Over 30 years ago I was delighted to see bubblemeister Tom Noddy perform his bubble tricks/creations on TV, and so was re-delighted to see he’s still around, appearing yesterday on CBS’s “Sunday Morning” show:
In turn, looking him up on YouTube I discovered that a new generation of bubble (or "bubbleology") artists are now out there performing, carrying on the fun for children and adults alike:
Though these show-meisters don’t get into the math involved, I can’t help but think that if Richard Feynman was in attendance watching he’d be hurriedly getting out a pen and pad to scribble down equations. ;)
If you do want a little more mathematical discussion, check out this take:
…seems like “bubbles” might be a good subject for Numberphile, Tadashi Tokieda perhaps, or possibly Mike Lawler and the boys could do something with them (apologies if any of you have already done so and I missed it). Bubbles represent a simple (or, maybe not-so-simple) everyday intersection of math and physics. Here's ZomeTool put to use exploring bubbles:
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ADDENDUM:Mike L. sends me a link to several videos he has indeed done previously with soap bubbles :)
“What one learns about mathematics in primary school corresponds to the alphabet. What one learns in high school corresponds to the sentences of a primer. What one learns in elementary college courses corresponds to simple little stories. Scholars alone are aware of the mathematics that corresponds to literature.”
And over five yrs ago I ran this just-for-fun post (entitled: "There is no title for this post."):
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This is the first sentence of the post titled, 'There is no title for this post.' This appears to be the sentence that follows sentence #1 of that post. This is the sentence following the previous sentence, but preceding the next sentence. This is the next sentence... or is it? Apparently this is sentence #5. This is the sentence you just finished reading. The last sentence of this post will come at the end. Thus, this is NOT the last sentence of this post. It is untrue that the prior sentence was false. This sentence begins with the word "this," followed by the word "sentence," followed by the word "begins," followed by the word "with," followed by the word "the," followed by the word "word," ...AND also ends with the word "word." And this is the sentence that informs you that the very next sentence is the final sentence of this post. This is the last sentence of the post, but why oh why does it end with a question-mark?
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We'll end with more humor, starting with a well-known, geeky aphorism:
"In order to understand recursion, one must first understand recursion."
...which reminds me in turn of one of mathematicians' favorite jokes:
Q: What does the "B" in "Benoit B. Mandelbrot" stand for?
A: Benoit B. Mandelbrot
Then, there is this thoughtful quote that I've used before:
"If my mental processes are determined wholly by the motion of atoms in my brain, I have no reason to believe that my beliefs are true... and hence I have no reason for supposing my brain to be composed of atoms."
--- J.B.S. Haldane, "Possible Worlds" (1927)
In a slightly similar vein, this famous refrain out of AI:
"If the brain were so simple that we could understand it, then we would be so simple that we couldn't."
There is always xkcd's classic treatment of self-reference:
“The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.”
An entranced Arthur Koestler, in "The Invisible Writing":
“I went on to recall Euclid’s proof that the number of primes is infinite… the scribbled symbols on the wall represented one of the rare cases where a meaningful and comprehensive statement about the infinite is arrived at by precise and finite means. I must have stood there for some minutes, entranced, with a wordless awareness that ‘this is perfect, perfect’, until I noticed some slight mental discomfort nagging at the back of my mind, some trivial circumstance that marred the perfection of the moment. Then I remembered the nature of that irrelevant annoyance: I was, of course, in prison and might be shot. But this was immediately answered by a feeling whose verbal translation would be: 'So what? Is that all? Have you got nothing more serious to worry about?' -- an answer so spontaneous, fresh and amused as if the intruding annoyance had been the loss of a collar-stud.”
