Posts

Three more stories about causation 2020-11-03T15:51:58.820Z
cousin_it's Shortform 2019-10-26T17:37:44.390Z
Announcement: AI alignment prize round 4 winners 2019-01-20T14:46:47.912Z
Announcement: AI alignment prize round 3 winners and next round 2018-07-15T07:40:20.507Z
How to formalize predictors 2018-06-28T13:08:11.549Z
UDT can learn anthropic probabilities 2018-06-24T18:04:37.262Z
Using the universal prior for logical uncertainty 2018-06-16T14:11:27.000Z
Understanding is translation 2018-05-28T13:56:11.903Z
Announcement: AI alignment prize round 2 winners and next round 2018-04-16T03:08:20.412Z
Using the universal prior for logical uncertainty (retracted) 2018-02-28T13:07:23.644Z
UDT as a Nash Equilibrium 2018-02-06T14:08:30.211Z
Beware arguments from possibility 2018-02-03T10:21:12.914Z
An experiment 2018-01-31T12:20:25.248Z
Biological humans and the rising tide of AI 2018-01-29T16:04:54.749Z
A simpler way to think about positive test bias 2018-01-22T09:38:03.535Z
How the LW2.0 front page could be better at incentivizing good content 2018-01-21T16:11:17.092Z
Beware of black boxes in AI alignment research 2018-01-18T15:07:08.461Z
Announcement: AI alignment prize winners and next round 2018-01-15T14:33:59.892Z
Announcing the AI Alignment Prize 2017-11-04T11:44:19.000Z
Announcing the AI Alignment Prize 2017-11-03T15:47:00.092Z
Announcing the AI Alignment Prize 2017-11-03T15:45:14.810Z
The Limits of Correctness, by Bryan Cantwell Smith [pdf] 2017-08-25T11:36:38.585Z
Using modal fixed points to formalize logical causality 2017-08-24T14:33:09.000Z
Against lone wolf self-improvement 2017-07-07T15:31:46.908Z
Steelmanning the Chinese Room Argument 2017-07-06T09:37:06.760Z
A cheating approach to the tiling agents problem 2017-06-30T13:56:46.000Z
What useless things did you understand recently? 2017-06-28T19:32:20.513Z
Self-modification as a game theory problem 2017-06-26T20:47:54.080Z
Loebian cooperation in the tiling agents problem 2017-06-26T14:52:54.000Z
Thought experiment: coarse-grained VR utopia 2017-06-14T08:03:20.276Z
Bet or update: fixing the will-to-wager assumption 2017-06-07T15:03:23.923Z
Overpaying for happiness? 2015-01-01T12:22:31.833Z
A proof of Löb's theorem in Haskell 2014-09-19T13:01:41.032Z
Consistent extrapolated beliefs about math? 2014-09-04T11:32:06.282Z
Hal Finney has just died. 2014-08-28T19:39:51.866Z
"Follow your dreams" as a case study in incorrect thinking 2014-08-20T13:18:02.863Z
Three questions about source code uncertainty 2014-07-24T13:18:01.363Z
Single player extensive-form games as a model of UDT 2014-02-25T10:43:12.746Z
True numbers and fake numbers 2014-02-06T12:29:08.136Z
Rationality, competitiveness and akrasia 2013-10-02T13:45:31.589Z
Bayesian probability as an approximate theory of uncertainty? 2013-09-26T09:16:04.448Z
Notes on logical priors from the MIRI workshop 2013-09-15T22:43:35.864Z
An argument against indirect normativity 2013-07-24T18:35:04.130Z
"Epiphany addiction" 2012-08-03T17:52:47.311Z
AI cooperation is already studied in academia as "program equilibrium" 2012-07-30T15:22:32.031Z
Should you try to do good work on LW? 2012-07-05T12:36:41.277Z
Bounded versions of Gödel's and Löb's theorems 2012-06-27T18:28:04.744Z
Loebian cooperation, version 2 2012-05-31T18:41:52.131Z
Should logical probabilities be updateless too? 2012-03-28T10:02:09.575Z
Common mistakes people make when thinking about decision theory 2012-03-27T20:03:08.340Z

Comments

Comment by cousin_it on Yoav Ravid's Shortform · 2021-02-25T10:44:10.934Z · LW · GW

This is a breathless article about something that's obvious to people who know the state of the art. (I've worked in geoinformational systems.) If you want a map that shows the shapes and sizes of continents without too much distortion, and don't mind having two circles, the Nicolosi globular projection is a thousand years old.

