architects, during the conquest. You go on to support this argument by pointing to the careers of two Ottoman architects Sinan and Mehmet Aga, and claiming that most of the mosques in Istanbul were built therefore by Christians. From this you draw the conclusion that muslims in the 11th century did not have the mathematical skills required to build large domes in the 11th century.

Your argument fails in a number of respects:

* The architects you reference flourished some 700 years after the first Muslim empire
* They were both active in a country that was not part of the Muslim Empire
* The Ottoman empire had been established for 200 years by the time of Sinan's birth, so he was not conquered
* Both architects were trained by the Ottoman army, so their skills were not acquired before a Muslim conquest
* Both architects were converts to Islam, not Christian as you state.

In addition, Islamic mathematicians were intrigued by the properties of Spheres, see, for example the work of Al Sijzi, who was active in exactly the time frame you claim Muslims were mathematically ignorant: http://www-groups.dcs.st-and.ac.uk/~history/Biogra phies/Al-Sijzi.html

Google: "Feynman mathematics"

A summary of Richard Phillips Feynman

Amazon search for Richard Feynman

--
Mod +1 informative -5 Karma Slut

Évariste Galois is the immediate, obvious choice.

Of course Albert Einstein would probably be in the library, but it's worth making sure there's a good biography that explains his struggles as a child, his annus mirabilis, how his Nobel was for the photoelectric effect, what E=mc^2 and relativity really are, how he was invited to be PM of Israel, etc.

I suppose it's entirely appropriate for 5th and 6th graders to know there was indeed a real Nicholas Flamel.

Another fascinating biography is that of Thomas Midgley, the poor soul who came up with three ideas that seemed brilliant at the time: leaded fuels, CFCs, and a system of ropes and pulleys in his bed that strangled him.

And what middle-schooler would not appreciate the toilet humor in the life of Tycho Brahe, so concerned for court etiquette that he let his bladder clog and kill him?

the submitter seems to have misplaced the incredulity. the important thing is that other mathematicians are amazed that someone would throw around important parts of the proof, not wait for credit and leave it to others to write it up. then again, knowing perelman they are not incredulous.

in mathematics, the trend has mostly been to keep the insights of a big result under wraps until the proof is written down properly and checked for bugs. that is the way to get yourself into the hall of fame. it is almost certain among mathematicians that fame is valued far more than money. money gets you graduate students, but mathematicians mostly think by themselves. fame gets you a theorem, or better yet, a chapter in the textbooks 400 years from now.

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Alan Turing devised most of the theoretical basis for computers in mathematics, but all the modern computers that we use are called Von Neumann machines for a reason.

Alan Turing devised most of the theoretical basis for computers in mathematics, but all the modern computers that we use are called Von Neumann machines for a reason.

I don't see how, unless the systematic errors are of such low magnitude that they're negligible in practice anyway.

Depends on the level of random errors and the statistical sampling that's used. Besides, "negligible in practice"? I'd prefer to leave no tamper margin, not just negligible tamper margin.

If you assume more realistic fraudsters, who weigh the chance of getting caught against the probability that they'll affect a race, what you'll really have is no fraud (of the sort we're discussing here).

If I was a very malicious person, what you'd do is allow the electronic systems to gain credentials, and then slowly reduce the quality checks in the crosscheck to allow the random error rate to creep upwards. So long as you stay under the crosscheck error rate, there's zero risk. How can something be "suspicious" when it's identical to a nonfradulent election?

That is, imagine the electronic voting system compares to the hand count to 1 in 1000 over 10 years of elections. The malicious person simply makes it so that the electronic counting outputs a result that is different from what it actually counted by 1 in 10,000. It'd take a very, very long time to notice that tampering. Then, of course, when things aren't noticed after two or three years, you work to reduce the quality of the crosscheck, allowing your tamper margin to go up.

