August 2014 - mathfun@mailman.xmission.com

[math-fun] Bogus Nobel prizes
by Warren D Smith 27 Aug '14

27 Aug '14

It seems that many Nobel Prizes were awarded that, in retrospect, were very bad decisions. It looks like the Physics & Chemistry prizes are pretty much free of embarrassment, but the Medicine, Peace, and Economic prizes include many howlers. [The Peace prize to H.Kissinger & Le Duc Tho in 1973 jointly, was amazing (Le Duc Tho actually refused it!) as was its award to B.Obama.] Anyway, here's a list of Medicine prizes: 1904 to Ivan Pavlov re digestion. Unfortunately Pavlov's main discovery was refuted in 1902 by EH Starling & WM Bayliss, and the refutors by discovering the first hormone, "secretin," actually accomplished something far more important (as well as correct this time), but they didn't get a prize... 1923 to Banting & Macleod for discovering the existence of insulin. But in 1962 the Nobel prize committee announced it had made a mistake since "Macleod had taken no active part in the work." 1926 to Johannes Fibiger for "discovering" that the cause of cancer was worms. He was totally wrong. 1927 to J.Wagner-Jauregg for "curing" dementia caused by syphilis by intentionally infecting patients with malaria. The patients that he cured, were defined to be cured, by him. 1949 to Antonio Egas Moniz for inventing the "revolutionary therapy" of lobotomy, aka intentional brain mutilation. (Which also was later used to "cure homosexuals.") 1952 to Selman Waksman for discovering streptomycin. Actually it was Albert Schatz, a doctoral student of SW's. They both were credited as discoverers on US patent and Schatz was 1st author of the paper, but Waksman grabbed all the royalties of about $350K in secret while giving Schatz essentially nothing (a "gift" of $1500) plus explained that Schatz had nothing to do with it and was only included on the paper & patent as a "courtesy." There then was a lawsuit, and Schatz was recognized as co-discover and awarded a 3:10 split of royalties with Waksman. This all happened before the Nobel award. 1997 Stanley B. Prusiner for "prions" and diseases they cause. However there remains some substantial fraction of scientists who do not believe prions really exist, so let's hope the Nobel Prize committee got this right. The prion detractors feel that the Award may have shut down anti-prion research, which, if prions really do not exist, was a very bad thing. It's very hard to prove it was prions and not anything else, and Prusiner's proof was necessarily not very convincing. However, based on this 2004 paper http://www.ncbi.nlm.nih.gov/pubmed/15286374 and several followup papers, where they synthesized prion protein than showed it caused disease, I think Prusiner must have been correct. So the Nobel committee got lucky on this one!

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[math-fun] Holometer (physics expt, hype for which pointed out by H.Baker)
by Warren D Smith 27 Aug '14

27 Aug '14

The whole mathematics underlying the whole holometer experiment (in the paper originally proposing it) is bullshit as I showed here: https://dl.dropboxusercontent.com/u/3507527/DistNoise.html I pointed this out to the holometrists, but mostly they did not want to know. One could, I suppose, argue that the experiment is still worth doing even if the whole mathematics underlying it was wrong. In fact, that was the best response I got.

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Re: [math-fun] Bogus Nobel prizes
by Henry Baker 27 Aug '14

27 Aug '14

The Medicine Nobel Prize committee made up a lot of lost ground with their 2005 award to Dr. Barry Marshall and Dr. Robin Warren of Australia for the activities of H. Pylori. https://en.wikipedia.org/wiki/Helicobacter_pylori The article below appears to be "retrospective ass-covering" at its best; Marshall & Warren had an incredibly difficult time getting funding for their controversial research; Marshall had to give himself H. Pylori gastritis & cure it with an antibiotic to make his point. Are we going to require researchers working on Ebola cures to cure themselves of Ebola? That sounds like a rather high bar for researchers; in particular, a bar far higher than just about any other Nobel field. --- "Bacteria, Ulcers, and Ostracism? H. Pylori and the Making of a Myth" "Medicines purported ostracism of the discovery of H. pylori has achieved a mythological quality. But it isnt true. After appropriate initial scientific skepticism, the hypothesis was accepted right on schedule." http://www.csicop.org/si/show/bacteria_ulcers_and_ostracism_h._pylori_and_t… --- To date, I'm not aware of any apologies by the medical community to their patients for the torture they put their stomach ulcer patients through. At 09:16 AM 8/27/2014, Warren D Smith wrote: >It seems that many Nobel Prizes were awarded that, in retrospect, were very bad decisions. >It looks like the Physics & Chemistry prizes are pretty much free of embarrassment, but >the Medicine, Peace, and Economic prizes include many howlers.

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[math-fun] How The Ancient Egyptians (Should Have) Built The Pyramids
by Henry Baker 27 Aug '14

27 Aug '14

FYI -- https://medium.com/the-physics-arxiv-blog/how-they-should-have-built-the-py… The Physics arXiv Blog on Aug 26 How The Ancient Egyptians (Should Have) Built The Pyramids Modifying square blocks to form dodecagons would have made them easy to roll, say physicists The Great Pyramid of Giza in Egypt is the only one of the seven wonders of the ancient world to survive largely intact. Almost 4000 years old, it is a vast structure constructed from 2.4 million limestone blocks, most about 2.5 tonnes but some weighing in at up to 80 tonnes. These were largely sourced from local limestone quarries. That raises a famous question. How did the Egyptians move these huge blocks into place? One theory is that the blocks were dragged along the sand which offers reduced friction when lubricated with water. But although the Great Pyramid is close to the Nile, many pyramids are not and this would have made the transport of water as big an engineering task as the movement of the blocks. Another theory is that the Egyptians attached quarter circle rockers to the flat surfaces of the blocks effectively turning them into cylinders and allowing them to be rolled. Experiments have shown that this method allows the blocks to be moved relatively quickly with just a few men. But this method also has a disadvantageÂ these cylinders would exert huge pressure on the ground causing considerable damage to roads. Modern estimates of the rate at which the pyramid was built suggest that workers put in place some 40 blocks per day. In that case, even well-engineered roads would have required considerable maintenance. Today, Joseph West at Indiana State University and a couple of pals suggest an alternative method for moving giant stone blocks. Their approach considerably reduces the ground pressure but at the same time allows the blocks to be moved with significantly less effort than dragging. They have even tested the idea to measure the amount of force workers would have had to use to move the blocks. Their idea is remarkably simple. They strap wooden rods to a block, turning its profile from a square into a dodecagon, which can then be moved more easily by rolling. West and co have tested their idea on a scale model consisting of a concrete block the shape of the square prism. This block was 20 cm square, 40 cm long and weighed almost 30 kilograms. They attached a set of three wooden dowel rods to each face of the block transforming its cross-section from a square to dodecagon. Finally, they attached a rope to the top of the block and measured the force required to set the block rolling. Their measurements indicates that the block experiences a coefficient of dynamic friction equal to 0.3, for a steady rolling motion. This would require the crew to apply force of only 0.15 times the weight of the stone to pull a rope wrapped around the block. They go on to calculate that a work crew of around 50 fit men would be required to move a block with a mass of 2.5 tonnes at the speed of 0.5 metres per second. ÂFor full scale pyramid blocks, the wooden ÂrodsÂ would need to be posts of order 30 cm in diameter, similar in size to those used as masts on ships in the Nile,Â say West and co. Of course, these researchers do not address the question of whether there is any evidence that the pyramids were constructed in this way, only that this would certainly seem a good option, not least because of the reduced wear and tear on the thoroughfares to and from the pyramid. Indeed, they say the mechanism would work without a formal, engineered road. ThatÂs an interesting, simple idea that might pique the interest of Egyptologists. Indeed, West and co say this idea, or something like it, needs to be studied in more detail. ÂIt would seem that some variation of rolling the blocks should now be considered to be among the ÂbestÂ and most likely method used to move the stones for the great pyramids,Â they conclude. A project for an Egyptologist with a little spare time. Ref: arxiv.org/abs/1408.3603 : How They (Should Have) Built The Pyramids http://arxiv.org/abs/1408.3603

