Physicist and dabbler in writing fantasy/science fiction.
Ben
Karma: 2,223
A nice post about the NY flat rental market. I found myself wondering, does the position you are arguing against at the beginning actually exist, or it is set up only as a rhetorical thing to kill? What I mean is this:
everything’s priced perfectly, no deals to sniff out, just grab what’s in front of you and call it a day. The invisible hand’s got it all figured out—right?
Do people actually think this way? The argument seems to reduce to “This looks like a bad deal, but if it actually was a bad deal then no one would buy it. Therefore, it can’t be a bad deal and I should buy it.” If there are a population of people out there who think this way then their very existence falsifies the efficient market hypothesis—every business should put some things on the shelf that have no purpose beyond exploiting them. Or, in other words, the market is only going to be as efficient as the customers are discerning. If there are a large number of easy marks in the market then sellers will create new deals and products designed to rip those people off.
Don’t we all know that sinking feeling when we find ourselves trying to buy something (normally in a foreign country) and we realise we are in a market designed to rip us off? First we curse all the fools who came before us and created a rip-off machine. Then, we reluctantly decide just to pay the fee, “get got” and move on with our life because its just too much faff, thereby feeding the very machine we despise (https://www.lesswrong.com/posts/ENBzEkoyvdakz4w5d/out-to-get-you ). Similarly, I at least have felt a feeling of lightness when I go into a situation I expect to look like that, and instead find things that are good.
You have misunderstood me in a couple of places. I think think maybe the diagram is confusing you, or maybe some of the (very weird) simplifying assumptions I made, but I am not sure entirely.
First, when I say “momentum” I mean actual momentum (mass times velocity). I don’t mean kinetic energy.
To highlight the relationship between the two, the total energy of a mass on a spring can be written as: where p is the momentum, m the mass, k the spring strength and x the position (in units where the lowest potential point is at x=0). The first of the two terms in that expression is the kinetic energy (related to the square of the momentum). The second term is the potential energy, related to the square of the position.
I am not treating gravity remotely accurately in my answer, as I am not trying to be exact but illustrative. So, I am pretending that gravity is just a spring. The force on a spring increases with distance, gravity decreases. That is obviously very important for lots of things in real life! But I will continue to ignore it here because it makes the diagrams here simpler, and its best to understand the simple ones first before adding the complexity.
If going to the right increases your potential energy, and the center has 0 potential energy, then being to the left of the origin means you have negative potential energy?
Here, because we are pretending gravity is a spring, potential energy is related to the square of the potion. (). The potential energy is zero when x=0. But it increases in either direction from the middle. Similarly, in the diagram, the kinetic energy is related to the square of the momentum, so we have zero kinetic energy in the vertical middle, but going either upwards or downwards would increase the kinetic energy. As I said, the circles are the energy contours, any two points on the same circle have the same total energy. Over time, our oscillator will just go around and around in its circle, never going up or down in total energy.
If we made gravity more realistic then potential energy would still increase in either direction from the middle (minimum as x=0, increasing in either direction), instead of being x^2 it would be some other equation.
The x-direction is position (x). The y-direction is momentum (p). The energy isn’t shown, but you can implicitly imagine that it is plotted “coming out the page” towards you and that is why their are the circular contour lines.
If you haven’t seen phase space diagrams much before this webpage seems good like a good intro: http://www.acs.psu.edu/drussell/Demos/phase-diagram/phase-nodamp.gif.
I am making a number of simplifying assumptions above, for example I am treating the system as one dimensional (where an orbit actually happens in 2d). Similarly, I am approximating the gravitational field as a spring. Probably much of the confusion comes from me getting a lot of (admittedly important things!) and throwing them out the window to try and focus on other things.
I am not sure that example fully makes sense. If trade is possible then two people with 11 units of resources can get together and do a cost 20 project. That is why companies have shares, they let people chip in so you can make a Suez Canal even if no single person on Earth is rich enough to afford a Suez Canal.
I suppose in extreme cases where everyone is on or near the breadline some of that “Stag Hunt” vs “Rabbit Hunt” stuff could apply.
I agree with you that, if we need to tax something to pay for our government services, then inheritance tax is arguably not a terrible choice.
