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Good math videos
Posted: 22 November 2011 07:56 PM   [ Ignore ]   [ # 31 ]
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How to Catch a Thief! - Scam School by Brian Brushwood.

SPOILER for the dial-up users: [ This magic trick sets up a drama with the participants numbers 1, 2, 3 each stealing a valuable.  The magician looks away as they do, and must figure out who has which valuable.  The magician gives them a few instructions, that have them perform some math (subtraction), and the result tells the magician were two of the valuables are.  Nearly fool-proof, but it has strict instructions needed to pull-off the illusion. ]

[ Edited: 22 November 2011 08:07 PM by jump_in_the_pit ]
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Posted: 13 December 2011 09:13 PM   [ Ignore ]   [ # 32 ]
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Physicist Edward Witten explains the history of modern physics and culminates with String theory.  He describes the mathematics of String theory as having “miraculous” abilites and it knows more about nature than humans do.

Witten hopes to find new particles at CERN.  These are his comments a year after CERN opened.  He doesn’t expect black holes, but only minuscule ones that do no harm if they appear.  He talks about other science projects, trying to detect dark matter.

Interview with Ed Witten on the Physics of the LHC

Spoiler for Dial-up users/notes: ((Maxwell’s equations said that light would move at the same speed regardless of the speed of the observer, Michelson and Morley tested the speed of light.  When Einstein’s Relativity it progressed this idea.  When according to classical physics the electron would collapse into the nucleus in about a millionth of a millionth of a second, physicists know that classical physics was wrong, that’s when Bohr came along in 1913.  Lots of discoveries and progress was made in the 1910’s.  The modern quantum ideas came in the 1920’s.  [7:40]Technology was advanced enough that they could test their ideas at that time as well, this was an amazing convergence of technology and intellect.  [8:20]In 1925, Davisson and Germer were able to observe the direction of an electron beam that was shined on a crystal, this allowed them to see particle versus wave behavior.  The technology came from television picture tubes (Cathode Ray Tubes).  ))

Edward Witten on modern physics I/V

Spoiler for Dial-up users/notes: (([00:15]Paul Dirac did most of the early work of relativistic-quantum mechanics.  When physicists took their photo plates up to the tops of mountains not only did they see protons but also anti-matter.  When matter and anti-matter collide they eliminate each other.  [03:50]There were a long chain of Nobel prizes awarded for the work on quantum field theory, which combined quantum with special (not general) relativity.  [04:15]In the 1930’s it became clear that general relativity and quantum couldn’t be combined in any obvious way.  [04:20]The non-linear mathematics that Einstein needed for general relativity simple doesn’t work well in quantum theory.  [04:50]So quantum theory, without relativity, solved it.  But adding relativity into the situation made things worse.  [05:10]The Nobel prize for Feynman, Schwinger, and Tomonaga, in about 1950 worked on the problem of why the electron didn’t spiral into the nucleus when including special relativistic quantum theory.  But general relativity still didn’t work with quantum theory, and that is what is understood today, so some part of it needs to be modified.  [10:36]Italian physicists Regge, Gabriele Veneziano, Sergio Piero Fubini, Virasoro, and many foresaw how they needed more and more energy to discover more and more particles in an accelerator.  The wanted an equation to describe the mess of discoveries.  The Vietciano formula was discovered, and physicists are still studing what the equation meant, moving beyond Vetciano’s understanding.  This leads to the theory that each particle can be represented by a vibration on one basic string. ))

Edward Witten - String theory 2/5

Edward Witten: 70 minutes of string theory (transcription)

Spoiler for Dial-up users/notes: (([00:10]In 1938-1964 physicists began to study string theory.  [05:43]Three crucial discoveries in the early period from ‘68-‘74.  Veneziano only described half of the particles in the world of strong interactions, not the ones that most people know.  A new structure had to be developed called Supersymetry.  Two other discoveries made String theory go into an eclipse, the progress of other theories made string theory seem unnecessary for particles of strong interaction.  [07:55]There was a new theory about building the strings out of quarks. [9:18]A small group of fans Juralsharts, Micheal Greene, Lars Brenken, and a handful more couldn’t believe that it was just a dead end when it had so miraculously held on until then, they kept it from eclipsing.  [10:00]Olive, Shirk, Schwartz then had the idea that a quantum theory with excess particles wasn’t needed the strong interaction of particles but was needed for reconciling general relativity. [12:21]String theory develops Supersymmetry in space and time and so string theory was revived with a new application of reconciling quantum theory with gravitational theory. [13:02]So, by the early ‘80’s it was clear, but it was know that there was more to String theory.  [13:55]First discovered in the ‘50’s and then integrated into quantum theory in the ‘60’s, that parody violations (that nature doesn’t look the same from the left side compared to the right side for particles of weak interaction) could be explained in String Theory, [14:35] among other things but not the most microscopic details.))

