denotational

The delayed-choice quantum eraser wasn’t carried out experimentally until 1999, so I think it’s a bit misleading to say this is what makes the double-slit experiment (first carried out with matter in 1927) so weird.

For me, the weird thing about the double-slit experiment for matter is that the excitations of the detector are discrete, i.e. we see individual particles arriving at the detector, as expected under the classical model of matter behaving like particles.

It’s only when we send many particles over time, that we can tell that we’ve been sampling from a distribution given by the interfering wave-functions.

This suggests that the particle is interfering with itself, thus behaving like a wave, but since we only detect each particle in a single place, it’s still behaving like a particle in some sense.

This is very different from the classical wave phenomena seen when we do the double-slit experiment in a water tank, where there is constant interference across the whole axis the whole time (there is no particle-like behaviour at all).

the usual garbage undergrad textbooks

Out of interest, please could you give some examples of textbooks you consider garbage, and some you consider not to be (undergrad or otherwise)?

Fair enough: I was reading the original comment as referring to (thermal) noise intrinsic to the amplifier design itself (as opposed to noise due to imperfections in DC supply or due to coupling with some external transmitter), but this makes more sense, and we should consider the whole system anyway.

I see, so you want to band-limit the noise, and are willing to accept potentially raising the noise floor in the band-limited range, the idea being that if the original noise is sufficiently broad-band, this will still increase SNR?

Off-topic, but can an RC circuit really reduce noise? I can see how it would reduce distortion (which is not the same as noise), but adding passives is surely going to increase thermal noise?

The paper that introduced the implicit lifetime mechanism suggests that std::launder is not required: https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/p05....

If the type is an implicit-lifetime type, then you can legally create an unsigned char array, and then reinterpret_cast a pointer to that to a pointer to the type.

See https://eel.is/c++draft/intro.object#def:object,implicit_cre....

https://eel.is/c++draft/intro.object#15 is an example showing this with malloc; the subsequent paragraph further permits it to work with an unsigned char array.

Hardware, see https://en.wikipedia.org/wiki/Tomasulo%27s_algorithm.

Yes -- in set theory sets can contain themselves

Which set theory? ZFC doesn't permit this.

Non-well-founded set theories are so non-standard that I think it's wrong, or at least misleading, to claim that unqualified "set theory" permits this.

Has anyone looked at using greywater for evaporative cooling? I couldn’t find much after a quick Google, aside from small scale domestic usage.

Given the “rightsholders” have no rights over OpenTTD (only the assets are copyrightable, and OpenTTD has had its own set of open-source assets for the past 15 years), I can’t agree with this.

I’m not sure how to interpret this other than Atari not wanting to compete with OpenTTD on Steam.

On another occasion much later, I learned by chance that putting certain provocative information on a security clearance form can greatly speed up the clearance process. But that is another story.

Presumably this is the famous (?) story of him listing his race as “mongrel” whenever asked?

Please could you elaborate?

It’s not really margin since there’s no leverage: the potential loss associated with the bet has to be deposited, so it’s fully collateralised.

* A set that isn't open isn't (necessarily) closed.

* A set that is open can also be closed.

Good publishing costs money

Good faith question: aside from hosting costs, what costs are there, given the reviewers are unpaid?

Right, but if you fill in the shorthand there’s no reason to think it’s circular; it’s just a normal definition at that point, albeit one without much motivation.

Do you mean specifically as consumer products?

There are loads of 10GbE switches from Cisco/Juniper/Arista/et al.

In its defence, the headline says "file operation" rather than "syscall", which makes it slightly less egregious: it's referring to `mmap` as a member of `struct file_operations`.

A null-pointer dereference in C will be just as fatal (modulo optimizations).

OCR errors?

It doesn't, at least on the version I have access to, as it is configured on that cluster.

I’m using Linux rather than AIX.

fcntl(2) locks are supported (as long as they aren't OFD), but flock(2) locks don't work across nodes.

Sadly GPFS still doesn’t support flock(2), so I still avoid it.

I think that's a pretty uncharitable take; I thought there were several interesting questions raised by the author:

1. Should conference "service" be something we expect of postdocs (and even PhD candidates) rather than established experts?

Often, as a result, the PC is staffed by junior, ambitious academics intent on filling their résumés. Note that it does not matter for these résumés whether the person did a good or bad job as a referee! [...] I very much doubt that the submissions of Einstein, Curie, Planck, and such to the Solvay conferences were assessed by postdocs. Top conferences should be the responsibility of the established leaders in the field.

