I didn't learn anything from this. It looks like there are things to learn here, but you seem to have deliberately chosen a writing style that does not permit it.

That is pretty annoying.

I think its spread through rationalist-land originated at this post by Alice Maz: https://alicemaz.substack.com/p/you-can-just-do-stuff

Though by following the trail of links from Haiku's comment one can find people saying similar things farther in the past.

Overall a nice insightful post, but recorded music is like upwards of a century old, so I don't think the timing works out. I was in a dancing club at one point and we used recorded music and I think that requiring us to use live music would have prevented the club from existing.

Yeah, there's definitely a few relevant things here:

• Representation theory is relevant (in particular representations of cyclic groups, which is basically the circle arithmetic you're talking about). Representation theory gives you matrices that use complex numbers, even for discrete finite groups. So number theory isn't the only place where complex numbers poke their nose into discrete business.
• There's apparently a whole theory of Dirichlet series and Dirichlet convolution which is analogous to Fourier series and Fourier convolution. Complex numbers are the nicest way to do Fourier series, so it makes sense that they're also the nicest way to do Dirichlet stuff.
• I guess just in general complex numbers are the best field and a lot of the math of number theory is turning things into vector spaces and linear operators and doing linear algebra on them. And if you're picking a field for your vector space, what better choice than $C$?
• A Dirichlet series is a function of a variable $s$, and complex functions can have complex analysis done on them, and complex analysis is uniquely nice, so why not make $s$ a complex variable?

The post author seems to already know a lot of math, so I guess they're looking for a deeper kind of answer.

Oh, cool, that's great.

I was referring to the older style of sailboat design, like this one, where the sails are all controlled by a bunch of ropes. Single rotating airfoil sounds a lot simpler. One advantage of an airfoil over a kite is that it would allow the ship to gain some propulsion, even when travelling at an angle upwind, right?

Obstacles to this idea:

• Hydrodynamic drag on many smaller hulls is larger than on one big one.
• Ports cost money. It seems hard to make a port which unloads individual 1-container vessels faster than a conventional port can pull containers off a large vessel using cranes. As for just making more numerous & smaller ports, it probably ends up being much more expensive.
• It's an existing technology for large ships to fly kites to save fuel when the weather is favourable and the wind is blowing in the right direction. I think most ships still don't do this, so I'm not sure if it's currently economical, but it at least demonstrates that making a ton of tiny sailboats is not the only way to take advantage of the wind. Sailboats have a lot of moving parts, and maintenance on so many of them would be a nightmare.
• Even though containers have taken over a lot of things, not all loads are containers even today, so we still need large ships for fuels and bulk cargo.

I'd be eager to hear about anything similar to this which is already discussed somewhere, if you know of anything.

I wrote a post in 2023 about somewhat similar ideas: https://www.lesswrong.com/posts/uDXRxF9tGqGX5bGT4/logical-share-splitting The market mechanism there is based on the formula P(A)+P(B)=P(A∧B)+P(A∨B) from probability theory.

In that post, shares aren't expected to have continuous-valued payoffs, but merely continuous-valued prices representing binary payoffs with some chance of happening. So that's a relevant difference that means the interpretation of $G\vee H$ is not quite the same (in particular, it doesn't involve a max function, since there are no continuous values to take a max of), though there's still a sense in which it's as good as having your choice between $G$ and $H$.

The conventional physics way of explaining this is as follows:

One way of asking "what is the current state of the universe?" is to pick a Cauchy surface. This is just a "slice" of the entire universe at a given time. There is a lot of freedom in the choice of slice: In Minkowsky space for example, there are slices corresponding to every choice of rest frame, and many more besides those. We just need to make sure that no points on the surface lie within each-other's light cones ($\Delta s^2<0$).

The information (about field values & derivatives) lying on any particular Cauchy surface is enough to predict the future and past from that surface. Pick any two Cauchy surfaces, and there's a unitary operator mapping one to the other. This is the relativistic version of a time-evolution operator.

Some Cauchy surfaces are entirely later in time than other Cauchy surfaces. (Though some pairs of Cauchy surfaces are partially later and partially earlier than each other.) We'll say that for Cauchy surfaces $A,B$, that $A<B$ exactly when for all points $a\in A,b\in B$, either $a$ is spacelike separated from $b$ or $b$ is in the future lightcone of $a$.

Let $S\left(\right)$ be a function that measures the entropy on a given Cauchy surface. The second law of thermodynamics then says that if $A<B$ then $S\left(A\right)\le S\left(B\right)$.

Thing likely being subtweeted: https://www.lesswrong.com/posts/dHLdf8SB8oW5L27gg/on-fleshling-safety-a-debate-by-klurl-and-trapaucius

1a3orn can correct me if I'm wrong. You're welcome, confused future readers.

I have read that some sequencing methods (nanopore) have a high error rate (comparing multiple reads can help correct this). Did you also spot-check some other genes that you have no reason to believe contain mutations to see if they look ok? Seeing a mutation in exactly the gene you expect is only damn strong evidence if there isn't a sequencing error in every third gene.

EDIT: Looks like this was checked, nice: https://www.lesswrong.com/posts/Hds7xkLgYtm6qDGPS/how-i-learned-that-i-don-t-feel-companionate-love