March 2015 - mathfun@mailman.xmission.com

Re: [math-fun] math-fun Digest, Vol 145, Issue 27
by Warren D Smith 09 Mar '15

09 Mar '15

> From: "Hilarie Orman" <ho(a)alum.mit.edu> > I've raved to people about an online course that took a year ago, but > apparently it is impossible for the generations to stay in step with > one another:> > "Why digital natives prefer reading in print. Yes, you read that right." > http://www.washingtonpost.com/local/why-digital-natives-prefer-reading-in-p… --tell us about your online course experience?

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Re: [math-fun] The Death of Textbooks? (Eric Angelini)
by Warren D Smith 09 Mar '15

09 Mar '15

Computer posing problems to students, grading them, and walking them thru a solution works pretty well... for simple fairly rote tasks. If the goal is to develop initiative and original planning, then the student would be working in some unanticipated way, not one of the preprogrammed computer patterns. And the student's way might actually be less efficient, but nevertheless the exercise of devising a plan, and seeing what happens, and what goes wrong, is valuable. Indeed without any originality, progress will end. Having a computer grade that, seems impossible until AI progresses a good deal further. So I think optimal teaching requires a substantial fraction of human feedback, and I do not think massive online courses with everything done by computer, can provide optimal teaching. If AI reaches the level where it can do this, then the debate will become irrelevant in the sense that humans will be obsoleted. That being said, I don't see why textbooks have to be heavy, expensive, and made of paper. If things keep going, wikipedia will become better than most textbooks. Free too.

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[math-fun] Crossword reconstruction
by Mike Speciner 08 Mar '15

08 Mar '15

Under what conditions/assumptions is it possible to recreate the geometry of a crossword puzzle from the across and down clue numbers?

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[math-fun] Fwd: Shirt
by meekerdb 08 Mar '15

08 Mar '15

-------- Forwarded Message -------- Now who else do I know who would appreciate this? http://teespring.com/pi-day-i-was-there?kw=wcsbMF30uL1nipur&&utm_campaign=p…

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[math-fun] The Death of Textbooks?
by Eric Angelini 07 Mar '15

07 Mar '15

Quote: >"I sat down with some students, and I thought this would be boring [to them], but I asked the kids and the kids said ‘no I really like that. I like working by myself and having these adaptive lessons and getting some cool feedback,’" Rice said. "They were really happy with it, which the textbook can never do for you." But that’s precisely what worries some educators the most: What was once a teaching model is transforming into a learning model. As Atwell put it: "Technology is a means; it’s not an end. And it’s become an end within this country." http://www.theatlantic.com/education/archive/2015/03/the-death-of-texbooks/… Best, É.

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[math-fun] more rants on ln, typography
by Warren D Smith 07 Mar '15

07 Mar '15

> Also, "ln" is distractingly hard to read because lowercase-l looks like capital-I and digit-1 and so forth and needs all the extra context it can get, and "ln" is harder to say than "log"; that agreement would be pretty much a pure loss for the pure mathematicians. --what hogwash. "harder to say." My heart bleeds for you. First of all, lg occurs in number theory and computer science, so the idea only ln occurs in pure math is hogwash. My personal convention, which is you will note is superior to Halmos (of whose opinions, I have a low opinion), is: always use ln, except if you are trying, intentionally, to convey the idea that some formula enjoys validity REGARDLESS of the base of the logarithm, in which case use log. You also will notice this is a superior convention for the purposes of pure mathematicians. If they are too stupid to realize that, it is their problem, not mine. Second, where do these pure mathematicians get off proclaiming there should be pure math books divorced from the rest of reality? And what's wrong with striving in every way possible to make work more accessible to Joe Schmoe? Rather than striving to make it less accessible? And even the pure mathematicians, you will notice, write their numbers in base 10. (Proving their total hypocrisy.) Every time I make a log-plot, I use base-10 logs to do it, and I dunno, I guess pure mathematicians never need to plot anything because that would be too applied? And finally, re "l" looking like "1" and "|", you know what? THIS WAS A MASSIVE MISTAKE by typographers. And while in many ways I love Don Knuth, he was a total idiot when he designed his fonts making u and v look too similar, as well as this. He should have intentionally striven to make them all look different. He then introduced "\ell" in LaTeX to try to compensate for his own idiocy, but it was too little too late. But there is nothing stopping somebody from designing a font suited to mathematics, for a refreshing change. (Maybe has already happened?). Knuth's font sure wasn't it, but one could. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] newton rotating liquid mirror
by Henry Baker 06 Mar '15

