Filtered for TIL
18.54, Monday 9 Feb 2015 Link to this post
A lot of prime numbers aren’t prime if you allow for imaginary numbers.
e.g., 13 can be factored as 2+3i x 2-3i.
It turns out that
this can happen to a prime if and only if after dividing by 4, we get remainder 1. So 5, 13, 17, 29… can all be factored if we add sqrt(-1), but 3, 7, 11, 19, 23… won’t.
Also, balanced ternary notation, which is counting in base-3, except the numbers are 1, 0, and -1.
The best-known application of balanced ternary notation is in mathematical puzzles that have to do with weighing. Given a two-pan balance, you are asked to weigh a coin known to have some integral weight between 1 gram and 40 grams. How many measuring weights do you need? A hasty answer would be six weights of 1, 2, 4, 8, 16 and 32 grams. If the coin must go in one pan and all the measuring weights in the other, you can’t do better than such a powers-of-2 solution. If the weights can go in either pan, however, there’s a ternary trick that works with just four weights: 1, 3, 9 and 27 grams. For instance, a coin of 35 grams-110(-1) in signed ternary-will balance on the scale when weights of 27 grams and 9 grams are placed in the pan opposite the coin and a weight of 1 gram lies in the same pan as the coin. Every coin up to 40 grams can be weighed in this way. (So can all helium balloons weighing no less than -40 grams.)
Habeas corpus… ancient right to not be imprisoned except if lawfully tried.
Habeas Corpus Act 1679,
one of the most important statutes in English constitutional history. Though amended, it remains on the statute book to this day.
It only passed the House of Lords because one of the tellers joked that a fat lord counted as ten, and the other teller didn’t notice.
Lord Grey and Lord Norris were named to be the tellers: Lord Norris, being a man subject to vapours, was not at all times attentive to what he was doing: so, a very fat lord coming in, Lord Grey counted him as ten, as a jest at first: but seeing Lord Norris had not observed it, he went on with this misreckoning of ten: so it was reported that they that were for the Bill were in the majority, though indeed it went for the other side: and by this means the Bill passed.
Incidentally, I like this exclamation people have nowadays, TIL, today I learned. It’s a way of passing on something that might be of curiosity, hey, TIL, [this], or a response to something surprising, well well well, TIL!
I was at a big model railway exhibition a couple of years ago, which is not a hugely regular occurrence for me. But interesting, yknow. Anyway, I got pretty into looking at the control panels for the layouts. Because the model makers would ad hoc together these sheets of wood with tracks drawn on them, lovely toggle switches for the points, big fat lights for the signals, etc, etc. All custom.
And I was in this massive crowd looking at this spectacular model of Liverpool Lime Street (1948), leaning over with my camera to take a picture of the control panel - which is actually in that video by the way, about 5:30 in - and behind me, one guy sees me and says to the guy next to him, “pshaw, it’s one of those control panel nerds.”
And then I was all: who are YOU calling a nerd you NERD, you’re the one at a railway modelling exhibition.
Note it’s called railway modelling, not model railways, because I don’t know why but it’s very important.
But actually I didn’t say anything because I AM a control panel nerd, really, in a casual sort of way, and he got me good. Nerd.
there’s no direct translation for the word “depression” in the Cambodian Khmer language. Instead, people may say thelea tdeuk ceut, which literally means “the water in my heart has fallen.”
Hinton may suggest an antidepressant that will “increase the water in the heart, so it will be like the rice fields after a storm.”
Bodies as land. With highlands and lowlands, and crops and weather.