Comment by cousin_it on Above the Narrative · 2021-02-25T09:46:36.724Z · LW · GW

I like Scott as much as anyone, but I think your post points people in a subtly wrong direction.

This mindset is nigh-incomprehensible to people of The Narrative who are used to being guided by a single source of truth enforced by social consensus.

Actually the left argue among each other bitterly and non-stop.

Its main proponent is Balaji Srinivasan, who wants Silicon Valley to tell its own narrative of “technological progressivism”. It is a story of humanity’s biggest challenges, from education to climate change to death itself, being solved by decentralized technological innovation as opposed to centralized institutional regulation.

That story is a myth. The internet came from ARPA, hypertext was invented by the director of OSRD, public key cryptography was invented at GCHQ, pagerank and blockchain come from academia. And if you look for big ideas in computing that didn't come from government/military/academia, your next stop will be AT&T Bell Labs and IBM, megacorps that are bigger than many governments.

That’s just handing your soul to the devil — the same devil that employs Metz.

Metz's side is just proselytizing faith. (I think what we're seeing today is the age-old conflict between proselytizing faith and everything else, which started with Christianity but isn't unique to it.) You can say many bad things about it, but it doesn't have a monopoly on doxing, narrative building, censorship and so on. The only thing it has a monopoly on is proselytizing, and sadly I hear echoes of that in Eliezer and Scott's writings as well. It's a hard habit to break.

Comment by cousin_it on Media Bias · 2021-02-22T22:06:41.813Z · LW · GW

Yeah, the last paragraph is very close to how I've been thinking about these things. Maybe instead of "attention" I'd focus on "importance". People propagate information based on what they consider important, but their importance judgments are themselves based on information received from other people. So the public conversation becomes a huge game of "importance telephone", leading to factions that hate each other for having "wrong" importance judgments.

Maybe effective altruism could be a way out of this mess? Agree on the QALY as a common yardstick of importance, and create QALY-centric news media. Has anyone tried that?

Comment by cousin_it on Google’s Ethical AI team and AI Safety · 2021-02-21T09:11:50.932Z · LW · GW

I can’t figure out why this is being downvoted.

Because the events are not related to AI alignment, but are the focus of a current battle in the culture war.

Comment by cousin_it on Using Betting Markets to Make Decisions · 2021-02-21T00:25:16.445Z · LW · GW

Decision markets seem to have tricky problems with manipulation, see this paper for example. And even prediction markets, which are simpler, might have problems as well. I'd like to understand this better, is there a simple scheme that avoids the problems?

Comment by cousin_it on The Glory System: A Model For Moral Currency And Distributed Self-Moderation · 2021-02-19T17:16:31.574Z · LW · GW

One aspect of laws and rights is a kind of agreement between people to not punish each other for wrongthink. Without such an agreement, people will jump on the opportunity to punish wrongthink.

Comment by cousin_it on The Glory System: A Model For Moral Currency And Distributed Self-Moderation · 2021-02-19T16:55:36.018Z · LW · GW

I think punishment should be based on codified rules. If you leave it up to individual discretion, that will lead to a lot of witch hunts and conformity.

Comment by cousin_it on The Median is Less than the Average · 2021-02-16T12:11:20.529Z · LW · GW

Increased information makes smart people smarter and stupid people stupider.

I can't think of any kind of information that has this effect. Technical information makes people smarter, all people. Entertainment, politics, and politics-entertainment (which together comprise most of the internet) make people stupider. The harm of entertainment is that you spend lots of time receiving stimuli without putting in any action or thought, and the harm of politics-entertainment is that you also end up resenting other people. And behind it all is the harm of advertising, which makes you want stuff you don't need and envy other people for having it. That's a lot of harm.

Comment by cousin_it on The Problem of the Criterion · 2021-02-11T10:40:13.250Z · LW · GW

I like particularism more than pragmatism, because all reasoning needs some kind of basis, but not all reasoning needs some kind of goal. For example, proving theorems in Peano arithmetic has a basis, but no goal.

More generally, I'd prefer not to ground philosophy in the notion that people follow goals, because so often we don't. Life to me feels more like something spinning outward from its own basis, not toward something specific.

Comment by cousin_it on Promoting Prediction Markets With Meaningless Internet-Point Badges · 2021-02-09T19:25:43.010Z · LW · GW

I think the first attack still kinda works. Create 1024 accounts, half of them bet on some hard-to-guess event, half against. Eventually you'll have an account that predicted 10 hard-to-guess events correctly.

Comment by cousin_it on Making Vaccine · 2021-02-09T09:47:55.750Z · LW · GW

Are you sure it will stop transmission?

Comment by cousin_it on The Fear Experiments · 2021-02-06T01:34:58.912Z · LW · GW

One evening last autumn I was traveling to our vacation place, got mixed up in trains, and ended up walking from the next town over at night. On open ground I could easily see everything by starlight, but when going through patches of wood, the darkness was so complete that I had to feel out the path with my feet. There were some bird and animal noises, but nothing especially large or scary, so it was a nice walk. Also I saw a meteor streak across the sky! You don't get that in inhabited areas.

Comment by cousin_it on Making Vaccine · 2021-02-06T00:43:12.440Z · LW · GW

By now, about 17 out of every 100k people aged 35-44 in the US have died from corona (source). Assuming this number doesn't grow a lot, "let's try an amateur medical thing" seems more risky, if only due to unknown unknowns. Am I missing something?

Comment by cousin_it on The Story of the Reichstag · 2021-02-05T16:08:02.036Z · LW · GW

It feels special to be in a place where layers of history just sit there, unerased.

One of our friends back in Moscow was a good tour guide, and I mean good tour guide. A typical yarn from him, just walking along a random street: "That side there used to be a graveyard, as the area was being rebuilt they cut up the headstones and used them for curbs. One time me and a friend flipped one over - " and he stops and points to a random curbstone with some old, old letters cut into it.

Comment by cousin_it on How to formalize predictors · 2021-02-03T11:36:15.259Z · LW · GW

I guess I just like game theory. "Alice chooses a box and Bob predicts her action" can be viewed as a game with Alice and Bob as players, or with only Alice as player and Bob as the shape of the game tree, but in any case it seems that option (2) from the post leads to games where solutions/equilibria always exist, while (1) doesn't. Also see my other comment about amnesia, it's basically the same argument. It's fine if it's not a strong argument for you.

Comment by cousin_it on Extracting Money from Causal Decision Theorists · 2021-02-03T10:38:09.472Z · LW · GW

Thanks! That's what I wanted to know. Will reply to the philosophical stuff in the comments to the other post.

Comment by cousin_it on The Lottery Paradox · 2021-02-01T11:45:27.796Z · LW · GW

it’s still more likely that you would lie to me than that this one random person would happen to win

What? If I generate a random number from 1 to n, then send it to you over a noisy channel that scrambles the number with probability p, you should be 1-p confident that you got the correct number. It doesn't depend on n at all.

Basically the sentence is trying to pull a fast one, comparing apples and oranges. Reminds me of how our physics teacher once asked us: "if the horse pulls the cart with force F, by Newton's third law the cart also pulls the horse with force F, so why don't they cancel out?" A friend of mine immediately replied: "the forces don't cancel out because they are applied to different bodies", and that was that.

Comment by cousin_it on The 10,000-Hour Rule is a myth · 2021-02-01T11:23:55.169Z · LW · GW

Classical piano is an extreme case that illustrates the problem. Almost no one makes a living as a classical pianist, because listening to a non-famous classical pianist just isn't the kind of entertainment that people will pay for. So in today's world, I think spending 10k hours on classical piano is a waste of time even if you have great musical talent, because other areas of music will give you better return on the same talent.

More generally in creative areas, even though they are competitive, you can somewhat control on what axis the competition happens. For example, many popular singers often miss notes, and many artists make a living without being able to draw a realistic human from imagination. Even though it only takes a few hundred hours for almost anyone to sing precisely or draw anatomy well. The reason people don't do it is because they can capture the audience by other means. So while you're spending your 10k hours on some creative pursuit, maybe it's worth spending one hour brainstorming these "other means".

Comment by cousin_it on Extracting Money from Causal Decision Theorists · 2021-01-30T13:19:22.254Z · LW · GW

Sure, and sometimes people can predict things like "the agent will use UDT" and use that to punish the agent. But this kind of prediction is "unfair" because it doesn't lead to an interesting decision theory - you can punish any decision theory that way. So to me the boundaries of "fair" and "unfair" are also partly about mathematical taste and promising-ness, not just what will lead to a better tank and such.

Comment by cousin_it on Extracting Money from Causal Decision Theorists · 2021-01-30T11:44:52.699Z · LW · GW

For example, the seller could put no money in any box if she predicts that the buyer will randomize.

This is a bit unsatisfying, because in my view of decision theory you don't get to predict things like "the agent will randomize" or "the agent will take one box but feel a little wistful about it" and so on. This is unfair, in the same way as predicting that "the agent will use UDT" and punishing for it is unfair. No, you just predict the agent's output. Or if the agent can randomize, you can sample (as many times as you like, but finitely many) from the distribution of the agent's output. A bit more on this here, though the post got little attention.

Can your argument be extended to this case?

Comment by cousin_it on A few thought on the inner ring · 2021-01-22T09:24:09.747Z · LW · GW

I think there are some desires that kinda make your soul smaller. Desire for money, certainly. Desire to be important, as you describe in the post. Desire for success: I remember when one of my favorite livejournal users, writing about her life woes in an amazingly personal way, suddenly wrote a post saying "I'm not getting any younger and gotta start thinking how to start publishing and become a recognized writer".

Maybe the common pattern is searching for fulfillment outside of yourself. Doing science to Be A Big Scientist, vs. doing science because some question just bugs you. Doing art to Be A Big Artist, vs. doing art to tease out some fleeting glimpse of beauty that you got.

The trouble then is that this is a very foundational assumption in the West, the dream of success and achievement and "you could be so much more" is seen as almost a synonym for happiness, even though most people who adopt it don't seem all that happy. So, like Lewis, I'd advise not tying your idea of happiness to that.

Comment by cousin_it on The True Face of the Enemy · 2021-01-21T14:55:58.943Z · LW · GW

I think culture, which includes teaching of kids by adults, is also a pretty fantastic computing device, and works better than letting every generation relearn everything in the school of hard knocks.

Comment by cousin_it on The True Face of the Enemy · 2021-01-19T14:23:44.022Z · LW · GW

I don't think freedom is the main factor here, because kids aren't fully developed. They start out with many desires that are bad for themselves and others: to eat lots of sweets, to watch lots of youtube, to torment each other. At some point growing up, kids learn self-control and start making decisions that actually make them better off. But until that point, parents are responsible for what's good for the kid, and giving kids freedom to make themselves worse off is a bad idea.

Comment by cousin_it on A Democratic Currency · 2021-01-19T12:28:27.586Z · LW · GW

As it happens, money does not measure value uniformly over all people; it measures what is valuable to those who already have a large supply of money

In what direction is it skewed? Do you think yachts cost too much when measured in bread, or too little?

Comment by cousin_it on The True Face of the Enemy · 2021-01-18T15:02:05.409Z · LW · GW

Going to school is a recent invention

Schools have existed for millennia, at first for children of rich parents, then expanded to everyone in the last few centuries.

Analogy between school and prison is excellent for this is exactly how many if not most children feel.

Children also feel that having to do chores is totalitarian, and getting only 1 hour of xbox per day is super totalitarian.

Comment by cousin_it on The True Face of the Enemy · 2021-01-16T22:32:02.378Z · LW · GW

Well, school isn't prison, anymore than time is money or property is theft etc.

If the complaint is that kids have to go to school, hey, kids live pretty controlled lives. For example, did I have the power to move to a different apartment? No, it was up to my parents. Does that mean my parents' apartment was a prison for me? Uhhh...

It's better to focus on real problems, like the fact that school often feels boring and pointless. That's what specialized schools try to solve, and often succeed.

Comment by cousin_it on The True Face of the Enemy · 2021-01-13T23:10:04.417Z · LW · GW

Maybe part of the solution is having more specialized schools. In Russia we have math schools, biology schools, sport schools and so on. Basically some subjects would get strong focus and the rest would be quietly neglected. The kids love it, I've heard from many friends how they felt disengaged in regular school, then moved to a specialized one and everything clicked. Maybe the system could be pushed further, by having schools focused on manual trades, commerce, etc.

Comment by cousin_it on Change My View: Incumbent religions still get too much leeway · 2021-01-09T07:57:30.447Z · LW · GW

Yeah. Hunter-gatherer beliefs maybe not so much, but I do have more respect for Greek and Roman polytheism (which led to achievements like a 50km long aqueduct, going under hills and over valleys, that descends at exactly 25cm per km) than for the successor religion that destroyed the aqueducts, burned the libraries, and introduced religious wars to the world. Then it took over a thousand years to mold Christianity into something compatible with human achievement, and just as it became more or less ok, the kids are replacing it with something worse again. This narrative is exaggerated, but I do tentatively believe something like it, and would be interested to hear arguments against.

Comment by cousin_it on Epistemic Warfare · 2020-12-11T09:04:53.038Z · LW · GW

Censorship can only be done by the powerful, who often lie at the same time. So I don't think it's wise to think of it as an antidote to lying.

Comment by cousin_it on Heel-and-toe drumming · 2020-12-11T08:23:19.837Z · LW · GW

To me, slightly raising or lowering the hi-hat is an essential dimension of playing, and double strokes / buzz strokes / rolls are important too, so drumming with only feet seems very limited. And why anyway? It's not so hard to find other people to play with. What I really want is for someone to figure out a hi-hat you can play standing up.

Comment by cousin_it on Notes on Endurance · 2020-11-27T15:58:53.013Z · LW · GW

I think endurance can sometimes be to your detriment, if people with power and authority try to manipulate you into enduring something that benefits them, when they don't have to endure much at all. I've often wished to have a little less endurance, more anger, and a stronger sense of self.

Comment by cousin_it on Writing to think · 2020-11-18T14:26:37.870Z · LW · GW

For some reason "writing to think" never worked well for me. I can only figure out stuff with nonverbal thinking and imagination, then try to put it in words.

Comment by cousin_it on Notes on Loyalty · 2020-11-16T16:24:07.896Z · LW · GW

A nice short story about loyalty is Friends in San Rosario by O. Henry.

Comment by cousin_it on When Hindsight Isn't 20/20: Incentive Design With Imperfect Credit Allocation · 2020-11-09T17:12:58.550Z · LW · GW

You could go further and say that when firms are too small, the level of trust is inefficiently low ("fly-by-night"), and when firms are too big, the level of trust is inefficiently high ("managerial feudalism").

