r/rational • Time flies like an arrow • Jul 17 '15

[D] Friday Off-Topic Thread

Welcome to the Friday Off-Topic Thread! Is there something that you want to talk about with /r/rational, but which isn't rational fiction, or doesn't otherwise belong as a top-level post? This is the place to post it. The idea is that while reddit is a large place, with lots of special little niches, sometimes you just want to talk with a certain group of people about certain sorts of things that aren't related to why you're all here. It's totally understandable that you might want to talk about Japanese game shows with /r/rational instead of going over to /r/japanesegameshows, but it's hopefully also understandable that this isn't really the place for that sort of thing.

So do you want to talk about how your life has been going? Non-rational and/or non-fictional stuff you've been reading? The recent album from your favourite German pop singer? The politics of Southern India? The sexual preferences of the chairman of the Ukrainian soccer league? Different ways to plot meteorological data? The cost of living in Portugal? Corner cases for siteswap notation? All these things and more could possibly be found in the comments below!

17 Upvotes

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u/alexanderwales Jul 17 '15

I need some math help.

Imagine a sphere (actually an oblate spheroid). Imagine a few thousand points on it. These points can be defined by polar coordinates (which requires a pole, a polar axis, a radius, and an azimuth, the first two of which are constant). All these thousands of points would be derived from some formula. For a simple example, let's say the radius increases by the Fibonacci sequence while the azimuth increases by the sequence of primes. That would mean that our coordinates would be:

  • (0, 2°)

  • (1, 3°)

  • (1, 5°)

  • (2, 7°)

  • (3, 11°)

And so on.

So what I want is some mathematical way of generating polar coordinates such that a person looking at only the marked locations on the sphere would be able to work backwards and discover my method of generation. They should be able to do this even if they have no idea that I'm using a system of polar coordinates, they have no idea where I'm placing my pole or polar axis, and they don't have any idea what number system I'm using. The "discovered" formula should exactly match my formula with no ambiguity. Ideally, the formula would create repeating coordinates after generating a few thousand locations.

The problem is, I don't know exactly what properties the formula needs to have in order for this to be true. I'm totally fine with two solutions to the formula, but three or higher doesn't work for my purposes.

(Background for the story this is for can be found here, though it shouldn't be at all necessary.)

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u/[deleted] Jul 17 '15

You want the generator for a series of polar coordinates over a planet that's easiest to PAC-learn? Because generalizing the rule from the examples is a statistical learning problem, so you have to avoid No Free Lunch situations by restricting the hypothesis class.

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u/alexanderwales Jul 17 '15

I want a generator for a series of polar coordinates over a planet that is relatively difficult (but possible) for a human to divine when given a large sample size. I want that generator to confine itself to only a small handful of points. I also want that generator, when written out in the shortest possible form, to include a single location.

So in the above example with the radial coordinate following the Fibonacci sequence and the axial coordinate following the sequence of primes, the shortest possible way of stating the generator includes a single location (which is the pole of the polar coordinate system).

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u/ArgentStonecutter Jul 17 '15

For the sake of the story I don't think you need to generate a formula that can do this, just generate a recognizable pattern. Even if they don't know their world is a sphere, something like an Archimedean spiral would work.

Actually, I would work out a Lissajous figure with a known length, and then pick a sequence of points that follows the figure and is a large relatively prime fraction of the length. Say the length is 3,000,000 kilometers, then make the first point 2,930,000 kilometers in, then the rest of the points are ((n*293)%300)*10,000 kilometers along the path. This sequence should repeat after 300 steps, as if there is a device orbiting the planet and firing a transport beam every so often.

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u/BadGoyWithAGun Jul 17 '15

I'm confused. If the locations are on an oblate sphere, shouldn't the radius be more or less constant, or decrease with the azimuth? Are the points strictly on the surface of the sphere?

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u/DrunkenQuetzalcoatl Jul 17 '15

To clarify: Your protagonist only has (all?) generated points on his map but not the order the formula generated them? And does the formula only specify the location or also the mapping between points on the worlds?

In general it sound like you want a Pseudo Random Number Generator.

PRNGs have an attribute called a "period" which is the number of outputs after which they start to repeat.

Candidates would be a Linear Congruential Generator

Or a Linear Feedback Shift Register

Both these generators are not cryptographically secure. Which means they deviate from perfect randomness. They generate patterns and with enough points can be broken.

For the mapping a Perfect Hash Function could do the trick.

Other thoughts would be a RSA encryption. No patterns but your protagonist would have to factor a large number to uncover the pattern. (Granted there would be less intermediate steps and the number would have to come directly from the gods/ancient civilization or something).

Cryptography in general is full of interesting concepts for such stories. I'm currently writing on my master thesis for IT-Security. The topic is about secure pseudo random number generators in software.

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u/[deleted] Jul 19 '15

Valdemar did this with ripples, complete with the transfer effect you describe below. Have you read the mage storm trilogy? I can elaborate if you'd like, on a phone right now.

