Monday, January 30, 2023

Lewis Carroll syncs

From the comments, promoted to post status for better searchability in the future.

On January 27, Ben Pratt wrote:

Today I was watching a math video (as one does) by Michael Penn that was his solution to a problem posed by Lewis Carroll (C. L. Dodgson) in the 1893 work Curiosa Mathematica II or Pillow Problems. Online I found a .djvu file of a reprint published in 1958 as The Mathematical Recreations of Lewis Carroll, which contains 72 problems Dodgson originally worked out in his head.

Problem 58 was originally worked out by Dodgson on the 20th of January 1884 and its text reads as follows:

"Three Points are taken at random on an infinite Plane. Find the chance of their being the vertices of an obtuse-angled Triangle."

Dodgson provides his solution in which he constructs a shape composed of two arcs and a line segment. Rescaling the triangle and equating its longest side to the line segment, all possible triangles (scaled appropriately) are contained within the shape. He also includes a semicircle with the diameter being the line segment.

Michael Penn follows the same basic approach in that he constructs the same shapes, but he includes their reflections across the line segment. This, of course, results in a drawing of a vesica containing a circle, a shape that has been in the syncs.

I also note that the infinite plane the three points are selected from is a "flat plane" as discussed above.

The next day, January 28, he added:

I was just reading a question and answers on Stack Overflow for something at work, and I happened to notice one of the Hot Network Questions in the right sidebar was "In honor of Lewis Carroll’s birthday, January 27."

When I submitted the above comment in both of our time zones it was January 27. I did not know that that is the birthday of Lewis Carroll until just now.

I replied the same day:

I didn't know that yesterday was Lewis Carroll's birthday, either. I read this passage in Green Doors yesterday. Petra, private secretary to a psychiatrist, is snooping in the doctor's files, looking for the records on a patient named McCloud.

Petra was pulling out the drawer marked in small black letters Mc. She pulled it slowly, as one might open a door onto an unknown landscape. She herself thought of Alice. "It might be the rabbit hole and here I am on the verge of tumbling down it." Indeed, she felt herself a second Alice and as if this deep drawer held a wonderland into which she was about to escape from the stifling hot afternoon of the upper world. Could she had known what it held for her, how different her hesitation in going on pulling out the drawer would have been, how much faster her heart would have beat!

And a few hours later I added:

Just saw on TV an ad for the show "Pawn Stars."

"Alice in Wonderland," said a voice and then, immediately, the scene changing, "Tyrannosaurus teeth are really rare."

Lewis Carroll, as a Victorian writer known for "nonsense," has much in common with his older contemporary Edward Lear

1 comment:

ben said...

Interesting January 20th with the math solution involving a vesica. Two disks, kinda like two doors, like DD, dove descending.

The January 20th just gone, well a dove descended, so to speak.

The expression is from John 1:32 (notice 132):

"And John bare record, saying, I saw the Spirit descending from heaven like a dove, and it abode upon him."

1320 (132 with an extra 0). 1:3:20 :: A:C:T. I already mentioned this somewhere. And this number is similar to the 2310 here:

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