"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck
"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)
******************************************************************** Rob Gluck
NOTE:This will be the last ‘Friday potpourri’ or post at MathTango. With the country in seriously deep-doo-doo I'd rather free up some collusion time to work on expunging orange-puppets or others who find 1930s Germany peculiarly appealing (…also, got some reading to catch up on ;). [Math-Frolic posts will also decrease substantially for remainder of year, until maybe, just perhaps, we get our country back.]:
1) This is an old (2003) piece, but Jordan Ellenberg pointed to it last week as his favorite magazine piece he ever wrote, and it is indeed wonderful:
Wasn’t sure if I would or wouldn’t compile a potpourri this week, but in the end (and with NO collusion, mind you, NONE, noooo collusion whatsoever) here it is:
1) “The biggest skill to learn moving forward…” (h/t Gary Davis):
Have been quite surprised by several of the outcomes thus far in the contest, either by who won, or by the margin of victory. A recent such surprising match was Edmund Harriss vs. Paul Taylor, with the former choosing to write about the Collatz conjecture and the latter about non-transitive dice. I thought this would be a very close match-up, but in fact Harriss ran away with it. Both topics are inherently very interesting and come up regularly on popular math sites, though I think the Collatz conjecture arises more frequently, in part because it is so easy to state and understand, yet fascinatingly eludes proof. Both the idea of it and the resultant pictures/graphics are “beautiful.” It probably makes everyone’s list of favorite topics, and Harriss offered up a nice standard rendition of it.
Still I ended up voting for Taylor, because he took that extra step of showing me something I’d not seen before, in his discussion of non-transitive dice, by bringing up "NON-non-transitive dice," an added side-twist, I found creative and interesting. In retrospect though, Harriss’s post is more strongly VISUAL, while Taylor’s post may require a bit more thinking/imagining/effort on the reader's part and perhaps that’s a handicap in such a contest.
So now I’m thinking that maybe in these matches an advantage comes to the competitor who presents the more visually-appealing (or at least less abstract) math bit.This may also help explain Zoe Griffith’s win over Evelyn Lamb — Evelyn hitting readers with high-dimensional spaces (that can’t be easily pictured or imagined) while Zoe stuck with Benford’s Law and numbers we can all relate to in everyday lives.
Despite those who argue anyone can learn math, I’ve long believed there is a large swathe of people who have real difficulties with “abstraction” (which is fundamental to math) and hit mental blocks because of it. I’ve known folks for example who if asked what “3 apples plus 2 apples” is, will immediately respond 5 apples, but if asked “what is 3x + 2x?” are immediately confused and uncertain, so powerful is this blockage when symbols are introduced.
One thing we don’t know is who the bulk of voters are in this contest… professional and/or amateur mathematicians, or is there a major contingent of lay people who just enjoy reading mathy stuff? I don’t know? But to the extent there is a latter group, easy-to-follow and visually-attractive posts may likely win out — or, hey, maybe I'm looking for patterns that don’t exist (and the results are much more random)! At any rate, participants turned in all there entries before the contest began, so nothing I say here can influence what they will be presenting.
My own actual daily picks have been fairly abysmal, picking only 4 out of the 12 winners (well, one not fully settled yet). As usual, I'm out of step with the masses. :(((
Anyway, we're almost down to the Final Four, and in one more week we'll know the names of the two final jousters. Better stock up on some popcorn and beer (or Guinness) now.
Been so busy this week watching Britain and U.S. race to see who can disintegrate first, that I didn’t have much time left over for compiling math bits, but here’s a few:
1) New Alex Bellos puzzle book now available in U.S.:
Well, it’s not the Thrilla-In-Manila, nor the Olympics, nor even the Soccer World Cup (to which, as an American, I can only say ho-hum), but a perfect, that is Lawson-Perfect, summer diversion for math geeks devised by The Aperiodical’s Christian Lawson-Perfect — intended to crown the "world’s most interesting mathematician" (well, at least of the 16 participating — and as Jim Propp notes, that real honor goes to John Horton Conway… so perhaps it should be called the "John Conway prize” ;)
With tons of interesting math bits to choose from, most of which are well covered, part of the fun is discovering exactly which intriguing bits various participants find most interesting (or at least think their readers will find most interesting), and then seeing exactly how they manage to present those bits.
I tried to look for some pattern or commonality among the winners thus far, but don’t really see one (does anybody???), though I haven’t yet run a complete astrological analysis ;).
But with Round 1 of the contest drawing near conclusion, a few general comments:
1) Even though this could be expected, still heartening to see so many entrants cite Martin Gardner for inspiration. Martin was not even a trained mathematician, yet as the saying goes, he “...turned 1000s of children into mathematicians, and 1000s of mathematicians into children.”
2) 16 seems a perfect number of competitors — not too many, to drag the contest out too long, potentially losing public interest, but enough for variety, diversity, and sustained interest.
3) It’s not just the topic an entrant chooses that is important, but the presentation is vital! Some folks chose ideas that were new to me and vote-worthy on that account, while others selected material that is more well-worn, but presented in such a clear, clever or creative manner that they got my vote.
4) One thing I’m not clear about is why vote totals vary so much from one matchup to another, ranging from ~180 to 878! — unless it’s just a case of some competitors having more nieces, nephews, friends, relatives, dogs and goldfish to draw upon for an assist than others!?
5) Some players gave relatively short presentations that just basically said ‘look at this, it’s interesting!’ while others gave more lengthy fleshed-out verbal descriptions and/or longer videos. I couldn’t tell that either approach was more consistently successful; seemed to me that clarity and creativity were more important than novelty, length, or technicality. Some topics were more abstract and some more hands-on, but again, I’m not sure either approach dominates — both can produce the “Aha!” moment Lawson-Perfect is seeking.
6) Finally, does anyone really WANT the burden of the title “World’s Most Interesting Mathematician” — think of the pressure, the stress, the nervous self-doubt and performance-anxiety!! Maybe just leave all that for John Conway, afterall (...he's already got gray hair).
In any event, so far it looks like 5 of my 8 initial bracketology picks will make it to the next round (from the “Sweet 16” to the “Elite 8,” as we would say in America), and what ought be a fun week ahead. Brits outnumber Americans and 2-syllable surnames outnumber all others! — so if you want to root for the underdog, then Lamb is your choice. ;)
Anyway, kudos to The Aperiodical folks for giving us at least a temporary distraction from the Brexit, Trump, and other insanities of daily news, with a contest that includes both wonderful writing and wonderful links. May it become an annual event!
…ALSO, I’d love to continue the fun by collecting a ‘Greatest Hits’ list of links from a wide variety of math communicators for a future post (NOT a competition, but just a sort of listing of single FAVORITE links contributed by great bloggers) — more on that in a future post over at Math-Frolic, but please be thinking what you might submit if asked to refer math fans to ONE single awesome old or new mathy link to read or view (NOT your own material) that they may have missed or forgotten about.
9) I was expecting a slow week over at Math-Frolic, BUT, lo-and-behold, ended up with varied posts on Mon., Tues., Wed., Thur., AND Fri.! (inspired by fluid dynamics, a quirky room, a Calif. teacher ;), a contest, and Sean Carroll). So please check out whatever you missed!
…Potpourri BONUS! (extra NON-mathematical links of interest):
1) h/t John Carlos-Baez for this fascinating ‘bit’ of info:
