Thursday, February 22, 2018

An Old Joke, a New Book, and a 42-year-old Film Clip

On Twitter the other day, Eugenia Cheng mentions this as one of her favorite “math jokes” (I’ve never thought of it as a joke per se, but do agree it is a favorite quickie logic puzzle):

3 logicians walk into a bar, and the bartender asks, “Would everyone like a beer?
The 1st logician says "I don't know.”
The 2nd logician says, “I don’t know.
The 3rd logician says, “Yes.

Richard Feynman once somewhat famously said, “Philosophy of science is about as useful to scientists as ornithology is to birds.” It’s not an uncommon sentiment among scientists. Nonetheless I do find some aspects of analytical philosophy and philosophy of science interesting, and a recent volume snagged my attention...
After all, how could anyone resist a book with the title “Exact Thinking In Demented Times”… yeah, it sounds like a volume about our current spiralling-to-fascism era, but is actually a historical account by Karl Sigmund (a math professor) of philosophy’s 20th century “Vienna Circle”. The Preface is written by Douglas Hofstadter, usually a significant endorsement in itself, though it turns out Hofstadter played a major role translating this volume from Sigmund’s original German, so has a stake in the book.  
But I am enjoying the volume thus far (less than 100 pages in), and haven’t even yet reached any discussion of the ideas and interactions of members of the famed Vienna Circle, which is what I am most looking forward to.
Anyway, to pique your interest I’ll pass along this bit that entertained me, where Sigmund recounts Ludwig Boltzmann presenting an address to the Philosophical Society with the “bland title On a Thesis of Schopenhauer,” and then opening his talk... 
“with the offhand comment that he had originally intended to use a somewhat more provocative title, to wit: Demonstration That Schopenhauer Is an Insipid and Ignorant Philosophaster Who, by Ceaselessly Propagating Hollow Twaddle, Spreads Nonsense Far and Wide and Forever Perverts Brains from Top to Bottom.  Amusingly enough, Boltzmann was actually giving Schopenhauer some of his own medicine, for none other than Schopenhauer had used exactly these same phrases to rail against the arcane writings of George Wilhelm Friedrich Hegel. Not that Boltzmann cared one bit for Hegel either.”
(I’ll assume this is just as humorous in the original German…;)

I may say more about the 400-page volume in the future.
(An MAA review of the volume is HERE.)


Lastly, speaking of demented times, and in honor of today’s young people (acting when grown-ups won’t!), some timely old cinema from the “I’m-a-human-being-goddamn-it-and-my-life-has-value” Dept.:

Tuesday, February 20, 2018

“Duck and Cover”

I grew up in the 1950s when our biggest fear in America was of a nuclear bomb blast -- though in reality, as a child, I felt few fears, and virtually none on a daily basis.

(ahhh yes, “worse than a terrible suntan”…)

I can’t even imagine sitting at a schoolroom desk, worried about being shot in the head (nor being the parent who must drop their child off at the school front door) — the daily reality of today’s students/parents — far scarier than my generation ever felt about the nuisance of a measly atomic bomb.

Sunday, February 18, 2018

Man vs. Computer

From Davis and Hersh (in "The Mathematical Experience"):
"To the philosopher, there is all the difference in the world between a proof that depends on the reliability of a machine and a proof that depends only on human reason. To the mathematician, the fallibility of reason is such a familiar fact of life that he welcomes the computer as a more reliable calculator than he himself can hope to be."

Thursday, February 15, 2018

“Tears In Heaven”

“Time can bring you down
Time can bend your knees
Time can break your heart
Have you begging please, begging please”

How can a nation, that so utterly fails safeguarding its children and youth, succeed into the future.…

( the Parkland, FL. victims, and the many, many, many, many more who will assuredly follow)

Wednesday, February 14, 2018

How Do I Love Thee…

Let me count the ways, employing the real numbers of aleph-one.…
(this might take awhile)

OK, actually for Valentines Day just a few (finite) links:

Starting with Ben Orlin covering it last year:

Jennifer Ouellette’s classic piece I used to link to every year, but haven’t for awhile (and ought not be missed):

…and lastly this from someone who’s gone completely ridiculously bonkers overboard:

Sunday, February 11, 2018

Mathematical Knowledge

From Ed Frenkel's "Love and Math":
“Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can’t be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what’s also amazing is that we own all of them. No one can patent a mathematical formula, it’s ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It’s too precious to be given away to the 'initiated few.' It belongs to all of us.” 

Tuesday, February 6, 2018

Miscellaneous RFI...