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[math-fun] We all live in a yellow submarine^H^H^H^H^H^H^H^H^Hhologram
by Henry Baker 27 Aug '14

27 Aug '14

FYI -- http://motherboard.vice.com/read/why-government-researchers-think-we-may-be… Why Government Researchers Think We May Be Living in a 2D Hologram Jason Koebler Staff Writer August 26, 2014 // 06:20 PM EST Operating with cutting-edge technology out of a trailer in rural Illinois, government researchers started today on a set of experiments that they say will help them determine whether or not you and me and everything that exists are living in a two-dimensional holographic universe. It sounds completely off-the-walls insane, but the incongruities between Albert Einstein's theory of relativity and some of Max Planck's discoveries about the nature of matter can only be explained if we're living in a Matrix-style holographic illusion, according to Craig Hogan, director of the Department of Energy's Fermilab Center for Particle Astrophysics. "For thousands of years, we have assumed that space is made of points and lines," he told me. "Maybe that is not rightÂ-it might be made of waves, the way that matter and energy are." In other words, space, and the universe, might not be entirely definiteÂlocations of things might not be completely definite and might be transmitted in quantum bits that vary ever so slightly. He likens it to the idea of "pixels" in a photo. From afar, you see one picture, but if you zoom in far enough, you see tiny points that make up the larger whole. Space, and everything that exists, might be the same, he theorizes. In other words, if you zoom in far enough on matter, on space, to a far-beyond subatomic level, you might see that existence is similarly blurry, and always moving slightly. It's heady stuff. In a paper explaining the theory (embedded below), he writes that "some properties of space and time that seem fundamental, including localization [where things are], may actually emerge only as a macroscopic approximation from the flow of information in a quantum system." If so, that would mean that the "real world is the ultimate 4-dimensional video display." In the paper, he says his team's hypothesis is that space and time are created from tiny bits of information that vary and that the relationship between space and time are created using information processing. So, that's the theory. Now how the hell do you go about testing it? In a lab called the Holometer, which uses ultra high-powered lasers, of course. Fermilab explained it better than I can in a release: Now operating at full power, the Holometer uses a pair of interferometers placed close to one another. Each one sends a one-kilowatt laser beam (the equivalent of 200,000 laser pointers) at a beam splitter and down two perpendicular 40-meter arms. The light is then reflected back to the beam splitter where the two beams recombine, creating fluctuations in brightness if there is motion. Researchers analyze these fluctuations in the returning light to see if the beam splitter is moving in a certain wayÂ-being carried along on a jitter of space itself. So, if the team detects movement, it's possible that the movement is being caused by space not being a completely set thing, in which case, we could be living in the Matrix. Hogan told me that, if we are indeed living in a hologram, "the basic effect is that reality has a limited amount of information, like a Netflix movie when Comcast is not giving you enough bandwidth. So things are a little blurry and jittery. Nothing ever just stands still, but is always moving a tiny bit." Hogan says the team will have initial findings within a year, but that's all they are sure of right now. "We don't know what we will find," he said. The full paper is embedded below: http://arxiv.org/abs/1307.2283

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[math-fun] Proizvolov identity
by Gustavus Simmons 25 Aug '14