This is assuming a simple paper receipt that can't be tracked to actual electronic votes: that is, the "paper counting" process is separate from the "electronic counting" process. This is the bad portion I'm talking about.

Registration fraud offers a much better return for the investment.

Sure. That doesn't mean I'm not going to worry about direct vote tampering. Someone else can worry about improving registration procedures.

And how do you ensure that the voter can't be associated with the ID? The ID would have to be invisible to the voter, but available to the vote counter.

How can you ensure the voter can't be associated with a ballot? They still have fingerprints on the ballot, for instance.

The ID would just be a random number - just to associate an 'electronic vote' with a 'paper vote' to link the two counting systems. There'd be no information in the system about who the voter was which placed each 'electronic vote'. While I guess you could, I dunno, do a forensic analysis of the system or something and figure it out somehow, you could conceivably do that with a paper receipt as well. In fact, the paper receipt would be a heckuva lot easier to track.

The real concern would be trying to keep the ID invisible to voters, so that they can't prove their vote (although to me, this is less of a concern) - and that you could do by having the paper be special - revealing the ID with a UV lamp, for instance.

That would mean no nice touch screen, no easy-to-use step-by-step interface, etc

Er? No it wouldn't. I could implement those things on bare metal in less than a month. This is a very simple system. It's essentially a state machine - which means just a bunch of flip flops. The only reason it's being implemented in embedded systems right now is because Diebold is extremely lazy and cheap.

If we're going to talk about that, we should begin by discarding plurality voting and use a system that doesn't disenfranchise anyone who isn't a fan of the two most popular parties.

There is such a thing as a fair count. There is no such thing as a fair voting system. Arrow's Paradox.

Sources... err, conversation with Dr. McKinna (who teaches the HCI course here): http://www.dcs.st-and.ac.uk/~james/

Apparently Helvetica was originally created for use by the Swedish railway, as they needed a font that would be easily readable on signs. As such, I'm told, it is ideally suited for use in small sections which need high visibility, while Times is better suited for large sections of text. So, for example, Helvetica is ideal for nice clear headings, while Times makes for easier to read article text...

Not sure about how being an electronic display changes that - is this a reading angle issue, contrast or resolution, do you know?

Correct me if I'm wrong but Einstein worked in the Bern patent office (see eg http://www-groups.dcs.st-and.ac.uk/~history/Mathem aticians/Einstein.html). Not in the USPTO.

I wish some of you would remember that this 'ere intarweb is global ... there are several patent offices. EPO, UKPO, ARIPO, ... if you mean USPTO then please say so.

>> "There have at least at some point in history been some brains in the patent office."

You're right. I used to work at the UKPO ... there are some extremely intelligent people working there! Not so many since I left of course ;0)>

I did go there --- it's a great place (and the bright red gowns are no longer compulsory, although you get free entry to the castle if you wear your gown). I did first year astronomy before realising that my maths weren't up to it and switching to comp sci; St. Andrews has some genuinely decent telescopes despite being at sea-level in a built up area. The Greg is deeply impressive to go and see. It's amazing just how big it is.

For those who don't know, St.Andrews is the third oldest university in the UK, after Oxford and Cambridge; it was founded in 1413, and totally dominates the town. (The university owns most of the town centre.) Going there is an experience totally unlike any other university in Britain... I had a room in a hall of residence five minutes walk from the town centre, perched high on a cliff top overlooking the North Sea. Great view.

Unfortunately, like Cambridge, St. Andrews has suffered from negative publicity as a result of its taking occasional pupils from failing schools and admitting them with A level scores which would not normally allow a student to be admitted. But at least it meant that some of the Windsors got access to higher education, so perhaps the policy is defensible.

Actually, things have changed. Until very recently, British students got their tuition fees paid by the state. Not long ago, however, the British parliament voted to make them pay a proportion --- but the Scottish parliament didn't. So students who go to a Scottish university get their tuition fees paid for them. As a result, all the Scottish universities have been inundated with students, and as the highest-prestige university in the country, St.Andrews can now basically name their price.

