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.
Thanks. I came up with this Python simulation that matches your 68%:
import random
def lying_flippers(num_flips=1_000_000):
"""
- Bob flips a coin and tells Alice the result but lies 20% of the
time.
- Alice tells me Bob's result but also lies 20% of the time.
- If I trust Bob, I know I'll be correct 80% of the time.
- If I trust Alice, how often will I be correct (assuming I don't
know Bob's result)?
"""
# Invert flip 20% of the time.
def maybe_flip_flip(flip: bool):
if random.random() < 0.2:
return not flip
return flip
def sum_correct(actual, altered):
return sum(1 if a == b else 0 for (b, a) in zip(actual, altered))
half_num_flips = num_flips // 2
twenty_percent = int(num_flips * 0.2)
actual_flips = [random.choice((True, False)) for _ in range(num_flips)]
num_heads = sum(actual_flips)
num_tails = num_flips - num_heads
print(f"Heads = {num_heads} Tails = {num_tails}")
bob_flips = [maybe_flip_flip(flip) for flip in actual_flips]
alice_flips = [maybe_flip_flip(flip) for flip in bob_flips]
bob_num_correct = sum_correct(actual_flips, bob_flips)
bob_percent_correct = bob_num_correct / num_flips
alice_num_correct = sum_correct(actual_flips, alice_flips)
alice_percent_correct = alice_num_correct / num_flips
# Trusting Bob should lead to being correct ~80% of the time.
# This is just a verification of the model since we already know the answer.
print(f"Trust Bob -> {bob_percent_correct:.1%}")
# Trusting Alice should lead to being correct ?% of the time.
# This model produces 68%.
print(f"Trust Alice -> {alice_percent_correct:.1%}")
print()
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.
No, that's just one of those made-up lies people repeat often enough online to become "true" because it's the top search result and because it makes them feel good about continuing to use that term.
> TO LET, Westmoeath Cottage and Garden, situated near to Cook's River, only
three miles from the city. the cottage contains
parlour and drawing room,and four large bed rooms ;
detached kitchen, bakehouse, landry, storeroom,
four stall stable and double coach-house, servants'
rooms neatly fitted up, together with hay-loft and
granary, school house and master's bed-room. A
cottage containing four separate rooms for overseer
and workmen ; two excellent wells of water on the
premises, about six acres of garden neatly laid out
and planted with the best vines and fruit trees,
'This property is fit for a family of the first
respectability.
You couldn't own slaves in London in 1845, and in any case the name derives from the "Master of the household", so if you want to be mad about it, you should call it sexist, not racist. Or you could just be chill, stretch the meaning a bit and say the couple together are the masters of the household.
But, now I'm curious: Where do you draw the line? You don't like git master branches and master bedrooms, but what about other uses?
You can have a master key, master record, master a skill, create a masterwork, be a master to an apprentice, join the toastmasters, be a master of ceremonies at a formal event, you can dress up for comic con as Master Yoda, Master Chief, or Dumbledore (the Headmaster of Hogwarts), you can be a Master Chief in the US Navy, be the dungeon master for a game of D&D, get a Masters' Degree and so on.
Which of these things are in your opinion bad and should be renamed?
This is very much like asking why are you focused on fixing one bug at a time in your software when you can fix every reported bug simultaneously?
I don't know man, maybe it's because fixing this one completely inconsequential bug faces so much backlash for no particular reason other than "change bad"?
And well done with using an example from a book series where the only Asian character is named Cho Chang and where there are elves with long noses in charge of the "central bank". That really works in your favour, you totally owned me [pun intended] with that one!
> A footman in his lordship's service stated he went into his master's bedroom [...]
isn't an example of the phrase "master bedroom".
I am also skeptical of "school house and master's bedroom". The main cottage has "four large bed rooms". Why would the "master bedroom", if it is meant to be read as it is today, be listed after the list of detached outbuildings?
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.
+1 on the train, mobile internet in the train is really bad. I kinda get it because you're in a faraday cage, moving between cells quickly, and frequently far outside of inhabited areas but still.
I'm pretty sure the in-train internet also relies on mobile networks, so that's unreliable too. Plus any bandwidth is taken up by people scrolling through tiktok.
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.
A huge value in having authors upload the original source, is it divorces the content from the presentation (mostly). That the original sources were available was sufficient for a large majority of the corpus to be automatically rendered into HTML for easier reading on many devices: https://info.arxiv.org/about/accessible_HTML.html. I don't think it would have been as simple if they had to convert PDFs.
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
This is the correct way - dynamic DNS servers frequently have very low TTLs set.
Serving DNS yourself is such an incredibly small bandwidth impact - most of the packets are in the 10's to 100's of bytes - and authoritative DNS servers do not do a lot of processing, just send back RR's from zones which are read at boot time, or updated in an in-memory database.
zdw mentioned an "authoritative" server, i.e. a content DNS server. CloudFlare is not talking about content DNS servers there. It cannot decide from paragraph to paragraph what it is calling the DNS servers that it is talking about, but it is talking about proxy DNS servers, that respond with the actual grunt work of query resolution done.
People like me have been recommending not running public proxy DNS servers for the entirety of the 21st century thus far, and the world has taken some notice, although more work is required, world!
In any case, ANY queries do not work nearly as well for amplification attacks as they used to. Many people have read RFC 8482. I, for example, changed all of the DNS servers in djbwares to respond to ANY queries per RFC 8482 back in March 2019.
The task at hand in this discussion only involves running a content DNS server, serving LOC records from some file/database or other.
You totally could use it for docking. A real ISS docking manoeuvre takes several hours. Orbits are very predictable and I'm quite confident that the error you'd get projecting your orbit 15min into the future would be good enough to get within close radar range for the final approach. In fact you probably could do it, even if your spavecraft doesnt have DNS at all, and you have to do the DNS resolve from a ground laptop before you board it. Soyez can dock within 3 hours of lauch. Orbits are very predictable in this timeframe.
If there's no timestamp, all you know is a Lat/Long that was accurate sometime in the last 15 minutes (or more, "best effort basis"). But you don't know when, and you don't know the altitude. That's gonna make using that information for docking...difficult.
I'd say the API can take up to half a minute to propagate, so API updates every minute is running up against their own performance. If you're a free customer, they may block you after a while, but first they'd have to notice you, and I doubt one update per minute would bother them.
At orbital speed of ~7.66 km/s, the ISS travels approximately 6,900 km during a 15-minute interval, which is indeed significant for precise location tracking.
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.
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