December 2012 - mathfun@mailman.xmission.com

Re: [math-fun] Antikythera
by Henry Baker 06 Dec '12

06 Dec '12

Thanks, Warren! Simple CF approximations: Mercury/Earth = 6/25, 7/29 Venus/Earth = 8/13, 235/382 Mars/Earth = 15/8, 32/17, 47/25 Jupiter/Earth = 83/7, 261/22 Saturn/Earth = 265/9, 1119/38 Just choosing the denominators of a few of these, I get lcm(9,7,8,13,25) = 163,800 or lcm(29,382,25,22,38) = 57,882,550 So just doing the planets alone would give us a period of at least 163,800 years, and possibly as much as 57 million years. Could we say that the Greeks had already approximated the k-T event at 65 million years ago? :-) At 08:57 AM 12/6/2012, Warren Smith wrote: >Here's some data I got from some random web page >http://www.princeton.edu/~willman/planetary_systems/Sol/ >giving alleged orbital periods in "years." > >Mercury := 0.2408467; >Venus := 0.61519726; >Earth := 1.0000174; >Mars := 1.8808158; >Jupiter := 11.862615; >Saturn := 29.447498; >#Greeks knew the above planets only >Uranus := 84.016846; >Neptune := 164.79132; >Pluto := 248.0208; > >eccentricities are known to only 3-5 figures, relative masses to only 4-5. > >Using continued fractions, you may enjoy spotting near-rational ratios >Venus/Earth=0.61518656 vs 8/13=0.61538461 >Mars/Earth=1.88078307 vs 1057/562=1.88078292

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[math-fun] antikythera device: an ancient computer
by Robert Baillie 06 Dec '12

06 Dec '12

a while back, someone posted a link to this youtube video of the antikythera device made out of legos: http://www.youtube.com/watch?v=RLPVCJjTNgk here is an interesting (58 minute) bbc documentary that explains in more detail how the device actually works, as far as we know today: http://www.youtube.com/watch?v=-rUsgL2VGeU many of the gears had a prime number of teeth. this was very helpful in figuring out what the device was used for, and how it worked. here are several shorter videos that might also be of interest: The Antikythera Mechanism - 2D (8 minutes) http://www.youtube.com/watch?v=UpLcnAIpVRA The Antikythera Mechanism - 3D (4 minutes) http://www.youtube.com/watch?v=L1CuR29OajI Antikythera mechanism working model.mov (4 minutes) http://www.youtube.com/watch?v=4eUibFQKJqI in case anyone passes through bozeman, montana, there is a great computer museum that has a replica of the antikythera device. the museum also has an old ibm 1620 computer, a curta calculator, and many other neat old things: http://www.compustory.com/ note: their rather primitive website doesn't do the place justice! bob baillie

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[math-fun] Antikythera
by Warren Smith 06 Dec '12

