Of Brittle and Broad Theories, and Science...

“….I responded with my view that all these theories are either vague enough to be adaptable to any data or precise enough to be evidently false with no data collection needed. This was what Lakatos noted: any theory is either so brittle that it can be destroyed by collecting enough data, or flexible enough to fit anything. This does not mean we can’t do science, it just means we have to move beyond naive falsificationism.”

                           — Andrew Gelman at end of a post on his blog a short while back

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

Statistics Is Where It's At

As many know, because of “big data,” the replication ‘crisis’ in psychology, concerns over p-values, frequentist vs. Bayesian debates, etc. etc. the field of statistics/probability has acquired a significance of late that it didn’t carry in earlier times. It takes a lot of background to fully understand and appreciate the arguments/nuances made in some of these discussions, but I (without that background) still find it interesting and important to follow.
Here are some of the statisticians I follow on Twitter, that you might find worth checking out, to keep up with the controversies (but there are a jillion more statisticians, often focusing on specific areas, on Twitter):

@F2Harrell

@StephenSenn

@d_spiegel
@StatModeling

@yudapearl

@learnfromerror

@EdwardTufte

@nbarrowman

@AlxEtz

This list gives a somewhat wide range of opinions across varying topics, though pretty heavily leaning Bayesian. And what is interesting is not just their tweets but the comment threads that often follow.

There are also of course many statistics websites/blogs/videos suitable for varying stats knowledge levels, and even some podcasts devoted to statistics, or in some instances more specifically to "big data."

In short, for anyone trying to better understand this newly-vital corner of mathematics in today’s world, there’s no shortage of assistance from the internet.

If you have other favorite stats people you find especially helpful in explaining the issues arising these days (especially to lay readers) feel free to mention in comments.

To whet your appetite, here's a somewhat lengthy sample (fairly technical) from a podcast some weeks ago with Bayesian Dr. Frank Harrell (starting at the 26:50 point, and focusing somewhat, but not entirely on clinical studies):
https://soundcloud.com/plenarysession/206-heart-failure-choosing-a-specialty-the-bayesian-approach-with-dr-frank-harrell#t=26:50

*********************
Addendum:  just yesterday Deborah Mayo posted a short entry, with several links, at her blog indicating the "turmoil" statistics finds itself in these days (I imagine the comments section may grow over time):
https://errorstatistics.com/2019/09/25/hardwicke-and-ioannidis-gelman-and-mayo-p-values-petitions-practice-and-perils-and-a-question-for-readers/

More Book Mentions...

Will just mention some books I’ve been perusing lately or that are in the queue (from old to new):

1)  Picked up John Derbyshire’s old (2006) “Unknown Quantity” for a buck at a used shop recently and very much enjoying it (popular treatment of algebra). 

For folks wanting a popular treatment of the Riemann Hypothesis, his “Prime Obsession” probably gets mentioned more often than the other mass audience works on the subject. Politically, Derbyshire is a right-winger so I actually hate recommending him! and favor instead du Sautoy’s “The Music of the Primes” or Rockmore’s “Stalking the Riemann Hypothesis,” but have to confess Derbyshire’s math writing is enjoyable and accessible. 

2)  Another older volume (2012) I just finished is Dana Mckenzie’s “The Universe in Zero Words,” a rapid flowing, succinct history of key mathematical achievements. Math history isn't one of my major interests, but this was an enjoyable read. Recommended, if you've never seen it.

3) Then a bit of synchronicity… I finally picked up Judea Pearl’s “The Book of Why” from 2018, a volume I’ve wanted for awhile. (I think the title is poor, but the subject matter, cause and inference, is important, interesting, and timely.) Then was surprised to discover that Dana Mckenzie is actually a co-author of this volume as well! Have barely begun it, but very much looking forward to it, and have a hunch that IF I had read it in 2018 it would’ve been high up on my year-end recommended list back then.

4)  Another 2018 book, but just now showing up in the U.S. is from Australian award-winning-teacher Eddie Woo: "It's a Numberful World," a fun journey into mathematics especially aimed at engaging young folks who might think themselves not interested in the field; a quick read (on well-known topics) for more experienced math fans, and a thoughtful introduction for math beginners.

5)  Finally, this week two new (as-always beautifully-produced) Princeton University Press volumes showed up in my mail, David Richeson’s “Tales of Impossibility” and Julian Havil's "Curves for the Mathematically Curious" anxious to sink into both when time permits!?  

Several other math-related volumes are recently-out or on-the-way. Don't know how many of them I'll have time for, and lots of old volumes at the moment I'm also wanting time to RE-read!

Always incredible to see the well-written bounty of instructive popular math books now regularly produced. There were certainly some good popular math volumes in my youth, but nothing like the yearly high-quality output we see these days. Not sure what the reason is… perhaps more mathematicians nowadays come out of well-rounded, liberal artsy educations, where they emerge not just good at math, but good at (and interested in) writing, as well. Or maybe it’s simply that word-processors and computers have made book-writing a far easier/pleasanter task than it once was; accessible to more people (not that writing a book is ever easy, but just easier/more efficient than it was decades ago). The internet also brings along a lot more collaboration, inspiration, rapid feedback, ideas, and contagious encouragement for writing.

Whatever the reason, math fans/students these days are blessed with an abundance of selections!

                                      

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

One of Sean Carroll's Many Worlds...

Here’s physicist Sean Carroll with Joe Rogan for 90 minutes touting the ideas in his new book, “Something Deeply Hidden” (many interesting segments if you can find time for a listen):

JRE #1352 - Sean Carroll from JoeRogan on Vimeo.

…ohhh, and if you don’t know who Sean Carroll is, well then I’ve got you covered on that ;)

https://math-frolic.blogspot.com/2019/04/sean-carroll-raconteur-expositor.html

RFI… Can Any Number Theorist (or others) Reply to This?

I can’t answer the following for one of my readers, but maybe someone else can (about a Fermat factoring variant)???

Well over 3 years ago I posted this little gem from Futility Closet:

"In 1643, Marin Mersenne wrote to Pierre de Fermat asking whether 100895598169 were a prime number.

Fermat replied immediately that it's the product of 898423 and 112303, both of which are prime.

To this day, no one knows how he knew this. Has a powerful factoring technique been lost?"

At the time, one comment came in (from someone named Walt), as follows:

“It is not that surprising if we assume that Fermat used what we call Fermat's factoring method. Upon multiplying by the cofactor of 8 (and using difference of pronic numbers instead of squares since the number is now even) he would find this pair of factors on the first try. (I am assuming that taking the square root of a 12-digit number was feasible. Also, I have no idea how difficult it was at that time for him to prove the primality of the resulting 6-digit factors.)
In fact, 8 * 112303 = 898424 = 1 + 898423. This is a remarkable coincidence and makes me wonder if Mersenne used this relation to construct the problem in the first place.”

Now (3+ years later) I’ve received an inquiry from a retired German mathematician, who recently ran across the post & comment, and asking in part about the:

“…. variant of ‘what we call Fermat's factoring method. Upon multiplying by the cofactor of 8 (and using difference of pronic numbers instead of squares since the number is now even) …’  I am wondering about (t)his remark to use differences of pronic numbers: I have never heard of that variant or read about it in any book. He [Walt] does not quote any references, so he seems to consider this variant as being well known. In fact, it is not too difficult to figure out the formula a*(a+1) - b*(b+1) = (a+b+1)*(a-b) that turns such a difference into a product, and to check that one may thus devise a factorization method for even numbers. I am wondering if this has been published anywhere.”

Can anyone provide an answer???

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

The Unreasonableness of.... Mathematicians? ;)

“How good is the evidence for the Riemann Hypothesis? To date, ten trillion zeros of the zeta function have been found, and they all lie exactly in the middle of the ‘critical strip,’ just where Riemann predicted. Any reasonable scientist, in any other subject, would have declared the problem solved long ago. However, in such matters mathematicians are not reasonable.”

                     — Dana Mackenzie in “The Universe In Zero Words”

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

Off to the Movies...

Feel like every few years (or at least until the Goldbach Conjecture is proven) I should re-run this mathematical short film, "The Calculus of Love," just for the entertainment of any who have yet to see it:
https://www.youtube.com/watch?v=_tVTodzvDSE




...and perhaps more befitting a Sunday morning meditative mood, this old Cristobal Vila piece aways worth another gander even if seen before:
https://www.youtube.com/watch?v=oVthC6neqVc