But a lot of your arguments seem a bit problematic to me. First, as a point of basic practicality, why 100%? Couldn’t most of your aims be achieved with a lesser percentage? That would also smooth out weird edge cases.
There is something fundamentally compelling about the idea that every generation should start fresh, free from the accumulated advantages or disadvantages of their ancestors.
This quote stood out to me as interesting. I know this isn’t what you meant, but as a society it would be really weird to collectively decide “don’t give the next generation fire, they need to start fresh and rediscover that for themselves. We shouldn’t give them the accumulated advantages of their ancestors, send them to the wilderness and let them start fresh!”.
I think I am not understanding the question this equation is supposed to be answer, as it seems wrong to me.
I think you are considering the case were we draw arrowheads on the lines? So each line is either an “input” or an “output”, and we randomly connect inputs only to outputs, never connecting two inputs together or two outputs? With those assumptions I think the probability of only one loop on a shape with N inputs and N outputs (for a total of 2N “puts”) is 1/N.
The equation I had ( (N-2)!! / (N-1)!!) is for N “points”, which are not pre-assigned into inputs and outputs.
These diagrams explain my logic. On the top row is the “N puts” problem. First panel on the left, we pick a unmatched end (doesn’t matter which, by symmetry), the one we picked is the red circle, and we look at the options of what to tie it to, the purple circles. One purple circle is filled with yellow, if we pick that one then we will end up with more than one loop. The probability of picking it randomly is 1⁄7 (as their are 6 other options). In the next panel we assume we didn’t die. By symmetry again it doesn’t matter which of the others we connected to, so I just picked the next clockwise. We will follow the loop around. We are now looking to match the newly-red point to another purple. Now their are 5 purples, the yellow is again a “dead end”, ensuring more than one loop. We have a 1⁄5 chance of picking it at random. Continuing like this, we eventually find that the probability of having only one loop is just the probability of not picking badly at any step, (6/7)x(4/5)x(2/3) = (N-2)!! / (N-1)!!.
In the second row I do the same thing for the case where the lines have arrows, instead of 8 ports we have 4 input ports and 4 output ports, and inputs can only be linked to outputs. This changes things, because now each time we make a connection we only reduce the number of options by one at the next step. (Because our new input was never an option as an output). The one-loop chance here comes out as (3/4)x(2/3)x(1/2) = (N-1)! / N! = 1/N. Neither expression seems to match the equations you shared, so either I have gone wrong with my methods or you are answering a different question.
This is really wonderful, thank you so much for sharing. I have been playing with your code.
The probability that their is only one loop is also very interesting. I worked out something, which feels like it is probably already well known, but not to me until now, for the simplest case.
In the simplest case is one tile. The orange lines are the “edging rule”. Pick one black point and connect it to another at random. This has a 1⁄13 chance of immediately creating a closed loop, meaning more than one loop total. Assuming it doesn’t do that, the next connection we make has 1⁄11 chance of failure. The one after 1⁄9. Etc.
So the total probability of having only one loop is the product: (12/13) (10/11) (8/9) (6/7) (4/5) (2/3), which can be written as 12!! / 13!! (!! double factorial). For a single tile this comes out at 35% ish. (35% chance of only one loop).
If we had a single shape with N sides we would get a probability of (N-2)!! / (N-1)!! .
The probability for a collection of tiles is, as you say, much harder. Each edge point might not uniformly couple to all other edge points because of the multi-stepping in between. Also loops can form that never go to the edge. So the overall probability is most likely less than (N-2)!!/(N-1)!! for N edge dots.
That is a nice idea. The “two sides at 180 degrees” only occurred to me after I had finished. I may look into that one day, but with that many connections is needs to be automated.
In the 6 entries/exits ones above you pick one entry, you have 5 options of where to connect it. Then, you pick the next unused entry clockwise, and have 3 options for where to send it, then you have only one option for how to connect the last two. So its 5x3x1 = 15 different possible tiles.
With 14 entries/exits, its 13x11x9x7x5x3x1 = 135,135 different tiles. (13!!, for !! being double factorial).
You also have (I think) 13+12+11+10+… = 91 different connection pieces.
One day, I may try and write a code to make some of those. I strongly suspect that they won’t look nice, but they might be interesting anyway.
