February 2015 - mathfun@mailman.xmission.com

Turing: The Imitation Game review
by Henry Baker 23 Feb '15

23 Feb '15

FYI -- Good review; good perspective. http://www.thedailybeast.com/articles/2015/02/21/the-imitation-game-can-thi… 02.21.15 ÂThe Imitation GameÂ: Can This Big Fat Cliche Win Best Picture? Instead of helping us with a role model, The Imitation Game hurts us with a hero. The most disappointing thing about the Oscar-nominated film The Imitation Game can be summed up in the way that Alan Turing, the brilliant mathematician played by Benedict Cumberbatch, answers his boss, Commander Denniston, when Denniston asks him why he needs to build a machine to crack the GermansÂ unbreakable code. ÂItÂs highly technical,Â Turing says, dismissive. ÂYou wouldnÂt understand.Â Turing may as well have been speaking to the audience, not just his sneering commander, because for a movie about a technological pioneer making a technological breakthrough, The Imitation Game barely deals with technology at all. Instead of an inventor, it shows a stereotype. Instead of a machine, it shows an obsession. And instead of inspiring us to follow in the footsteps of a person who shaped technology, the film inspires us only to get out of the way of the next genius who can. As a movie, The Imitation Game is beautiful. As a missed opportunity, itÂs sad. At a time when we need to take power over the technology that runs our livesÂ-think privacy, hackers, net neutrality, surveillanceÂ-The Imitation Game gets the perfect subject and tells the wrong story. First, to Turing. THE STEREOTYPE The Alan Turing of The Imitation Game matches our eraÂs stubborn stereotype of the awkward and isolated computer scientist. ÂIÂm afraid these men will only slow me down,Â the filmÂs Turing tells Denniston when the commander tells him to work together with the other members of his team at BritainÂs Bletchley Park. Right in front of them, of course. But the stereotype fits too well. The Imitation Game changed aspects of the real Alan TuringÂs personality to conform more closely to our idea of the solitary nerd. The real Alan Turing could be warm and funny, his colleagues have said. And he worked with his team from the beginning, unlike the arrogant Turing of the film who stumbles into collaboration only after another character, Joan Clarke (played by Kiera Knightley), tells him itÂs the only way he can finish his work. Stereotypes are useful as a kind of shortcut: The more we feel we know a character, the faster we can get to the drama. And so the film fudged the details so the picture was familiar. The result? The Imitation Game falls in line with the tired idea that only outcasts could love computers, rather than the reality that one of the pioneers of the field was a shy but nice enough guy who could work in a team. THE TECH As for explaining the science behind TuringÂs code-breaking machine, the movie doesnÂt bother. Other than a couple broad allusions to what we now know as a computerÂ-an Âelectronic brain,Â in one quick sceneÂ-we are given no idea how this thing works. In a couple scenes the tech talk is just ending as we come in, and we catch the last bit of a sentence before the movie moves us on from Âhighly technicalÂ things we couldnÂt possibly understand. In one scene, mathematical formulas are visible for an instant on a cafÃ© table between Turing and Clarke before their colleaguesÂ entrance changes the subject. Skimming the science isnÂt a big deal in most films that have it in the background. In many, the science is silent because itÂs bad science, a plot device to justify extraordinary circumstances. But if invention doesnÂt deserve top billing in this story, where the technology at its heart is not only historically significant but hugely resonant in our lives today, then I donÂt know where it would. You donÂt need to understand what Turing did, the movie seems to say. You only need to appreciate it. No sequence is more telling on this point than the montage that shows Turing beginning to design his machine. Shots of him working at his desk are cut with shots of him jogging. He draws some dots in circles. Runs. Draws more circle dots. Runs again. Stares at a wall full of pinned-up dots in circles. Runs faster than ever. ThereÂs a race against the clock element to the code-breakersÂ work. Allied soldiers and sailors are dying every day they donÂt crack it. But the jogging shots are all that give those work shots meaning, because without them, it would be too obvious that they have none. The movie doesnÂt tell us what the circles of dots means because it doesnÂt bother to seek drama in the actual work of invention. We have no idea what Alan Turing is doing and barely realize it. All the movie needs us to know is that itÂs very important, and very, very hard. THE OBSESSION In real life, TuringÂs code-breaking machine was called the Bombe. In the film, itÂs called ÂChristopher.Â Christopher Morcom is the name of a close friend and supposed early love interest who died while they were in school. The movie chose to carry this biographical tidbit all the way to the machine in Bletchley Park. Why? To paint a portrait of TuringÂs machine as his singular obsession. The real Alan Turing built his machine with help. A man named Gordon Welchman made a significant improvement to it. In The Imitation Game, Welchman does not exist and colleagues enter the barn where Turing tinkers with Christopher like they would enter the lived--in art studio of a fragile eccentric. The filmmakers, who saw the replica of the actual Bombe in England, ran more red wires through the machine to resemble nerves and bloodÂ-thatÂs how sentimental they wanted to make this. ÂWhat happens now?Â one of TuringÂs colleagues asks when Turing turns the machine on. The question is a plot driver: Here, at least, the movie bothers to explain something about the machine to the audience (as blandly as possible: It Âshould work out the dayÂs Enigma settings,Â Turing responds). But the question also shows TuringÂs obsession with his machine for the fiction it is. If theyÂd finally come around to working with Turing on this thing, and wouldnÂt they know just a little bit about it? Earlier in the film, when colleague Hugh Alexander tries to break the machine over its belief that it does no good, TuringÂs invented mad scientist persona emerges. ÂMy machine will work,Â he tells Alexander, brimming with conviction but offering no explanation, absolutely no case. Later, when Denniston turns off the machine and threatens to fire him, Turing explodes: ÂYou will never understand the importance of what IÂm creating here!Â At the end of the film, Joan Clarke, TuringÂs straight love interest and former fiancee (itÂs complicated) finds him broken from the hormone therapy the government forced on him for being homosexual. ÂAlan, you do not have to do this alone,Â she tells him. ÂIÂm not alone,Â he says. Behind him is another machine, another Christopher, taking up half a room. You donÂt have to obsess over your work to make it great. It just makes it more entertaining. A ROLE MODEL HereÂs the crux of the problem IÂm trying to describe: The Imitation Game gives us Alan Turing the hero when what we need is Alan Turing the role model. The message of the movie is that the uncommon man can do amazing things, but the message we need is that the common man, woman, anybody can and should tinker with the technology that manages our whole world. To dramatize the hero, you have to dramatize the heroic act. To place Turing into a hero narrative, The Imitation Game brought the historical Turing closer to his machine, farther away from his colleagues and into a stereotypical personality that puts him and his achievements at a greater distance from us and what we imagine for ourselves. I believe that the movie set out to make people appreciate Turing, but did not set out to make people believe they can be Alan Turing. It doesnÂt think weÂd want to. It doesnÂt think itÂd be any fun. It doesnÂt think weÂd understand. And that is a damned shame.

