May 2018 - mathfun@mailman.xmission.com

[math-fun] What is this function? puzzle
by Dan Asimov 12 May '18

12 May '18

Define a function f : [0,oo) —> R via f(x) = sqrt(1 + x*sqrt(1 + (x+1)*sqrt(1 + (x+2)*sqrt(1+... Evaluate f(x) in closed form. —Dan

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[math-fun] "The Busy Bee"
by James Propp 11 May '18

11 May '18

This may be a folie-a-deux, but both Serge Troubetzkoy and I have recollections of my having written a preprint that neither of us can find any trace of in the on-line or off-line universe. It was called "The Busy Bee", and it was a follow-up to my articles in the Mathematical Intelligencer (cowritten with David Gale, Scott Sutherland, and Serge Troubetzkoy) on the Langton Ant and variations thereon. The article was about what happens when you replace the square grid of the Langton Ant by an hexagonal grid. As in the square grid case, you can set up the rules and the initial conditions so that the bee builds ever-larger symmetrical structures in its universe. Well, sort of. I was able to prove that bilateral symmetry reasserts itself infinitely often, but I was never able to show that the structures grow without bound. That is: I wasn't able to rule out the possibility that at some point the structures start to shrink and the universe returns to its initial configuration. Does anyone have a copy of this article? (I'm guessing that I wrote it as a preprint, then discovered that my results were already in work of E.G.D. Cohen, and then let it languish.) Jim Propp

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[math-fun] Fwd: Fill in the blank.
by rwg 11 May '18

11 May '18

gosper.org/√blank.png --rwg

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[math-fun] Spam subject line typo implies disturbing alternative
by Marc LeBrun 10 May '18

10 May '18

Spam subject line typo implies disturbing alternative: "Discrete, Beautiful, Women Waiting For You"

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[math-fun] Musical parallelotopes, climbable tesseracts, etc.
by James Propp 10 May '18

10 May '18

Do any of you know of passages of music that represent 2-dimensional projections of 3- or higher-dimensional parallelotopes if one plots time against the log of frequency? A simple way to generate such a passage is to start with a two-note figure. Create a four-note figure consisting of the original two-note figure followed by a transposed version of same. Now create an eight-note figure consisting of that four-note figure followed by a transposed version of same. The eight notes can be conceived of as the vertices of a musical parallelohedron (projected into a 2D space). Apply the construction again and you’ve got a sixteen-note projection of the vertices of a 4D parallelotope. (More interesting variants exist, but that’s the basic idea.) Has this sort of geometrically-inspired scheme for organizing pitches in time been exploited by any composers to create music worth listening to? I ask because I’m working on an essay about the hypercube, so musical embodiments would fit in nicely. For that matter, has anyone built a 3D jungle gym based on 4D structures? (As I’ll mention in the article, jungle gyms were invented by the same guy who coined the term “tesseract”, and the idea of making higher dimensions more kinesthetically accessible was a goal of his.) Thanks, Jim Propp

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[math-fun] A review of using cell phone email in Albuqerque
by Hilarie Orman 09 May '18

09 May '18

The app, Is crap. The service, Worse. Hilarie --- "Nevertheless, she persisted."

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Re: [math-fun] math-fun Digest, Vol 183, Issue 17
by Hilarie Orman 08 May '18

08 May '18

----- Original Message ----- From: math-fun-request(a)mailman.xmission.com To: math-fun(a)mailman.xmission.com Sent: Mon, 07 May 2018 12:00:02 -0600 (MDT) Subject: math-fun Digest, Vol 183, Issue 17 Send math-fun mailing list submissions to math-fun(a)mailman.xmission.com To subscribe or unsubscribe via the World Wide Web, visit https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun or, via email, send a message with subject or body 'help' to math-fun-request(a)mailman.xmission.com You can reach the person managing the list at math-fun-owner(a)mailman.xmission.com When replying, please edit your Subject line so it is more specific than "Re: Contents of math-fun digest..."