I still find the effect weird, but something that I think makes it more clear is this phase space diagram:
We are treating the situation as 1D, and the circles in the x, p space are energy contours. Total energy is distance from the origin. An object in orbit goes in circles with a fixed distance from the origin. (IE a fixed total energy).
The green and purple points are two points on the same orbit. At purple we have maximum momentum and minimum potential energy. At green its the other way around. The arrows show impulses, if we could suddenly add momentum of a fixed amount by firing the rocket those are the arrows.
Its visually clear that the arrow from the purple point is more efficient. It gets us more than one whole solid-black energy contour higher, in contrast the same length of arrow at the green position only gets us to the dashed orbit, which is lower.
Visually we can see that if we want to get away from the origin of that x, p coordinate system we should shoot when out boost vector aligns with out existing vector.
A weird consequence. Say our spaceship didn’t have a rocket, but instead it had a machine that teleported the ship a fixed distance (say 100m). (A fixed change in position, instead of a fixed change in momentum). In this diagram that is just rotating the arrows 90 degrees. This implies the most efficient time to use the teleporting machine is when you are at the maximum distance from the planet (minimum kinetic energy, maximum potential). Mathematically this is because the potential energy has the same quadratic scaling as the kinetic. Visually, its because its where you are adding the new vector to your existing vector most efficiently.
I am not sure that is right. A very large percentage of people really don’t think the rolls are independent. Have you ever met anyone who believed in fate, Karma, horoscopes , lucky objects or prayer? They don’t think its (fully) random and independent. I think the majority of the human population believe in one or more of those things.
If someone spells a word wrong in a spelling test, then its possible they mistyped, but if its a word most people can’t spell correctly then the hypothesis “they don’t know the spelling’ should dominate. Similarly, I think it is fair to say that a very large fraction of humans (over 50%?) don’t actually think dice rolls or coin tosses are independent and random.
That is a cool idea! I started writing a reply, but it got a bit long so I decided to make it its own post in the end. ( https://www.lesswrong.com/posts/AhmZBCKXAeAitqAYz/celtic-knots-on-einstein-lattice )
Celtic Knots on Einstein Lattice
I stuck to maximal density for two reaosns, (1) to continue the Celtic knot analogy (2) because it means all tiles are always compatible (you can fit two side by side at any orientation without loosing continuity). With tiles that dont use every facet this becomes an issue.
Thinking about it now, and without having checked carefully, I think this compatibilty does something topological and forces odd macrostructure. For example, if we have a line of 4-tiles in a sea of 6-tiles (4 tiles use four facets), then we cant end the line of 4 tiles without breaking continuity. So the wall has to loop, or go off the end. The ‘missing lines’ the 4 tiles lacked (that would have made them 6′s) would have been looped through the 4-wall. So having those tiles available is kind of like being able to delete a few closed loops from a 6s structure.
I might try messing with 4s to see if you are right that they will be asthetically useful.
That’s a very interesting idea. I tried going through the blue one at the end.
Its not possible in that case for each string to strictly alternate between going over and under, by any of the rules I have tried. In some cases two strings pass over/under one another, then those same two strings meet again when one has travelled two tiles and the other three. So they are de-synced. They both think its their turn to go over (or under).
The rules I tried to apply were (all of which I believe don’t work):
Over for one tile, under for the next (along each string)
Over for one collision, under for the next (0, 1 or 2 collisions, are possible in a tile)
Each string follows the sequence ‘highest, middle, lowest, highest, middle lowest...’ for each tile it enters.
My feeling having played with it for about 30-45 mins is that there probably is a rule nearby to those above that makes things nice, but I haven’t yet found it.
I wasn’t aware of that game. Yes it is identical in terms of the tile designs. Thank you for sharing that, it was very interesting and that Tantrix wiki page lead me to this one, https://en.wikipedia.org/wiki/Serpentiles , which goes into some interesting related stuff with two strings per side or differently shaped tiles.
Celtic Knots on a hex lattice
Something related that I find interesting, for people inside a company, the real rival isn’t another company doing the same thing, but people in your own company doing a different thing.
Imagine you work at Microsoft in the AI research team in 2021. Management want to cut R&D spending, so either your lot or the team doing quantum computer research are going to be redundant soon. Then, the timeline splits. In one universe, Open AI release Chat GPT, in the other PsiQuantum do something super impressive with quantum stuff. In which of those universes do the Microsoft AI team do well? In one, promotions and raises, in the other, redundancy.
