kmm

I like the temperate graph halfway down the page. It looks like two decaying exponentials alternating every ~40 minutes, with the downward one steeper than the upward one. It's a neat visualization of hysteresis, where the thermostat presumably has a different temperature threshold for turning off or turning on (or perhaps there's a minimum time between state switches). Without the scale it's hard to know for sure.

Russian used to have dual pronouns too, but they all were lost somewhere in the 13th century, as in all other Slavic languages other than Slovenian.

The system used for small numbers is probably a broad extension of an earlier dual number for nouns, i.e. something like a plural but just for two things. For (some) male nouns, the nominative dual ending was the same as the genitive singular, which was then extended to all other nouns even when this correspondence didn't hold, and from just 2 things to 3 and 4 as well. Nowadays the dual has been completely forgotten for nouns, and the only interpretation of the rule is that it's a genitive singular.

Curiously, Old English unc is actually not related to German uns, at least, not after the Germanic language family had already formed. Old English at some point underwent a sound change[1] where the -n- sound disappeared before fricatives (sounds like s, f, v, z, sh, etc...). So "us" comes from an older common form "uns", which German inherited basically unchanged. This sound change also explains other correspondences between English and German where the n is missing, like mouth-Mund, tooth-Zahn, other-ander, goose-Gans or five-fünf.

1: https://en.wikipedia.org/wiki/Ingvaeonic_nasal_spirant_law

Everytime people extoll the virtues of high noon, I ask the same question: why does it matter if the sun reaches it highest point near 12 o' clock? You're awake for 4-6 hours before 12, and you remain awake for 10-12 hours after it. Noon isn't the middle of the day for nearly anyone in the western world.

I understand the argument for having an early sunset, clearly having sunlight when you're awake has an effect. But who cares about having an early high noon, when there's still two thirds of the day left at best?

That's correct, but it's pretty well-hidden because at first sight there is no term that's just the year modulo 7. That's because a Gregorian calendar cycle of 400 years is coincidentally an integer amount of weeks long, so after the term modulo 400 you don't need another correction anymore.

To recover the fact that 365 % 7 == 1 from the given formula, one can notice that the sum of the coefficients 5+4+6=15, which modulo 7 is 1.

That's only if you delay renewal until the last day of the lifetime of the certificate. If you renew at day 30 you'd only get in trouble if there's more than two weeks of downtime.

Hah, the capitalization of the title of this post only just now made me realize why the GPU farm at my job is called "barracuda". That's pretty funny.

And a megabyte is depending on the context precisely 1000x1000=1,000,000 or 1024x1024=1,048,576 bytes*, except when you're talking about the classic 3.5 inch floppy disks, where "1.44 MB" stands for 1440x1024 bytes, or about 1.47 true MB or 1.41 MiB.

* Yeah, I read the article. Regardless of the IEC's noble attempt, in all my years of working with people and computers I've never heard anyone actually pronounce MiB (or write it out in full) as "mebibyte".

I think I have some sort of intuition why all the probabilities are the same.

Imagine you're standing on a randomly chosen vertex on the ring which is not right next to the starting position. At some point, the ladybug will be guaranteed to appear either to the left of you or to the right of you for the first time, and this cannot happen as the second-to-last step, because then the ladybug would have had to have visited both of your neighbors. At this point, for your vertex to be the one last visited, the ladybug would have to turn around and loop all the way around the circle to your other neighbor. But this means the previous trajectory of the ladybug and which vertices were visited before is irrelevant, as the ladybug will have to pass by them anyway. By symmetry, this situation is completely equivalent to being at the very start of the process on one of the vertices neighboring the starting position. Hence any randomly chosen vertex not next to the starting position has to have the same probability of being visited last as those two vertices. Hence all vertices have to have to same probability of being visited last.

In that case following Alice's input is still the best strategy, but you'll be worse off: you'd only be right if both tell the truth, at 80%80%=64%, or both lie, at 20%20%=4%, for a total of 68%.

