All of Ben's Comments + Replies

It says "I am socially clueless enough to do random inappropriate things"

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 offe... (read more)

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 dea... (read more)

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: $E=\left(1/2\right)p^2/m+\left(1/2\right)k{x}^2$  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... (read more)

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 t... (read more)

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... (read more)

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 ... (read more)

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 ... (read more)

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 ... (read more)

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 )

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 ... (read more)

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)
• Ove

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.

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 th... (read more)

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). ... (read more)

That is very interesting! That does sound weird.

In some papers people write density operators using an enhanced "double ket" Dirac notation, where eg. density operators are written to look like |x>>, with two ">"'s. They do this exactly because the differential equations look more elegant.

I think in this notation measurements look like  <<m|, but am not sure about that. The QuTiP software (which is very common in quantum modelling) uses something like this under-the-hood, where operators (eg density operators) are stored internally using 1d vectors, and the super-operators (maps from... (read more)

Yes, in your example a recipient who doesn't know the seed models the light as unpolarised, and one who does as say, H-polarised in a given run. But for everyone who doesn't see the random seed its the same density matrix.

Lets replace that first machine with a similar one that produces a polarisation entangled photon pair, |HH> + |VV> (ignoring normalisation). If you have one of those photons it looks unpolarised (essentially your "ignorance of the random seed" can be thought of as your ignorance of the polarisation of the other photon).

If someone el... (read more)

 What is the Bayesian argument, if one exists, for why quantum dynamics breaks the “probability is in the mind” philosophy?

In my world-view the argument is based on Bell inequalities. Other answers mention them, I will try and give more of an introduction.

First, context. We can reason inside a theory, and we can reason about a theory. The two are completely different and give different intuitions. Anyone talking about "but the complex amplitudes exist" or "we are in one Everett branch" is reasoning inside the theory. The theory, as given in the ... (read more)

Just the greentext. Yes, I totally agree that the study probably never happened. I just engaged with the actualy underling hypothesis, and to do so felt like some summary of the study helped. But I phrased it badly and it seems like I am claiming the study actually happened. I will edit.

 I thought they were typically wavefunction to wavefunction maps, and they need some sort of sandwiching to apply to density matrices?

 Yes, this is correct. My mistake, it does indeed need the sandwiching like this  ${\rho }_{new}=a{\rho }_{old}{a}^{†}$.

From your talk on tensors, I am sure it will not surprise you at all to know that the sandwhich thing itself (mapping from operators to operators) is often called a superoperator.

I think the reason it is as it is is their isn't a clear line between operators that modify the state and those that represent measurements... (read more)

The way it works normally is that you have a state $\rho$, and its acted on by some operator, $a$, which you can write as  $a\rho$. But this doesn't give a number, it gives a new state like the old  $\rho$ but different. (For example if a was the anhilation operator the new state is like the old state but with one fewer photons). This is how (for example) an operator acts on the state of the system to change that state. (Its a density matrix to density matrix map).

In dimensions terms this is:  (1,1) = (1, 1) * (1,1)

(Two square matrices of size... (read more)

You are completely correct in the "how does the machine work inside?" question. As you point out that density matrix has the exact form of something that is entangled with something else.

I think its very important to be discussing what is real, although as we always have a nonzero inferential distance between ourselves and the real the discussion has to be a little bit caveated and pragmatic. 

I think the reason is that in quantum physics we also have operators representing processes (like the Hamiltonian operator making the system evolve with time, or the position operator that "measures" position, or the creation operator that adds a photon), and the density matrix has exactly the same mathematical form as these other operators (apart from the fact the density matrix needs to be normalized). 

But that doesn't really solve the mystery fully, because they could all just be called "matrices" or "tensors" instead of "operators". (Maybe it gets... (read more)

There are some non-obvious issues with saying "the wavefunction really exists, but the density matrix is only a representation of our own ignorance". Its a perfectly defensible viewpoint, but I think it is interesting to look at some of its potential problems:

1. A process or machine prepares either |0> or |1> at random, each with 50% probability. Another machine prepares either |+> or |-> based on a coin flick, where |+> = (|0> + |1>)/root2, and  |+> = (|0> - |1>)/root2. In your ontology these are actually different machines

I just looked up the breakfast hypothetical. Its interesting, thanks for sharing it.

So, my understanding is (supposedly) someone asked a lot of prisoners "How would you feel if you hadn't had breakfast this morning?", did IQ tests on the same prisoners and found that the ones who answered "I did have breakfast this morning." or equivalent were on average very low in IQ. (Lets just assume for the purposes of discussion that this did happen as advertised.)

