Saturday, January 18, 2020

Our Fragile Nation



American democracy is fragile, yet resilient. We'll soon see if Republicans turn the impeachment trial of demagogue Donald Trump into a farcical sham (as they'll no doubt attempt to do). How many Republican Senators will refuse to cave to money, power, and autocracy, and actually seriously consider the Constitution, rule-of-law, and founding principles?....

Today (because it seems timely) I am just re-posting, with minor changes, an entry from close to a year ago:

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Most readers here likely know the famous story of Kurt Gödel’s 1947 visit to an examiner’s office to apply for U.S. citizenship — it’s been briefly told many places, as I did back HERE.

Gödel, logician that he was, thought he’d found a 'logical flaw' or 'contradiction' in the U.S. Constitution that would allow a dictator to take power in the U.S., not unlike what Europe had witnessed. Friends, Oskar Morgenstern and Albert Einstein, talked Gödel out of bringing this up at his examination, believing, according to some accounts, that his worry was 'far-fetched and outlandish.'  No one knows for sure what his qualms centered upon, but the most widespread guess is that he was concerned about Article V of the Constitution allowing for amendments to the Constitution… even amendments that might weaken/eliminate various checks-and-balances and hand more authority to a despotic leader. We could theoretically amend ourselves right into a dictatorship.
The appeal of this explanation is that it reflects Gödel's well-established interest in self-reference: i.e., the Constitution could be amended, the amendments could be amended, the amendments to the amendments could be amended, etc.
While certainly possible, I’ve never been fully comfortable with that ‘guess’ of Gödel’s thought process, because Kurt probably realized what a slow, arduous, unwieldy path amending the Constitution actually is… with ample opportunity along the way to redress or put the brakes on ill-founded changes.

I’ve begun to wonder if just perhaps what Gödel had in mind was, alternatively, something far simpler, more direct, and more mathematical:
He would’ve clearly understood the math of the Electoral College (as spelled out in Amendment XII of the Constitution), and recognized that a demagogic individual could become President with a minority of the citizens' vote (not even a plurality, let alone a majority) by simply concentrating on a handful of key states. Then, with backing of a subservient Party he might run roughshod over most checks-and-balances simply with the judicious use of Executive Orders, Executive Privilege, emergency measures, martial law, judicial appointments, and the President’s function as Commander-In-Chief of the military... may or may not be a better explanation than the Article V focus, and might or might not be viewed as a 'logical flaw.'

In the oft-quoted words of Sinclair Lewis (who was contemporaneous with Gödel):
 "When fascism comes to America it will be wrapped in the flag and carrying a cross."
In short, if enough of the electorate is naive and ignorant enough to elect one, isn’t every democracy at risk of putting a despot-to-be into power, and made even easier with our Electoral College system? The German experience may be more 'normal' than we care to contemplate...
Is THAT what Gödel realized 72+ years ago?

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Thursday, January 16, 2020

More Book Lists…


Book lists always make good space-fillers! So here we go ;)

Awhile back I stumbled upon an 8-year-old post from prolific author Ian Stewart listing his  “Top 10” popular math books:

In 2012 that list was as follows (no particular order):

The Man Who Knew Infinity  — Robert Kanigel
Gödel, Escher, Bach  — Douglas Hofstadter
The Colossal Book of Mathematics  — Martin Gardner
Euclid and The Rainforest  — Joseph Mazur
Four Colors Suffice   — Robin Wilson
What Is Mathematics, Really?  — Reuben Hersh
Magical Mathematics    — Persi Diaconis and Ron Graham
Games of Life   — Karl Sigmund
Mathematical Tales of Mathematical Wonder   — ed. by Rudy Rucker
The Mathematical Principles of Natural Philosophy   — Isaac Newton

(don't know what Stewart might add to that list in the dozen years since it appeared)
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This made me start looking around the Web for other favorite popular math book lists. There were fewer than I expected.

This 13-member list comes from math teacher Ali Kayaspor:
  • Zero: The Biography of a Dangerous Idea — Charles Seife.
  • Prelude to Mathematics — W.W. Sawyer.
  • Measurement   — Paul Lockhart
  • The Joy of X — Steven Strogatz.
  • An Imaginary Tale — Paul Nahin.
  • Proofs From the Book  — Aigner and Ziegler
  • Things to Make and Do in the Fourth Dimension    — Matt Parker
  • What is Mathematics?   — Courant and Robbins
  • A History of Pi    — Petr Beckmann
  • e: The Story of a Number    -- Eli Maor
  • Imagining Numbers   -- Barry Mazur
  • Journey Through Genius   -- William Dunham
  • Prime Obsession   -- John Derbyshire
Kayaspor also has a separate book-list "for math people and designers":

