1 Sep 2011, 15:57

A couple of days ago I tried to coax some pigeons into feeding from my hand. They had descended en masse to eat some bread, and when they had devoured it they just walked around the garden aimlessly. I threw bits out to them so that they'd learn me throwing things is safe for them and provides tasty food. Eventually I threw the pieces closer and closer to me. They kept flying off at the slightest noise or sharp movement, though, to land on my roof. I'd look up and I'd see six or seven pigeons peering over the edge of the roof at me. One even dropped a bit of bread just by me.

At some point a ringed dove joined them. That one was quite tame, and I managed to get it to come very close to me. I also stretched my hand out holding a load of bread to try to get it to take some, but none of the pigeons, even the quite tame dove, would do so. In the London parks they routinely come and sit on your hand to feed, but there they're more used to it.

What I liked most about the garden pigeons is that they walked around moving their heads in a very quizzical manner, as if to say, whatchoo doing? The dove especially would walk in a kind of semicircle, checking me out, then come back and get a little bit of bread from by my hand, and walk off in the semicircle again. Eventually they stopped flying back down from the roof, probably because I'd given them so much bread that they were happy and full.

1 Sep 2011, 15:15

A while ago I came up with the idea that lightweight markup languages should use emphasis as the basis of their link syntax:

“When converted to hypertext and rendered in a browser, links are typically underlined and coloured, with the default colour being blue. Since this is a kind of emphasis, why don't these languages use their default emphasis as the core of their link syntax?”

The script I use for that is on gist, with the catchy name *Emphasis style hypertext, lightweight format script*. https://gist.github.com/1186399

31 Aug 2011, 17:02

The imaginary numbers weren't found solely because of the root operator, and there's nothing particularly interesting about the root operator. It's a consequence of negative numbers and multiplication. Specifically, -1 * -1 performs a 180° transformation, but nobody thought of it that way. This shows that people didn't fully understand what they were doing with negative numbers, even though they had these subset conventions of the big picture. Presumably the people who came up with the convention that -1 * -1 = 1 had a subset of the kind of insight that was required to come up with the *Argand plane*. en.wikipedia.org/wiki/Complex_plane

It's a lot easier to think about this in terms of polar coordinates than with cartesian coordinates. This is because polar coordinates are better for multiplication, and cartesian coordinates better for addition. So my question about why I can't imagine a -25 amount of things being ordered with 5i or -5i sides is obvious. When you think about the polar representation of 5i and -5i, their length component is just 5 units. That gives you the sides, but then you have to create the negative sign, and you do that with the i transformation, which is the rotation from the origin on the positive real azimuth. So you can imagine √-25 because you just imagine the length component in terms of the geometry, and then the quarter rotation being the thing that gives the half rotation in the result of 5i².