I enjoyed Mathematical Footprints, though there were parts that I did not understand. For example, the suggestion that there did not used to be a square root of negative 15 but now there is is hard for me to grasp. That it hadn’t been discovered, okay. It took a long time before people thought of zero, after all, but not because it didn’t exist. Nothingness was around before we had a symbol for it. Bertrand Russell suggested (and is quoted doing so in this book) that it probably took a long time for people to consider that two days and a brace of pheasants were in any way the same thing. But the suggestion that some not-very-real number came into existence at some time baffles me.

I also find that my eyes slide off the page when there are lots of numbers all together, so I missed out on the discussion of fractals, and the pictures of four dimensional shapes continue to look two or perhaps three dimensional to me, no matter how hard I stare at them. I’ve seen those things in three-dimensional models, in fact, and they still don’t look four dimensional. 

“Where’s the four dimensional part?” I asked the builder of one.
“You can’t see it,” he said, pityingly.

 The mathematical explanation of Magic Eye pictures was quite fascinating, though, and I now know a lot more about bar codes than I ever expected to.

But it may well be that the thing I will remember best from this book is the method of determining longitude on a ship using powder of sympathy.

You start by getting a wounded dog. There is no suggestion that you should wound the dog intentionally, but it is hard to escape the thought that this must have been part of the plan sometimes, in cases where there was no wounded dog around and the ship was otherwise ready to set sail. You put a bandage on the dog’s wound. When the dog is better, bring it on the ship with you, leaving the bandage behind on land.

Are you with me so far?

Now, enlist someone back on land to put powder of sympathy (a weird 17th century cure, usually applied to weapons that had hurt someone) onto the bandage at precisely noon every day. The dog will react to this sympathetic magic in some way, at which point you merely determine what time it is on your ship at that moment (by looking at the sun, I suppose), and swiftly calculate your longitude by comparing the time where you are to the time back in Portsmouth or wherever you left the bandage.

The author mentions that this method doesn’t work, possibly in case we were planning on trying it out.

Fortunately, the invention of portable clocks in the late 1700s made the wounded dog method obsolete. You could set the time in Portsmouth and the clock would keep it for you as you sailed about.

There was also a method which involved observing the moons of Jupiter, a difficult task at any time, let alone on a ship, and another which seemed to require putting into port and asking what time it was there. I really don’t see that one. If you are in port, surely you could just ask where you are, at which point you could look up your longitude in a trice.

For the solstice, let’s sing “The Holly and the Ivy.” This is a nice 14th century English carol, lots of fun to sing, and filled with pagan imagery in case you are going to that kind of party.

My next party is on Saturday morning, at Partygirl’s, and she has promised me champagne. Really, she serves champagne more than anyone else I know. You can just drop by her house on the way to the grocery store and find that she has champagne going. I am not supposed to drink alcohol, what with my triglyceride numbers being imperfect, but I make an exception for champagne at Partygirls’ house, much as one would go ahead and eat the sheep’s eyeballs if that were the custom in the country in which you were traveling.

Last night after choir practice (most memorable line from the rehearsal: “There I was singing the first verse over,  cranberriesbig as Dallas.”), #2 son and I made Cranberry Caramel Bars. We got the recipe from Southern Living, but this site provides just about the same recipe. They are good, and just the thing if you are having a party.

The picture here is of their prettiest stage. Then #2 son covered them with caramel and I sprinkled a crumb topping on and we baked them some more and they ended up looking less colorful but tasting terrific.

Add champagne, sing pagan carols — you’re set.

Oh — the meeting with the teacher became a meeting with the teacher, then the counselor, and then the counselor and the principal together, and it reminded me of the story of The Blind Men and the Elephant. #1 son feels that he is incapable of grasping chemistry and needs a Special Class. His teacher says he behaves as though he is an Artist and above petty things like chemistry, but is certainly capable of doing the work if he chooses to. His counselor says he is “adorable” and she and the principal (who said chemistry is like a wall for some students) fixed it up to move him into the class of a nice lady teacher. His dad says it is all the fault of the computer. He didn’t have computers in his day, and he always did his homework.

He didn’t have electricity, either, I pointed out. That might not have been tactful of me. It was shortly after that that he said he was going to buy a new car and move to Wyoming. He has taken that back. I have pointed out to #1 son that no matter how adorable he is and how nice the lady teacher, he still won’t pass if he never does his assignments.