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[math-fun] death rates
by Warren D Smith 22 Feb '15

22 Feb '15

http://www.cdc.gov/nchs/data/dvs/MortFinal2007_Worktable310.pdf gives death counts, USA, year 2007, at each age 0-120. The file http://www.cdc.gov/nchs/data/dvs/MortFinal2007_WorkTable210R.pdf gives death rates in each 5-year age group, USA, year 2007. Also broken down by race, sex, and into 113 popular causes of death. Now I will try to give the all-races, all-sexes, all-causes year-2007 death rates from that file and also http://www.cdc.gov/nchs/data/dvs/LCWK7_2007.pdf for below 1 year old: age rate/100K/yr ln(rate) 0-1 675.1 6.51 1-4 28.6 3.35 5-9 13.7 2.62 healthiest age; monotonic increase from here on: 10-14 16.9 2.83 15-19 61.9 4.13 20-24 98.3 4.59 25-29 99.4 4.60 30-34 110.8 4.71 35-39 145.8 4.98 40-44 221.6 5.40 45-49 340.0 5.83 50-54 509.0 6.23 55-59 726.3 6.59 60-64 1068.3 6.97 65-69 1627.5 7.39 70-74 2491.3 7.82 75-79 3945.9 8.28 80-84 6381.4 8.76 85-199 12946.5 9.47 I attempted to draw a graph of this data, and the line ln(DeathRate)=(31/375)*Age+1.856 happens to agree with the data pretty well for ages 5-14 and 30-84. This confirms "Gompertz's law." I believe it also works well at ages 85-95. However, it does not work at ages <5 and 15-29. Perhaps you can produce better laws. I suspect ages 20-95 could be fit well by DeathRate = A + exp(B*age+C), which I think is called Gompertz-Makeham law. Also, I think there are papers out there about very old people's death rates perhaps also deviating from Gompertz law (ages>95), but the CDC does not seem to provide that data. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Divisor question
by David Wilson 22 Feb '15

22 Feb '15

m^2 + n^3 | m^3 + n^2 => m | n?

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[math-fun] parametrically enclosed spherical area
by Bill Gosper 22 Feb '15

22 Feb '15

The plane area inside (x(t),y(t)) = ½∫x dy - y dx. E.g., the usual picture of the area under f(x), a<x<b becomes four line integrals--the three axis-aligned segments plus the actual curve of f, traversed anticlockwise: Integrate[f[x],{x,a,b}]==(Integrate[a - 0, {t, f[a], 0}] + Integrate[t*0 - 0, {t, a, b}] + Integrate[b - 0, {t, 0, f[b]}]+Integrate[t*D[f[t], t] - f[t]*D[t,t], {t, b, a}])/2 == (b f[b] - a f[a] + Integrate[t f'[t] - f[t], {t, b, a}])/2 , which follows from integration by parts. E.g., if f:=Exp, In[55]:= % /. f -> Exp Out[55]= -E^a + E^b == 1/2 ((-2 + a) E^a - a E^a - (-2 + b) E^b + b E^b) In[56]:= Simplify@% Out[56]= True What about on a sphere? Suppose we have a a unit vector X(t):=(x(t),y(t),z(t)) describing a closed curve on a sphere. (X(0)=X(1), say.) What's the area? There ought to be some nice thing analogous to ½∫x dy - y dx. --rwg

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Re: [math-fun] "Achromatic metasurface" breakthrough in lens technology?
by Warren D Smith 21 Feb '15

21 Feb '15

If for example you had 3 diode lasers (red,green,blue) and wanted to make a projector to display images on the wall, these lenses would be perfect. In the old days it used to be that if your fancy lens design worked at 3 wavelengths, then you regarded it as probably handling all other wavelengths well enough, hence were happy. However, perhaps although that thinking was good enough for old style lenses, it is not valid for these funny new kinds of lenses (?). I do not know since I don't really understand how these work. Perhaps somebody can explain it to me. It seems to be a very cool idea, but exactly how does it work, how could you design your own, what design would be "optimal" (whatever that should mean), what happens at other wavelengths, and how expensive to manufacture... all these things are unclear to me.

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[math-fun] "Achromatic metasurface" breakthrough in lens technology?
by Warren D Smith 21 Feb '15

21 Feb '15

This looks very interesting and potentially revolutionary. Think depends how expensive it is to manufacture these. http://www.seas.harvard.edu/news/2015/02/perfect-colors-captured-with-one-u… -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Hollywood Fudged the Relativity-Based Wormhole Scenes In Interstellar
by Henry Baker 20 Feb '15

20 Feb '15

FYI -- http://science.slashdot.org/story/15/02/20/1956237/why-hollywood-fudged-the… Why Hollywood Fudged the Relativity-Based Wormhole Scenes In Interstellar "The problem was that the view of the other side when travelling through a wormhole turns out to be visually indistinguishable from a conventional camera zoom and utterly unlike the impression Nolan wanted to portray, which was the sense of travelling through a shortcut from one part of the universe to another. So for the final cut, special effects artists had to add various animations to convey that impression." http://arxiv.org/abs/1502.03809 http://arxiv.org/pdf/1502.03809v2 Visualizing Interstellar's Wormhole Christopher Nolan's science fiction movie Interstellar offers a variety of opportunities for students in elementary courses on general relativity theory. This paper describes such opportunities, including: (i) At the motivational level, the manner in which elementary relativity concepts underlie the wormhole visualizations seen in the movie. (ii) At the briefest computational level, instructive calculations with simple but intriguing wormhole metrics, including, e.g., constructing embedding diagrams for the three-parameter wormhole that was used by our visual effects team and Christopher Nolan in scoping out possible wormhole geometries for the movie. (iii) Combining the proper reference frame of a camera with solutions of the geodesic equation, to construct a light-ray-tracing map backward in time from a camera's local sky to a wormhole's two celestial spheres. (iv) Implementing this map, for example in Mathematica, Maple or Matlab, and using that implementation to construct images of what a camera sees when near or inside a wormhole. (v) With the student's implementation, exploring how the wormhole's three parameters influence what the camera sees---which is precisely how Christopher Nolan, using our implementation, chose the parameters for \emph{Interstellar}'s wormhole. (vi) Using the student's implementation, exploring the wormhole's Einstein ring, and particularly the peculiar motions of star images near the ring; and exploring what it looks like to travel through a wormhole.