In the general case of n intermediate occasional liars, the odds of the final result being accurate goes to 50% as n grows large, which makes sense, as it will have no correlation anymore to the initial input.

That's actually a message from the (Arch) initramfs[1], in case it can't mount the root filesystem or find an init to hand off to.

The kernel has a different error message: "No working init found. Try passing init= option to kernel."[2]

1: https://github.com/archlinux/mkinitcpio/blob/2dc9e12814aafcc... 2: https://github.com/torvalds/linux/blob/d358e5254674b70f34c84...

That alignment is only necessary to do the Grand Tour, to visit all four outer planets in one mission. Voyager 1 actually didn't do the Grand Tour, it only visited Jupiter and Saturn, you're thinking of Voyager 2. This alignment is also not even necessary to attain the highest speed, Voyager 1 is even faster than Voyager 2.

A flyby of both Jupiter and Saturn can be done every two decades or so (the synodic period is 19.6 years)

https://en.wikipedia.org/wiki/Grand_Tour_program

There are many more kinds of masters than just owners of slaves. The word "master bedroom" only appeared in 1920, it has absolutely nothing to do with slavery.

Interesting to see you have a different experience. I'm not sure I would call it stellar. On the train route between Den Haag and Amsterdam, one of the busiest routes in the country presumably, reception is constantly dropping out. I'd love to be able to work on the train, but it's completely impossible if you need a network connection for anything.

Perhaps the route being so busy is the cause of the connectivity issues, but it's still baffling to me how bad it is, given that the amount of mobile devices trying to connect must be very predictable.

In Newtonian gravity, the relation between the orbital period T and the semimajor axis a of the orbital ellipse is a^3 / T^2 = GM / 4π^2, where M is the reduced mass of the system (in this case, with 99% of the mass being in one of the two black holes, it's simply the mass of the heavier one).

Plugging 12 years and 18e9 solar masses gives about 2e12 kilometers, or roughly a fifth of a lightyear. This also means the smaller black hole is zipping around the bigger one at around 6% of the speed of light, which is low enough that the Newtonian approximation is probably reasonable accurate (at least to give a rough idea of how large the distances must be).

I sort of understand the reasoning on why Arxiv prefers tex to pdf[1], even though I feel it's a bit much to make it mandatory to submit the original tex file if they detect a submitted pdf was produced from one. But I've never understood what the added value is in hosting the source publicly.

Though I have to admit, when I was still in academia, whenever I saw a beautiful figure or formatting in a preprint, I'd often try to take some inspiration from the source for my own work, occasionally learning a new neat trick or package.

1: https://info.arxiv.org/help/faq/whytex.html

I understand there are API limitations, but isn't 15 minutes a lot for an object that orbits around the entire Earth in 90 minutes? On average you're going to be off by about a twelfth of the circumference of the Earth, or roughly the distance between Lisbon and Istanbul

I don't see how the size of Wikipedia has any bearing on the 50MB figure given for pre-20th century literature by the parent.

Perhaps that's meant to be 50GB (and that still seems like a serious underestimation)? Just the Bible is already 5MB.

Without taking into account dark energy or a cosmological constant (so on scales smaller than a few hundreds of millions of lightyears), in the usual cosmological model you can see the expansion of the universe simply as a remnant of the initial kick all matter got from the Big Bang. There is no active pushing anymore, it's just matter moving apart, constantly slowing down due to the mutual gravitational attraction.

So for our bodies, planets, solar systems, even galaxies and clusters, because these are bound (either electromagnetically or gravitationally), the influence of the expansion of the universe on them is not just negligible, it's non-existent.

It's a little different when wo do include dark energy and other mechanisms more complicated than a simple matter or light content. For your intuition, you can think of this as a constant omnipresent negative pressure. We have no idea how it works on scales smaller than those of the observable universe, but if we imagine it works the same on every scale, then it's an extremely tiny force constantly pulling your body apart.