Some real miscellany for today!:

1)  start with some actual mathy-ness: 
The continuum hypothesis involves a well-known conundrum (considered undecidable without new set theory) among mathematicians over whether any infinite sets exist between aleph-zero and aleph-one. But I don't recall hearing any arguments over whether there could be infinite sets between any other alephs (say, aleph-three and aleph-four) — of course these higher sets are all power sets, but I can’t recall ever reading any “proof” that there can be no set in-between… I assume this is a long-settled simple question, but am not sure what the simple answer is! or is it somehow axiomatic with no real proof... or does it not even much matter since there's already an infinity of infinite sets???

ADDENDUM:  I've now posed this question to a local retired math professor/number-theorist and he didn't know the answer, so at least I feel better at this point that it may not be a simple or dumb question to ask! (but have not heard from anyone else)

2)  Next, no math, just a question that I asked on Twitter but got little response to, so will try here:
Google search has given me sporadically crappy results for several weeks (sometimes NO results, and sometimes results having no or little bearing on what I’m searching for), so I’ve switched over to Bing for now, but just wondering what search engines other math-types are happy with (it’s not a privacy issue or any other concern, strictly quality/relevance of results)? And are others experiencing issues with Google search — seems like some real glitch involved?

3)  Finally, just a note… Two of the the greatest television shows ever when I was younger were Carl Sagan’s “Cosmos” and Jacob Bronowski’s “The Ascent of Man.” I’ve sometimes used Bronowski quotes and videos here on the blog, and just as “Cosmos” was re-done a few years back I feel like “Ascent of Man” should be re-run or re-done for each new generation.
Anyway, I stumbled across Bronowski on the Web a few days back and suddenly realized that he was trained as a mathematician (somehow I had him pegged in my mind as a physical scientist). Also didn’t realize he had died at the age of 66 (much younger than I thought) just one year after “Ascent…” was completed in 1973. Additionally discovered that “Ascent…” was originally commissioned by Sir David Attenborough. Just all interesting tidbits to me… and here is Dr. Bronowski voicing some of his thoughts about mathematics:

Sunday, February 4, 2018

"Mathematics is the music of reason"

Paul Lockhart provides this Sunday reflection:
“Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.” 

Thursday, February 1, 2018

Two That Bear Repeating

Today, am just re-citing 2 of my very favorite long, rich blogposts that I’ve previously linked to, one from Lior Pachter a couple years back and an even older one from Tim Gowers. New people/teachers are constantly entering the math blogosphere, so for any who may have missed these earlier on I think they bear re-posting/re-reading:

Monday, January 29, 2018


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 NumberphileTadashi 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:

ADDENDUM:  Mike L. sends me a link to several videos he has indeed done previously with soap bubbles :)

Sunday, January 28, 2018

Math Courses

Sunday reflection...

“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.”
— Carl Stoermer

Thursday, January 25, 2018

A Tweet, A Post, and a Survey

Some miscellany from the current week for your entertainment:

1)  Just a funny Twitter thread that, if you read the comments all the way down, may offer some potential grist for classroom discussions:

2)  ICYMI, Ben Orlin tackled a thorny debate yesterday (school math requirements), with his usual aplomb (and round-faced colleagues):

3)  A New Zealand researcher is studying attitudes toward mathematics — you may wish to help out by filling out their survey questions:

Monday, January 22, 2018

A Re-run on Self-reference

Short on time for new posts right now but will re-run (slightly modified) this old one on self-reference from MathTango some years back:

"This sentence contains ten words, eighteen syllables, and sixty-four letters." (from J. vos Post)

While researching the above sentence I came across this entertaining list of 150+ recursive or self-referential sentences:

In a related note, earlier this week Futility Closet posted about a new pangram or autogram in Lee Sallows' tradition:

Meanwhile, there are plenty more self-referential sentences at these pages:

And over five yrs ago I ran this just-for-fun post (entitled: "There is no title for this post."):


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?


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:

And then this bit of parody-absurdity:

Lastly, this is the final sentence of this particular post, which would appear to end with the word, hippopotomonstrosesquipedaliophobia.

Sunday, January 21, 2018

Of Heavens and Math

From G.K. Chesterton:
“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.” 

Friday, January 19, 2018

Fly Away

Is snow keepin’ ya inside, or are you otherwise bored, or down with a cold/flu, than a post just for you today, full of practical application ;)

… a few videos (making similar claims), for constructing long-flying paper airplanes.
 Do it!:

[...for a little more mathy content a short, new Friday potpourri is now up at MathTango ]

Tuesday, January 16, 2018

Stayin' Alive...

May be busy with a project for awhile, possibly slowing down blogging... but will try to keep y'all entertained, somehow... oh yeah!:

Sunday, January 14, 2018

'I was in prison and might be shot'

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.”

Friday, January 12, 2018

A Suggestion for Nigerian Email Scammers

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…