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[math-fun] approximation to pi in base-(e^i)
by Henry Baker 07 May '18

07 May '18

Notice the big gap between 344 and 51109. Once again, pi has certain excellent approximations. 'rapprox' uses the greedy algorithm in an attempt to minimize the largest power; the 2nd argument is an epsilon. (%i1) rapprox(%pi,0.0000001); (%o1) [468856, 364508, 260515, 52529, 51109, 344, 77, 33, 30, 14, 11, 5, 1, 0] (%i2) rexpand(%); 468856 364508 260515 52529 51109 344 77 33 30 (%o2) r + r + r + r + r + r + r + r + r 14 11 5 1 1 1 1 1 1 1 1 1 + r + r + r + r + - + -- + --- + --- + --- + --- + --- + ---- + ------ r 5 11 14 30 33 77 344 51109 r r r r r r r r 1 1 1 1 + ------ + ------- + ------- + ------- + 1 52529 260515 364508 468856 r r r r (%i3) %,r=exp(%i); 468856 %i 364508 %i 260515 %i 52529 %i 51109 %i (%o3) %e + %e + %e + %e + %e 344 %i 77 %i 33 %i 30 %i 14 %i 11 %i 5 %i %i + %e + %e + %e + %e + %e + %e + %e + %e - %i - 5 %i - 11 %i - 14 %i - 30 %i - 33 %i + %e + %e + %e + %e + %e + %e - 77 %i - 344 %i - 51109 %i - 52529 %i - 260515 %i + %e + %e + %e + %e + %e - 364508 %i - 468856 %i + %e + %e + 1 (%i4) %,rectform; (%o4) 2 cos(468856) + 2 cos(364508) + 2 cos(260515) + 2 cos(52529) + 2 cos(51109) + 2 cos(344) + 2 cos(77) + 2 cos(33) + 2 cos(30) + 2 cos(14) + 2 cos(11) + 2 cos(5) + 2 cos(1) + 1 (%i5) bfloat(%); (%o5) 3.141588840097392b0

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[math-fun] Spelling correction (ASLR?) on DNA sequences
by Henry Baker 07 May '18

07 May '18

It appears that using "CRISPR" technology, it is possible to "correct the spelling" of various DNA *protein coding subsequences* to replace all coding triplets for a particular amino acid with a single, canonical triplet for that amino acid. This "spelling correction" of an organisms's genome apparently *does not harm* the creature, since precisely the same proteins are still constructed in precisely the same way. However, this "spelling correction" seems to play havoc with a majority of the usual viruses that want to attack the organism, and may provide some degree of immunity -- at least until the viruses evolve to recognize & take advantage of this new/canonical coding triplet sequence. This "spell checking" is analogous to, but simpler than, the "Address Space Location Randomization" which is used to stymie computer computer viruses & malware. Of course, ASLR-type randomization may soon be required in humans & other organisms when the biological viruses begin to recognize a canonical coding. Speaking of viruses, it also appears that tens of *complete viruses* are encoded in animals' DNA -- e.g., pigs -- in such a way that theses viruses can escape from the DNA and become fully active. Typically, these pigs are already immune (or partially immune) to these hidden viruses, but *other organisms* -- e.g., humans -- who come in contact with them may not be. This "hidden virus" problem makes transplanting *pig organs* into humans much more difficult, as transplantation requires *immunosuppression*, which then makes the human recipient completely vulnerable to these hidden viruses. Apparently, CRISPR can also be used to remove these hidden viruses, and thus produce pigs whose organs don't harbor such viruses. https://after-on.com/episodes/024 Episode 24: George Church | Bioengineering After On Podcast #24: The Astounding Present and Dizzying Future of Synthetic Biology (from Boing Boing) George Church's Harvard lab is one of the most celebrated fonts of innovation in the world of life sciences. George's earliest work on the Human Genome Project arguably pre-dated the actual start of that project. Subsequently, he's been involved in the creation of almost a hundred companies - 22 of which he co-founded. Much of George's most recent and celebrated work has been with a transformationally powerful gene-editing technique called CRISPR, which he co-invented. ...

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[math-fun] Mars probe remarks
by Bill Gosper 07 May '18

07 May '18

(I think) last week's launch was the first from Vandenberg to achieve escape velocity. Surprising to me: The launch trajectory was significantly posigrade. Launched from Vandenberg because the complicated, multisegment launch window was incompatible with the "congestion" (huzzah) at Canaveral. And because they had excess oomph to compensate the lack of full posigrade. Contrary to headlines, Insight is not a rover. (What if it lands on a slab of rock?) If I were more studious, I would know whether it will repeat Curiosity's crazy skycrane landing stunt. And whether it will similarly ditch hundreds of pounds of tungsten ballast beforehand. (Or maybe the price of tungsten has rebounded with the re-legalization of incandescent bulbs?) Ballast! On Mars! Who remembers the 1950s, when Vanguard couldn't put a grapefruit in low earth orbit, and nobody could believe Sputnik weighed 180 pounds? --rwg oomph ~ ∞MPH

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