Which is ironic, considering that the 1950s were long before the internet boom. The internet didn't even exist yet, let alone dial-up modems.

I was curious and looked this up: https://en.wikipedia.org/wiki/Modem#1950s

Mass production of telephone line modems in the United States began as part of the SAGE air-defense system in 1958, connecting terminals at various airbases, radar sites, and command-and-control centers to the SAGE director centers scattered around the United States and Canada.

Shortly afterwards in 1959, the technology in the SAGE modems was made available commercially as the Bell 101, which provided 110 bit/s speeds. Bell called this and several other early modems "datasets".

Aside from the fact that such calculations aren't necessarily applicable anyway, it is incorrect because they would most likely have continued to use and have to pay for Evernote for more than just the one year.

That really depends on which country you're in.

The solution is that the probes were built by a long ago technological civilization on Earth as a desperate measure in an interstellar war.

The probes are out there and were programmed never to come back to Earth.

That's a solid plot device and sounds like a fun story! It definitely doesn't pass the customs inspection for use in speculation about the real world, though.

FWIW, it's part of the plot of Andreas Eschbach's Lord of all Things. (IMHO one of his weaker novels, but weirdly one of the few that were translated into English)

You forgot about branch predictors.

'cough' could share a root with 'keuchen' (IANAL)

That has a different sound though. But yes, it might be a cognate.

The operations could be short-circuiting.

Agreed. There is no sane reason why live translation and/or its privacy properties should depend on the specific headphones used. Even if the live translation were to happen in the headphones themselves, that should only tie the availability of the feature to the headphones. The privacy implications ought to be orthogonal.

I see three possibilities. Either the whole thing is made up entirely by Apple for bad faith reasons. Or some non-technical person with bad faith motivations at Apple suffered from some internal misunderstanding. Or somebody at Apple made some incredibly bad technical decisions.

Basically, there's no way that this isn't a screw up by somebody at Apple in some form. We just can't say which it is without additional information.

Official communications to an international governmental agency are surely checked by multiple employees and subject to review by lawyers, marketing, C suite, etc.

Apple said what they said. It wasn't a mistake. It was attempted deception.

It's misleading to compare a desktop GPU against a data center GPU on these metrics. Blackwell data center tenor cores are different from Blackwell consumer tensor cores, and same for the AMD side.

Also, the size of the native / atomic matrix fragment size isn't relevant for memory bandwidth because you can always build larger matrices out of multiple fragments in the register file. A single matrix fragment is read from memory once and used in multiple matmul instructions, which has the same effect on memory bandwidth as using a single larger matmul instruction.

Affine transformations don't change relative density.

You can think of it this way. There's a density function on the shapes in question. Whenever you transform the 2d space, you have to adjust the density at the same time to preserve "volume" (area times density).

Non-linear transforms, such as interpreting a square as polar coordinates to obtain a disk, will expand or shrink area differently in different parts of the space, which means that if you start with a uniform density, you end up with a non-uniform density. But linear/affine transforms affect area the same everywhere in the space, and so if the density is uniform to begin with, it remains uniform.

Thanks, I should have reminded myself that my intuitions are often non-mathematical. I don't even know how I decided that a change in angle would have a non-linear effect on density.

I also had an intuition that the aspect ratio change would squish the distribution. I guess this aspect ratio doesn't matter for the density distribution of dimensionless points.

But, if doing something like splatting a pixel/sprite at each point coordinate, would the sprite shape need to be transformed to match...?