2. Should programme chairs strive to maintain exclusivity of their conference track, or look for important ideas that deserve to be communicated?

As a simple example, consider a paper that introduces a new concept, but does not completely work out its implications and has a number of imperfections. In the careerist view, it is normal to reject it as not ready for full endorsement. In the scientific view, the question for the program committee (PC) becomes: is the idea important enough to warrant publication even if it still has rough edges? The answer may well be yes. [...] Since top conferences boast of their high rejection rates, typically 80% to 90%, referees must look for reasons to reject the papers in their pile rather than arguments for accepting them.

3. Is computer science suffering from a focus on orthopraxy rather than scientific method?

What threatens to make conferences irrelevant is a specific case of the general phenomenon of bureaucratization of science. Some of the bureaucratization process is inevitable: research no longer involves a few thousand elite members in a dozen countries (as it did before the mid-1900s), but is a global academic and industry business drawing in enormous amounts of money and millions of players for whom a publication is not just an opportunity to share their latest results, but a career step.

What do you think about these?

BB(764) is an integer (!) that I know is uncomputable

I meant BB(748) apparently.

To elaborate on this point a bit, I specifically mean uncomputable in ZFC. There may be other foundations in which it is computable, but we can just find another n for which BB(n) is uncomputable in that framework since BB is an uncomputable function.

Two Dedekind reals (A, B) and (A', B') are equal if and only if they have identical representations. […] Can you elaborate on how you're thinking about decidability?

Direct:

Make one of the sets uncomputable, at which point the equality of the sets cannot be decided. This happens when the real defined by the Dedekind cut is itself uncomputable. BB(764) is an integer (!) that I know is uncomputable off the top of my head. The same idea (defining an object in terms of some halting property) is used in the next proof.

Via undecidability of Cauchy reals:

Equality of Cauchy reals is also undecidable. The proof is by negation: consider a procedure that decides whether a real is equal to zero; consider a sequence (a_n) with a_n = 1 if Turing machine A halts within n steps on all inputs, 0 otherwise; this is clearly Cauchy, but if we can decide whether it’s equal to 0, then we can decide HALT.

Cauchy reals and Dedekind reals are isomorphic, so equality of Dedekinds must also be undecidable.

Hopefully those two sketches show what I mean by decidable; caveat that I’m not infallible and haven’t been in academia for a while, so some/all of this may be wrong!

I’m not who you replied to, but:

The equivalence classes of integers: pairs of naturals with (a, b) ~ (c, d) := (a + d) = (b + c).

The equivalence classes of rationals: pairs of integers with (a, b) ~ (c, d) := ad = bc.

It’s “easy” to tell whether two integers/rationals are equivalent, because the equivalence rule only requires you to determine whether one pair is a translation/multiple resp. of the other (proof is left to the reader).

Cauchy sequences, on the other hand, require you to consider the limit of an infinite sequence; as the GP points out, two sequences with the same limit may differ by an arbitrarily large prefix, which makes them “hard” to compare.

We can formalise this notion by pointing out that equality of integers and rationals is decidable, whereas equality of Cauchy reals is not. On the other hand, equality of Dedekind reals isn’t decidable either, so it’s not that Cauchy reals are necessarily easier than Dedekind reals, but more that they might lull one into a false sense of security because one might naively believe that it’s easy to tell if two sequences have the same limit.

I don’t really know what a “calculus” class is since here (the UK) that term isn’t really used for university-level mathematics; we’d usually say “analysis” instead, but I know that “analysis” is a class in the US too, so I don’t know if calculus is closer to what we would do just prior to university (a bit of limits, differentiation, Riemann integrals, a bit of vector calculus).

Virtually every first year UK undergraduate analysis course will start with a construction of the reals via Dedekind cuts, and this is about the level that this book is pitched at.

The original commenter suggested that “least upper bounds” is a simpler approach, and that Hardy’s book is outdated by using Dedekind cuts; it may be that constructing the reals is not something that would be done at “calculus”-level in the US, but clearly the book isn’t aimed at that level.

Dedekind cuts (or Cauchy sequences) are totally standard, and I don’t think it’s fair to criticise their use at all.

Seconded, the “least upper bound” method for constructing the reals that I know about is… …Dedekind cuts.

Mario Carneiro’s MS Thesis has a good overview of the type theory and how it compares to Coq: https://github.com/digama0/lean-type-theory/releases/downloa...