25 Aug '14

A Proizvolov arrangment of the 2n integers, 1 through 2n, consists of an arbitrary subset A of n of the integers arranged in increasing order, matched in pairs with the remaining n integers, subset B, arranged in decreasing order. The Proizvolov identity says that Sum/ai - bi/ = n2. Without regard for whether the smaller integer in a pair was in set A or set B, index pairs by the integers 1 through n in increasing order. The other integer in each pair is the one the index was paired with in the Proizvolov arrangment. Call this ordered set C. The only way construction C could fail to be possible is if some Proizvolov pair consisted of two integers, both less than or equal to n. Let x be the largest integer less than or equal to n in A. Assume it is in position i, indexed from the left. Then there are n - i integers less than or equal to n to be placed in ascending order – from the right – in B. But this says the smallest integer that could be paired with an integer less than or equal to n is n+ 1. Therefore construction C is always possible.. Clearly Sum/ci - i/ = Sum/ai - bi/ since at most the order of the summands has been altered. If the Proizvolov arrangement had been the trivial one in which no integer was derranged the sum of the integers in any pair would have been 2n + 1 and the difference would have been 2n - i, where i is the index. Sum(2n - i) = n2 in this case. If ci is not 2n - i + 1, interchange ci with 2n - i + 1 in the pair, say (j, 2n - i + 1), in which it occurs. This cannot affect Sum(ci - i ) since the ci by construction are all larger than n, so the change in the value of ci - i is exactly offset by the change in cj - j. Continue in this way interchanging the ci where necessary to cause the ci to all be 2n - i + 1. Since no interchange affects the sum, the final result is the trivial Proizvolov arrangement and Sum/ai - bi/= n2 as was to be shown. 　　　 Here is an example to illustrate the procedure. Let the Proizvolov arrangment be: 1 3 7 8 9 11 12 15 16 14 13 10 6 5 4 2 The C arrangement will be 1 2 3 4 5 6 7 8 16 15 14 12 11 9 13 10 The first sum preserving interchange needed is for index 4 when 12 and 13 must be interchanged. At index 5, 11 and 12 must be interchanged etc. __________ Information from ESET Smart Security, version of virus signature database 10315 (20140826) __________ The message was checked by ESET Smart Security. http://www.eset.com

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Re: [math-fun] cos(x) = x question
by Leo Broukhis 25 Aug '14

25 Aug '14

Simon Plouffe wrote: > Hello, > > Yes, this is the argument, the length of the proposed approximation > is about the length in number of digits of precision. > Indeed, the Elias (or Levenshtein) codes for 160 and 13 by themselves almost cover the 21 bits of precision, no code space is left for pi or the operations. > Just a coincidence, and there are others, very few can be explained fully. > > > here are a few of them : http://mathworld.wolfram.com/AlmostInteger.html > It used to be there; now it is mentioned here: http://mathworld.wolfram.com/DottieNumber.html > http://fr.wikipedia.org/wiki/Nombre_presque_entier (in french), > > http://en.wikipedia.org/wiki/Almost_integer > Thank you, Leo

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[math-fun] Time Capsule quirks
by Bill Gosper 25 Aug '14

25 Aug '14

One just saved my tush. Time remaining: 26 hours and 59 minutes. ... 26 hours and 2 minutes. 25 hours. 24 hours and 59 minutes. *Never* X hours and 1 minute. Maybe it feared saying "and 1 minutes." But most haunting was the huge blowup of the Time Capsule icon, showing exactly four-and-a-half o'clock on the hour. (Well, conceivably 0900 on a 24 hr dial.) --rwg

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[math-fun] "Proizvolov's identity"
by Gareth McCaughan 25 Aug '14

25 Aug '14

A recent post on the (excellent) blog "Futility Closet" http://www.futilitycloset.com/2014/08/21/proizvolovs-identity/ cites without proof the following theorem: Take the numbers 1..2n. Divide them into two subsets of size n. Write one in ascending order and the other in descending order. Then the sum of |a_i-b_i| is always n^2. This isn't difficult to prove, but the proof I found not-difficult to find isn't terribly elegant. Is there a neat "bijective" proof? (There are two proofs at http://www.cut-the-knot.org/Curriculum/Games/ProizvolovGame.shtml neither of which seems very elegant to me. Both are better than my proof, which proceeds by induction on n.) -- g

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[math-fun] Better Living Through Transcendence
by ho＠alum.mit.edu 25 Aug '14

25 Aug '14

http://hilarie.orman.name/photos/mathathome.jpg Hilarie

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