An interesting corollary to this is that even if the future trajectory of a general 3-body orbit is predictable in theory using numerical methods (and infinite precision calculations), in practice the use of finite-precision floating point means that after some time the trajectory predicted by an ODE solver will diverge from the mathematically-true trajectory. Even symplectic integrators have this problem. More details on the general case of chaos are provided by this insightful blog post:
I'll add one more piece of ham lore to this thread. The gigantic electronic component distributor DigiKey got its start when the founder designed and marketed a Morse code key to the ham radio audience. DigiKey was originally a mail-order business selling to hams.
The point is that the ham radio hobby is very intertwined with the electrical engineering profession. It's very technical ... not just a bunch of guys talking to each other over the radio (although it's that too).
The thing which seems to be overlooked -- both in the linked article and in the HN comments -- is that at one time ham radio was a hobby for folks wanting to play around with state-of-the-art technology. It was more than just a bunch of guys chatting with each other over a radio. At one time most people had to build their own ham rig from piece parts. One had to have a serious amount of engineering ability to do so ... or at least be able to read a schematic published in a magazine and solder together a radio, not a small feat. As a hobby it was all about becoming proficient in electrical engineering, then enjoying your proficiency by chatting with -- and showing off to -- like-minded guys around the world.
Ham magazines like QST and 73 published schematics and other how-to articles which amounted to an excellent education in practical electrical engineering. 73 magazine in particular was very technical -- it assumed you had good working knowledge of many common RF and audio circuits. Also, to get a ham license you needed to take a test demonstrating a good level of proficiency. For the lowest rung "novice" license you just had to demonstrate knowledge of Morse code at a slow but reasonable pace. For higher rungs of the achievement ladder like "advanced" or "extra" you needed to pass an exam about electronics as well as receive and send Morse code at a fast clip. The license presented a barrier to entry which didn't exist in CB radio -- which some hams looked down upon as a cesspool of unwashed, technically illiterate bozos.
My exposure to ham radio really started in the 1970s since my dad had been a ham playing with homebuilt radios since he was a kid in the 1930s. In the '70s the hobby was trifurcating. On one hand were the hard-core guys who built their own rigs, sometimes for the challenging high-frequency bands. Some also participated in designing and launching a ham-radio satellite via the ARRL. Early forms of digital encoding over radio were also big. Those guys were the real engineering types, and I admired them. On the other hand, commercial outfits were selling ready-to-use radios ... no engineering skills needed. In the middle were guys assembling and using stuff from Heathkit -- a great way to learn about electronics.
The ham hobby has been fading away for many years. I think the thrill of building a radio and then talking to somebody on a different continent with it has diminished in the face of cheap international calling, cell phones, Skype, etc. The only thing left for hams to do these days involves disaster relief -- and the remaining ham mag QST plays up that theme (or at least did the last time I looked). Meanwhile, the young nerds who used to take up ham radio now occupy themselves with various open-source software projects. I suppose that's natural.
You mentioned the cost of tools a couple of times. What's wrong with using MOSIS, which is free? Just asking, since I don't know anything about this area except that MOSIS was mentioned multiple times when I was in grad school back in the 1980s.
I will probably get downvoted for pointing this out, but the reality is that the geometric algebra approach to E&M, while interesting for its own reasons, will not replace the formalism based on Gibbs's vector calculus. One reason is simply that vector calculus is pretty intuitive and easy to learn. The major reason, however, is that the vector calculus approach is totally entrenched in the worlds of engineering and physics. After 100 years, nobody actually practicing those disciplines will make the notation change just so they can replace the 4 Maxwell's equations with one geometric algebra equation.
Also, Gibbs's vector calculus is used in fluid dynamics and other engineering disciplines, and as far as I know, nobody it touting the advantages of geometric algebra to folks working in fluid dynamics. I can be pretty sure that some HN reader will show me I am wrong about this by pointing out one lonely researcher who has found a way to express the Navier-Stokes equations using the geometric product ... but so what? ... My main point is that traditional vector calculus is a language everybody knows how to speak, geometric algebra is just another way to say the same things, so why would anybody change?
Besides these test functions I am curious to know if anybody uses the CUTE/CUTEr/CUTEst framework for testing. It's not clear to me how much the CUTE* packages are used in industry or by developers of optimization software.
I worked at the Arch Mach at MIT for a very short period in the very early 1980s. The Arch Mach was the predecessor to the MIT Media Lab. I made absolutely no impact there, but I do recall one of the successes of the lab was a kind of prototype of today's Google Maps Street View, where you could drive around Aspen, Colo on the computer and look at image taken from a car driving around the town. You could choose to drive forward, then turn left or right at an intersection as desired. You could thereby explore the entire town via the computer. It was regarded as extremely cool at the time. It's clearly the inspiration to today's Google Street View. Although I didn't work on it myself, I was able to play with it.
The images were stored on a laserdisk, and as you drove down the street the laserdisk player would pull the appropriate images off the disk and show them to you on the computer monitor. The images were stored on laserdisk because they were large files and at the time the only way you could store a lot of such large files was on a laserdisk since it was designed to hold video. For the 1981-1982 time-frame the Aspen exploration system was very forward-looking, but I do recall a delay between the time when you'd hit the button to move ahead, and the image would appear on the monitor. The delay had to do with first seeking, then reading the image off the disk.
I just looked around the web, and found this link describing the system:
I see a bunch of names I recognize in the Wikipedia article, so here's a shoutout to all the folks I worked with while I was an insignificant undergrad.
The reason Americans use cups and spoons (instead of e.g. grams) to measure ingredients is a matter of history. Tradition says Fannie Farmer wrote the "Boston Cooking-School Cook Book" in 1896, and for the first time in a cookbook used precise measurements (instead of "a jigger of this" or "a pinch of that") to specify how much of each ingredient to use. Nobody at that time would have a weight scale in their kitchen, so Ms. Farmer measured her proportions using tools which were readily available in any kitchen -- cups and spoons.
Her cookbook achieved immediate success and she became a household name in America. Even I had heard of her, long before I became a feeble student of history. Her measurement system is totally entrenched in American cooking culture, so I expect it won't ever be displaced by metric measurements except perhaps amongst high-end commercial kitchens and with people who want to make the effort to convert to grams and liters when cooking.
https://www.stochasticlifestyle.com/how-chaotic-is-chaos-how...