By coincidence, shortly before our Il Duce was referencing “shithole” countries I was re-reading an old Presh Talwalkar post from a few years back that I always enjoyed on ‘Nigerian’ email scammers. It explains, as many know by now, why ’Nigerian’ email scams got stupider and stupider over the years, full of misspellings, bad grammar, poor English, outrageous narratives, etc. — the scammers wanted to make their messages SO obviously fraudulent that only the most gullible, naive, unthinking people would even respond (why waste time on thinking-folks wary enough to not follow through with the scam):
Anyway, I have a suggestion for how the scammers can be even more efficient: Just buy a copy of the mailing lists used by the Republican National Committee -- boy, talk about a sucker-list…
Yo, logic enthusiasts, when I saw a post entitled, “Smullyan and the President’s Sanity” listed on the mathbogging.org feed this morning it caught my attention. Have fun:
Sunday reflection: Bedraggled old man: "....5, 1, 4, 1, 3 -- DONE! at last." Passerby: "You look exhausted; what did you just do?" B.O.M.:"Recited the complete decimal expression of pi backwards." -- old Wittgenstein joke
For Sunday reflection, this passage from Stephon Alexander's "The Jazz of Physics": "I walked into his spacious office and saw Dr. [Chris] Isham relaxing on a reclining armchair with his feet up... Notes on topos theory -- incredibly complicated algebraic-type manipulations of rules on topological spaces -- decorated the board behind him, so grand, they couldn't possibly fit on A4 paper. He was smiling warmly. He wasted no time and got straight to the point. 'Why are you here?' he asked. I responded, with some nervousness in my voice, 'I want to be a good physicist.' Chris then surprised me. 'Then stop reading those physics books. You need to develop your unconscious mind; that's the wellspring of a great theoretical physicist.' As if his scientific repertoire weren't impressive enough, what I didn't know at the time was that he was both seriously spiritual and philosophical. He calmly and earnestly told me that he had trained his mind to do tedious calculations while he was dreaming. He followed that remarkable revelation with another question: 'What are your hobbies?' Dumbstruck by his feats during slumber (I just slept at night), I distractedly replied, 'I play jazz at night.' There was a pause. 'You should play more music. I sing. I find that music is an ideal activity to engage the unconscious.' Another pause. 'You see these books here?' He pointed to the complete volumes of Carl Jung's writings, the founder of analytical psychology. 'I have fifteen years of training in Jungian psychoanalysis. Read volume nine, part two, Aion: Researches into the Phenomenology of Self. There is a mystical side to doing physics.'"
Isn't this a time! Isn't this a time! A time to try the soul of man... -- Pete Seeger
As the year is closing out, will again just post a list of some folks to follow on Twitter in 2018, as America's kabuki dance with demagoguery, plutocracy, and Russian puppetry continues: Seth Abramson
Today just a space-filling retrospective of a few of my favorite simple posts (from the two blogs) in the year gone by (though only a few actually contain math!). In no special order:
didn't do a lot of puzzles this year, but here were a couple of quick ones:
"The trouble with college math classes -- which classes consist almost entirely in the rhythmic ingestion and regurgitation of abstract information, and are paced in such a way as to maximize this reciprocal data-flow -- is that their sheer surface-level difficulty can fool us into thinking we really know something when all we really 'know' is abstract formulas and rules for their deployment. Rarely do math classes ever tell us whether a certain formula is truly significant, or why, or where it came from, or what was at stake. There's clearly a difference between being able to use a formula correctly and really knowing how to solve a problem, knowing why a problem is an actual mathematical problem and not just an exercise." -- David Foster Wallace
A mind-bender showed up on Twitteryesterday from a logic blogger. It's very similar to a puzzle that went viral a couple years back, which you may well remember (...but will likely still require some thoughtful-time to solve again). I’ve slightly adapted yesterday's Twitter version as follows:
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Alice and Bob are each given a different fraction of the form 1/n where n is a positive integer. Each of them knows their number (fraction) but does not know the other’s number (but does know they are different). Assume each participant thinks in a perfectly logical/rational manner (and understands the other individual is doing so as well), the following conversation takes place:
Me: I gave each of you separately a different fraction of the form 1/n that you have had a chance to look at. Which of you has the larger number (fraction)?
Alice: I don’t know.
Bob: I don’t know either.
Alice: I still don’t know.
Bob: Yes, now I know who has the larger number.
Alice: In that case, so do I, AND I know both numbers!
What numbers (fractions) were they each handed?
[yes, there is one exact, correct solution... have fun]
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I find this puzzle especially appealing because of a sort of 3-tiered evolving process it likely follows for most solvers:
1) Upon first reading, it doesn’t seem like it will be solvable.
2) Upon further contemplation it appears partially solvable, but seems like multiple solutions are possible.
3) The final step needed to reach the one correct solution requires a bit of recursive thought that, once made, is both illuminating and very satisfying.
If you make math videos you can’t do much better than get a thumb’s-up recommendation from Grant Sanderson (of 3Blue1Brown). Recently, Grant recommended a youngish YouTube site called “Think Twice” that's putting up some nice, short little animated math videos. Here's one example (feel free to explore more!):
“All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They’re adults in the crystalline world, infants in the real one.”
I'll have a Friday potpourri tomorrow morning at MathTango, but just to make sure you have enough to read/hear ;) below are some lists I've come across recently that may be of interest:
a) Fine list of online math resources (including free online math-related magazines) that was tweeted out this week:
