vikingerik

Yes, Parker used gravity assists, several passes by Venus.

The cheapest way in terms of delta-v in the real solar system is actually to use Jupiter, launch to there and slingshot against your incoming velocity to cancel it out and drop towards the sun. Parker considered this, but decided not to because it would complicate the spacecraft design to handle operations at Jupiter (cold) and at the sun (hot).

And yes, without assists, it's harder to get from Earth to the sun than to anywhere else. Solar escape velocity is 42 km/s at the altitude of Earth's orbit. Earth's orbital speed is 30 km/s, closer to escape velocity than to the near-0 you would need to drop all the way to the sun.

Bit of a nitpick - Jupiter tends to shield the inner solar system from comets that originate far out, but not necessarily asteroids. For bodies in the asteroid belt, there's some thought that Jupiter perturbs as many to a perihelion near Earth's orbit as it diverts away. And without Jupiter, the asteroid belt itself would have accreted into a terrestrial planet instead of remaining loose. Jupiter's overall effect on shielding Earth is uncertain.

Right. It's not a word game, it's an area-control game with 150,000 rules for legal placement of your resources.

Codenames is a word game. Scrabble is about arbitrary sequences of glyphs.

And on the Atari 2600, the fastest way to write to consecutive video registers is to set the stack pointer to its address and do push instructions. You take advantage of getting the stack pointer decremented for free on each push. The stack pointer can be hijacked for this since the machine has no interrupts.

The 2600 can also run self-modifying code in RAM, which I did: http://www.dos486.com/atari/

And the retro arcades are really bars for their business model. The profit is all in the $9 beers and $16 nachos, not the admission charge or coin drops. The games are just the crowd draw like live music or trivia or whatever.

Redemption games get families loading up $50 per kid at the card machine (and then $50 more after the kids blow it in twenty minutes); retrocades aren't pulling that from anybody.

Yeah. Here's another: Space Invaders is now closer in time to the Gamecube than the Gamecube is to today.

Similarly, Windows 95 is now closer in time to the Intel 4004 microprocessor than to today.

If the relevant part was that you didn't see an ace... fun semantic question: is it counting if the only number you track is 0?

As for why a casino might let a counter stay: many try but not all are good at it so they're still losing money. A counter might not be accurate, or misplay other decisions like splits and doubles, or not bet bigger enough when it's favorable, or tilt after some bad luck and bet bigger when it's not favorable enough.

Counting is always possible, nobody can tell if you're just counting in your head. What's detectable and counterable is the way to get advantage from it: you must make your bet much bigger when the count is favorable. That behavior pattern alone is enough for a casino to choose to toss you - they don't even have to prove that you were counting.

Counting works in general because the player's advantage is concentrated into a small number of possible hands. Almost all of your profit comes from blackjack hands paying 3:2, with a bit more from some particular cases like splitting aces and doubling on 11. For everything else, you lose more hands than you win (the asymmetry is that if player and dealer both bust, dealer still takes your money), and you're just trying to tread water to get to the good stuff. The good stuff all requires aces and tens, and counting is to identify the cases when there are more of those available.

Besides counting, the other way to play blackjack profitably is shuffle tracking. It's possible to watch as aces go into the discard pile and visually track them through the shuffle. When you know an ace is coming up soon (even within a range of the next 20 cards), bet big since even a 5% extra chance of an ace makes the expected value of that hand profitable in your favor. Casinos also know to foil this and will eject you in the same way, for a pattern of suddenly making big bets even if they don't necessarily know or prove you're doing it.

Keyboards are easily replaceable - why not just leave off from the sunk cost here and get one that's more to your liking?

It would take a benefactor who wants to pay for running it for its own sake and not for profit. As soon as there's a profit motive, enshittification sets in since you're serving whoever pays rather than your users.

Seems likely it would change. Here's another way to think about it:

0 rotations is more likely than 1 rotation, since there is a wider range of rotation speeds that lead to exactly 0 rotations than to exactly 1. Similarly, 2 flips is more likely than 3, 4 is more than 5, and so on. So you're always biased towards an even number of flips and the starting side.

Take out the 0 case by your conditional, and you're left with 1 > 2, 3 > 4, 5 > 6, and so on, now biased towards an odd number and the non-starting side.