06 Dec '12

>Henry Baker: Does anyone here know what the fundamental _period_ of the antikythera device is? I.e., by all reports, this device is a "planetarium in a box". So how many years of simulated time does it take for this device to return to its initial configuration ? If we start the antikythera device in 70 B.C., which appears to be approximately the date of its demise, how far into the future can this device "see" ? --I do not know. However, if my speculation the device was intended by its designer (Archimedes?) as an experimental navigation aid, is correct, then this does not terribly matter. The way you then would want to use such a device, is you would reset it to the truth, whenever you had access to the truth, i.e. whenever your ship came to a place (1) whose location was known, and (2) where they were making accurate astronomical observations -- such as Greenwich. The device then would only need to keep good accuracy during the duration of your sea voyage (<2 months?) which is a precision and math level the Greeks might have been capable of. The Greeks were unaware of Newton & Kepler laws of motion hence tremendous accuracy was not possible, but they were aware of a correction to the "constant speed circular" model which made the speed and radius nonconstant, and they evidently had enough observational accuracy to be confident of the need for that, and the device is known to incorporate a "pin in slot" mechanism which seems intended to cause that effect. If this device had been further developed (which apparently it was not) in concert with astronomical records being kept, then it seems to me it would have been possible, working semi-empirically, for them to get one capable of enough accuracy for useful navigation, at least in principle. Whether that level was ever actually achieved, I do not know. >Let's assume that the device was used on a daily, weekly or monthly basis. Presumably, the position of the wheels would be indicative of the last time it was used. This is essentially equivalent to being able to determine the exact time of an earthquake from the position of the hands of clocks which stopped as a result of the earthquake. --since some parts of the device are missing, corroded, damaged, broken off, I doubt that is possible. Also, related question: using today's computers and data, are we capable of extrapolating 2000 years with enough accuracy to tell this? Here's some data I got from some random web page http://www.princeton.edu/~willman/planetary_systems/Sol/ giving alleged orbital periods in "years." Mercury := 0.2408467; Venus := 0.61519726; Earth := 1.0000174; Mars := 1.8808158; Jupiter := 11.862615; Saturn := 29.447498; #Greeks knew the above planets only Uranus := 84.016846; Neptune := 164.79132; Pluto := 248.0208; eccentricities are known to only 3-5 figures, relative masses to only 4-5. Using continued fractions, you may enjoy spotting near-rational ratios Venus/Earth=0.61518656 vs 8/13=0.61538461 Mars/Earth=1.88078307 vs 1057/562=1.88078292 ... Neptune/Uranus=1.9614081 vs 51/26=1.9615385 Pluto/Neptune=1.50506 vs 3/2=1.5 and 149/99=1.505050505... etc. How many of these are "flukes" vs how many are "real"? One way to tell would be, I suppose, to examine the statistics of partial quotients & compare with Gauss-Kuzmin distribution expected for generic reals. Due to tidal effects presumably the solar system has ratios "closer to rationals" than generic reals. Such rational approximations would have been one thing limiting the accuracy of a Greek device; and other effects like inter-planet interactions, noncircularity, etc. too.

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Re: [math-fun] Can't you follow directions?
by Adam P. Goucher 06 Dec '12

06 Dec '12

> My father's favorite example: a sign that says "No Parking Allowed". > > So, it's OK if you don't park there. But can you park there if you want to? That's an interesting demonstration that our language is non-associative (specifically, No (Parking Allowed) != (No Parking) Allowed). It's also non-Abelian (a truncated triakis tetrahedron is not the same as a triakis truncated tetrahedron). >> I've liked the roundabouts I've used in the U.K., Australia, and >> Boston. But the idea is to turn into the circular flow of traffic >> without stopping. I don't see how they can work if the traffic isn't >> all clockwise (in the U.K., counterclockwise in the U.S.). It's all clockwise if you think of it as six disjoint roundabouts instead of one large compound roundabout. Theoretically, you could assemble these magic roundabouts recursively to produce an even larger clockwise one. http://en.wikipedia.org/wiki/Antoine%27s_necklace Sincerely, Adam P. Goucher http://cp4space.wordpress.com

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Re: [math-fun] Can't you follow directions?
by Adam P. Goucher 06 Dec '12

06 Dec '12

On the other side of the Atlantic, we have a cycle of six mini-roundabouts with radiating roads, one of which fissures into two: http://en.wikipedia.org/wiki/Magic_Roundabout_(Hemel_Hempstead) This is not an individual occurrence, by the way; there are analogous cycles of five mini-roundabouts in Colchester and Swindon. Sincerely, Adam P. Goucher http://cp4space.wordpress.com

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Re: [math-fun] Can't you follow directions?
by Henry Baker 05 Dec '12