From the GoodReads website comes this list of a dozen math-related books:

Gödel, Escher, Bach — D. Hofstadter
Fermat’s Enigma  — Simon Singh
Flatland  — Edwin Abbott
The Code Book  — Simon Singh
Zero    — Charles Seife
The Man Who Loved Only Numbers  — Paul Hoffman
Journey Through Genius  — W. Dunham
A Beautiful Mind   — Sylvia Nasar
The Drunkard’s Walk   — Leonard Mlodinow
How to Lie with Statistics  — Darrell Huff
Euclid’s Elements — Euclid
What Is Mathematics   — Courant and Robbins

The FiveBooks site offers this (2018) list of 10 best math 'history' books:

Prime Obsession  — J. Derbyshire
Mathematics for the Nonmathematician   — Morris Kline
Zero  the biography of a dangerous idea   — Charles Seife
A Concise History of Mathematics   — Dirk Struik
Unknown Quantity  — J. Derbyshire
The Math Book   — Clifford Pickover
A History of Mathematics   — Merzbach and Boyer
God Created the Integers   — Stephen Hawking
Fermat’s Enigma   — Simon Singh
Journey Through Genius   — W. Dunham

The Fivebooks site has several other science/math related listings possibly worth perusing:
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This list comes from Peter Flom on Quora:

A Mathematician's Lament — Paul Lockhart
Out of the Labyrinth — Robert and Ellen Kaplan
Conversations with a Mathematician — Gregory Chaitin
Proofs and Refutations  — Imre Lakatos. 
Mathematics: Coffee Time in Memphis — Bela Belobas
The Measure of Reality: Quantification and Western Science 1250-15400 — Alfred Crosby
Godel Escher Bach — Douglas Hofstadter
The Proof and Paradox of Kurt Godel — Rebecca Goldstein
Group Theory in the Bedroom and Other Mathematical Diversions — Brian Hayes
 Pretty much anything by Martin Gardner or Ian Stewart
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Here's one of several Reddit threads related to favorite math books:

Simon Singh offers up a long list of recommendations here:

And finally, I’ll add my own tentative baker's-dozen list (in no special order, and subject to change on a different day-of-the-week) to the mix:

The Prime Number Conspiracy  — ed. by Thomas Lin
Single Digits   — Marc Chamberland
Math With Bad Drawings  — Ben Orlin
Things To Make and Do In the Fourth Dimension  — Matt Parker
How Not To Be Wrong   -- Jordan Ellenberg
The Language of Mathematics — Keith Devlin
The Colossal Book of Mathematics   — Martin Gardner
How Mathematicians Think  — William Byers
The Music of the Primes  — Marcus du Sautoy
Mathematics For Everyone   — Laurie Buxton
Grapes of Math   — Alex Bellos
Unknown Quantity   — John Derbyshire
The Penguin Book of Curious and Interesting Mathematics  -- David Wells

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3 additional books are among my all-time favorites, but their subject matter crosses so many boundaries that I don’t really think of them as ‘popular math books’:

The Outer Limits of Reason  — Noson Yanofsky
Gödel, Escher, Bach    — Douglas Hofstadter
When Einstein Walked With Gödel — Jim Holt
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By the way, for those whose taste runs to fiction Alex Kasman maintains a large site of recommended math-related fiction/novels:
http://kasmana.people.cofc.edu/MATHFICT/
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Honestly though, all of these barely scratch the surface of the wonderful math reading that is out there. Indeed, I think we're currently experiencing a kind of golden age for popular math!




Monday, January 13, 2020

ASMR Monday


OK, to start your week, the first ASMR post of 2020. One genre of ASMR I only stumbled upon a few months back (and quickly became a favorite type) is often called "fast and aggressive ASMR," generally involving rapidly produced and changing auditory stimuli. Because the focus is on the audile and not visual aspect it can simply be played in the background while doing other things online, or simply closing one's eyes and listening. Here is one example:




Thursday, January 9, 2020

Lies, Damned Lies, and....


(via Wikipedia)
                                                    
One of the late chapters in David Spiegelhalter’s fine volume, The Art of Statistics,” focuses on the problems and reproducibility crisis in psychology research.

This sentence gave me a bit of a startle: “In a 2012 survey of 2,155 US academic psychologists, just 2% admitted to falsifying data.” The part that gave me a gasp was the phrase, “just 2%” as if that was a small figure. I’m not surprised that 2% have falsified data; I’m surprised that that many would admit to it! Indeed, I feel sure (though am only guessing) that the majority who have done it would NOT admit to it, and that the true figure is therefore probably at least double the 2% given — that would be at least 4% who haven’t just made mistakes, or fudged a little, or spun their conclusions, but outright falsified data! 