Yes, I wrote that short for brevity. If you must have the full thing spelled out: New Horizons nearly got enough velocity at Jupiter to eventually overtake Voyager. 4 km/s is "nearly" in astronomical terms. New Horizons wasn't really trying to optimize for speed at Jupiter (its closest approach was over 10m km), and a spacecraft that did could easily overtake Voyager using Jupiter alone and not need an alignment with Saturn or anything else.

Breaking that down: Voyager itself couldn't have reduced velocity, it had nowhere near enough reaction mass to do that. Hypothetically a spacecraft could but you might be talking about orders of magnitude more reaction mass. (Which means multiples more of the fuel to launch and accelerate that mass itself, which could quickly escalate beyond any chemical rocket capabilities.)

It also likely wasn't possible to get to Pluto on some future Pluto orbital pass. The limiting factor is likely that Voyager's incoming trajectory to Neptune was already too far beyond solar escape velocity to get into that narrow elliptical orbit you propose. (You'd have to slingshot so close to Neptune's center that you'd hit the planet instead.)

Designing from the beginning to come in slower to Neptune and adjust to encounter Pluto on some future Pluto orbital pass was probably possible, but yeah you might be talking about time scales of Pluto's entire orbit or even multiples of that. (We do similar things for inner solar system missions, like several encounters with Venus separated by multiple Venus-years, but that's on the order of single-digit years and not hundreds.)

The common answer to a lot of these outlandish slingshot questions is usually, yes it's eventually possible by orbital mechanics, but it gets so complicated and lengthy that you may as well just build another separate spacecraft instead. We talk about Voyager's grand tour alignment because it's captivating, but realistically if that hadn't happened we would have just done separate Jupiter-Uranus and Jupiter-Neptune missions instead.

The sun's motion relative to the galaxy doesn't matter for any of this - nothing else in the galaxy is remotely close enough to affect anything, the nearest star is still over 1000x Voyager's distance.

The alignment isn't what matters for overtaking Voyager. Jupiter alone is enough, and New Horizons nearly did. Jupiter accounts for the vast majority of any gravity-assist plan. Saturn has 30% the mass and 2/3 of the orbital velocity, so it could only add 20% more over what you get from Jupiter alone, and the ice giants are smaller and slower yet.

The scenario where a gravity assist doesn't work is if turning sharply enough would require your minimum planetcentric approach distance to be less than the radius of the planet - you'd crash into it instead.

This is why Voyager 2 couldn't also do Pluto - it would have needed to change course by roughly 90º at Neptune, which would have required going closer to the center of Neptune than Neptune's own radius.

The most unusual gravity-assist alignment that we did was for Pioneer 11 going from Jupiter to Saturn. The encounters were separated by roughly 120º of heliocentric longitude. Pioneer 11 used Jupiter to bend its path "up" out of the ecliptic plane and encountered Saturn on the way back "down". Nowadays we wouldn't bother doing that (we'd wait for a more direct launch window instead), but the purpose of this was to get preliminary Jupiter and Saturn encounters done in time before Voyager's launch window for the grand tour alignment.

I'd also venture that the profile of Tesla drivers is also a factor along with those other two brands. I'd be pretty sure that Tesla owners collectively drive more aggressively than the average car on the road. Teslas aren't being driven by soccer moms and careful grandmas.

It's easy for them to have that intention, but then the realities of operating from bankruptcy court or receivership or being assimilated by Microsoft or Sony could be much different.

I choose to only buy stuff for like $8 and under where I can expect to get my money's worth of gameplay in a short time frame and so not have to worry about any long term sunsetting. That's a reasonable middle ground between fully trusting the platform or fully abhorring it.

Right, this is a bi-elliptic transfer, which is delta-v-cheaper than a Hohmann transfer for widely separated orbits. https://en.wikipedia.org/wiki/Bi-elliptic_transfer

In practice in the real solar system, the cheapest way to get from Earth to the Sun is to use Jupiter. Launch to there and reverse-slingshot to cancel out the orbital velocity and drop directly towards the Sun. The Parker Solar Probe would have done this, although decided not to because of the complications in designing to handle both the cold of Jupiter and the heat of the Sun.

The same thing can happen on some Rubik's cuboids - it seems unsolvable with a parity problem, then the answer is to swap two seemingly identical elements.

I know it happens on the 3x3x4 cuboid - each of the 3x4 faces has two centers that appear identical, but if you have exactly two such unsolved pieces, it's unsolvable because it's impossible to exchange exactly two of them - what you need to do is cycle 3 of them where 2 appear identical. I remember this happening on some other shapes and sizes as well.

