pontus

There's another version of the Monte Hall problem that highlights why this is such a counterintuitive problem.

Imagine that after you pick your box, Monte Hall invites an audience member up on stage and instructs them to choose one of the remaining two doors to open. This audience member doesn't know anything at all and just randomly picks one of the two doors. When their door is opened we see that it's empty. You're now given the option of switching just like in the standard game. Should you?

Cosmetically everything is identical with the standard game, but if you analyze the game carefully this time you're left with a 50/50 shot so there's no benefit of switching.

I think most of the arguments in this article would appear to work for this modified version of the game which means that they're not actually getting to the heart of the problem.

For completeness, the reason this now reduces to 50/50 is that there's also now a chance that the spectator opens the door with the car behind it, something that couldn't happen in the original Monte Hall problem. Put another way, there's actually a little bit of information that's conveyed to you when you see that the spectator happens to not open the door with the car and this extra information exactly cancels the usual benefit you get from eliminating the other empty door. In the example of "scaling up" in the article, if you did this with 20 doors and the spectator randomly picks 18 of the 19 unopened ones to open and then happen to not stumble upon the car, you might actually think that you could have been lucky all along. Ultimately you're left with a 50/50 chance.

So stuff like precious metals, commodities (energy, corn, pork, ...), stocks that don't pay dividends, etc are then also equally worthless?

I don't think holding a barrel of oil or a bar of gold, or a share of Berkshire Hathaway will generate any income for me. I'd need to sell it to someone else for me to get my money back.

Isn't that true of anything that doesn't include the fed? I mean unless you can print money, you can't change the amount of fiat in any subset of the economy. You can still add value though which would be evident by more people wanting a piece of whatever pie there is, driving more fiat into the subset and/or creating paper gains which is a sort of money in itself, but this is true for crypto as well.

For example, I can draw a circle around Google and make the same argument: "I can see how fiat can flow into Google (investments, debt, advertiser dollars, ...) but I can't see how Google can create new fiat to flow back to the rest of the economy." The best I can see is that higher demand for a share of Google creates paper gains but then that's true for crypto as well.

Thanks for this! That being said, I think that makes it an even better slogan. Taking something that was well known and using it in a new context where the meaning was, in fact, reversed. Kind of brilliant.

Each product's value can be judged along many different dimensions. The fact that a product is not the top most used in a category does not mean that it is inferior along all dimensions. For example, many people here on HN would say that they prefer DuckDuckGo over Google because it doesn't track you in the same way. However it's not the number one product in the search engine category. It does, however, win along at least one dimension: privacy. So, if you value that then maybe DDG is for you. The same privacy argument could be made for protonmail, Tor, and Signal.

Just because something isn't AWS doesn't mean that it's useless. I think that's part of the point the OP was making: people keep moving the goal post and because of that, their argument is not falsifiable.

It's amazing to see people on both sides of this debate speak with such intense and unapologetic certainty. In 10 years or so one side will be found correct and say things like "I told you so, this was obvious from the beginning. People were just sheep!".

Why would one expect Bitcoin which is more-or-less trying to disrupt the world order to be stable at this point in its evolution? Maybe in 20 years it'll be stable, but now? Sort of like saying that there was political instability in US following the revolutionary or civil wars and that therefore the US would never be a country that could be depended upon for international trade.

It's a fun idea, but I found it super frustrating because it gets harder and harder to come up with consistent words.

I'd personally like an "easy setting" where there's another key color that indicates if a letter is viable. So when there are only say 10 possible words left it'd highlight the letter the word could start with. Maybe it's just me though.

Right, I mentioned above that the resolution to this is that the expected value of both envelopes is infinite before you open anything and thus the difference is undefined. Once you open one, the difference becomes well defined.

I still think it's quite unintuitive that one needs to open an envelope in order to regularize things this way. The fact that you will always decide to switch, regardless of what you see in the first envelope, yet you still have to open it is what I find paradoxical.

The point I'm making is that if you open the envelope you will always conclude that it's advantageous to switch regardless of what you see in that envelope. In the case where you see $1, you're guaranteed that switching is a good idea. If you see anything other than $1 you come to the same conclusion but you have to rely on a probabilistic argument using expected values. Now, if you will decide to switch regardless of what you see in the envelope, then why even bother opening it? But, if you don't open the envelope, then you're back to the original problem where the symmetry argument is valid.

No, k >= 0 in my example. In one case you know for sure that you have the smallest envelope since you see that it has $1 in it. I'm this case you should absolutely switch. In all other cases, you should still switch although you can't be completely sure.

That being said, even if you let k go negative I think it's still a paradox.

If you're curious the resolution to this is that before you look in the envelope the expected value of both envelopes is infinite. Only after you look inside one of them does that collapse to two finite values that you can subtract.

There actually is a paradox:

Select a power of 2 according to the probability

P(2^k) = 0.2 * 0.8^k

i.e. p(1) = 20%, p(2) = 16%, p(4) = 12.8%, etc.

Then place this amount in one envelope and twice that I'm the other envelope.

Then, randomly shuffle the envelopes and select one and open it. Say you see the number 16. It could have landed there in two ways: Either 16 was generated and the other envelope has 32. This happens with probability 0.2*0.8^4 ~ 8.192%. Alternatively 8 was generated and the envelope you have is already the largest one. This happens with probability 0.2*0.8^3 ~ 10.24%. Given that you see 16 already, the relative probability becomes 4/9 vs 5/9. In other words the chance that you have the largest envelope already is 5/9. The expected value of the other envelope is then 5/9*8 + 4/9*32 = 18.67 > 16 so you should switch.

