Sunday, November 19, 2017

A Little Self-referential Humor

for Sunday reflection... just an old, classic joke:
“There are three kinds of people in the world: those who are good at mathematics and those who aren’t.”

[...also, a new post over at MathTango today in honor of Thanksgiving approaching.]

Thursday, November 16, 2017

Sunday, November 12, 2017

Playing Games

From the inimitable John Conway:
“You get surreal numbers by playing games. I used to feel guilty in Cambridge that I spent all day playing games, while I was supposed to be doing mathematics. Then, when I discovered surreal numbers, I realized that playing games IS mathematics.”

Thursday, November 9, 2017

Happy Birthday Carl

It’s Carl Sagan’s birthday today; an apt time to re-read some of his words and view classic video:
    “If you wish to make an apple pie from scratch, you must first invent the universe.”
“Extinction is the rule. Survival is the exception.”
    “The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in     
    our apple pies were made in the interiors of collapsing stars. We are made of starstuff.” 
“We live in a society exquisitely dependent on science and technology, in which hardly
anyone knows anything about science and technology.”
    “The dangers of not thinking clearly are much greater now than ever before. It's not  
    that there's something new in our way of thinking -- it's that credulous and confused  
    thinking can be much more lethal in ways it was never before.”
Science is more than a body of knowledge; it is a way of thinking. I have a foreboding of an America in my children's or grandchildren's time -- when the United States is a service and information economy; when nearly all the manufacturing industries have slipped away to other countries; when awesome technological powers are in the hands of a very few, and no one representing the public interest can even grasp the issues; when the people have lost the ability to set their own agendas or knowledgeably question those in authority; when, clutching our crystals and nervously consulting our horoscopes, our critical faculties in decline, unable to distinguish between what feels good and what's true, we slide, almost without noticing, back into superstition and darkness. The dumbing down of America is most evident in the slow decay of substantive content in the enormously influential media, the 30-second sound bites (now down to 10 seconds or less), the lowest common denominator programming, credulous presentations on pseudoscience and superstition, but especially a kind of celebration of ignorance.
In memory...

Wednesday, November 8, 2017

Perception of Streaks

H/T to Dan Goldstein (on Twitter) for pointing out an Interesting plotting of (likely and VERY likely) “streak” probabilities:

The author looks mostly at "coin-tossing"-like scenarios, but notes such analysis potentially relates back to other theoretical discussions (such as "hot hand" observations). One can imagine a lot of other ways to play with similar data (and the author presents R code for doing such).

Tuesday, November 7, 2017

Twitter Quirkiness

Just a quirky episode from the other day... below is a verbatim copy of a tweet that someone posted (I've taken their name off) which I read quickly, thought was kind of fun, and re-tweeted to my followers, giving no more consideration.  If you've not already seen it, take a quick look, and then scroll further below for the little follow-up:


the non-commutativity of custard, according to . i'm going to have to try this. so weirddd  

A smidgen interesting I thought, but did you catch the error? (and no, I don't mean the spelling of the word "weird" which was clearly deliberate)... because it slid right by me, despite being rather obvious! And it interests me because of the way language and words function cognitively (psycholinguistics, including speech processing, was my primary focus decades ago).
So, in case, like me, you didn't notice it, the graphic example shown above is one of associativity, and is clearly labelled as such. Yet the poster's description calls it an example of "non-commutativity" (which of course it is NOT).
I simply found interesting the tendency (on my part anyway) to be so drawn to the graphic as to read right through the clear, posted words and not have them accurately register -- you think you know what they say, but the precise meaning may be translated in one's mind quite otherwise, overridden by expectation or the simple speed of processing (part of it too I think is just the mental 'appeal to authority,' resulting from invoking Eugenia Cheng's name, even though she is NOT the one who makes the error). It's almost like an optical illusion that you "see" one way, but is really another -- here, a word takes on an illusory effect.
Anyway, this may be of interest to no one else; I'm just eternally intrigued/concerned by how language plays with our minds (and often in far more deleterious ways!).
p.s.: Brian Hayes was the one who first pointed out the error above to me, and the author of the post apparently heard from several other folks as well; so to many, the mistake no doubt jumped right out.

In any event, I'm in the mood for some custard. :)

Monday, November 6, 2017

Sunday, November 5, 2017

The Dismal Science

Sunday reflection:

To put it bluntly, the discipline of economics has yet to get over its childish passion for mathematics and for purely theoretical and often highly ideological speculation, at the expense of historical research and collaboration with the other social sciences. 
...This obsession with mathematics is an easy way of acquiring the appearance of scientificity without having to answer the far more complex questions posed by the world we live in

-- Thomas Piketty

Sunday, October 29, 2017

Keeping It Short

One of the shortest Sunday reflections ever, courtesy of Paul Erdös:

"If numbers aren't beautiful, I don't know what is."

