improbable22

27 ms·

271.
by improbable22 9y ago
You can do general matrices too, what do you have in mind? aa[x_] = {{1, 2}, {3, 4}} x bb[x_] = {x^2, x^3} D[ a[x].b[x] , x, x] (* for any suitable tensors *) % /. {a -> aa, b -> bb}
272.
by improbable22 9y ago
This is what index notation is good for, and I encourage everyone to learn it. Jacobians are dx_a/dx_b, two indices, and clearly b belongs to the derivative. Whether it's rows or columns is an implementation detail of how you&#x27
273.
by improbable22 9y ago
Like this, perhaps? A = {{1,2},{3,4}} vec = {x^2, x^3} D[vec.A.vec, x] Or perhaps like this, again the table of derivatives: xvec = {x1,x2} Table[ D[xvec.A.xvec,x] ,{x,xvec}] (all untested... one typo caught...)
274.
by improbable22 9y ago
Mathematica can absolutely do all of this! D[ matrix ,x] ... or things like this: f[x_,y_] := x^2 + Sin[y] vars={x,y}; Table[ D[f[x,y],var1, var2], {var1,vars}, {var2,vars}] // MatrixForm
275.
by improbable22 9y ago
America has plenty rules which aren't written down, too. You just lack a good word for them, having decided to use constitution to mean a particular bit of paper, which is periodically found to contain rights unknown to its authors. A
276.
by improbable22 9y ago
Or perhaps to put that another way: In a city with great public transport, lots of the person-miles are done on full trains, running back to back all rush hour, in a way that nothing else can really replace. But for the system to be useful,
277.
by improbable22 9y ago
Re "the 2-5 person capacity mass transit vehicle": Lots of cities have enough density to support good dense tram / train / bus networks in the centre, during the day. But quite a lot of the people who would use that, als
278.
by improbable22 9y ago
Indeed. Frameworks seem like embryonic languages, which are extremely awkward to work with (compared to Python) but easy to compile to the GPU. A relevant essay: "On Machine Learning and Programming Languages" https://
279.
by improbable22 9y ago
It's certainly possible to find such views in theoretical physics. But typically not from very serious people. In my understanding the big shift was the understanding of renormalisation, Kadanoff and Wilson, around 1970. This took airy
280.
by improbable22 9y ago
"much smaller today" meaning literally smaller: Navier didn't know about atoms, 10^-10 m, but now we know about things at 10^-18 m or so. Sure, our awareness of how much we don't know has grown over time. The point I was
281.
by improbable22 9y ago
Human limitations is one reason, but there's something much deeper going on here. Navier and Stokes worked before we were sure that atoms existed, certainly before we had any idea of how many there were. Nevertheless they were able to
282.
by improbable22 9y ago
Isn't AIC just an approximation to cross-entropy, in the simplest possible case of gaussian noise? It's a rule of thumb which is useful in much simpler cases (a few parameters, lots of data) than typical for say neural nets. Not t
283.
by improbable22 9y ago
Certainly these improvements led to overall population growth, which accelerated over a few centuries. But the pattern that richer people had more kids than poor is a different thing. I believe this persisted until Victorian times in Englan
284.
by improbable22 9y ago
Yes this seems to be the story today, both in the west and in some developing countries (e.g. India). But this was not the historical pattern. Firstly, it's my understanding that richer families started having fewer kids than poor ones
285.
by improbable22 9y ago
For England I want to say the crossover is about 150 years ago, could be 200, from memory. France & Germany a generation or two later, most other places later still. The US frontier may well be different -- having almost infinite land m
286.
by improbable22 9y ago
This 3% or whatever from 0.5^n is a lower bound. To get close to it, all your other relatives would need to come from completely somewhere else. But in reality, many of your other ancestors were probably related to him, because they had liv
287.
by improbable22 9y ago
Chromosomes don't stay intact like (it sounds like) jonsen is assuming. Instead they cross-over or re-combine to make never-before-seen strands -- the new strand has one end from one copy & the other end from the other copy. There
288.
by improbable22 9y ago
Well I found the graph I was remembering: https://www.economist.com/node/21732803 Although I'm not actually sure exactly what the time scale this is measuring. Data is from is here, I believe: http://ww
289.
by improbable22 9y ago
No, this is not true. Or rather, it's true today (in the west) but this is historically very unusual. We actually have surprisingly good records of such things, and digging them up demolished lots of commonly held beliefs. For instanc
290.
by improbable22 9y ago
You're more strongly descended from royalty (or at least nobility) than this. Because rich people had more children for most of history, and thus their offspring tended to displace those of the poor. For instance, if the top 10% have f
291.
by improbable22 9y ago
My first point about mass was that some are tempted to imagine the mass of the BH as residing in the matter of the neutron star or whatever that formed it. This is misleading, it is better to think of that matter as no longer existing, and
292.
by improbable22 9y ago
Certainly normal matter (like the earth) has mass and warps spacetime. But a black hole is a purely gravitational object, there need not be any normal matter involved. The mass of a black hole is something that's really only defined fr
293.
by improbable22 9y ago
No, not really. Just about everything we say about black holes is talking only about the exterior, the region of spacetime outside the horizon. The simulations through which we model the merging of two black holes only model the exterior of
294.
by improbable22 9y ago
There isn't exactly one moment of collision like snooker balls, the two spiral and merge and then settle down to look like one bigger black hole. But the time during which most of the energy is radiated is quite short, like 0.1s. The m
295.
by improbable22 9y ago
For black holes these aren't separate concepts. An apple and the earth each have rest mass, and gravity means there is also potential energy in their separation. But a black hole is an object with rest mass which is made purely out of
296.
by improbable22 9y ago
This is also true. I don't see how they're making money off their extensive knowledge about me. When I make the mistake of buying something online in a browser logged into facebook, then I get adds for a week trying to sell me wha
297.
by improbable22 9y ago
But why does this mean they have power? The hiring committee at their next job has real power. The administrators who could fire them have some power too (although failing to impress the former is almost as bad as being expelled by the latt
298.
by improbable22 9y ago
Oh they have much more than this. Messenger asks nicely to upload your whole address book, and since half your college buddies clicked yes they know when and where you studied, and who you knew, and your parents landline thus some idea of t
299.
by improbable22 9y ago
Lots of good replies. I'd like to add that incentives seem a better explanation than power: The professor's incentives are entirely towards thinking up and pulling off big long-term projects. The tenure committee is not going to k
300.
by improbable22 9y ago
> tax that consumers pay No, you should think of the tax man standing between the customer and the seller. Whether he takes the bank notes from the customer's hand just before, or from the seller's hand just afterwards, really

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