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[math-fun] Moon as tape recorder for events on Earth
by Henry Baker 20 Feb '15

20 Feb '15

FYI -- It would be fabulous to find bits from the k-T boundary (65Mya) on the Moon. http://www.airspacemag.com/daily-planet/ancient-life-moon-earth-180954282/ Ancient Life on the Moon Â From Earth The possibility that terrestrial fossils are preserved in Moon rocks makes lunar exploration even more appealing. It was once said the Moon acts as a cosmic tape recorder, quietly and continuously collecting a detailed history of the Earth-Moon corner of the universe over the last 4 billion years. Now we are discovering that this geologic tape recorder holds an even more impressive collection of ÂtunesÂ than we had previously imagined.

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[math-fun] Sodalite (is it sugar-free?)
by Fred Lunnon 17 Feb '15

17 Feb '15

As a schoolboy (I know --- it's difficult to imagine!) I became interested in a Euclidean d-space polytope I'll call TKD_d : the convex hull of points assigned the same value of multinomial coefficient, in some layer of the obvious generalisation of Pascal's triangle from binomials to d+1 variables (assuming most general position). Another way to envisage its vertices and edges is the Cayley graph of permutations on n+1 symbols, generated by adjacent transpositions. TKD_d has (d+1)! vertices, 2^(d+1) - 2 facets (if d > 1 , at any rate). TKD_1 is a just line segment; TKD_2 is a regular hexagon; TKD_3 is an Archimedean tetrakaidecahedron (truncated octahedron) with 6 square and 8 hexagonal faces; TKD_4 has 120 equal tetrahedral vertices, 180 edges, 90 faces, 30 cells comprising 10 tetrakaidecahedra and 20 hexagonal prisms. Two questions: For what d does TKD_d tile d-space? (It surely does so for d = 1,2,3 --- what about d = 4 ?) Is (the edge-skeleton of) such a tiling O'Keeffe's "d-dimensional sodalite" net, described cryptically as "holes in the A_d^* lattice" on page 2387 of J. H. Conway, N. J. A. Sloane (1997) "Low–dimensional lattices. VII. Coordination sequences" http://neilsloane.com/doc/Me220.pdf ? Fred Lunnon

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Re: [math-fun] Defective Sandisk uSD cards
by Henry Baker 16 Feb '15

16 Feb '15

I'm using the Linux "disk utility" benchmark function. I've done some more benchmarking on a variety of flash SD cards and USB flash drives. I'm seeing various kinds of performance. I tried a 16GB Sandisk "Ultra", which has excellent read rates (35 MB/s) and lousy write rates (3.4 MB/s avg). At 08:53 AM 2/15/2015, Tom Rokicki wrote: >Can you tell us how you tested? Secure Digital is very >complicated internally and the speed rating is based on >a very specific usage pattern. > >While I'm sure you understand this, many forms of >"testing" can actually have the effect of slowing down >the cards dramatically. > >On Sun, Feb 15, 2015 at 7:19 AM, Henry Baker <hbaker1(a)pipeline.com> wrote: > >> I purchased 4 32GB uSD cards from Costco yesterday, and found to my amazement >> that one of the devices was faulty: while the maximum write rate was >20 MB/s, >> its minimum write rate was 1.2 MB/s, with an average write rate of 5.1 MB/s. >> >> While I suspect that this defective device will function correctly as a memory, >> I was amazed to find that perhaps 25% of these devices did not meet their speed >> requirement. >> >> BTW, if you run Linux, there is a "benchmarking" function for the disk formatting >> program which is quite useful. >> >> Now I'm going to have to test all of my SD cards in advance prior to using them. >-- >-- http://cube20.org/ -- [ <http://golly.sf.net/>Golly link suppressed; ask me why] --

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