Yes, the two train track pieces are the same lengths. I know this because we have a basket of toy train tracks, and I took two identical curves and lined them up for the outline of this sketch. But it's easy to be fooled and think the one at the top is shorter than the one at the bottom.

While there may be other factors to help explain the ring-segment illusion, a common one is that our brains compare the short inner side of the top track against the longer outer side of the lower track leading us to believe the top one is shorter. Aligning the top track to the outer left point of the lower track enhances the illusion by increasing the horizontal contrast.

I like the ring-segment illusion as the name for it. It's also known as the Jastrow illusion after the Polish-American psychologist Joseph Jastrow, also known for the ambiguous figure of the rabbit-duck, who published a tapered version of the ring-segment illusion. In his paper, he gives a related example of how a square sitting on a point can look larger than one sitting on a side as we subconsciously compare the longer diagonal length with the shorter side length. You can test that in the sketch.

The ring-segment illusion

Richard Feynman was one of the great scientists of the 20th century, making significant contributions to physics and other related fields. Part of what made him stand out was his gift for teaching. He had a remarkable knack for explaining some of the most complex things in ways anyone could understand. He was also a model of the desire to deeply understand how things worked, often deriving a result in several ways to be more confident he was right.

The Feynman learning technique is typical of how he approached understanding something deeply and helps explain some of his teaching skills.

Spend time writing about a topic as if explaining it to someone.

Then practice explaining it, speaking and drawing as if you were a teacher at the front of the class. You may figure out some other aspect wasn't as clear as you thought and need to look into something.

Refine any gaps you reveal until you can share the topic fluently and clearly.

Then, simplify your language by replacing complex words and ideas with simpler ones and considering analogies to help people relate.

Now, you can explain it because you deeply understand it, too.

"You can know the name of that bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird."

— Feynman's father, from Surely You're Joking Mr Feynman?

I loved the Fun to Imagine interviews to experience some of Feynman's joy and skill for teaching.

The sketch was inspired by this excellent animated video of the Feynman Learning Technique.

Though he was primarily a theoretical physicist, Feynman also made lasting contributions to the field of computation. If you want to get into those, you might enjoy the Feynman Lectures on Computation from the last course he taught at Caltech, edited, no less, by my Dad.

The Feynman Learning Technique

What does biweekly mean to you? How about bimonthly or biannually?

While each of us will have our own, perhaps unambiguous, reaction to it, the word biweekly is interpreted as "twice a week" or "once every two weeks." I know this from personal experience of confusing people en-masse. The dictionary even carefully, if unhelpfully, defines it as meaning either. It's a strange quirk of the English language. But it's so handy, what to do? An excellent concise solution is the word fortnightly.

Fortnightly has the helpful unambiguous quality that it means "once every fortnight," so "once every two weeks." And it's also just one word. If something happens "two times a week," I think you need to spell it out or use "twice a week" or perhaps "every Monday and Thursday."

The same source of confusion applies to the words bimonthly and biannually—to be sure of being understood correctly, it's best to avoid them. Phrases like "every second month," "every two months," "twice a month," or "two times each year" are helpful here.