That doesn't explain Prince William, however, who is by all accounts not very bright.

So many cultures discovered / realised / deduced things that western eurpoeans had to discover / realise / deduce again later .

The early Indian astronomers are largly forgotten but around 500AD a guy called Àryabhata taught that the earth is a sphere and rotates on its axis, and that eclipses resulted from the shadows of the moon and earth.

If you are interested the Archaeogeodesic achievements of the Ancients then that whole site is a good reference : http://www.jqjacobs.net/astro/aegeo.html

The Islamic scholar Abu Arrayhan Muhammad ibn Ahmad al-Biruni probably read Àryabhata's works 500 years later, he certainly wrote of Indian astronomy in his work "India". This is the same al-Biruni who calculated the radius of the earth to be 6339.6 km using the angular incidence of shadows.

The Indians did more than invent 0, they contributed much of the numerals which we often mistakenly label Arabic in origin, al-Biruni writes : "What we [the Arabs] use for numerals is a selection of the best and most regular figures in India."

Ancient true black African contributions are a little less well documented, the writings struggling to survive the 5000 years necessary, even if someone bothered to patent "I have discovered how to make a rotating disk from three pieces of wood such that they can aid in transporting goods", but it's legacy lives on in your mouse : the wheel. As well as the agricultural revolution, copper, tin, bronze (the ore for which was transported from Asia & Syria), the potters wheel ("the first really mechanical device").

I, for one, thank our black African ancestors, our Islamic discoverers (one of whom even made a pin-hole camera using a whole room, it might have been al-Biruni but I can't find a cite !) and our Indian scholars.

Even today we can't even get the history of science right. The NYT recently published a story with the summary : Robert P. Crease, a member of the philosophy department at the State University of New York at Stony Brook and the historian at Brookhaven National Laboratory, recently asked physicists to nominate the most beautiful experiment of all time.

I here's a non-NYT link to the list :
http://physics.nad.ru/Physics/English/top10.htm

See what's number 2. Pfft, he didn't even do that demonstration, let alone discover the phenomena.

The Belgian-Dutch mathematician, Simon Stevinus, did the demonstration in 1586.

Ironically, the article does have a great lesson : "he [Galileo] had demonstrated the importance of taking nature, not human authority, as the final arbiter in matters of science."

So many cultures discovered / realised / deduced things that western eurpoeans had to discover / realise / deduce again later .

The early Indian astronomers are largly forgotten but around 500AD a guy called Àryabhata taught that the earth is a sphere and rotates on its axis, and that eclipses resulted from the shadows of the moon and earth.

If you are interested the Archaeogeodesic achievements of the Ancients then that whole site is a good reference : http://www.jqjacobs.net/astro/aegeo.html

The Islamic scholar Abu Arrayhan Muhammad ibn Ahmad al-Biruni probably read Àryabhata's works 500 years later, he certainly wrote of Indian astronomy in his work "India". This is the same al-Biruni who calculated the radius of the earth to be 6339.6 km using the angular incidence of shadows.

The Indians did more than invent 0, they contributed much of the numerals which we often mistakenly label Arabic in origin, al-Biruni writes : "What we [the Arabs] use for numerals is a selection of the best and most regular figures in India."

Ancient true black African contributions are a little less well documented, the writings struggling to survive the 5000 years necessary, even if someone bothered to patent "I have discovered how to make a rotating disk from three pieces of wood such that they can aid in transporting goods", but it's legacy lives on in your mouse : the wheel. As well as the agricultural revolution, copper, tin, bronze (the ore for which was transported from Asia & Syria), the potters wheel ("the first really mechanical device").

I, for one, thank our black African ancestors, our Islamic discoverers (one of whom even made a pin-hole camera using a whole room, it might have been al-Biruni but I can't find a cite !) and our Indian scholars.

