[The morning of Sam and Kip's wedding, and I have a little downtime, so I thought I'd squeeze in another couple of posts.]
I found this object in the Santa Barbara Botanical Gardens. What is it?
I've never seen a sundial like this one—a very clever design that surely must have been known in Isaac Newton's time and probably much earlier. But it's not the kind of thing we science students got to study in the 20th Century. It's all new to me.
The dial itself is about 15" in diameter. It's made of brass. The gnomon (the fishtail shaped hook) can be rotated, moving the two arrows that point to the time.
To tell the time, you rotate the gnomon until the shadow falls on the figure eight-shaped curve engraved on the curved plate—the one that has the names of months alongside. You make the notch in the shadow line up with the section of the curve that corresponds to the current month, in this case, October.
This alignment causes the arrows to point to the correct position on the time dial. Here I have aligned the notch to fall precisely on the winter side of the curve.
Note that there are two arrows, one for Daylight Saving Time, revealing that despite its patina, this is a modern sundial.
The figure eight shape is called an analemma and is a curve generated by the tilt of the earth's axis and the fact that its orbit is elliptical, not circular. Here's the analemma for London, England.
By incorporating the analemma into a precisely crafted and sufficiently large sundial, it's possible to read the correct time to better than one second on any sunny day of the year.
An analemma is not just some abstract mathematical curve. It's an actual pattern made by the sun in the sky, and it has been photographed by opening the shutter on a fixed camera at the same time of day once a week or so for an entire year.
This pattern was known to the ancients, but to this modern-day semiconductor engineer, it was a mystery until today.
A century ago, kids were taught stuff that gets skipped over today. Can you multiply two large numbers by casting out nines? Can you extract a cube root by hand?