05 Dec '12

Video camera-based road sign "readers" have now become commonplace in Europe in BMW's, etc. I wonder what these cameras would make of Gosper's "arrow only" signs? ----- Vauxhall Insignia sports all-seeing front camera system [w/VIDEO] Safety technology has become a major selling point for car shoppers, and a new front-sensing camera co-developed by Vauxhall and Opel will give GM's European brands something to brag about. The new camera, which will be available on the Opel/Vauxhall Insignia beginning early 2009, is located between the wind screen and the rear-view mirror. The camera sees what's ahead at 30 frames per second and uses two processors to both read road signs and tell drivers when they're straying from a lane. The road sign reader works by scanning the road ahead for recognizable shapes and signals, then displaying information like speed limits or no passing zone signs in the digital display in the middle of the gauge cluster. Depending on conditions, the camera can recognize signs up to 100 meters away. http://www.autoblog.com/2008/06/19/vauxhall-insignia-sports-all-seeing-fron… 6. Road sign reader This is the latest in a new generation of safety technology. The new Vauxhall Insignia has cameras which can read road signs and warn the driver of a change in speed limit, allowing them to concentrate purely on the road ahead. http://www.techradar.com/us/news/car-tech/10-life-saving-car-technologies-4… Missed that speed-limit sign? Your GM car could see it for you http://content.usatoday.com/communities/driveon/post/2010/05/missed-that-sp… At 05:52 PM 12/4/2012, Bill Gosper wrote: >You know those black and white traffic signs at stoplights that say, >e.g., "U Turn from left lane only" only the only text is "ONLY" and >the rest is various arrows? Can you top this <http://gosper.org/arrows.JPG>? California has >legalized driverless cars. As a step toward mandating them. > >--rwg

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[math-fun] Iridium & Indium (inside future analogue of light bulbs?)
by Warren Smith 05 Dec '12

05 Dec '12

Iridium is 40x rarer than gold and total world production is only about 10 tons annually. Indium is also pretty rare, but not as rare: 1000 ton annual production. So I think if iridium is a substantial component of solid plastic lighting source then that will not be a useful technology for Average Joe Consumer. I would think you'd want ingredients common enough for million-ton production. If they can remove the need for Iridium and other rare elements, the general concept sounds excellent as a future lighting source. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] New lighting technology breakthrough?
by Henry Baker 05 Dec '12

05 Dec '12

(Full disclosure: my father worked for Ford Motor Co., Edsel Division(!), in the 1950's.) The "Federal Motor Vehicle Safety Standard 108" is online (referenced from Wikipedia), and is a perfect example of too much detail embedding obsolete technology into law. For example, headlights are restricted to 55-70 watts at 12.8 volts. Elsewhere, the brightness is limited in candela. There is a very detailed specification of the abrasion resistance of the headlamp cover, including the size of the abrading grains, or the coarseness of the steel wool. In the 1940's, Edwin Land, the inventor of the Polaroid instant photography, tried unsuccessfully to polarize headlights and windshields in orthogonal axes; he finally gave up in 1947. I estimate that his invention could likely have saved ~10^6 lives during the past 70 years. Billings, B.H. and Land, E.H. "A comparative survey of some possible systems of polarized headlights". J. Optical Soc. of America, 38(10), 819-829, Oct. 1948. The 1948 Tucker had steerable headlights. Steerable headlights were subsequently banned, and precluded the importation of the innovative Citroen SM into the US until its steerable headlights (& many other features) could be disabled. The US auto lighting regulations also discouraged "non sealed beam" headlights, which completely stalled vehicle lighting innovation for 30-40 years. These obsolete regulations were used (successfully) by the U.S. auto manufacturers to keep out foreign cars and protect domestic manufacturers. --- Here are the specifications for the vehicle light colors, referencing the CIE color chart: Red. Red is not acceptable if it is less saturated (paler), yellower, or bluer than the limit standards. Yellow (Amber). Yellow is not acceptable if it is less saturated (paler), greener, or redder than the limit standards. White. White is not acceptable if its color differs "materially" from that of CIE Source A. Red. The color of light emitted must fall within the following boundaries: y = 0.33 (yellow boundary) y = 0.98 - x (purple boundary) Yellow (Amber). The color of light emitted must fall within the following boundaries: y = 0.39 (red boundary) y = 0.79 - 0.67 x (white boundary) y = x - 0.12 (green boundary) White (achromatic). The color of light emitted must fall within the following boundaries: x = 0.31 (blue boundary) y = 0.44 (green boundary) x = 0.50 (yellow boundary) y = 0.15 + 0.64x (green boundary) y = 0.38 (red boundary) y = 0.05 + 0.75x (purple boundary) --- There must be a chart showing these regions on the CIE diagram, but I couldn't easily find such a chart. There is a way to convert these specifications into wavelengths, but it's a bit complicated, because the specifications are specified with tristimulus coordinates. At 11:21 PM 12/3/2012, Bill Gosper wrote: >[Not math, but hopefully fun] >Automotive lights: Besides the traditional yellowish white headlights, >we're seeing cold white, and pale green, blue, pink, >and lavender. Plus those annoying prismatic things. But crawling down >I280 tonight, I was struck by the uniformity of >the red in the miles of taillights stretching out before me. Both LED and >conventional. Is there some strict spectral >standard? Or does my color discrimination roll off fast at the red end?

