Tuesday, March 15, 2022

A Post From Pi Day

 "If our world presently stops existing, 7817924264 will be the last digits of {\pi} that we know."

https://rjlipton.wpcomstaging.com/2022/03/14/are-these-the-last-digits-of-pi/

"Emergence" in mathematics....



Thursday, March 3, 2022

Puzzletime

 Here’s a puzzle I’ve lifted from THIS blog (who got it from Facebook poster Millie Johnson):


Arrange the digits 0‑9 into a ten-digit number such that the leftmost n digits comprise a number divisible by n. For example, if the number is ABCDEFGHJK, the three-digit number ABC must be divisible by 3, the five-digit number ABCDE must be divisible by 5, and so on.


answer below:

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.


3816547290


Saturday, February 26, 2022

"Crap" in Science....

 Wow!... this isn't focused on math per se, but no doubt there is math included in the subjects referenced in this piece (H/T to Ivan Oransky):

https://www.science.org/content/blog-post/how-much-published-crap-will-we-put


Wednesday, February 16, 2022

Midweek ASMR

 Haven't posted an ASMR video for a bit, so here's a recent Turkish head & body massage one:

https://www.youtube.com/watch?v=wTeTf9hUNMk



Monday, February 7, 2022

Start The Week Off With Grant and... of course Wordle

 Lest you miss it, Grant Sanderson (3blue1brown) has entered the Wordle fray now:

https://twitter.com/3blue1brown/status/1490351572215283712

[Less empirically, I wrote a little about Wordle less than a week ago HERE.]

One thing I'm not completely clear on, BTW, is when many of these recent pieces analyzing Wordle talk about "letter frequency" is whether they are simply employing well-published figures for letter frequency in English, or are they in fact using (as they ought be) letter frequency specifically in 5-letter words, as easily computable from the Wordle corpus of use? I would expect those two figures to be similar but not the same, and hopefully they are using the latter.

Also, there's tremendous emphasis placed on first word choice in the game, and more and more second word choice seems key to me for winning in 3 to 4 guesses. At least I'm finding increasingly that I can generally get the target word in 4 tries almost regardless of my first word choice so long as I spend enough analysis time on my 2nd and 3rd choices. Certain first word options simply incrementally increase the chance of 3rd guess winners.

It would be interesting to actually run a competition between some real word-maven aficionados (who have a "feel" for the game) versus some strictly (brute force) algorithmic programs and see who would achieve best scores (no time limit), and by what amount.




Wednesday, February 2, 2022

May I Have a Wordle With You...



Everybody seems to be doin' it, thinking about it, or just seein' and wonderin' about it!  Longish piece from The Aperiodical on the latest online viral hit game, "Wordle":

https://aperiodical.com/2022/02/a-mathematicians-guide-to-wordle/

Though, like many, they compare it to the classic game "Mastermind," for at least a few of us oldsters it is even more reminiscent of "Jotto," my favorite (word) game growing up in the 50's and 60's, and still available in online versions (in fact, I find it a bit ironic and funny that some guy has suddenly made a ton of $$$ with Wordle, when Jotto has been quietly around for... well, a verrrry much longer time!)

As to "best" starting words for Wordle (a much discussed/theorized topic) I'm surprised that more people haven't settled on my two starters: "ADIEU" or "AUDIO" -- with these starters I rarely require more than 4 entries to get the target word, and probably at least 20% of the time 3 entries suffice (...but then I'm a pretty good guesser once I get it down to 4 or fewer word possibilities).

The 2nd word choice obviously is also very key to this game, but it is highly dependent on the results of the first word choice. Most often though, my second word will derive from these letters: r, s, t, y, either o or e, and one of the letters pinpointed by the 1st word guess; however, c, h, l, or n, may end up subbing for one of those choices in some instances; and the exact results of the first word choice may, more rarely, lead to still other letter choices for guess #2.

Now, with the NY Times purchasing Wordle for a tidy little sum, not certain what its future will be, for the game or its millions of addicts for whom Wordle is as much a start of the day as is coffee.

------------------------------------

ADDENDUM  (2/6/22):

Having read a number of articles now touting various "best" starting words, pointing to the sort I used to use based upon letter frequency, I went back and tried that approach again, fairly successfully. Then I started trying unlikely starting words (zebra, radar, oozes, queen, excel, etc.), and what I'm largely discovering is that I can most often solve Wordles within 4 guesses by the careful, thoughtful selection of the 2nd and if needed 3rd guess, REGARDLESS of the first word choice! 'Rules' for the selection of the 2nd & 3rd word choice are what really need to be spelled out, though they are difficult because they are so dependent upon the the highly variable results of first word choice. Anyway, it all says something interesting about the redundancy and patterning of language.


Monday, January 17, 2022

From Bad Soup to Fuzzy Logic

 As someone who has always found the “Law of the Excluded Middle” a bit nonsensical, some years ago I tried to find someone who could say a little about “fuzzy logic,” (as opposed to Aristotelian logic) only to be surprised by how few folks (mathematicians, at least) cared to address it (perhaps it falls more into the realm of philosophy, logic, or even computer science). Anyway, happy to see Jim Propp touching upon it (well, scratching the surface) in his latest piece here:

https://mathenchant.wordpress.com/2022/01/17/bad-soup/


The one sentence in the piece though that somewhat made me cringe is an almost offhand, parenthetical remark where Jim says "Well, you don’t always have to be careful, but when things are fuzzy, you’re aware that they’re fuzzy and you value the removal of the fuzz" (bold added). Actually, I think the problem that arises so often is that people DO NOT consciously or fully recognize "the fuzz" which is what allows them to speak so dichotomously (and strongly, but wrongly) about matters that are not so cut-and-dry as presented.  Even if at some level there is 'awareness' of the fuzz, if it is not fully acknowledged, then it may tend to be ignored, swept under the mental carpet like so many dust bunnies (instead of genuinely removed). And while 'fuzziness' is a particular problem in the social/behavioral sciences it can also creep stealthily into math, engineering, and their outgrowths.


Thursday, January 13, 2022

Teens Learning Taxes

 Frankly, I’ve always been surprised (i.e., disappointed) at how little really practical and needed life experience is taught in our high school years (taxes, mortgages, job hunting/applications, budgeting, banking, childrearing, civics/laws, traveling, health, etc.).  We are left instead to largely learn about such matters by happenstance on our own.

But hey, here’s a start:

https://www.scaffoldedmath.com/2022/01/how-to-file-a-1040-tax-return.html



Friday, January 7, 2022

Aussie Math

 They say 'don't judge a book by its cover,' but I don't know, this one looks interesting and made me chuckle:

https://blog.tanyakhovanova.com/2022/01/a-dingo-ate-my-math-book/