snarkconjecture

No, multiplying the incidence by 1.05 is incorrect. The 5% figure is additive.

ICRP Publication 103 is pretty unambiguous; e.g. Table A.4.2 gives total figures of about 400-600 "cases per 10,000 persons per Sv".

It would be astonishing if it were a mistake.

And yes, it's a detectable signal. "in a large population-based cohort it was found that up to 4% of brain cancers were caused by CT scan radiation" --somewhere on Wikipedia

CT scans vary in dosage. Wiki gives ~10 Sv for an abdominal CT; I don't know where Scott got 30, but maybe the kidney screening is multiple scans or otherwise higher dose. Or he was wrong by a factor of 3, which is not a factor of 100.

CT scans aren't done frivolously, and the current rate of scans is hotly debated for exactly this reason. I'm a little surprised that kidney donation involves CT over MRI by default, but I'm not an expert.

You did it wrong.

One Sv increases your absolute risk of fatal cancer by an added 5% or so. It doesn't multiply it by 1.05.

Quoting Wikipedia: "According to the International Commission on Radiological Protection (ICRP), one sievert results in a 5.5% probability of eventually developing fatal cancer based on the disputed linear no-threshold model of ionizing radiation exposure."

Also, where on earth did you get 1% as a "depressing" upper bound from? For lifetime risk of dying of cancer? It's over 15% in the US.

All of the graphs in the literature suggest a positive second derivative. Why do you say negative? AIUI the model is that hormesis kicks in even for extremely small amounts of radiation, but has a limited effect and is overwhelmed by the negative effects of larger amounts.

I was trying to give a conceptual understanding on the level of the person I was responding to, not instructions for doing actual calculations.

I didn't mean to suggest euclidean metric, I just thought "3+1" would be extra jargon.

The person asking questions was confused because they'd heard that "mass causes curvature" in GR, and that gravitational waves involve curvature. I figured it would help to explain that these are different kinds of curvature.

I think I was totally wrong re: Ricci curvature. I was thinking "oh, GW carry energy and there's nonlinear evolution..." and got carried away, whoops.

If you want to give a more accurate explanation (that makes sense to someone who's never taken a GR class) please do!

There are many ways for spacetime to warp, which can be put into two categories. The simpler kind, Ricci curvature, is the only kind of curvature in <4 dimensions and is produced by mass-energy, momentum, pressure, and shear stress, according to general relativity. The other kind, Weyl curvature, only exists in 4 or more spacetime dimensions and can exist in a vacuum.

Gravitational waves are Weyl-curvature distortions of spacetime that propagate in a vacuum according to general relativity.

(Also, gravitational waves do carry a little bit of energy, so they cause a small amount of Ricci curvature, but this is a secondary effect.)

Yes, it's a little buried but the article says

> The energy turnover results from the coupled heating power multiplied by the duration of the discharge

The numbers:

> The energy turnover of 1.3 gigajoule was achieved with an average heating power of 2.7 megawatts, whereby the discharge lasted 480 seconds

Also:

> Within a few years, the plan is to increase the energy turnover at Wendelstein 7-X to 18 gigajoules, with the plasma then being kept stable for half an hour

i.e. 10 megawatts for 30 minutes

You can't specify the time derivative of the wavefunction independently, because the Schrodinger equation is first-order (unlike classical dynamical laws which are second-order).

I think that's not quite it.

The relevant theorem is that variance(position-space function f) * variance(Fourier transform of f) >= some constant.

A wavefunction is a wavefunction, it doesn't have more frequency components at the classical scale. It's just that what looks like a large position spread at the quantum scale is pretty tiny compared to classical length scales, and what looks like a large momentum spread (variance of the Fourier transform) is pretty tiny compared to classical-scale momenta.

You shouldn't think of a wavefunction as being perfectly localized, with infinitely spread out frequency components, because that would mean the particle's momentum is infinitely uncertain. Instead, think of a Gaussian function, whose Fourier transform is a Gaussian. The widths of those two Gaussians are inversely proportional to each other.

Also, you should think about continuous Fourier transforms, not discrete Fourier series. Periodic wavefunctions are only the norm in situations like crystals where the environment itself is periodic.

They got the article from the OP article -- it goes on a diversion into the circle-squaring thing at the end.

1/7 ≈ 1/8.2 + 1/47 gives about half the error (<.3%) with half the resistor count.

Or the greedy approach: 6.8+.22 in parallel with 2700 gives you 7.0018 with .026% error.

> one cannot feasibly produce resistors with values as elements of a dense subset of the real line, being, as analysis taught us, an uncountable set

The rational numbers are an example of a countable dense set.

Unfortunately, countably-infinite product catalogs are still a bit unwieldy.

Unless one of the leaks caused all the others, it seems like a hell of a coincidence for them to all happen on the same day by chance after sitting there for years.

Disclaimer: not a linguist.

Languages don't really become systematically simpler over time, or they would've had to start out incredibly complicated. They have some tendency to cycle between lots of grammatical forms (like Latin) and few grammatical forms with lots of helper words (like English).

("Simple" and "complex" is debatable; English's snarl of helper words is infamously hard to learn.)

It's obvious how you go in the "less inflection" direction, but how do you go in the "more inflection" one? The answer is that you start with helper words, which evolve into enclitics (fragments of words attached to other words, like the n't in 'can't' and 'shouldn't'), and eventually those become suffixes and prefixes, and then merge into the words they're attached to, creating grammatical inflections!

This process is where all(?) of the grammatical forms in Greek/Latin/etc are thought to have come from, afaik. Proto-Indo-European, one of the earliest languages we can reconstruct, seems to have been pretty close to the apex of this process, having just consolidated a bunch of enclitics into grammar.

So the goofy internet 'verbn't' trend is actually a possible glimpse of how English could acquire a negative verb form like Japanese has!

What does this achieve that posting "text me and I'll tell you if I have a crush on you" doesn't?

Or texting your crush directly?

I suppose it's a useful commitment mechanism for proving you aren't telling everyone they're your only crush, but that seems a bit of a niche use case.