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[math-fun] Lasr Hormander
by Michael Kleber 04 Dec '12

04 Dec '12

Seen on Google+, https://plus.google.com/110050584459359486755/posts/7WGEpW3Lw2A, from Bruce Schechter: The Swedish mathematician, Lasr Hormander died a few days ago. I'm researching an obituary on him for the the NY Times and need to speak to people who knew him and who can explain the importance of his work. I'm on an extremely tight deadline, so if you know of someone, please contact me ASAP. Thanks! --Michael -- Forewarned is worth an octopus in the bush.

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Re: [math-fun] New lighting technology breakthrough?
by Henry Baker 04 Dec '12

04 Dec '12

To a first approximation, today's "white" LED and today's "white" fluorescent light are the same: They both excite a fluorescent dye with a blue/ultraviolet light. They differ in how the blue/ultraviolet light is created. The visible "white" color (or color "temperature") is dependent upon the type of dye. The dyes can be made from "quantum dots", which can be engineered to have the appropriate spectrum. "White" light can also be made using 3-4 colored LED's (green LED's are less efficient, so you tend to need RGGB instead of just RGB); this is used in large LED billboards and for LED TV's. Since you need 2 G's anyway, you can use G's with 2 different wavelengths to get a wider "color gamut" -- RGG'B. There are some LED TV's that utilize this idea. There are now LED stage/studio lights whose colors can be computer-programmed for different colors using these combinations. I would speculate that white light made from LED's of individual colors _might_ be more efficient (in terms of electrical power) than the white light from downconverted UV, but I haven't been able to confirm this. My best guess is that downconverted UV is cheaper/simpler to use, because it requires only one type of bulb, and because it draws upon a century of fluorescent light technology. At 04:50 PM 12/3/2012, Warren Smith wrote: >The news hype media is full of stuff about how David Carroll, prof. at Wake Forest Univ. >in NC, has invented new wondrous lighting technology, environmentally >friendly, efficient as LEDs and "at least twice as efficient as fl.tubes," but simpler and looks better, >wholy solid state, simple, most any shape (sheets, rods, bent rods,...), glowing capacitor using magic nanoparticles >embedded in plastic, no toxic mercury like fl.tube has, long lived (>10 years), will be commercialized with in 1 year. > >I tracked it to this press release > http://news.wfu.edu/2012/12/03/taking-the-buzz-out-of-office-lights/ >and this pre-paper of some ilk: > http://www.sciencedirect.com/science/article/pii/S1566119912004831 > >What the media hype machine never mentioned in about 10 articles I saw, >but is revealed in the latter document, is that they incorporate >substantial amounts of Iridium and Indium. That sounds like an >immediate major lose right there. > >-- >Warren D. Smith >http://RangeVoting.org <-- add your endorsement (by clicking >"endorse" as 1st step)

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