Even today we can't even get the history of science right. The NYT recently published a story with the summary : Robert P. Crease, a member of the philosophy department at the State University of New York at Stony Brook and the historian at Brookhaven National Laboratory, recently asked physicists to nominate the most beautiful experiment of all time.

I here's a non-NYT link to the list :
http://physics.nad.ru/Physics/English/top10.htm

See what's number 2. Pfft, he didn't even do that demonstration, let alone discover the phenomena.

The Belgian-Dutch mathematician, Simon Stevinus, did the demonstration in 1586.

Ironically, the article does have a great lesson : "he [Galileo] had demonstrated the importance of taking nature, not human authority, as the final arbiter in matters of science."

Paolo Ruffini made extremely significant contributions to this problem before Abel was even born, only to be largely ignored by the leading mathematicians of the day:

http://www-groups.dcs.st-and.ac.uk/~history/Mathem aticians/Ruffini.html

Are you at all familiar with the theory of general relativity? True, it's only been around for about a hundred years, but it's pretty well accepted these days.

The upshot of the whole thing is, any frame of reference can be taken as stationary (motionless) and the universe continues to make sense. Now, this doesn't mean that the earth has sufficient gravity to drag the sun around all over the place, however, within any bounded system, the motion of the unaccelerated objects within that system should be able to be accounted for (from any frame of reference) from inertia and sources of gravity. Someone correct me if I'm wrong here.

So, according to Einstein, you can take the earth as a stationary object and speak of the sun as moving around it. Don't like that? Argue with Einstein, not me.

Further, even in Newtonian physics, the Earth doesn't properly revolve around the sun, but the earth and the sun both move around a common center. That's forgetting the other planets, asteroids, comets, galaxies, etc., which would, of course, complicate things.

Besides, what does "around" mean?

In just a short 100 years since people really started thinking seriously about computation, the whole science has progressed to the point that it is a well-understood field (well, maybe not to freshmen).

Make that 200 years - Many concepts were introduced by mathematicians such as Euler, Fourier, and Laplace, to name but a few.

A more detailed list

In just a short 100 years since people really started thinking seriously about computation, the whole science has progressed to the point that it is a well-understood field (well, maybe not to freshmen).

Make that 200 years - Many concepts were introduced by mathematicians such as Euler, Fourier, and Laplace, to name but a few.

A more detailed list

In just a short 100 years since people really started thinking seriously about computation, the whole science has progressed to the point that it is a well-understood field (well, maybe not to freshmen).

Make that 200 years - Many concepts were introduced by mathematicians such as Euler, Fourier, and Laplace, to name but a few.

A more detailed list

In just a short 100 years since people really started thinking seriously about computation, the whole science has progressed to the point that it is a well-understood field (well, maybe not to freshmen).

Make that 200 years - Many concepts were introduced by mathematicians such as Euler, Fourier, and Laplace, to name but a few.

A more detailed list

Of course, India has managed to produce one of the most oddly brilliant mathematical geniuses of all time Srinivasa Aiyangar Ramanujan.

Being a 1st world country does not give you any monopoly on intelligence. Generally speaking (though the US is a strong counterpoint to this) your educational system is better. But I wouldn't go discounting Indians who've gotten an MS in mathematics in their own country. The books needed to learn it aren't exactly expensive.

Everything is predictable scientifically. It's just that there's too many variables to do it practically

An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it (...) for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes

There has recently been proposed a limit on the computational power of the universe, ie the ability of Laplace's Demon to process an infinite amount of information. The limit is based on the maximum entropy of the universe, the speed of light, and the minimum amount of time taken to move information across the Planck length, and the figure turns out to be 2130 bits. Accordingly, anything that requires more than this amount of data cannot be computed in the amount of time that has lapsed so far in the universe.

It is Lorentz, but not the same Lorenz (as it's usually spelled) of "Lorenz attractor." Lorentz was a contemporary of Einstein. Lorenz is a meteorologist and mathematician who discovered the Lorenz attractor from weather research in the 1960s.