Comment by cousin_it on Competitive Universal Basic Services? · 2020-11-09T14:32:53.080Z · LW · GW

The binary is true though: either you bid up the price of a good by subsidizing purchases, or you bid it down by collective bargaining (or you do both and they cancel each other out to some extent). Vouchers, along with measures like college loans, seem to be on the first horn of the dilemma; OP is more interested in the other horn.

Comment by cousin_it on When Hindsight Isn't 20/20: Incentive Design With Imperfect Credit Allocation · 2020-11-09T12:13:45.475Z · LW · GW

Yeah, markets aren't very nice when they have mostly one-shot, fly-by-night interactions. You could fix that with punishments, but a less wasteful alternative is reputation. Sellers of used cars can join into bigger companies that are incentivized to uphold their reputation and provide warranties; workers in critical jobs can bring references from previous jobs where they proved their quality; owners of vacation homes can benefit when Airbnb lets future renters see the reviews written by past renters.

Comment by cousin_it on Where do (did?) stable, cooperative institutions come from? · 2020-11-04T16:38:13.322Z · LW · GW

Is there some number that reflects the decline in cooperation you're seeing?

Comment by cousin_it on Notes on Piety · 2020-11-04T11:22:33.716Z · LW · GW

I think the focus on ultimate values comes from the Christian mindset. It's worth contrasting with the Greek mindset, where piety is more about actions that show respect to your gods, rulers, or parents, with an expectation of good treatment in return.

Comment by cousin_it on Three more stories about causation · 2020-11-03T23:13:31.621Z · LW · GW

The thermostat pattern is everywhere, from biology to econ to climate etc. I learned about it years ago from this article and it affected me a lot.

Comment by cousin_it on Bucket Brigade Singing · 2020-11-03T23:04:27.130Z · LW · GW

True. I've been doing this with the 4XCamera app on iPad, it's clunky and doesn't have live collaboration, but for take by take recording it's ok. I heard Acapella was better, but the subscription model turned me off.

Comment by cousin_it on Three more stories about causation · 2020-11-03T21:15:36.249Z · LW · GW

For most real-world phenomena, the graphs aren’t that regular nor repeating, so there are more hints about direction and lag.

Yeah, though I think "at fourth glance" stands as it is: in the long run any bounded function will have zero correlation with its derivative.

#3 is a communication failure—we forgot to say “compared to what” when we say “increases” risk of death.

Compared to the control group. People often measure the effect of variable X on variable Y by randomly dividing a population into experiment and control groups, intervening on X in the experiment group, and measuring the difference in Y between groups. Well, I tried to show an example where intervening on X in either direction will increase Y.

Comment by cousin_it on Three more stories about causation · 2020-11-03T20:57:05.141Z · LW · GW

Yeah. Thanks for the front door link, I'll take some time learning this!

Maybe to reformulate a bit, in the second sub-scenario my idea was that each person has a kind of "tar thermostat", which sets the desired level of tar and continually adjusts your desire to smoke. If some other factor makes you smoke more or less, it will compensate until your level of tar again matches the "thermostat setting". And the trait that determines someone's "thermostat setting" would also determine their cancer risk. Basically the system would counteract any external noise, making the statistician's job harder (though not impossible, you're right).

The third scenario, about skydiving, hints at a similar idea. The "thermostat" there is the person's desire for thrill, so if you take away skydiving, it will try to find something else.

Comment by cousin_it on Bucket Brigade Singing · 2020-11-03T16:43:30.698Z · LW · GW

Nice! My friend group was looking for just this kind of thing a few weeks ago, ideally with video as well, and saving a multiscreen recording at the end.

Comment by cousin_it on Non Polemic: How do you personally deal with "irrational" people? · 2020-11-03T16:33:24.212Z · LW · GW

One aspect of intelligence/rationality is estimating the productiveness of a conversation before it happens. Another is expressing your views in a way that sounds palatable even to those who disagree. Another is recognizing that on any given topic there are more knowledgeable people than you, and seeking them out. Another is directing most of your effort and emotion toward things you can influence. You can't learn these things from a book though, you have to practice them.

