January 16, 2016 at 01:57AM

Today I Learned: 1) A metric space* is *complete* if for every convergent series in the space, the thing to which that series converges is also in the space. Intuitively, this means that it doesn't have any holes. Example -- [0,1], the set of real numbers from zero to one, including both zero and one. An example of a set that is almost-but-not-quite a complete metric space is (0,1), which is all of the real numbers from zero to one but not including either. In (0,1), for example, you can consider the series 1/2, 1/4, 1/8, 1/16/,... which converges to zero. Since zero isn't in (0,1), (0,1) isn't a copmlete metric space. A non-complete set can be "completed" by adding one or more points, which are the "completion" of the set. * a metric space is a set of stuff on which you can define a measurement of distance with some reasonable properties like the triangle inequality. Thanks to Dawna Bagharian!!!!! for setting me down a path of wiki articles to this information! 2) The Living Computer Museum! It's a museum of old computers, from the early 1960s through the early 90s, and almost all of them are functional and interactive. So you can go in and mess around on old 70s and 80s computers, or punch out punch cards with an IBM card-punching machine from 1964. It was a ton of fun to play around in. A couple things that stood out from browsing all the computers: 1) Very few of them had arrow keys! This made sense, though, since very few of those computers had any notion of backspacing. Several literally printed out your commands via typewriter as you typed, so an arrow key would probably just be ridiculous. 2) There was a lot of variety in auxilury key placement on keyboards (shift, ctrl, alt, break, insert, delete, those kinds of things). Even stuff like number and punctuation placement differed surprisingly between different keybaords up through the 70s computers. 3) The ergonimics of old keyboards were really different. The type-feel was in some ways much more like a typewriter than, say, my current macbook. 4) Mice are really recent! Also, they've gotten a lot better since they were introduced. 3) ...a story about how Microsoft got into the operating system business. Rumor has it Microsoft originally made some little auxilury software for IBM, which they sent representatives to IBM to give a talk about. Whatever IBM people saw it liked it, and went from that talk to a different company that was making an OS for them. The IBM reps didn't like what they saw, so they went back to the Microsoft team and asked if they could sell IBM an OS. The Microsoft team said they didn't have any OS, but they knew a guy who was working on one and could probably convince him to finish it, and then they could sell it to IBM. And thus, DOS was born.