Wednesday, October 25, 2017

The Universe... Even or Odd

I should be writing a blurb about the various 2017 mathy books that have passed my way the last few months, but instead the volume I just finished reading is an older classic, Roy Sorensen’s 2003 A Brief History of the Paradox. Toward the end comes a ‘paradox’ (perhaps known by some as 'the odd universe' paradox) I was unfamiliar with and frankly don’t quite understand, though it doesn't appear too difficult. Am passing it along because some of you may find it interesting (…or be able to explain it better to me!).
Verbatim from the book (I’ve bolded a few bits that I especially have difficulty following):
“Meanwhile, Nelson Goodman kept sharpening the knife of nominalism. In 1951 he published The Structure of Appearances. This book contains a logic of parts and wholes. Goodman denies that there are sets. Instead, there are fusions built up from smaller things. Unlike a set, a fusion has a position in space and time. You can touch a fusion. I’m a fusion. So are you. Goodman’s ‘calculus of individuals’ says that there are only finitely many atomic individuals and that any combination of atoms is an individual. Objects do not need to have all their parts connected, for instance, Alaska and Hawaii are parts of the United States of America. Goodman does not let human intuition dictate what counts as an object; he also thinks that there is the fusion of his ear and the moonIn a seminar Goodman taught at the University of Pennsylvania around 1965, John Robison pointed out that The Structure of Appearances implies an answer to ‘Is the number of individuals in the universe odd or even?’ Since there are only finitely many atoms and each individual is identical to a combination of atoms, there are exactly as many individuals as there are combinations of atoms. If there are n atoms, there are 2n - 1 combinations of individuals. No matter which number we choose for n, 2n - 1 is an odd number. Therefore, the number of individuals in the universe is odd! The exclamation point is not for the oddness per se. Aside from those who think the universe is infinite, people agree that the universe contains either an odd number of individuals or an even number of individuals. What they find absurd is that there could be a proof that the number of individuals is odd. ‘Is the number of individuals in the universe odd or even?’ illustrates the possibility of one good answer being too many. Our expectation is that this question is unanswerable. The lone good answer confounds beliefs about what arguments can accomplish.”
Anyway, seems like an interesting thought exercise to play with.
(If you can explain it any more lucidly in the comments feel free to give it a go. The primary part I'm unclear about is, in the 2nd part that I've bolded, why does the 2nd sentence necessarily follow from the prior sentence?)

Monday, October 23, 2017

Gauss... the Rodney Dangerfield of Mathematics?

A John Golden tweet this weekend reminded me that I should check in on GaussFacts every now-and-then (…like when Trumpsky makes me want to slit my wrists, or, even more assuredly, his) for a few guffaws.
It's one of my favorite ongoing math-humor bits, but truly Gauss gets a lot more respect than Rodney ever did:

Sunday, October 22, 2017

The Minds of Brilliant Mathematicians

A Sunday reflection from Kaja Perina in a piece on Alexander Grothendieck:
“The minds of brilliant mathematicians are of perennial fascination. But in the onrushing era of synthetic neurobiology and genomic reconfiguration, the possibility that genius and mental illness are intertwined takes on monumental significance. If scientists are eventually able to alter living brains or edit human embryos with an eye to mitigating conditions such as autism and schizophrenia, do we risk excising brilliant outliers from the gene pool? Isaac Newton, John Nash, and Alexander Grothendieck are low-frequency, high-impact minds; they advanced civilization in the domain on which they trained their high beams. It is worth turning the high beams of scientific inquiry on those same unusual minds.”

Friday, October 20, 2017

Foundations, Randomness, Free Will, the Aaronson Oracle

To end the week, another wonderful new episode from PBS's Infinite Series, this time on the foundations of mathematics:

Also, sort of cool… in the commentary after the episode the show host, Kelsey Houston-Edwards, briefly mentions the Aaronson Oracle, which I was unfamiliar with, and which interactively demonstrates the difficulty of 'randomness.' It's a program from Scott that predicts a choice (generally succeeding well-over half the time, with two possible choices) that you will make in attempting to randomly press two computer keys:
Read a little about it here:
...and then try it out here:

Thursday, October 19, 2017

Crazy... Like A (Cunning, if Unstable, Mentally-Ill) Fox

I suspect one reason Dotard Trump was so willing to let Steve Bannon, Seb Gorka, Reince Priebus (and others) depart his Administration is because of the amount they were leaking, for their own benefit, to the press.
The crazy stories that eke out of this White House, may of course indeed reflect craziness within the West Wing, but more and more they look orchestrated and planted selectively just to see which ones end up reaching manipulated media outlets, thus signifying who is doing the ongoing leaking (which is NOT to say that there isn’t still much real craziness within the Oval Office)… all of which was hinted at by this puzzle post I did just a couple of months back:

If, alternatively, there is no method to the madness of this White House, then we are left with just pure unstable, narcissistic sociopathy in the midst of enablers. Oy.

Tuesday, October 17, 2017

Fawnzie Nguyen…

Yesterday afternoon I noticed my Twitter feed popping up with accolades for Fawn Nguyen’s keynote address to the Northwest Mathematics Conference. Unfortunately, it wasn’t recorded so those of us not in attendance have missed out.
I don’t have anything special in the works for posts this week, so it seems like a good time to refer any readers who have never read it to my 2014 interview with Fawn, which has always been one of my favorite interviews here (especially since at the time I knew relatively little about her). The same insightful, funny, inspiring spirit she exhibits on stage (and in writing and in the classroom and on Twitter) comes through I think in her answers here:

Also, in the interview I asked her about her favorite own postings of all time and she referenced just one (from 2012), which if you’ve not read before, you must:

Worth noting too that Ms. Nguyen has a book on teaching math coming out in the future.

p.s.… Twitter posters yesterday kept referring to the “last line” of Fawn’s keynote (apparently very memorable and powerful!), but I don’t know what it was??? :-(
So hey, can someone tell us what that line was with maybe enough context to get a full sense of it (or will it not carry as much weight without hearing the talk preceding?). Or, maybe Fawn or someone else can post a transcript of her keynote. Puhhh-leeeeze!

Sunday, October 15, 2017

The Darkness of Axioms

A little Sunday reflection from Bernhard Riemann:
“It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it.” 

Friday, October 13, 2017


End of another crappy week for America, democracy being dismantled day-by-day; will just re-reference a previous post from 5+ months ago…: