Distracted, busy
It has a been a bit since I posted anything - sorry: been working on learning how to use blender/godot = 24/7 frustration because I just don't understand enough about the jobs these tools are used for. Plus my son got hit by someone running a red light and Allstate Insurance is not covering themselves with glory on this one.
About five years ago I hit a deer - night time; it was being chased by a dog and came over a berm right in front of me. On that one Allstate was wonderful: fast, helpful; absolutely hassle free. This time? we could end up in court because the kid's dash cam record is completely exonerating and they still want to hold him 50% responsible.
The crash, by the way, could be used to illustrate everything Volvo claims about safety: she was the second vehicle to run the red light, came from behind a stopped pickup, and hit the front 9" or so of his (by then nearly stopped) car at about 40mph. Her SUV folded, his Volvo (S60 R-design) was suddenly ugly, but drive-able.
Ilhan Omar
No sitting congresscriter has ever yet sought refuge in a foreign country. Ilhan Omar has a good chance, I think, of being the first - wonder where she'll go? I'm sure Carney et al in Ottawa would love to have her: not only are they birds of a feather but the sheer glory of being seen protecting her from the bad orange man would be irresistible.
Drones
People I know, many of whom should know better, keep droning on about how drones are the future of warfare and impossible to stop. Well, duh, except it's nonsense. Drones are better artillery -longer range; more accurate; less launch exposure; and more adaptable but, in the end, it's a numbers game and that, oddly enough, means that you're better off being targeted by 100,000 drones than 10,000 shells.
Why? because a shell on a ballistic trajectory is essentially unstoppable while we can, as I assume the U.S. is, build lasers that will cook off very large numbers of incoming drones very quickly indeed.
The numbers tell the future: if a mobile laser can take out about 10 drones per second at about 1000 yards then the enemy will make them faster, smaller, lower flying, and more resistant to spot over-heating. And what that means is that the cost per offensive unit will go up while volume, technical change, and training drive costs down for defenders to eventually produce yet another equilibrium with these things integrated into everyday doctrine.
Alberta 51
One of the Alberta independence referenda petitions has reached the signature level needed to get on the ballot. Unfortunately it's the "Stay Free Alberta" one - the one that gets media attention and support largely because, I think, it's a sure loser guaranteed to strengthen the federal government's hand in dealing with us.
Personally I don't want to see Canada break up, but do want a separatist referendum to pass here with a whopping majority because the feds, right now, see us the way feudal lords saw their serfs: valuable because productive, but essentially subhuman and certainly not to be treated as equals.
Meanwhile the streaming services we watch at home are being inundated by taxpayer funded commercials obviously intended to promote Canadian anti-Americanism - my favorite is one in which we're told Canada is a Nation of Builders - in reality we haven't built anything of substance since -well, the ad cites the St.Lawrence Seaway (completed in 1958! with 30% of the money and nearly all of the engineering coming (via Montreal, of course) from the U.S.).
Most fundamentally, Carney has bet the country on Trump losing the midterms -and if that doesn't happen (and please God don't let it happen!) the bills he's running up both in terms of cash and, more importantly, in terms of national unity and social cohesion are going to come due. If I had any money, I'd be shorting Canada about now -it's an escalating bad bet and there's nobody to call a halt to it.
Math
(FYI: somebody did but the first copy of Frames and sent me an email asking why the computers use continued fraction arithmetic instead of floating point. Here's why.)
From a practical, everyday engineering, perspective the single most important concept in mathematics is that of a limit. Want to know where the shell will land? how fast the airplane will go; how much fuel gets exhausted instead of burnt; or whether a bridge mount will hold in a high wind? and you will be using approximations based on limits.
But.. there's a problem, known since at least Euler: a limit like (pi squared)/6 isn't really a limit: it's an invitation to pick a point beyond which change doesn't matter.
For example, 3.141592 is 0.000092 greater than 3.1415 - and an estimate for pi out to a billion digits is smaller than one done with ten billion digits. Saying it's (pi squared)/6 is good enough for most purposes, of course, but one reason nobody has been able to prove stuff like Riemann is simply that many limits are like that: approachable, but not reachable. Not a big deal, right? except maybe when it is - for example, the gravity exerted by a planet, star or galaxy doesn't vary with some radius R, but with abc, where a, b, and c, are the axis lengths for a better approximation to the object's real shape.
So what? well all of the calculations we do on orbits are dependent on limits best considered approximations. If, for example, the earth's orbit around the sun were circular we could find its length to within a meter or two with 14 digits of pi; but it isn't circular and the effects of gravity from other sources on our orbit don't map smoothly to spherical surfaces either, so 14 digits won't get us within several hundred miles of the right length - and the tan(x) calcs required are themselves dependent on limits..
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