It is interesting. I think in conversation people very often hear the question they were expecting, and ... (read more)

The question of "why should the observed frequencies of events be proportional to the square amplitudes" is actually one of the places where many people perceive something fishy or weird with many worlds. [https://www.sciencedirect.com/science/article/pii/S1355219809000306 ]

To clarify, its not a question of possibly rejecting the square-amplitude Born Rule while keeping many worlds. Its a question of whether the square-amplitude Born Rule makes sense within the many worlds perspective, and it if doesn't what should be modified about the many worlds perspective to make it make sense.

I agree with this. Its something about the guilt that makes this work. Also the sense that you went into it yourself somehow reshapes the perception.

I think the loan shark business model maybe follows the same logic. [If you are going to eventually get into a situation where the victim pays or else suffers violence, then why doesn't the perpetrator just skip the costly loan step at the beginning and go in threat first? I assume that the existence of loan sharks (rather than just blackmailers) proves something about how if people feel like they made a bad choice or engaged willingly at some point  they are more susceptible. Or maybe its frog boiling.]

On the "what did we start getting right in the 1980's for reducing global poverty" I think most of the answer was a change in direction of China. In the late 70's they started reforming their economy (added more capitalism, less command economy): https://en.wikipedia.org/wiki/Chinese_economic_reform.

Comparing this graph on wiki https://en.wikipedia.org/wiki/Poverty_in_China#/media/File:Poverty_in_China.svg , to yours, it looks like China accounts for practically all of the drop in poverty since the 1980s.

Arguably this is a good example for your other point... (read more)

I don't think the framing "Is behaviour X exploitation?" is the right framing. It takes what (should be) an argument about morality and instead turns it into an argument about the definition of the word "exploitation" (where we take it as given that, whatever the hell we decide exploitation "actually means" it is a bad thing). For example see this post: https://www.lesswrong.com/posts/yCWPkLi8wJvewPbEp/the-noncentral-fallacy-the-worst-argument-in-the-world. Once we have a definition of "exploitation" their might be some weird edge cases that are technicall... (read more)

The teapot comparison (to me) seems to be a bad. I got carried away and wrote a wall of text. Feel free to ignore it!

First, lets think about normal probabilities in everyday life. Sometimes there are more ways for one state to come about that another state, for example if I shuffle a deck of cards the number of orderings that look random is much larger than the number of ways (1) of the cards being exactly in order.

However, this manner of thinking only applies to certain kinds of thing - those that are in-principle distinguishable. If you have a deck of bl... (read more)

I found this post to be a really interesting discussion of why organisms that sexually reproduce have been successful and how the whole thing emerges. I found the writing style, where it switched rapidly between relatively serious biology and silly jokes very engaging.

Many of the sub claims seem to be well referenced (I particularly liked the swordless ancestor to the swordfish liking mates who had had artificial swords attached).

Other Ant-worriers are out there!

""it turned out this way, so I guess it had to be this way" doesn't resolve my confusion"

Sorry, I mixed the position I hold (that they maybe work like bosons) and the position I was trying to argue for, which was an argument in favor of confusion.

I can't prove (or even strongly motivate) my "the imaginary mind-swap procedure works like a swap of indistinguishable bosons" assumption, but, as far as I know no one arguing for Anthropic arguments can prove (or strongly motivate) the inverse position - which is essential for man... (read more)

I suspect there is a large variation between countries in how safely taxi drivers drive relative to others.

In London my impression is that the taxis are driven more safely than non-taxis. In Singapore it appears obvious to casual observation that taxis are much less safely driven than most of the cars.

At least in my view, all the questions like the "Doomsday argument" and "why am I early in cosmological" history are putting far, far too much weight on the anthropic component.

If I don't know how many X's their are, and I learn that one of them is numbered 20 billion then sure, my best guess is that there are 40 billion total. But its a very hazy guess.

If I don't know how many X's will be produced next year, but I know 150 million were produced this year, my best guess is 150 million next year. But is a very hazy guess.

If I know that the population of X's... (read more)

I remember reading something about the Great Leap Forward in China (it may have been the Cultural Revolution, but I think it was the Great Leap Forward) where some communist party official recognised that the policy had killed a lot of people and ruined the lives of nearly an entire generation, but they argued it was still a net good because it would enrich future generations of people in China.