(Pic for reference: https://www.grubiks.com/images/puzzles/30/small.png . This puzzle exists as do many other NxMxH cuboids. Rectangular but non-square faces can only make 180º turns.)

If what's fun is the reasoning, then the thing to do is other shapes and styles of puzzles besides the cube.

This is my collection: https://imgur.com/v9OuYNw

Like you, I learned the 3x3x3 in high school via memorized algorithms, and that was only so interesting. Years later my brother got me a Megaminx (the dodecahedron equivalent to the 3x3x3 cube, third one in the top row there) and I was absolutely fascinated by learning to solve that by porting what I knew from the cube. From there I got all those other shapes as well. The most interesting ones to search by name: Dayan Gem 3 (the one that looks like the Star of David), Face-Turning Octahedron (last one in the second row), Helicopter Cube (to the right of the 3x3x4), Rex Cube (right from the Helicopter Cube).

The lineup barely matters for gravity assist. Jupiter is the vast majority of the total you can get. Saturn has 30% of the mass and 2/3 the orbital velocity, so adding Saturn gets you only 20% more above using Jupiter alone (and the Voyagers didn't really try), and the ice giants are smaller and slower yet.

We could easily overtake Voyager via only Jupiter if we wanted to (and New Horizons eventually will), and Jupiter-to-any-target launch windows come at least every 12 years.

Moon-dwelling Muslims would go by the phases of Earth, if they wanted to match Earth timing but not rely on communication with Earth. The Earth as seen from the Moon exhibits the opposite phase as the reverse. Ramadan would begin when the Moon-dweller sees the Earth as being just past full. If you wanted, you could synch it with a particular timezone on Earth, by watching for when that location on Earth (Mecca or whatever) just rotated past the terminator so it experienced sundown. (Of course none of this can be directly observed if you're on the far side.) (And I get your joke about seeing the moon when you're on it; this is the practical alternative.)

Same here. I only use and want a single monitor setup. I can alt-tab between windows faster and more comfortably than turning my head to another screen.

Also a dual/multiple setup bothers me for losing the mouse boundaries when it crosses to another screen - I'd rather have the mouse bounded on one screen for faster access to menu bars at the edges.

One reason I and a number of people do that: to cover the possibility you might be at the wrong door/house or ringing the wrong doorbell.

I had both of those problems at my previous residence. It was an apartment complex with some N½ addresses. Visitors would often miss that bit and be at the wrong door. On top of that, the doorbells were counterintuitive: they were arranged vertically, but the bottom doorbell would ring the top apartment and vice versa, so I forever had visitors and deliveries ringing the wrong bell (and actually mostly for the other units ringing mine.)

I had the same thought and did put a finger on it. It's because we don't trust Amazon or any of the other media companies for "buying" content online - we don't trust that the purchase is really permanent, eventually the company will go away or discontinue that service or lose the rights to that content or whatever. Since we don't trust them for buying, we don't trust them for renting either, even if we'd expect the rental transaction to be over in a day or two.

Where in the world did you get that 30% number? Even on Boeing's worst planes, the chances of any incident are still much more like 0.003% or something like that. "30%" is just fearmongering.

Your second paragraph is correct and may be where the previous poster's intuition was disagreeing, that the method doesn't necessarily hold for repeated iterations in a physical system where one trial starts from where the last one ended.

It's not even really "spooky" - all you need is a flipping apparatus that's biased towards an odd number of rotations, and so then THTH is more common than THHT and you get a bias towards repeating your last result.

It's customary in astronomy because it correlates more directly with observation. An object 10 parsecs away exhibits a parallax shift of 1/10 arcsecond.

You've always got the standard way to get fair random numbers from a fairness-unknown coin. Flip it twice. Restart if you get both heads or both tails. If you get H then T or T then H, those are equally probable, so take the first one of those as the final outcome.

This generalizes to a die of N sides. Roll it N times. If you don't get all N distinct results, restart. If you do, then take the first result as your final outcome.

(That may take a lot of trials for large N. It can be broken down by prime factorization, like roll 2-sided and 3-sided objects separately, and combine them for a d6 result.)

The problem with directing tax heat towards assets is that you chase away the assets to more favorable jurisdictions (ie, overseas.) Real estate / property tax works because land can't be moved. But if you tax capital in the US, the capital holders will simply leave the US.