Edward Witten - String theory 3/5

Spoiler for Dial-up users/notes: ((1994-95 Witten found the the five theories of string theory, although they were an important advance over when there were infinite theories, were too many for one universe, and so Witten found that there was really only one.  People didn’t like extra dimensions, but they turned out to be [08:22]they turned out to be a lessing in disguise.  It had a new mission, not merely to describe the weak interacting particles, but to describe everything.  [07:45]You need the extra dimensions of freedom to vibrate the strings, that gives it they ability to form all the variety of particles that were being seen in particle accelerators.  [09:15]The two-dimensional projection of a three-dimensional image is missing some information because you can’t see all the way around the object.  Holograms have three dimensions. ))

Edward Witten - String theory 4/5

Spoiler for Dial-up users/notes: (( [00:18]Witten believes that String theory is on the right track.  It miraculously hangs on.  He tried to prove that it was inconsistent, that wound up proving it.  He believes that String theory knows more than humans do about physics, and he wants to understand.  By 1997, techniques advanced enough to realize that the expansion of the universe is accelerating.  The energy of the vacuum of space is positive, not zero.  The energy density is roughly the rest mass of one atom per cubic meter.  Einstein predicted this, but rejected it because there was no evidence in his day.  [3:30]So as the universe expands, the objects that we can see today will not be there in the future, and so there were probably more object within vision in the past.  [09:10]Supersymetry is, at least, an important facet of String theory.  [10:30]When ions are collided, thousands of particles are produced.  Even though the equations that describe this exist, they are hopelessly hard to solve.  String theory offers another solution, where comparing the theory where gravity is not important, and the theory where gravity is important, [11:05]and modeling the droplet produced in a heavy ion collision as an evaporating black hole.  So this is a striking success, where String theory knows about equations, and gives physicists remarkable insights in quantum phase transitions, and dense matter, and there are other insights.  [12:09]Critics say String Theory is too ambitious, that we can’t have the experimental data needed to work out the details of the theory, and they might be right.  [13:02]But Witten thinks that it has miraculously held together, it gives us too many good ideas about physics and geometry, it forces gravity upon us where quantum denies gravity, and [13:34]“it qualitatively gives us in an astonishingly effortless way, a good rough draft of the elementary particles.”)) 

Edward Witten - String theory 5/5

[ Edited: 14 December 2011 10:06 AM by jump_in_the_pit ]
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Posted: 29 December 2011 08:11 PM   [ Ignore ]   [ # 33 ]
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Archimedes of Syracuse was an ancient Greek and a great scientist.  Some of his greatest works include The Method, The Stomachion, On Floating Bodies, and On Sphere and Cylinder,  these are some of his mathematical treatises.  He lived in the third century B.C.E. and being Greek he did his math in the traditional way: he did geometry rather than the analytic math.  In his book The Method, he took several steps towards discovering modern calculus!  Because he did it 2,000 years before Newton and Liebnitz, because he did it the hard way using the Greek method of exhaustion, because he wrote so many mathematical books and is credited with so many engineering works, he is regarded as one of the greatest scientists the world has ever known.

The way that ancient writings survive, so that we can read them today, is by copying them.  The reason that a book can survive for hundreds of years is because it is written on parchment (animal hide) rather than paper.  A palimpsest is a parchment book that was erased, and the pages re-used to write a new book, parchment is tough enough to survive this scraping process, but scraping removes the ink.  Today the Archimedes Palimpsest is a goatskin parchment copy of some of Archimedes’ greatest books, it is the world’s only surviving manuscript of some of those books, it was lost for nearly a century, and there has never been an English translation of Archimedes directly from a Greek manuscript which includes his all-important geometry diagrams.  But on April 13, 1229 C.E. in Jerusalem Johannes Myronas erased the Palimpsest from history, the value of the codex reduced down just to the parchment pages it was written on, then he cut it in half, one half being lost, and wrote a Christian prayer book on top of the surviving half.  Since that time the Palimpsest has been damaged by extensive mold, by fire, pages lost, and the ravages of time… now Archimedes is just a ghost of what he was when the Palimpsest was first written in the Byzantine Empire, probably in the late tenth century at Constantinople.  There is no other more valuable source for Archimedes greatest works in the world.  There are other books in the Palimpsest also, like Hyperides’ speeches.  To read the ghostly writing, it takes special imaging and lighting techniques to read the under text.