Yea, look what this guy did (or didn't)

Ooops!

garcia: I'm not certain of your position on this. I hope you don't think your views ("What American workers need to do is not allow their personal lives to intermingle with their daily work grind.") should be adopted by everyone. I don't think people should be forced to associate outside working hours but I think they should have the right to do so if they wish. My situation may be relatively unique (or perhaps not) but I don't have a daily work grind; even though this is not the legal arrangement, I view myself as an "independent contractor" and I consider my work to be for my benefit (and the benefit of my employer). I could "work" 15 hours per week (which almost never happens) or 70-80+ hours per week and my employer would not know the difference; of course, I am on a modest salary (over $80K) and I "work" all the time. This is not me but his description ("I like to lie down on the sofa for hours at a stretch") kind of fits my "work."

It was not the Greeks, however, who put it all together. According to this interesting article it was the Indians and perhaps the Chinese who concocted the place value system.

The Arabs of course are the ones who maintained this knowledge throughout the death of the Roman Empire and brought the place value system to Europe.

Somewhere, perhaps in a paper from the Santa Fe Institute, I read an exchange between a physicist and an economist. The economist derided the physicist saying that a career in physics did not last much beyond the physicist's 30th year. The economist went on to ask the physicist what he'll do after his 30th birthday. The physicist replied he'd likely become an economist

Sorry to reply to myself, but a search for Fermat's Last Theorem in Google returns this URL as the first result, and it mentions the proof I was talking about right at the end:

http://www-groups.dcs.st-and.ac.uk/~history/HistTo pics/Fermat's_last_theorem.html

Either information exists or it doesn't.

Say that we have evidence that information does not exist. Then, it can only be expressed through information.

However, if there is evidence that information doesn't exist, then the only real explanation is that we lack the proper language to express that information. Thus, with no proper language to adequately express itself, information appears to not exist.

This reminds me of an anecdote about the famous mathematician G. H. Hardy (it's been credited to others as well):

Hardy once said that he could prove anything if it given a contradiction to begin with. McTaggart denied the consequence: "if 2+2=5, how can you prove that I am the pope?" Hardy replied: "if 2+2=5, 4=5; subtract 3; then 1=2; but McTaggart and the pope are two; therefore McTaggart and the pope are one."

In other words, Hardy argued, and most philosophers would agree, given one false idea or inconsistency you can prove anything.

More on Ramanujan at St. Andrews
Also at physorg.
It all deals with the Partition function.

The Abel prize was introduced as a sort of "Nobel Prize of math" where people are rewarded for results and achievements that have shown themselves to be of lasting value in the field. Alfred Nobel did not want a Nobel Prize in math since he himself saw little scientific value of math! The most prestigious prize in math before the Abel came into being is the Fields medal, but this prize is only given to younger mathematicians (belove the age of 40) that has made break-through results and show promise for the future. The Fields medal is handed out every 4 years while the Abel is handed out every year (first prize was handed out in 2003).

It would have been ironic for Abel if he were to know that such a huge money prize is to be given out in his name, when his whole life he had to live in poverty and fight to get time and money to do his scientific work. The irony of Abel's life is also that Abel himself finally got a professorship in Berlin; but too late, the letter was sent to him two days after his death.

This great practically self-taught Indian mathematician might have said differently.

Also, a brief look into the history of mathematics will reveal a decimal system in use in India around 2100BC, the development of theories of a solar-centric solar system, and pi around 500 AD, and tangible proof of the development of zero and negative numbers around 650-ish AD (the 7th century, and yes, this is a huge accomplishment nit-wit). Additonally, the term sine is derived from an Indian word, as trigonometry originated there, though you likely never made it through algebra.

The contributions made by the people of the Indian subcontinent are far from trivial. Sounds like someone also needs a history lesson.