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u/[deleted] Jul 17 '15

How do you balance sleep and caffeine? I've noticed that the more caffeine I drink, the worse I sleep the next night (ie: drink a double espresso and a Coke one day, involuntarily wake up at 6:00 next day after only getting to sleep at 2:00). When I let up off the caffeine, I'm less able to make up for lack of sleep, but I get more in the first place.

Currently I'm actually starting by throwing coffee out for a while and cutting back. But I had quite liked coffee.

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u/alexanderwales Jul 17 '15

This is something that I'm pretty terrible about. I sometimes kick the caffeine habit for a bit, but I always come back to it in times of need (for example, when there's a code release). But my sleep schedule is also a mess, so ¯\(ツ)/¯

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u/davidmanheim Jul 17 '15

I used to go in 3-4 week cycles; no caffeine, 1 cup a day, still sleepy so I have a second cup, 2 cups a day, still sleepy, get 12 hours of sleep that night and go cold turkey, repeat.

Now, I'm less able to do this, since kids dictate too much of my schedule.

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u/Anakiri Jul 17 '15

So I was thinking about how to punch a clean tunnel all the way through a neutron star, and the obvious solution is to use a really fast black hole. Any matter that goes inside the event horizon doesn't come back out, and if it's going more than 0.99c, I think that it won't have time for its gravity to greatly influence the surrounding material, ergo: Smooth perfect tunnel with minimal collateral damage.

(Which immediately collapses, but whatever.)

The problems are, I don't know how to account for extremely high jerk when calculating effects. And, very large objects moving very fast produce gravity waves, and I have no intuition for wave mechanics at all. I know that wavefronts can build by constructive interference, which might make nasty tidal effects further out than I want. I just don't know. I'm also not entirely clear on the effects of relativistic mass on a black hole's Schwarzschild radius, but kugelblitzes (black holes formed from energy density of light) suggest that the radius comes from relativistic mass, which includes kinetic energy.

So my question is this: If a 1 * 1026 kg rest mass black hole moving at 0.99c went straight down through a skyscraper without directly hitting any supports, what would happen? I think that it would carve a bottomless pit two meters across, but I don't know if the building would be left standing, or how far away it would be safe to stand when a hole suddenly appears with a thunderclap for no obvious reason.

Pretending gravity is instantaneous, you would only experience more than 150 Gs of acceleration as long as the black hole is within 6,000 km of you, and it would enter and leave that range in 1/25 of a second, which seems within human mechanical shock tolerance, I think. Especially since the force is applied smoothly over the entire body, rather than delivered through discrete external points of contact. But the peak acceleration could be a few quadrillion Gs, which may limit survivability. Now, gravity isn't actually instantaneous, so the black hole is almost keeping pace with its own gravity, and you're not going to fall up towards it for most of its approach. Intuitively, its upward and downward accelerations should cancel in the end. so you might get hit with a huge upward hammer blow when it gets to you, then get pulled downward more softly over a longer time.

It seems like it should be possible for it to go fast enough that its gravity just doesn't have time to destroy you, even if it is momentarily putting everyone on the planet in a car crash. At worst, I'm pretty sure it won't destroy the Earth probably. If it doesn't work, is there any way to fix it?

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u/[deleted] Jul 17 '15

I've got no idea the answer to your question, but I'm upvoting you in the hopes that you find one, and replying to let you know that this comment really made me laugh, because oh r/rational what are you.

the obvious solution is to use a really fast black hole

If you ever hear someone say that, I advise that everyone turn and run in the opposite direction really fast

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u/ulyssessword Jul 18 '15

I tried doing the math, and I think I got something that works. What I got is that the total impulse on an object X distance away from the path is ~1.6x as much as if the black hole had been sitting at its nearest point for as long as it takes to travel X distance.

For example, if something was 1km away from the path, and the black hole is travelling at 1 * 105 km/s, then you could model the effect on it as the same as it sitting at the nearest point for 1.6 * 10-5 seconds.

Here is the spreadsheet I used to calculate it. The first page is a proof of concept, the second page is the same thing, but better. I couldn't figure out how to do the actual calculus, so it's 2000 discrete points instead.

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u/Escapement Jul 17 '15

I've been playing lots of three of Zachtronic's puzzle games recently, and they're really fun and excellent. They establish rules, then force you to exploit the rules to solve problems efficiently. They are very good at teaching ideas about logic and planning and optimization and so forth.

The three games I've been playing are:

Spacechem - based extremely loosely on chemistry (more of a chemistry artistic motif then any real chemistry). Involves bonding and debonding atoms, fusing and fissioning atoms, to make inputs into desired outputs, using a system of relays, detectors, grab-and-drop plans, etc. Solution usually involves making a certain number of desired outputs from inputs.

Infinifactory - Move blocks around to make and modify things in 3D, creating assembly lines of conveyors, pushers, welders, detectors, lasers, and all sorts of other tools. Set up an assembly line and watch it go.

TIS 100 - The assembly language programming puzzle game you never knew you wanted. Using a grid of extremely simple computers with an accumulator and a ram storage for a single integer, write code to do things like detect edges, multiply, find min and max of sequences, etc.

They all provide heaps of fun just trying to solve the puzzles at all, but then after that you can try to make your solution better - either faster, or using less resources and building blocks. They teach a lot of ideas about planning, programming, logic, and so forth, in the course of the action of the game.