I don’t know how many total academic psychologists there are, but depending where they are and how much they publish, 2 - 4+% represents a pretty serious problem in my mind.  And while psychology is probably especially vulnerable to such falsification this doesn’t even address how much may additionally go on in biological, medical, and physical science fields. Spiegelhalter goes on to note that 94% of those in the study admitted committing at least one of 10 "questionable research practices" looked at.  Of course there are many reasons for such a state of affairs, but ultimately none very defensible. The award-winning site "Retraction Watch" has been tracking, for years now, published scientific papers that are retracted due to various issues, including fraud -- and they never seem to run out of material! :(( (definitely a site worth following and supporting if you're not already).

I was a psychology major myself 45 years ago and complained, to deaf ears, about the sloppiness of the field, but sloppiness and fraud are almost separate issues. Still, glad to see it all attracting more attention these days.

The study Spiegelhalter cites is here (with a lot more details):



Sunday, January 5, 2020

Reuben and Martin...


     “The working mathematician is a Platonist on weekdays, a formalist on weekends.”  
                                                                                      — Reuben Hersh

Mathematician and popular prolific writer Reuben Hersh died on Jan. 3, apparently in Santa Fe, NM., but I haven’t seen any details about his demise or major tributes as yet on the Web (no doubt forthcoming).  Hersh started off with a B.A. in English literature in 1947, and only later returned to school to attain his Ph.D. in mathematics in 1962.

Hersh’s writing was almost always interesting and thought-provoking (advocating what he termed a “humanist” view of mathematics) whether one agreed with him or not. He famously feuded with recreational mathematician/writer Martin Gardner as exemplified in a well-known and critical 1997 review Gardner wrote about Hersh’s popular volume, “What Is Mathematics, Really?” Gardner was a vocal and sharp-tongued "Platonist;" Hersh was not. Definitely worth a read if you’ve never seen it (the review):
https://www.latimes.com/archives/la-xpm-1997-oct-12-bk-44915-story.html


Gardner leads off saying he has “such high respect for [Hersh] as a mathematician and such low respect for his philosophy of mathematics.” And it gets harsher from there.
Hersh did eventually reply to Gardner though I couldn’t find a direct, free link to it on the Web (if someone knows of one let us know). This page offers up the first page of Hersh’s response and means for seeing the rest if you so wish:
https://www.deepdyve.com/lp/springer-journals/reply-to-martin-gardner-1IRiQyGw5c

==> ADDENDUM: Thanks to .mau (in comments below) for finding this unformatted link to Hersh’s response:

Many of Hersh's other articles are here:

Martin Gardner, who like Hersh died in his 90's, wanted to believe there was an 'afterlife' following death. Perhaps if there is, he and Reuben are carrying on their fascinating debate somewhere in the great beyond... or, better yet, maybe they've found a final answer.




Saturday, January 4, 2020

It's A Contest!


MoMath
                                                
I’m sure word of this is getting disseminated adequately without my little added promo for it, but if you haven’t heard yet the National Museum of Mathematics has announced the "Steven H. Strogatz Prize for Math Communication" for applicants between 15 and 18 years of age. How cool is that! Read all about it here:

The contest is worldwide, and I’ll bet there are going to be some sensational, maybe mind-blowing entries -- so much untapped creativity across the globe. But deadline for submissions is April 22, 2020, not all that far off. All sorts of forms of communication are encouraged, falling into various categories, and will be judged on the basis of “content, creativity, communication.” There will be cash prizes and of course posting of winning entries on the Web.

What a great idea to encourage young math minds early on along their path. Hope/assume this will be an annual event.



Wednesday, January 1, 2020

Twitter Resolve….


                                   


It's that ridiculous time of year again for well-intended (if improbably-kept) resolutions:
1)  Re-read more math and statistics books… and, peruse less politics on Twitter
2)  Lift more weights, do more back exercises… and, tweet less. 
3)  Play more pickleball/tennis… and, post fewer re-tweets. 
4)  (Pretend to) play my guitar more… while responding on Twitter less.  
5)  Eat fewer carbs, breakfast pastries, and treats… resist growling, grumbling over tweets.   
6)  Dwell more on the awesome and transcendent… and less on the terse and snarky.
…catch my drift; there's a theme here (now if someone would hold me to it).
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...With an impeachment trial soon underway (I presume) and state primaries little over a month away I may be too distracted by politics for awhile to blog much (though I do have plenty of ASMR videos saved to post sporadically!). So IF posts become sparse it just means that I'm busy with other things (...like, you know, saving democracy!), and not gone into hiding.



