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.
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.
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 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)
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.
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.