For individuals you weigh up the risk/rewards of differing your resource for the future. But, as a society asking individuals to give up a lot of potential utility for unborn future generations is a harder sell. It requires coercion.

I think we might be talking past each other. I will try and clarify what I meant.

Firstly, I fully agree with you that standard game theory should give you access to randomization mechanisms. I was just saying that I think that hypotheticals where you are judged on the process you use to decide, and not on your final decision are a bad way of working out which processes are good, because the hypothetical can just declare any process to be the one it rewards by fiat.

Related to the randomization mechanisms, in the kinds of problems people worry about with pre... (read more)

I see where you are coming from. But, I think the reason we are interested in CDT (for any DT) in the first place is because we want to know which one works best. However, if we allow the outcomes to be judged not just on the decision we make, but also on the process used to reach that decision then I don't think we can learn anything useful.

Or, to put it from a different angle, IF the process P is used to reach decision X, but my "score" depends not just on X but also P then that can be mapped to a different problem where my decision is "P and X", and I u... (read more)

I like this framing.

An alternative framing, which I think is also part of the answer is that some art is supposed to hit a very large audience and give each a small amount of utility, and other art is supposed to hit a smaller, more specialized, audience very hard. This framing explains things like traditional daytime TV, stuff that no one really loves but a large number of bored people find kind of unobjectionable. And how that is different from the more specialist TV you might actually look forward to an episode off but might hit a smaller audience.

(Obviously some things can hit a big audience and be good, and others can be bad on both counts. But the interesting quadrants two compare are the other two).

Random thoughts. You can relatively simply get a global phase factor at each timestep if you want. I don;t think a global phase factor at each step really counts as meaningfully different though. Anyway, as an example of this:

$f(x_{k-1},x_k,x_{k+1})=x_{k-1}$

So that, at each (classical) timestep every single element of the CA tape just moves one step to the right. (So any patterns of 1's and 0's just orbit the tape in circles forever, unchanging.). Its quite a boring CA, but a simple example.

We can take the quantum CA that is exactly the same, but with some complex pha... (read more)

After finding a Unitary that comes from one of your classical Cellular Automata then any power of that unitary will also be a valid unitary. So for example in classical logic their is a the "swap" gate for binary inputs, but in quantum computing the "square-root swap" gate also exists. 

So you can get one of your existing unitary matrices, and (for example) take its square root. That would kind of be like a quantum system doing the classical Cellular Automata, that is interrupted halfway through the first step. (Because applying the root matrix twice i... (read more)

I think the limitations to radius set by material strength only apply directly to a cylinder spinning by itself without an outer support structure. For example, I think a rotating cylinder habitat surrounded by giant ball bearings connecting it to a non-rotating outer shell can use that outer shell as a foundation, so each part of the cylinder that is "suspended" between two adjacent ball bearings is like a suspension bridge of that length, rather than the whole thing being like a suspension bridge of length equal to the total cylinder diameter. Obviously ... (read more)

If this was the setup I would bet on "hard man" fitness people swearing that running with the spin to run in a little more than earth normal gravity was great for building strength and endurance and some doctor somewhere would be warning people that the fad may not be good for your long term health.

Yes, its a bit weird. I was replying because I thought (perhaps getting the wrong end of the stick) that you were confused about what the question was, not (as it seems now) pointing out that the question (in your view) is open to being confused.

In probability theory the phrase "given that" is a very important, and it is (as far as I know) always used in the way used here. ["given that X happens" means "X may or may not happen, but we are thinking about the cases where it does", which is very different from meaning "X always happens"]

A more common use woul... (read more)

That Iran thing is weird.

If I were guessing I might say that maybe this is happening:

Right now the more trade China has with Iran the more America might make a fuss. Either complaining politically, putting tariffs, or calling on general favours and good will for it to stop. But if America starts making a fuss anyway, or burns all its good will, then their is suddenly no downside to trading with Iran. Now substitute "China" for any and all countries (for example the UK, France and Germany, who all stayed in the Iran Nuclear Deal even after the USA pulled out).

"given that all rolls were even" here means "roll a normal 6 sided dice, but throw out all of the sequences that included odd numbers." The two are not the same, because in the case where odd numbers can be rolled, but they "kill" the sequence it makes situations involving long sequences of rolls much less likely to be included in the dataset at all.

As other comments explain, this is why the paradox emerges. By stealth, the question is actually "A: How long do I have to wait for two 6s in a row, vs B: getting two 6's, not necessarily in a row, given that I am post selecting in a way that very strongly favors short sequences of rolls".