evanb

They did consider it, got a contract that affirmed that the military would be bound by the same pre-existing terms of service as every other user, and want to resist the military's pressure to renegotiate.

Surely that might be naive but the entire issue is that they want to stick to the original contract, which is of course the purpose of a contract in the first place.

IANAL but it seems 3rd-amendment-adjacent.

I'll try to find it; thanks!

I'm using these to teach an intermediate mechanics class, and my only regret is that there are no problems. The flip side is that sometimes Feynman skips over the derivations of certain things, and that makes good assignments ("Fill in the steps between [these assumptions] and [this result]").

Feynman's writing of course is stellar. The order is a bit unusual and not really designed for a "standard" university-level course. I can pick and choose, but I wish I could easily reorder the material.

“Pining for the fjords?”

> Winter rain, now tell me why

> Summers fade and roses die

> The answer came, the wind and rain

> [...]

> Circle songs and sands of time

> And seasons will end in tumbled rhyme

> And little change, the wind and rain

Fare thee well, Bob.

or

3) there's a misunderstanding about ordinary least-squares.

You think it was primarily poor people who were driving their cars into Midtown?

These are nice! I had never seen the 1/5 spiral before!

I animated these and related 'proofs' some time ago

    1/3 = 1/4 + 1/16 + 1/64 + ...

https://evanberkowitz.com/images/2014-03-15-quarters/SquareA...

https://evanberkowitz.com/images/2014-03-15-quarters/Triangl...

    1/7 = 1/8 + 1/64 + 1/512 + ...

https://evanberkowitz.com/images/2014-03-16-eighths/EighthsA...

    1/8 = 1/9 + 1/81 + 1/729 + ...

https://evanberkowitz.com/images/2014-03-17-ninths/NinthsAni...

Careful what you wish for. Negating the predicate of "A COMPUTER CAN NEVER BE HELD ACCOUNTABLE. THEREFORE A COMPUTER MUST NEVER MAKE A MANAGEMENT DECISION" might open us up to the consequence.

I think it's a reference to https://xkcd.com/353/

Indeed, but if I had called it the Nazi salute I'd have been begging the question---or something like it.

In Germany it hits home when someone gives the Roman salute with an angry scowl on your face during a moment of transition of power.

A dot product is a weighted sum of two vectors, but not in the way the author suggested. The author's use is that one of the vectors is the weights and the other is 'the' vector, so the dot product is the weighted sum of ONE vector. It just so happens that because the author is not interested in the geometric interpretation of the dot product that they forgo the metric.

On the other hand, it is common to need a metric, which is actually the set of weights in the dot product. If `g` is the metric,

    dot(a, g, b) = np.einsum('x,xy,y->', np.conj(a), g, b)

g doesn't have to be diagonal, but if you want the dot product to be symmetric in a and b it ought to be self-adjoint. Then you can find a basis where g is diagonal with real diagonal elements, which you can interpret as the weights.

> A small change in the parameter a can lead to vastly different particle trajectories and the overall shape of the attractor. Change this value in the control panel and observe the butterfly effect in action.

I think this is slightly inaccurate. The butterfly effect is about the evolution of two nearby states in phase space into well-separated states. But the parameter a is not a state. To see the butterfly effect by changing a we would need to let the system settle down, give the parameter a small change, and then change it back. The evolution during the changed time acts as a perturbation on states.

Instead, showing that the attractor changes qualitatively as a function of the parameter is more akin to a phase transition.

No, you cannot escape the conclusion of the limitations on measuring the one-way speed of light.

While the video doesn't touch on this explicitly, the discussion of the different path lengths around 25:00 in is about the trigonometric effect of the different distances of the beam from the camera. Needing to worry about that is the same grappling with the limitation on the one-way speed.

I was always surprised that when we talk about BHs mass, charge, and spin that we really mean U(1) (electromagnetic) gauge charge and not charges from global symmetries. (If BHs had global charge, you could at least say that this or that black hole was made out of N baryons, or whatever.)

But it's really so---according to GR, black holes don't have global charges. So even if you see a star made out of baryons collapse into a black hole, once the BH settles down into a steady state you can't say it's "really" got baryons inside: the baryon number gets destroyed.

(Of course, a different model of gravity that preserves unitarity might upset this understanding.)

I thought all this machine learning stuff was about minimizing the loss?

That’s correct, but being forced out of academia is a good way for scientists to disappear from research and publication.

If you find Jane Goodall inspirational, you may be delighted to learn about Anne Innis Dagg [0], whose studies of wild giraffe predates Goodall's study of chimps. The documentary "The Woman Who Loves Giraffes" [1] is fantastic and has 100% on Rotten Tomatoes. The reason you might not know Dagg's name is essentially that she was denied tenure for being a woman.

[0] https://en.wikipedia.org/wiki/Anne_Innis_Dagg

[1] https://thewomanwholovesgiraffes.com/

This map is a neat visualization but is incomplete so far as there are some missing jurisdictions. Puerto Rico and the Virgin Islands, for example.

If you're interested in HMC, we showed how to apply it to the Ising model in https://arxiv.org/abs/1912.03278 with code available in https://github.com/HISKP-LQCD/ising_hmc

What if the property with 1 hectare of area were 0.1m x 10^5 m? The meter is bigger than the field is wide.

Or, more to the point, suppose someone came with a different system of units and said: look, one of our standard lengths is 10^-6 of one of yours, but one of our standard areas is defined just like yours: 1 ha = (100m)^2 and (1 of our areas) = (100 of our lengths)^2.

In other words, their standard length = 10^-6m; their area = 10^-12 ha = 10^-8 m^2.

Is their standard area bigger or smaller than their standard length?

Notice that in proportion the lengths and areas are the same.

Which is bigger: a meter, a hectare, or a liter?

I agree; the fair comparison is the nth root of the hypervolume in n dimensions, (V(n))^(1/n). This monotonically decreases from n=0, which shows the counterintuitive point that people often want to make anyway: an n-sphere takes up less and less of an n-hypercube. The peak at n~=5 is illusory.

Another fair comparison is between dimension-dependent lengths is the ratio of the (hyper)volume to the surface (hyper)area V(n)/A(n). This monotonically decreases from n=1.

I really thought the :) at the end would be enough.

This is a nice analog but unfortunately I think it breaks down in a way the "π" calculation does not.

In the article 2π(d) = the ratio of the circumference to the radius. This is dimensionless, in the sense that the circumference and the radius are both lengths (measured in meters, or whatever), so 2π(d) is really just a number.

But the (hyper)volumes you're talking about depend on dimension, which is exactly why you say "hyper". In 2 dimensions the volume is the area, πr^2, which has dimensions L^2 [measured in m^2 or whatever]. But in 3 dimensions the volume is 4/3 πr^3, which has dimensions L^3. The 5 dimensional (hyper)volume has dimensions L^5, and so on.

So, "comparing" these to find out which is bigger and which smaller is not really meaningful---just like you shouldn't ask which is the bigger mass: a meter or a second? Neither is, they aren't masses.

I can think of a font that’s only 1 pixel high. Invented by Samuel Morse, takes a bit of practice to read :)

HMC was essentially designed to mix random walks (the momentum refresh step) with gradient descent (that is, the state likes to 'roll down the potential' ie. minimize the action (loss)).