Yet more fun with phase lag

It's still warm here in Philadelphia. Highs are in the eighties this week, which is slightly above average for early September.

Walking home from campus yesterday, a little before 7 PM, the sun was low in the sky. I found myself digging for my sunglasses. And I remembered the circumstances under which I bought the sunglasses -- in late March and early April I was having the same problem. (I live west of campus, so I could actually have this problem twice a day, as I walked east in the mornings and west in the evenings.)

But wasn't it cold then, I thought?

But the position of the sun doesn't depend on the cold. The position on the horizon at which the sun rises and sets depends only on the distance of the current day from the summer solstice. Yesterday was the 75th day after the summer solstice (I'm using June 21 here); the 75th day before the solstice was April 7. The high temperature in Philadelphia that day was 41 degrees. (The average high then is 59.) (The declination, which is the celestial analogue of latitude, varies essentially sinuisoidally, but that doesn't mean the position of sunrise varies sinusoidally because there's another circle to deal with.)

In short: in terms of insolation right now is like early April, but in terms of temperature it's like early June. Maybe this sort of asymmetry explains why spring and fall feel different, since we're sensitive to both temperature and amount of light.

Of course, it's hard to know for sure, because you also have to take into account the derivatives of insolation and temperature; in the spring they're both increasing, and in the fall they're both decreasing. (A Jewish friend of mine once said that he doesn't think it's coincidence that Yom Kippur, when Jews are obliged to fast from sundown to sundown, falls near the autumn equinox; that makes the fast a few minutes less than it would be if it fell near the spring equinox.) And there's a big psychological factor, as well. Right now, an hour and ten minutes before my first class of the year, I feel exhilirated intellectually; in, say, May I'll feel exhausted. There's not much of a way to control for the cycles we humans have imposed on the year.

But what would it be like to live in a world where the season with the most sunlight was the cold season? I suspect we'll never know, because the only way to create that sort of world is to isolate people from the natural world for a very long time, and if you're willing to pay people to live in your cave for a while you can probably think of more worthwhile things to find out by using them as test subjects.