People recognise this instinctively. Changing companies is much faster and easier than changing specialities. So people care primarily about their speciality doing well, their own specific company is a secondary concern.
A fusion expert can expert at a different fusion company way faster and more easily than they can become an expert in wind turbines. Therefore, to the fusion expert all fusion companies are on the same side against the abominable wind farmers. I suspect this is also true of most people in AI, although maybe when talking to the press they will be honour bound to claim otherwise.
I wonder if any of the perceived difference between fusion and AI might be which information sources are available to you. It sounds like you have met the fusion people, and read their trade magazines, and are comparing that to what mainstream news says about AI companies (which won’t necessarily reflect the opinions of a median AI researcher.).
I think economics should be taught to children, not for the reasons you express, but because it seems perverse that I spent time at school learning about Vikings, Oxbow lakes, volcanoes, Shakespeare and Castles, but not about the economic system of resource distribution that surrounds me for the rest of my life. When I was about 9 I remember asking why ‘they’ didn’t just print more money until everyone had enough. I was fortunate to have parents who could give a good answer, not everyone will be.
Stock buybacks! Thank you. That is definitely going to be a big part f the “I am missing something here” I was expressing above.
I freely admit to not really understanding how shares are priced. To me it seems like the value of a share should be related to the expected dividend pay-out of that share over the remaining lifetime of the company, with a discount rate applied on pay-outs that are expected to happen further in the future (IE dividend yields 100 years from now are valued much less than equivalent payments this year). By this measure, justifying the current price sounds hard.
Google says that the annual dividend on Nvidia shares is 0.032%. (Yes, the leading digits are 0.0). So, right now, you get a much better rate of return just leaving your money in your bank’s current account. So, at least by this measure, Nvidia shares are ludicrously over-priced. You could argue that future Nvidia pay outs might be much larger than the historical ones due to some big AI related profits. But, I don’t find this argument convincing. Are future pay outs going to be 100x bigger? It would require a 100-fold yield increase for it to just be competitive with a savings account. If you time discount a little (say those 100-fold increases don’t materialise for 3 years) then it looks even worse.
Now, clearly the world doesn’t value shares according to the same heuristics that make sense to a non-expert like me. For example, the method “time integrate future expected dividend pay outs with some kind of time discounting” tells us that cryptocurrencies are worthless, because they are like shares with zero dividends. But, people clearly do put a nonzero value on bitcoin—and there is no plausible way that many people are that wrong. So they are grasping something that I am missing, and that same thing is probably what allows company shares to be prices so high relative to the dividends.
In a sense I agree with you, if you are trying to signal something specific, then wearing a suit in an unusual context is probably the wrong way of doing it. But, the social signalling game is exhausting. (I am English, maybe this makes it worse than normal for me). If I am a guest at someone’s house and they offer me food, what am I signalling by saying yes? What if I say no? They didn’t let me buy the next round of drinks, do I try again later or take No for an answer? Are they offering me a lift because they actually don’t mind? How many levels deep do I need to go in trying to work this situation out?
I have known a few people over the years with odd dress preferences (one person really, really liked an Indiana Jones style hat). To me, the hat declared “I know the rules, and I hereby declare no intention of following them. Everyone else here thereby has permission to stop worrying about this tower of imagined formality and relax.” For me that was very nice, creating a more relaxed situation. They tore down the hall of mirrors, and made it easier for me to enjoy myself. I have seen people take other actions with that purpose, clothes are just one way.
Long way of saying, sometimes a good way of asking people to relax is by breaking a few unimportant rules. But, even aside from that, it seems like the OP isn’t trying to do this at all. They have actually just genuinely had enough with the hall of mirrors game and have declared themselves to no longer be playing. Its only socially clueless if you break the rules by mistake. If you know you are breaking them, but just don’t care, it is a different thing. The entire structure of the post makes it clear the OP knows they are breaking the rules.
As a political comparison, Donald Trump didn’t propose putting a “Rivera of the Middle East” in Gaza because he is politically clueless, he did so because he doesn’t care about being politically clued-in and he wants everyone to know it.