Comment by cousin_it on Notes on Honesty · 2020-11-03T09:40:52.986Z · LW · GW

Recall how he tricked Achilles into dropping his woman disguise (by sounding a war trumpet outside). That's a lie, but I can't seem to find anything wrong with it. It's not an edge case and doesn't need authorial fiat - many people have done similar tricks in reality, like the Sokal hoax.

Comment by cousin_it on Kelly Bet or Update? · 2020-11-03T09:34:41.787Z · LW · GW

“Bet or update” assumes the possibility of taking either side of the bet.

It doesn't. I wrote the "bet or update" post, so I'd know =)

Comment by cousin_it on Kelly Bet or Update? · 2020-11-03T07:59:19.645Z · LW · GW

A fun subtlety about "bet or update" that just came to my mind. If you refuse to bet that X is true, you're supposed to update enough that the bet becomes unprofitable. But that doesn't always mean updating away from X - sometimes you update toward X.

Imagine there's a million doors, with a pot of gold behind one of them. The host indicates one door and asks "would you like to bet a dollar at even odds that the gold is behind this door?" You know the host's algorithm was as follows: he selected the true door with the gold and two other random doors, then selected randomly between the three. Then you would refuse to bet (because you lose a dollar with probability 2/3) and also refuse to update away (in fact you'd update strongly toward the door being the one with the gold, as now it has probability 1/3 instead of 1/million).

Comment by cousin_it on Notes on Honesty · 2020-10-28T08:36:06.976Z · LW · GW

There seem to be two meanings of honesty: the kind that's designed to help you (avoiding boastfulness and such), which was valued by the Greeks, vs. the kind that's designed to help other people at your expense, which comes more from Christian morality. Modern defenses of honesty usually equivocate between the two. Personally I think Odysseus was pretty cool, even though he lied a lot, so a list of virtues that says "you can't be Odysseus" is a no go for me.

Comment by cousin_it on Stupid Questions October 2020 · 2020-10-28T08:08:57.808Z · LW · GW

Imagine a 2D plane where x is space and y is time. Let's say the Earth is stationary at x=0, so its trajectory is the y axis, and the metric of spacetime is "curved" near it.

We can represent the metric visually by sprinkling a bunch of sand near the y axis. Then lines of inertial movement ("geodesics") can be understood in two ways:

  1. Given a pair of points, a geodesic is the line between them with the least sand (this represents the line being shortest according to the metric).

  2. Given a starting point and velocity vector, keep moving so as to keep equal amounts of sand on your nearby left vs. nearby right - in other words, curve toward more sand.

Surprisingly, these two views are equivalent! For example, consider the geodesic from (1,0) to (1,1). It will bulge slightly away from the y axis, to avoid sand, and so at each point it will be curving toward more sand.

Now we can answer your original question. Place an object at (1,0) with velocity vector (0,1) (zero spatial velocity) and let it go. It will keep moving in the positive y direction, but curve toward the y axis where there's more sand, and eventually cross it at an angle. Then it will curve back by symmetry, and so on, oscillating back and forth in the x coordinate while moving forward in time.

Can that really be a shortest line between two points? Why not. Say the object makes one full oscillation, traveling from (1,0) to (-1,1) to (1,2). If you try to "straighten" the line by pulling on the endpoints, the midpoint will be pulled toward the y axis and catch more sand. So it might well be a local minimum.

Comment by cousin_it on Notes on Courage · 2020-10-25T18:27:17.946Z · LW · GW

I think the archetypal form of courage is courage before physical enemies. Can't say I have it permanently, but a few times in my life I managed to muster it and it feels amazing. But I have no idea how you can deliberately develop it in a safe Western country. The boxing ring gives a diluted experience, because you know there are limits and no real enmity. Things like climbing or public speaking are even more diluted, you can be good at them but turn to jelly when a street situation comes up.