Zero and Infinity

A triangle has three corners.

A pentagon has five. A decagon has ten.

As the number of corners becomes large, the polygon becomes more "circular".

When the number of corners is infinity, the polygon is a circle - a shape with zero corners!

Links

1. Stay in the Game: There is hope in humanity!

2. Kevin Simler's graphical essay on going critical

3. The force of Gilbert Strang

4. Strogatz's "Beauty of Calculus" Lecture

QuickTip: Linux Convert Color PDF to GrayScale

Using GhostScript (source). The first line sets name of output file ("output.pdf" here)

gs \
 -sOutputFile=output.pdf \
 -sDEVICE=pdfwrite \
 -sColorConversionStrategy=Gray \
 -dProcessColorModel=/DeviceGray \
 -dCompatibilityLevel=1.4 \
 -dNOPAUSE \
 -dBATCH \
 input.pdf

Second-Level Thinking

James Holzhauer's epic run on Jeopardy came to an end.

While the human drama around that is entertaining, one of the best pieces of analysis was this write up "Did James make the right Final Jeopardy bet?" on one of my favorite websites.

At one level, his explanation made perfect sense, and did play out in the way the leader (Emma) bet.

But here's the "she knows what he knows what she know's" second-ordered thought (what the author calls the "mindfuck" strategy).

But Emma could have figured out his thinking, and bet a smaller amount, ensuring she won regardless of whether she got the question right or wrong (essentially sealing her victory).

Of course, one could take this type of reasoning one or more levels higher.

Hawk Attack

Yesterday, as I was hiking down a trail in Tom Brown park, I was attacked by a hawk.

Bizarre, I know!

For an instant, as I felt the scratching on my head, I thought an old twig had fallen off a tree. But my confusion was dispelled a nanosecond later, as I saw the hawk's wide wings swooshing right in front of my forehead. From there, it swooped up like a jet taking off on a runway, and perched itself on a nearby tree, watching!

The claws had inflicted a minor scratch, but nothing serious (I finished the remaining 3 miles of my hike). Later, I called the nurse, just to see if I should take antibiotics or tetanus shot.

To my mild surprise, she told me that I was up to date on my tetanus shots. She said "your chart says you had your last shot in 2016."

Ah! The sting ray accident, I remembered!