Monday, December 28, 2020

Thinking Outside the Box...

 A new round of always-fun lateral thinking puzzles from Futility Closet today:

...and here's an hour-plus of science-writer John Horgan talking to science-writer Amanda Gefter:

Friday, December 25, 2020

25th Amendment....

 No math today, just a Sunday deadline:

(...while wondering if Nashville is an isolated tragedy or a presage of the next 4 weeks in America)

Thursday, December 24, 2020

Monday, December 21, 2020

"Torturing Data".... and, the price of tea in China

 Once again on the all-too-common practice of 'torturing the data':

"This is one reason why artificial intelligence (AI) is often brittle. AI algorithms can torture data faster than any human and can find an essentially unlimited number of idiosyncrasies that humans might overlook. Computers don’t get tired and they never say no."


Friday, December 18, 2020

Friday ASMR

 Taking you into the weekend with some stairway cleaning/brushing:

Monday, November 30, 2020

Let The Shopping Begin

 Usually toward the end of the year I do some sort of review of popular math books from the year gone by, including choosing a “Book of the Year.”  That tradition ends this year as I have read no math books (and very few books at all) since last March, having been so distracted by covid and the insane politics of America… moreover that rascal Ben Orlin didn’t put out a book this year, so what is the point of naming a book-of-the-year!  Just kidding, there were once again many fabulous books out in 2020 for the dedicated math fan. The four I did look at, and absolutely loved (and recommend), early in the year were, in no special order:

Mathematics for Human Flourishing

Humble Pi

Sleight of Mind

Do Dice Play God

Five more recent volumes that have definitely caught my eye are:


  Cut the Knot

  Best Writing On Mathematics 2020

  Games For Your Mind

  Why Study Mathematics

…. but many other math volumes appeared in the course of this year and if math books are part of your holiday shopping list you ought have no trouble finding several to select from. Indeed, this almost seems like a Renaissance period of math exposition, with the problem being over-choice, not scarcity!

ADDENDUM:  will go ahead and add this volume I just learned of today:

Frank Ramsey: A Sheer Excess of Powers

Friday, November 27, 2020

Friday ASMR

 I shouldn't let November get by without an ASMR post, so without further adieu...:

Wednesday, November 11, 2020

Benford & Biden, etc.....

ICYMI, in a timely video, Matt Parker has taken on Benford's Law as it relates to elections:

Sunday, November 1, 2020

Continuum Hypothesis via Scott Aaronson


Bored with the headlines, folks?... Is election news getting you down?... Or the blitz of political ads scraping on your last nerve?... Is that what's buggin' you, kiddies??? 

Well, OK, this won’t be everyone’s cup-a-tea, or fun distraction, but in a longish post (first of multiple) Scott Aaronson tackles the independence of the Continuum Hypothesis:

I knew it would be a great read when he started off with this quote from Bertrand Russell:


“in adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics.”

Wednesday, October 21, 2020

Sharing the Wealth....

We live in an age when the need for critical/logical thinking has never been more vital… and yet (it seems to me) is hardly taught or emphasized in our education system. Perhaps no field of study more greatly nourishes such an ability or objective than mathematics.  In that vein I recently asked on Twitter what organizations and non-profits math people themselves would encourage giving charitable donations to in order to help further foster mathematics and the skills it entails. 

Below are the suggestions, in no particular order, that I received (some of which I was unaware of), and I’m still happy to hear of even more, so feel free to add in comments:

Gathering For Gardner Organization

Julia Robinson Math Foundation

Bridge to Enter Advanced Mathematics (BEAM)

Edge For Women

National Council of Teachers of Mathematics


National Association of Mathematicians

American Institute of Mathematics

'Math circles,' active in many areas of the country (check your local area), were cited.

additionally, someone mentioned that there are likely several math-related Patreon accounts taking donations… some are HERE.

Lastly, I was a bit surprised that no one mentioned the Art of Problem Solving group, so I’ll throw it into the mix  as well.

As we head into the year-end charitable-giving season maybe keep such groups in mind right alongside all the more traditional names you'll hear from in your mailbox or otherwise.

Sunday, October 11, 2020

From Pencil & Paper to Zoom... Teaching and the Age of Covid


"There’s a minimalism to teaching and learning math that I’ve always loved. With just a pencil and paper I can become a mathematician. With just one good question I can launch a math class. But now there’s a lot more I have to rely on, and plan for. And it’s all beyond my control."

  -- Patrick Honner

Sunday, September 27, 2020

Friday, September 25, 2020

Covid at Cornell

 Covid... the Cornell experience:

Early success, but Kaiser Fung does caution at the end:

"Whether the success will last is an open question. It's only three weeks into the term."

Saturday, September 12, 2020

"Dear p-values...."

 Taking the p-values pledge:

"Based on this latest experience and my exhaustion with dealing with p-values, I am making a pledge:

There will be no p-values in any paper that I co-author in the next 12 months."
-- Adrian Barnett

Sunday, August 30, 2020

Sir Roger...

From ASMR (prior post) to an hour+ of Roger Penrose, courtesy of Numberphile:

More on the podcast and Penrose here, from AMS:

Friday, August 28, 2020

Birdie ASMR

Approaching the end of another hell-of-a-month with another ASMR....
Who knew that cockatoos were dogs!:

Wednesday, August 26, 2020


Okay, Mikhail Shubin replies to an Andrew Gelman post with this comment:

“Should you reply all to stop the annoying reply-to-all cycles? I think this is a case on an interesting moral dilemma!
You want to protest against something, but the only way to express your protest is to participate in the thing you want to protest against! The other examples:

* Should you fly to the conference on preventing the climate change?
* There is too many meeting in the company. Should you call a meeting to discuss this situation?
* Should you protest violently against violence?
* You believe the elections, organised in your county, are illegitimate. Should you still participate in the elections?
* You suspect you have COVID. Should you take a public transport across the city to get tested?”

And to see what he’s responding to you can check out the post here:

Monday, August 17, 2020

The Slippery Fish of Social Science...

when we’re doing social and behavioral science, we’re not looking for a needle in a haystack; rather, we’re trying to catch a slippery fish that keeps moving.  All this is even harder in political science, economics, or sociology. An essential aspect of social science is that it understands people not in isolation but within groups. Thus, if psychology ultimately requires a different model for each person (or a model that accounts for differences between people), the social sciences require a different model for each configuration of people (or a model that accounts for dependence of outcomes on the configuration).

I enjoyed this statistical (or almost meta-statistical) piece from Andrew Gelman yesterday on  social/behavioral science research, where the same concerns seem to re-occur again and again over time:

Sunday, August 16, 2020

Feeling Like a Pawn...

" I was terrified. It’s really scary to speak up in a room like that, and to call out literally everyone I work with. And I regret that I took half an hour to say something. I still can’t understand why no one else spoke up.... The message in that meeting was crystal clear. My school’s commitment to health and safety is a lie."
One teacher's experience as schools around the country attempt to open:

Difficult to see how this ends well... and how this wasn't all foreseen ahead-of-time by bureaucrats in charge.

Thursday, August 13, 2020

This Looks Interesting… (Keith Conrad)

I’d not heard of Keith Conrad (University of Connecticut mathematics professor)… until today that is, when R. J. Lipton referenced him:

Here’s Conrad’s homepage with what looks like lots of fun, interesting, miscellaneous stuff:

Monday, August 10, 2020

Fooling the Eyes


For awhile now I’ve used the above wonderful static optical illusion (of non-existent black dots appearing-and disappearing at grid intersections) as a header for my Twitter account, always presuming it was an example of the “Hermann grid illusion,” but I just recently discovered it is actually a slight variation known as the “scintillating grid illusion.” You can read a tad more about it here:

Friday, August 7, 2020

Wednesday, August 5, 2020

"Misplaced Confidence" in Statistics

This non-linear scaling is hard to grasp intuitively. It leads people to underestimate just how noisy small samples can be, and hence to conduct studies that lack the statistical power needed to detect an effect….
One thing is clear: conventional training in statistics is insufficient, or even counterproductive, because it might give the user misplaced confidence.”

Dorothy Bishop on cognitive/confirmation bias in stats:

The first principle is that you must not fool yourself and you are the easiest person to fool.”  
   — Richard Feynman

Monday, August 3, 2020

The Culture of Mathematics

"The idea that there is a single body of knowledge or a single way of thinking that we call 'mathematics' is a myth."
Maneuvering the path between Platonism and non-Platonism... Keith Devlin discusses the "culture" of mathematics (with interesting set of questions toward the end):

Sunday, August 2, 2020

Data, Science, News... and Bullshit

"At the same time as we are going through this populist political movement there is a technocratic worship of data. Arguments are being presented in an increasingly quantitative way: people are using data to bullshit."
-- Carl Bergstrom (co-author of Calling Bullshit: The Art of Scepticism in a Data-Driven World), on data, science, news… and B.S.:

Saturday, August 1, 2020

30+ Free Articles...

The latest wide-ranging issue of the Journal of Humanistic Mathematics is out -- a journal whose "emphasis is on the aesthetic, cultural, historical, literary, pedagogical, philosophical, psychological, and sociological aspects as we look at mathematics as a human endeavor." All articles are web-accessible (PDFs):

Wednesday, July 29, 2020

Monday, July 27, 2020


The always-interesting Liv Boeree going meta:

Sean Carroll had physicist, poker-player, thinker, tinkerer, Boeree on his Mindscape podcast almost exactly 2 years ago here:

Wednesday, July 22, 2020

Matt Parker Messes With Your Mind

Just a little puzzle from insidious Matt Parker today regarding David and Anton ( case you have no better way to while away the afternoon):

(...despite my understanding that corporal punishment has been banned in Britain for a few decades, anyone available has my permission to spank Matt mercilessly)

Tuesday, July 21, 2020

"Carpe diem..."

It was Robin Williams' birthday today... I can't let that pass unrecognized....

So Much Winning....?

Mehhh, just a few numbers on the TrumpVirus:

New Covid-19 cases in the last week: Mainland China: 172 Norway: 50 Greece: 186 Japan: 3516 France: 4377 Australia: 1831 Italy: 1394 United Kingdom: 5239 South Korea: 259 Canada: 2969 United States: 465,027

Presidential 'task force'(LOL) pr(opaganda)ess conference on tap for later today. ~5pm.

Friday, July 17, 2020

Friday ASMR

Yet another horrible week for the worldwide laughingstock that the USA and its joke leadership has become... maybe a good time to end with some ASMR... once again courtesy of a shoeshiner:

Tuesday, July 14, 2020

Wolchover on Gödel

Natalie Wolchover has a new piece on Gödel’s Incompleteness Theorem at Quanta Magazine:

As usual Natalie does a great job. I’m too lazy right now to look it up, but my favorite explanation of Gödel is probably Raymond Smullyan’s that he gives in one or more of his volumes. Rudy Rucker also does a good job for the layperson in at least one of his volumes, and Ms. Wolchover mentions the Ernest Nagel/James Newman short older volume “Gödel’s Proof” as another good source.

Lastly, I’ll re-post a quote/tribute I’ve used before from Freeman Dyson in "The Scientist As Rebel":

"Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.
"It is a curious paradox that several of the greatest and most creative spirits in science, after achieving important discoveries by following their unfettered imaginations, were in their later years obsessed with reductionist philosophy and as a result became sterile. Hilbert was a prime example of this paradox. Einstein was another…

"Science in its everyday practice is much closer to art than to philosophy. When I look at Gödel's proof of his undecidability theorem, I do not see a philosophical argument. The proof is a soaring piece of architecture, as unique and as lovely as Chartres Cathedral… The proof is a great work of art. It is a construction, not a reduction. It destroyed Hilbert's dream of reducing all mathematics to a few equations, and replaced it with a greater dream of mathematics as an endlessly growing realm of ideas. Gödel proved that in mathematics the whole is always greater than the sum of the parts. Every formalization of mathematics raises questions that reach beyond the limits of the formalization into unexplored territory."

Saturday, July 11, 2020

Shearer Delight....

Most readers here likely already know of Catriona Shearer's incredible geometry problems regularly presented on Twitter (though they travel around the Web elsewhere), but if you don't, time to get started with this recent fun one:

Saturday, July 4, 2020

Ahhh Yes, the Research Literature…. ;))

Cleaning out some old files I stumbled across this vintage piece from sometime in my 1970s academic career (I believe at the time I adapted this from some other original source?). Am sure most of you have seen such parodies before. I do find it noteworthy that several of the issues taken quite seriously in statistics and research methodology currently were already being hinted at and joked about by we grad students 40+ years ago….:


A Guide to the Reading and Understanding of Research Literature

"it has long been known that…."                                                    

Really means:
I haven’t bothered to look up the original references

"…of great theoretical and practical interest"

interesting to me

"the … reagent was chosen as especially suitable for the experimental procedure"

the fellow in the next lab over already had some made up

"subjects for the study were randomly chosen"

students in Psych. 101 were asked to participate as a prerequisite for passing the course

"three of the samples were selected for detailed study"

the results on the others didn’t make any sense

"accidentally strained during mounting"

dropped on the floor

"handled with extreme care throughout the experiment"

not dropped on floor

"typical results are shown…"

the best results are shown

"the data revealed a linear correlation"

we took a ruler and drew a line

"agreement with the predicted curve is:"
excellent  (means fair)
good  (means poor)
satisfactory  (means doubtful)
fair  (means imaginary)

"the values are correct at least within an order of magnitude"

the values are wrong

"statistically significant"

possibly plausible

"it is suggested that…”

I believe

"it may be that…”

I think

"It is generally believed that….”

a couple of other guys think so too

"it is clear that much additional work will be required before a complete understanding…”

I don’t understand it

"unfortunately, a quantitative theory to account for these results has not been formulated”

neither does anyone else understand it

"while it has not been possible to provide definite answers to these questions…”

the experiment didn’t work, but I figured I could at least get a publication out of it

"further work in this area is warranted…”

I intend to get a second publication out of this data

"special thanks are due to R. Stoodle for technical assistance and to J. Goober for valuable discussions”

R. Stoodle did the work and J. Goober explained what it all meant