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

May We All Have a Mr. Keating In Our Educational Lives (perhaps more than one)

No Friday music today and no mathy-ness either.  This month marked the 5-year anniversary of Robin Williams' death, and didn't want to let that pass without a little commemoration. Back at the time I wrote a tweet, simply quoting another person’s tweet that I found interesting, even though I wasn’t even sure I understood their exact point? To my astonishment it became the most retweeted tweet I've ever had (I posted briefly about it HERE). Their tweet included this quote posted by someone else (the original tweet having since been removed):

5 years later I still don’t know for sure precisely what they meant… but I know we miss Robin. Hey, the world could use a little more zaniness these days.

Anyway, still one of my favorite movie scenes ever, from “Dead Poets Society”:

Have a good weekend all....

What is Bob's number?....

ICYMI, I loved this logic riddle that Brilliant.org tweeted out last weekend — it’s a take-off of earlier similar puzzles in this genre (I've very slightly modified):

Alice and Bob are both logical and truthful, and each has complete knowledge that the other is logical and truthful. They are each given a distinct one-digit positive number in secret, and then they make these statements in the order given:

Alice: I don’t know who’s number is bigger.

Bob: I don’t know who’s number is bigger.

Alice: I still don’t know who’s number is bigger.

Bob: I still don’t know who’s number is bigger.

Alice: Now I know Bob’s number!

What is Bob’s number?

the answer is below; if you need further explanation go visit the comments to the original tweet here:

https://twitter.com/brilliantorg/status/1164885101148139521


....And as a bonus here's a problem Presh Talwalkar posted about yesterday that apparently went viral in India (it's a take-off on some older similar math riddles you may well be familiar with):
https://mindyourdecisions.com/blog/2019/08/26/worlds-toughest-riddle-explained/
.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

 answer:  Bob's number is 5

2 Book Blurbs

1)  Wasn’t familiar with this new book (“Calculus Reordered”) from David Bressoud, nor ever saw any 'buzz' about it, but yet ANOTHER in the stream of volumes in this seeming 'year of calculus' for math fans:

https://amzn.to/31YPcqj

Looks interesting, and comes with some wonderful endorsements on the back cover (K. Devlin, Wm. Dunham, and John Stillwell, who says, "As far as I know, there is no other book that integrates the history, theory, and pedagogy of calculus as well as this one"...), AND it comes from Princeton University Press, which alone implies how good it must be!

So, if you haven't overdosed by now on the topic, probably another volume you should give a whirl.

2)  Meanwhile, the volume I’ve most recently finished is Graham Farmelo’s “The Universe Speaks in Numbers” which has received rave reviews and ought be of interest to any interested in the history and current state of affairs of theoretical physics. With that said, I can’t help but think that what one writes in this arena is very dependent upon both one's initial assumptions and who one talks to. Farmelo certainly speaks with many outstanding physicists for this volume, yet some significant names seem to be missing, and the disagreements/debates within theoretical physics these days are so deep and contrary it’s difficult for a layperson to know how to weigh the contrasting viewpoints. I would have liked to have seen just a little more of the cosmology mathematics involved described in the volume (although admittedly difficult to do in a general audience work), and a little more specificity of the clear disagreements among physicists themselves, but still a very worthwhile read for the physics-inclined.