06 Mar '15

Situation 1: Non-rotating Earth. The child's circular pool (R=~3') is placed on a lazy susan and rotated at 1 revolution per day. Result: concave parabolic surface. This is the canonical Newton telescope, except for the extremely slow rotational rate. Situation 2: Rotating Earth; child's pool located at the South Pole. Pool still rotates at 1 revolution per day. Pool & water within pool can't tell the difference between situation 1 and situation 2. Result: same concave parabolic surface. If you rotate a child's pool, the water will rush towards the edges; the only thing keeping the water from flowing out is the pool wall, hence the pool wall will feel not only the static load of the water, but also an incremental force due to the centrifugal force of the rotating water within the pool. Thus, it is the _constraint_ of the pool wall which keeps the surface of the pool water in a more-or-less parabolic shape. At 06:27 AM 3/6/2015, Andy Latto wrote: >So the shape of the surface near the center of the pool is not >determined by the local forces on the water at the center of the pool, >but by some kind of "spooky action at a distance from the pool walls? >And accurate measurement of the water at the center of the pool can >determine the size of the pool? Can it also determine the shape of the >pool? This sure sounds wrong to me. > >Suppose the pool is 100 feet in diameter. Consider the circle 50 feet >in diameter around the center of the pool. No water is flowing in or >out of that circle. So if we introduce a new boundary there, there >will be no change in the height of water inside or outside that >circle. > >Andy > >On Fri, Mar 6, 2015 at 8:21 AM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> No, I wouldn't expect a lake at the south pole to have a concave area in the center, but I would expect a child's round swimming pool at the south pole to have a concave surface. >> >> There will be forces against the side of the pool to keep the edge of the water higher than the middle. In the middle of a lake, these forces will be dissipated because the water will move away from the center. >> >> At 09:40 PM 3/5/2015, meekerdb wrote: >> Would you expect a large lake at the south pole to have a concave area in the center, but match the geoid elsewhere? >-- > Andy.Latto(a)pobox.com

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Re: [math-fun] junk dna
by Warren D Smith 06 Mar '15

06 Mar '15

On 3/6/15, Henry Baker <hbaker1(a)pipeline.com> wrote: > [Just us.] > > We used to think that the spleen, the tonsils and the appendix were "junk > organs". > > We now know that the spleen & the tonsils are involved in the immune system, > the > spleen is involved in stockpiling red blood cells, and the appendix is > involved > in recreating the microbiome after dysentery-like diseases. --you can live without these 3 organs. I do like the spleen and tonsils, but, I suspect the appendix is worse than junk in the sense you are actually better off on average without it. (Ditto wisdom teeth.) There is in many herbivores a region of their digestive system, the "caecum," in which cellulose-digesting microbes live. This enables them usefully to eat cellulose, which we humans cannot. Perhaps the appendix is a relic of that. Wisdom teeth are definitely a relic. > "Junk" is stuff that we don't _currently_ have a recognized use. --there are example of two closely related animals (e.g. both similar frogs?) one has like 10X the DNA of the other frog. I do not care what you babble about possible unrecognized uses. This is junk. There is no way the 2nd frog has any reasonable unrecognized use for 10X more DNA which it suddenly developed in time epsilon. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] junk dna
by Warren D Smith 06 Mar '15

06 Mar '15

http://www.nytimes.com/2015/03/08/magazine/is-most-of-our-dna-garbage.html?… the NY Times article is enjoyable but fails to mention that closely related species can differ in DNA by large factors. Which is very convincing evidence a lot of the larger one's DNA, must be junk. I'm not saying everything currently thought to be junk necessarily is -- the NYT article mentions the highly interesting "hotair" counterexample -- but there can be no doubt that well over 50% of some organisms' DNA is junk. One researcher quoted in the NYT piece says the old estimate 99% of the human genome is junk, is in his view now really 92%.

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[math-fun] u uersvs v, trisectrix, ellipsoids
by Bill Gosper 06 Mar '15

06 Mar '15

Wasn't v created from u by lazy Roman stonecutters? Mens et Manvs -- William Barton Rogers (Ovr Fovnder). No matter what font you are using for math, I think it would be a good idea to avoid mixing u and v closely. There are so many other good pairings to choose from. -Hilarie Lost cause! Integration by parts. Do you prefer "e^u du/dx, takes the place of normal sex, ..." ? Trisectrix: I've mentioned Julian's lovely http://gosper.org/tripenta.gif here before, but in off-list conversation added: The angle being "sected" is between the x axis (not shown) and the short green rotor, whose length is 1/4. The angle's three trisectors are the cyan radii of the lesser moving circle (radius 3/4), determined by its intersection with the (unit radius) astroid (= quadricuspid hypocycloid). There are five additional intersections (magenta) whose significance we've never determined. The (quadricuspid) epicycloid is a pentasectrix when intersected with the moving circle of radius 5/4. The five legitimate pentasectors are dark blue, with three mysterious bogons in red. If you have a theory for the red or magenta bogons, Neil, Julian, & I are all ears. Also I once posed here: Given its three girths, what are the semiaxes of an ellipsoid? No closed forms? I could only find (three) series solutions (for each semiaxis). At least they converge rapidly. --rwg

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