Monday, December 30, 2019

Yes or No


Been reading a review copy of a wonderful new book (due out in March) by Matt Cook from MIT Press, entitled “Sleight of Mind,” all about one of my favorite topics… paradoxes. It’s chockfull of them, and I’ll do a fuller review closer to the publication date, but will entice you with just a few fun, simple one-sentence logic puzzles (variations of the “liar paradox”) that appear near the start of one section of the volume:
“Answer truthfully, yes or no: Is ‘no’ the correct answer to this question?" 
“Now answer this one truthfully: Is ‘yes’ the correct answer to this question?” 
“What about, ‘Does this question have an answer?”
…and I’ll leave you to contemplate these on your own. 
(but essentially, for one of them neither answer works, for one of them both answers work, and for one of them only one answer fits).


Monday, December 23, 2019

Bye Bye Bayes…


                                           
One tidbit I found especially interesting/surprising (and had never heard about) from David Spiegelhalter’s current “The Art of Statistics” volume, is that Bayes' Theorem or Bayesian inference/reasoning has been banned in British courts… yeah, you read that right Nate Silver, BANNED in court! ;)  As if statistics weren’t confused and misused enough by lawyers, one of the most common and vaunted modern approaches to probability isn’t even allowed, and this decision goes back at least 8 years.

Here are a few of the links that talk about the decision:





If any of our friends from across the pond can tell us more about how much controversy or debate this prohibition has produced in UK (or is it 'settled law' at this point?) I’d be curious to hear.


Sunday, December 15, 2019

Calming Canine ASMR


With the House impeachment vote looming in a few days perhaps I should squeeze in another relaxing ASMR clip before the never-ending Republican bullsh*t hits the proverbial fan & airwaves... 
Did an earlier ASMR with a feline, so here's one with Simba, a big, gorgeous Shetland Sheepdog... enjoy:





Tuesday, December 10, 2019

Of Ed Witten and Donald Trump



Just a little clash of thoughts in my mind recently….

By chance I’ve read several books/articles lately where Ed Witten’s name pops up; always of course in glowing terms, i.e., ‘the most brilliant scientist of our time,’ ‘the most important thinker alive,’ ‘the greatest living theorist,’ etc. Indeed, many of the other leading thinkers of our time admit that Witten is a person with ideas they can barely comprehend or keep up with. He is a mathematical physicist (and a Fields Medalist, among many awards), and I won’t even try to offer a bio or synopsis of him here (other than to say he and I were born in the same year, after which our lives diverged considerably ;) — most readers no doubt know basically who he is.

But what struck me in seeing his name so much recently, is that most Americans (outside the astute readers of this blog of course ;)) likely have no idea who Ed Witten is — his name would be largely unknown I bet to 90++% of all literate Americans. 
I suspect, in his day, and certainly now, the name “Albert Einstein” was known to most all Americans. Even names like Heisenberg, Bohr, and others probably are somewhat recognizable to a majority of again literate Americans. Late in life, and especially following his death, “Richard Feynman” became very well-recognized among masses of American citizens. And of course there's Stephen Hawking too. Yet this current ‘most brilliant man alive’ exists somewhat in virtual obscurity outside of the scientific community that reveres him. 
I’m not someone who thinks we should place individuals on pedestals (in fact I dislike the practice of building monuments/statues to individuals, or even naming buildings/streets after them, etc.), but I do wish our education system and press made citizens more aware of such major contributors to our knowledge and progress. I can’t help but think what a splendidly better country this would be if more of the electorate knew the name “Ed Witten” than knew the name “Kim Kardashian.” We might even then be a nation that would not elect (more tragically than laughably) an incompetent, authoritarian demagogue to the highest post of the land… and take 3 damn shattering years to impeach his autocratic ass. ...ehh, just some idle thoughts for this Tuesday. ;)




Sunday, December 8, 2019

Sunday Illusion


OK, for your Sunday entertainment and perspicacious pondering I’ll pass along this optical illusion that seems to be making the rounds — it’s somewhat cool, and I didn’t recall seeing it before:


It works better for some folks than for others, and there are actually multiple ways to make it work besides the “breathing” routine. Despite being passed around a lot right now, when I tried to learn more about it I found it went back to at least 2015, but still haven’t found the originator or precise explanation for how it works. In fact, for something that’s been out there for at least 4 years I’m surprised how little I could find about it on the Web. Maybe the best explanation (and still not all that incisive or neurologically revealing) is this comment placed on one site:
“The dots aren't moving. There are two sets of dots in alternating points around the circle, and they're flashing between the two sets. The illusion of movement comes from the suggestion to the viewer that the dots are moving, resulting in subconsciously following in the chosen direction.”
Anyway, if you know more about it feel free to elucidate in the comments below! ;)