Content-Type: text/shitpost

Julie Moronuki asked why left adjoints are left and right ones are right, and I had to admit that I always get them mixed up also. My grasp of spatial relations is excellent, but I often get handedness backwards.

As a kid I learned left-hand from right-hand quite late, and depended for a long time on the trick of holding up my hands to see which one looked like the letter “L”.

On one memorable occasion my sister was driving and I was navigating, and I told her to turn left at the next traffic light. As she began to turn, I got very agitated. “No, left! Turn left! … sorry, I meant right.” I hadn't mixed up the route. I knew which way I wanted her to turn, and it was the correct turn, but I used the wrong word for it.

Strangely, I have never had any trouble with clockwise and counter-clockwise. For many years I was not always sure which one would turn the water on and turn the water off, but I could remember that counter-clockwise is for un-screwing a screw, and I would picture the faucet mechanism in my mind and imagine the screw and the washer moving upward up to let the water in, so I always got that right.

I couldn't help Julie with the left and right adjoints. I said:

I have a similar problem with "left" and "right" group actions. My hold on the concept of group actions is quite solid, but if someone talks about "left" or "right" group actions I suddenly feel at sea.

On the other hand I have no trouble with limits that exist from the left but not from the right; my association of left with positive and right with negative works just fine. I don't know.

Er.

Left with negative and right with positive.