Through the generosity and foresight of the anonymous owner of the Archimedes Palimpsest (who purchased it a Christy’s auction house in New York for two-million dollars), and the works of many, there is a rescue effort happening to recover what’s left of Archimedes.  It is held by William Noel, curator of manuscripts and rare books at the Walter’s Art Museum in Baltimore, MD, and the publications are being done with Reviel Netz professor of classics at Stanford University, and others.  They have just published the second volume of their scholarly work on imaging and restoring Archimedes, published through Cambridge.  They work to restore text that hasn’t been seen in over seven-hundred years. They have a bank of their images of the Palimpsest on-line too.

[2:18]“There’s a philosopher called [Alfred North] Whitehead who very famously said that Western philosophy is nothing but a series of footnotes to Plato.  I’m going to make the case very briefly, that Western science is nothing but a series of footnotes to Archimedes.  What do I mean by this.  What I mean is that Archimedes is the guy who first got abstract problems and attached them to the physical world.”

[6:37]“Now, if you can apply abstract physical models to the physical world, and if you can calculate curves, eventually you can send a rocket to the moon, which is why Archimedes is the most important scientist who ever lived.”

The Archimedes Palimpsest: Google TechTalk 1 (1:04:04) (Scroll down below the middle (60%) of the page.)

Now, in addition to the pop book, there is a two-volume scholarly publication also.

“To coincide with the exhibition’s opening, two volumes, each priced at $125, of a projected scholarly five-part series documenting the findings of the Archimedes Palimpsest Project will be published for the Walters by Cambridge University Press. The first volume surveys the Palimpsest’s history and the projects’ scientific findings. The second volume provides transcriptions of the hitherto unknown texts contained in the Palimpsest, accompanied by facsimiles of the processed images from which these transcriptions were constructed.”
Walters Art Museum: Lost and Found: The Secrets of Archimedes

Parchment and Pixel: Blog of Will Noel

NOVA beta: Inside the Archimedes Palimpsest Posted 09.30.03

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Posted: 17 September 2012 02:25 PM   [ Ignore ]   [ # 34 ]
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In Richard Feynman: Relation of Mathematics and Physics (Part 4/6):

[02:13] “But Newtonian laws were wrong.  There’s no forces, its all a lot of baloney, the particles don’t have orbits, and so on…  Yet the analog, the exact transformation of this principle about the area, the conservation of angular momentum is true for the atomic motions, in the Quantum Mechanics, and is still, as far as we can tell, is exact.  So we have these wide principles which sweep across all the different laws, and if one take too seriously his derivations, and feels that this [an initial principle] is only valid because this [a second principle] is valid, you cannot understand the different branches of physics.  Someday, when physics is complete, then maybe with this kind of argument we can know all the laws we can start with some kind of axioms, (and no doubt somebody will figure out some particular way to do it) and then all the deductions will be made.”

[09:22]“If these various alternatives are mathematically not exactly equivalent, and if, for certain ones, there are different consequences than for others, that’s perfectly alright then because we have only to do the experiments to find out which way nature actually chooses to do it.  Mostly people come along and they argue philosophically they like this one better than that one, but we have learned from much experience that all intuitions about what nature is going to do FAIL, it never works.  What one has to do is just work out all the possibilities and just try all the alternatives.”

Each one is just a few minutes long.

Richard Feynman: Relation of Mathematics and Physics (Part 1/6)

Richard Feynman: Relation of Mathematics and Physics (Part 2/6)

Richard Feynman: Relation of Mathematics and Physics (Part 3/6)

Richard Feynman: Relation of Mathematics and Physics (Part 4/6)

Richard Feynman: Relation of Mathematics and Physics (Part 5/6)

Richard Feynman: Relation of Mathematics and Physics (Part 6/6)

[ Edited: 21 September 2012 07:51 AM by jump_in_the_pit ]
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