In fact, try this for different initial envelopes and you'll see that you should always switch.

But, if you should always switch, why even look inside the envelope?

But, then you're back at the symmetry / no information argument.

I did a pretty deep analysis of this problem a while back here in case you're interested: https://mindbowling.wordpress.com/2020/09/14/two-envelope-pa...

Yeah, I agree. This setup though is the one to which the original "naive" argument applies which is why I think it's interesting to ponder.

It depends on how the envelopes are prepared. If the two envelopes have x and 2x in them and one is randomly handed to you, there's a symmetry between them that tells you there is no benefit in switching.

However, suppose x is placed in an envelope and handed to you. Then a fair coin is flipped. If it comes up heads, 2x is placed in another envelope and if it comes up tail, x/2 is placed in that envelope. Then you should switch.

It's a subtle difference in how the envelopes are prepared, but it makes all the difference.

I wrote a pretty detailed analysis about this problem here in case you're interested:

https://mindbowling.wordpress.com/2020/09/14/two-envelope-pa...

It all depends on how the envelopes are prepared.

I wrote up a pretty detailed analysis of this problem a while back here: https://mindbowling.wordpress.com/2020/09/14/two-envelope-pa...

At the end I constructed a super weird example where regardless of what you see in your envelope, you should switch (this seems to go against the symmetry argument, but is sort of saved by a divergence in the expectation value).

This is quite outdated, I believe. With the launch of NU5/Halo2 in a couple of weeks, all transactions will be private by default. Plus, even without that change, the shielded pool is way larger these days. Finally, a fairer comparison with Monero would have been to trace a shielded to shielded transaction. This should be literally impossible with Zcash.

Both of these are no longer a thing with NU5 / Halo 2

Well, if you want true privacy you should try Zcash.

I mostly agree with you. Just to play devil's advocate though, I wonder if this is just an artifact of him being overly open / verbose. In other words, I suspect that all this stuff would normally happen behind closed doors anyway during due diligence. Similarly if you look at his performance in Tesla / SpaceX is terms of hard metrics I guess he's doing pretty well even though he might be talking about self driving being a year away all the time.

Because of scale? Tech is an insane force multiplier. Instead of deceiving ~100 people by talking to them face-to-face you can now deceive ~10k, 100k, maybe millions. The cost is also so low to allow pretty much anyone to engage in this behavior.

I came here to write the exact same thing. Amazing content.

No, that's not at all what I'm saying. I'm saying that if someone seated next to me is allergic to my pet (or for whatever reason doesn't want to sit next to it), then they could relocate either me or that person so that we're sufficiently far apart not to cause any issues.

The argument presented to me in the past (and also the argument in comment I was replying to) is that since some people are allergic to pets or otherwise dislike them, we should completely disallow traveling with pets in a blanket fashion. I'm simply saying that I think that's too extreme and that a middle ground can be found.

If we're going to completely ban pets on airplanes, then we should consider also banning flying with a cold because of immunocompromised people (in fact this is perhaps more warranted given the severity of the situation).

When I used to fly with my dog (~10lbs so they were allowed in the cabin) I had to pay $200 for them which is fine. But then it turns out that the dog also counted toward my carry-on! WTF!? I mean either charge me or have it count toward my carry-on, but both??

I used to have a dog and got this feedback from people quite often.

As far as I understand, pet allergies are not like peanut allergies in that they're not actually lethal (correct me if I'm wrong!) As such, I feel like it's just one of those things that people might just need to deal with when they're part of a shared space much like sitting next to someone with bad body oder, someone chewing loudly, or someone laughing out loud when they're watching their tv. If it's too much of an annoyance maybe one can try to get moved to a different seat?

What a ridiculous oversimplification of life...

I disagree. If there really is only one universe which is 3D, this argument does not in any way explain why it is 3D.

If you use Bayesian probability, you would in this case start with p(3d) = 1 since there's only one universe which is 3d and then end with p(3d | life) = 1. In other words, there's no explanatory power in the observation that there's life.

If instead you say that p(3d) = 1/1000 because maybe the multiverse has all sorts universes out there but you also say that life is only possible in 3d, i.e. p(life | 3d) > 0, but p(life | not 3d) = 0, then you go from p(3d) = 1/1000 to p(3d | life) = 1. In other words, the observation of life does have explanatory power.

I know you explicitly asked for non-string theory answers, but I have to give one anyway -- sorry!

There's an argument in string theory called the brandenberger-vafa mechanism that I think is pretty clever:

Imagine that a bunch of particles and antiparticles travel along in one dimension. Because they can't spread out, they'll eventually collide and annihilate. However in 2d that's not the case: they're more likely to just miss each other all the time.

If you increase the dimension of the "particles" to strings, you can make a similar argument. In 2 (compactified) dimensions, strings will find each other but not in three.

Then if you start with some compactified space of 10d with a bunch of strings wrapped around various 2d subspaces, they will naturally constrain that space so that it can't expand. However, as strings move around randomly they'll tend to collide and unravel, allowing various 2d subspaces to cease being constrained and therefore expand.

If you analyze this carefully you can show that in fact three of the spatial dimensions will tend to expand while the six remaining ones will remain compactified.

Anthropic arguments only work if there's a mechanism for generating other versions besides the one you're observing. For example, you could use the anthropic argument to explain why earth is in the "goldilocks zone" because there are plenty other planets out there at varying distances from their sun.

So, if you want to make the argument that 3d is preferred for some reason you need to acknowledge that there are other universes out there with 2d, 4d, etc that just can't sustain life and that therefore life only finds itself in the subset of universes that have three dimensions.