I wrote this on the plane: number theory

Dumb little explorations in number theory. As I've mentioned, I sometimes fall asleep by calculating squares in my head. I go quickly through the ones I have memorized, and hit the higher numbers where the long multiplication starts to put me to sleep. At times I've done variants, like calculating each one twice: first by multiplication, then by taking the last square and adding 2n+1, double checking myself. It's just a way to fill up all my short-term memory registers with numbers so I can't worry about work or delve into the many repulsive attributes of myself.

A couple of nights ago I was extra stressed, and decided to convert each square to base 7. That added enough novelty that I started really low: with 3, whose square is 9, which in base 7 is "12".

And higher and higher. As my extremities started to go numb with falling asleep, I converted 64 into base 7 to get "121" and smiled… sleepily… because that's a square number in base ten, too, of course, and isn't that pretty. I made some kind of math mistake as I converted 81, and then flickered out like a light.

The next night I told heisenbug my discovery, and then I did the whole thing again, except I thought: hey, maybe I should convert the number to base 7 first and then square it, doing the math in base 7. well, that was pretty damn straightforward. 7 in base seven is "10", which squares to "100" which means 49.

8 in base 7 is "11", which squares to 121:

 11
x11
---
 11
11
---
121

And of course, of course, 11 will always do that, and so "121" is a square of (base + 1) in pretty much any base. Except base 2 where there is no 2 digit and the addition part of the long multiplication will cause a carry-over.

Likewise, the square of "12" is always going to be "144" as long as there's a 4 digit (base five and up). The square of "13" requires base ten or higher, and the square of 14, well, it already involves a carry-over in base ten. In hex it would, too, so geez… you need base 17.

It would be fun to generalize: if you're squaring a two-digit number, in what base b do you need to be doing the math such that the answer will be the same in all bases b or higher?

I wrote this on the plane too: life, Nala

In mid-air, writing because I don't feel like reading. I could be watching The Company Men, but the headphones at my seat don't work, so I've limited myself to other in-flight entertainment, especially enjoying the dexterity and timing game of Order Coffee During Turbulence. I also finished knitting a hat, and immediately put it on my head because it's chilly up here.

And of course, looking at silly magazines and catalogues. I do like some of these rings by Alex Sepkus. Wormy rings that look like a small alien invasion.





And I  also  kind of want to buy this shirt from Skymall customized with a 0. "mommy of 0". Wonder if I could get it before Mother's Day.

Here is my sad news: it turns out Nala is hyperthyroid. ("Of course," I said, "the rest of her is hyper, so why would her thyroid not be?") I researched treatments, and found to my relief that there is a very good one-shot cure available. It's around $1000, and involves leaving her in a special facility for 3-5 days while she's radioactive (seriously), butgets her away from the prospect of a pill twice a day for the rest of her life. So that's what we'll do, although we can't do it until she has been on the pills for a month or so (to make sure her high metabolism isn't masking any underlying liver problems) and then back off the pills again.

This is her first major health problem, and I'm glad she doesn't know she has a problem. She vocalizes and runs around a lot, but then, she's always done that. I am calling her my hypercat.