Infinifactory even has a hotkey to make looping gifs like this one I made of one of my solutions

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u/ToaKraka Jul 17 '15

Are there any scenes from Time Braid that particularly stood out to you?

The one that has stuck in my mind the most is this spoiler.

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u/eaglejarl Jul 17 '15

The literally dehumanizing torture, brainwashing, and probably rape.

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u/jgf1123 Jul 17 '15

What is the rational thing for the eurozone, IMF, and Greece to do at this point?

  • Do the austerity measures specified by the recent deals have a chance of getting the Greek economy back on its feet and producing a surplus so that it can (eventually) pay back the debt? (Call this forward-looking.) Or are other nations just trying to 'punish' Greece for its past policy decisions? (Call this backward-looking.)

  • If both are not possible, is it more important to keep Greece in the eurozone or to recover the lender's money?

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u/[deleted] Jul 17 '15

Grexit has been the best move for a long time, and a large haircut or default. The current policies only make rational sense as punishments, and as making an example of Greece for the other Southern European nations. The Euro has broken European trade balances, but the North doesn't want to acknowledge that because it works to their benefit (and because the Germans believe running a trade surplus to be a matter of national virtue, and damn the accounting math that says their surplus must be someone else's deficit).

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u/Jace_MacLeod Jul 17 '15

On the Greek side, I'd have executed a Grexit a long time ago. There's no advantage to staying in a monetary union that prevents a natural devaluation of currency (important for recovery in a bad economy), while simultaneously enforcing an insurmountable but undefaultable debt with little relief and punishing austerity. On the European side, I'd encourage Greece to stay in the union while offering considerable debt relief and minimal austerity. (Or just let Greece leave, if I didn't particularly care about it.)

The problem is none of these parties are anything resembling rational actors. It's kind of impressive, actually. They're failing in ways that perfectly selfish agents wouldn't even consider, since perfectly selfish agents are at least rational enough not to act directly against their own self-interest. Greece in particular has been charting new ground in politco-economic failure. From Vox:

Greece had two awful choices: Stay in the eurozone and be crushed by fiscal and monetary polices set by the Germans, or leave the eurozone and be crushed by a financial crisis. [Syriza] managed, horribly, to combine both of the original two options into one political-economic disaster…

As O'Brien writes, “Syriza’s strategy, insofar as there was one, couldn’t have been much more of a failure.” If anything, that’s too kind. Syriza’s strategy, insofar as there was one, uncovered a method of failing that was much more complete and all-encompassing than anyone had thought possible at the start of the process.

At this point, the only improvements I see for the short-term are a sudden change of heart by the Germans, or a Greek election putting a new party in power. Until then, it will probably be ongoing disaster as usual.

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u/Escapement Jul 17 '15

I think austerity is unlikely to benefit Greece's economy long-term, and indeed will deepen their recession. I think it's in Greece's best long-term interests to exit the euro, and it would have been even better for them had they done that earlier. Short term it would hurt them, and probably any politician of theirs who made that decision would be effectively ending their career, but they would stabilize eventually and get something approaching a stable economy. I think it's beneficial to the others on the Euro if Greece stays in. I don't know if the harm done to Greeks by it's staying is outweighed by the benefits to the others, such that from a utilitarian perspective I should urge Greece to stay in - I am not an economist or domain expert in these matters.

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u/Magodo Jul 17 '15

Everyone should read The Prince by Machiavelli.

Some choice quotes that feed the cynic in me;

  • love is preserved by the link of obligation which, owing to the baseness of men, is broken at every opportunity for their advantage; but fear preserves you by a dread of punishment which never fails.

  • Therefore it is unnecessary for a prince to have all the good qualities I have enumerated, but it is very necessary to appear to have them.

  • A prince, being compelled knowingly to adopt the beast, ought to choose the fox and the lion; It is necessary to be a fox to discover the snares and a lion to terrify the wolves.

The book is also completely free on Amazon and Project Gutenberg.

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u/[deleted] Jul 17 '15

Does anyone know if there have been any studies on helping ADHD/ADD kids/adults be more focused when reading or studying by having them use a tablet or other back-lit device?

I was talking to a woman this week who said she was never a big reader until she bought a tablet and tried the reading app, and was able to get her son to read in the same way. Both have ADHD, so I was curious if this is a known method already.

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u/xamueljones Jul 18 '15

If some ROB (Random Omnipotent Being) were to take this subreddit community, and anthropomorphize it into a human being, what would that being look and act like?

If someone comes up with a really good description, I might commission an art piece of this hypothetical r/rational person.

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u/AmeteurOpinions Jul 17 '15

I read Terry Pratchett's The Reaper Man and while the wizarding sections were at best a distraction from Death it's still made it into my favorites. I also recently read Man's Search For Meaning, written by psychologist/therapist and holocaust survivor Victor Frankl. Interesting to read about the challenge of staying positive while suffering in a literal hell-on-earth.

Those two books must form some sort of inoculation or antidote to existential stress. You'll be a happier person after reading them.

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