Is it really that siloed? The condition mentioned in the article (there being a global timelike Killing field) is discussed in all introductory texts on quantum field theory in curved spaces, it's even present in the first few paragraphs of the relevant Wikipedia article[1]. Even if it doesn't apply here, the authors ought to have mentioned why not.

I don't think they were stupid per se, nor malicious, but perhaps cavalier in pushing a result with such unexpected consequences without getting a consult.

1: https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved...

I thought coffee for people who don't like coffee was instant coffee? The linked Clever Dripper seems like it's comparatively a bit more effort and waste.

Apart from the advantage of instant preparation, to my undiscerning palate instant coffee has got all the qualities and taste of coffee I enjoy, and not being a coffee-connoisseur, I can't be disappointed by its apparent blandness or one-dimensionality.

Out of curiosity, what do the backticks and ellipsis do here?

The body of the question makes it abundantly clear what the OP is asking, which has nothing to do with the plural form of the noun "zero". You could suggest an improvement to the title, but answering "zeroes" and pretending it's the only correct answer is being deliberately obtuse.

"will" used to mean "to want", like its cognates in Dutch or German still do. However, it's not really unusual, it's quite common for desiderative forms of verbs to evolve into expressing a future tense, something similar happened independently in a few Indo-European language families, like Greek, Albanian, Celtic etc...

According to the etymology section on the Palau Wikipedia article, there is no relation. Palauans calling themselves Belau makes the similarity less remarkable as well.

https://en.wikipedia.org/wiki/Palau#Etymology

You cannot decay if you don’t experience time

That's a common misconception, there's no a priori reason a particle without a restframe can't decay. For all known particles with a finite lifetime we give this lifetime as measured in its restframe (i.e. with the particle standing still), but in principle it is an observer-dependent quantity, faster moving particles will take longer to decay. If we, for example, assume the lifetime of a massless particle is proportional to its energy, we retain the same expected Lorentz covariance.

Of course, if you actually go through the math, the known massless particles in our universe, photons and gluons, turn out to be stable.[1]

1: https://arxiv.org/abs/hep-th/9508018

The Hubble constant is not necessarily derived from the cosmological constant. To be clear, it's not even a constant either, it's a proportionality factor between the recessional velocity of distant objects and their distance from us. Though in some usages it refers to the value of this factor at the current time, which would in fact make it a constant. Regardless, even without a cosmological constant, after the Big Bang you'd still have an expanding universe, possibly collapsing or endlessly expanding, and I like to think of the Hubble constant/parameter in this case as representing the "momentum" the matter in the universe has left from the Big Bang.

The cosmological constant does in fact have to be constant within the constraints of general relativity. The mathematical machinery of GR only allows two parameters: Newton's constant G, representing the coupling of matter to gravity, and the cosmological constant. Both have to be true constants, numbers with a unit.

However, this is only true of the most basic theory of dark energy, where you directly add a constant to the general relativistic lagrangian. More complicated theories, like, for example, quintessence, involve adding new dynamical fields to the theory. The "effective cosmological constant" associated to such theories, quantifying the effect these fields are having on the expansion of the universe, can dynamically change over time, and some of these theories are proposed to solve the Hubble tension. To be clear, although none of these theories are fringe or pseudoscience, they haven't been accepted as a final explanation either, resolving these issues is still a work in progress, at this point they're all simply interesting hypotheses.

Being easy to prove doesn't make it unremarkable. Lots of theorems, including this one, have straightforward proofs once you are given the exact formulation. The tricky part is coming up with the idea for the theorem itself. I remember being (mildly) shocked when I was taught this in undergrad, it just seemed too good to be true.

That doesn't sound right. Relativistic mass as a concept is avoided in modern physics because it doesn't yield much insight and is hard to keep consistent. Involving gravity only makes it worse, because it's very hard to consistently include gravity in special relativity. For one, does the relativistic mass gravitate or not?

And if you actually do go through the calculations, you find that you do not get the observed result. This paper[0] sums up a few of them.

0 (PDF): http://kirkmcd.princeton.edu/examples/perihelion.pdf