It's more complicated.

For the Fermi paradox version of the 'Dark Forest' to work, you need civilisations to actively go out and destroy any other form of life they find announcing themselves:

> The "dark forest" hypothesis presumes that any space-faring civilization would view any other intelligent life such as theirs as an inevitable threat and thus destroy any nascent life that makes itself known. As a result, the electromagnetic radiation surveys would not find evidence of intelligent alien life.

Wikipedia has a section on game theory etc.

Without this additional element (basically the version you describe), the dark forest theory doesn't explain the Fermi Paradox: it's just another filter that might perhaps exclude 90% of civilisations, but many civilisations would still be dumb enough to announce themselves. Humans certainly did and keep doing so: it only needs a some people to send a message, and near unanimity to not send anything.

(And that's completely ignoring that our very atmosphere with its chemical imbalance has been sending a strong message of "there's probably life here" for billions of years now. Even our own technology, still in its infancy, is increasingly able to pick up clues about the chemical composition of the atmosphere of exoplanets ever further away from us. And we are still getting better quickly.)

If you add the element that other civilisation are hiding, but come out of hiding just to strike, that breaks down as soon as you have more than two players. Or even just the faint possibility of more than two players.

When you know there are only at most exactly to players, and you are the lurker and find someone else being 'noisy': yes, you have an incentive to strike. When there might be other third parties lurking, you better stay quiet, lest you invite a strike by a third party against you.

You mean place a stick flat on the ground? (Singapore is pretty much on the equator.)

It's pretty easy to get right, if the provider allows you to go (slightly) negative before cutting you off.

> Also, can you imagine the kind of downtimes and complaints that would inevitably originate from a fully synchronous billing architecture?

Doesn't need to fully synchronous.

No need to retire API keys.

I don't see the connection.

Sorry, how does that work?

Well, you need to harden everything, the attacker only needs to find one or at most a handful of exploits.

Huh, no?

I would have hoped that by now it was obvious that we are talking about a _specific_ weak form of the EMH that takes friction into account?

What is your whole first paragraph about? Who are you trying to convince? Where's the strawman that claimed that the strongest version of EMH that you can imagine is literally true?

There's no single weak form of EMH that could be accurate or inaccurate: there are many versions of the EMH in various strengths and dimensions (that can be accurate or inaccurate).

To be more specific: Jane Street believes (or acts lie they believe) that markets are at least efficient enough that it takes a lot of effort for them to make money. As a very, very weak form: someone doing chart astrology, eh, I mean technical analysis, on S&P 500 stocks won't beat the market. But even much stronger versions than this are defensible.

The real strong forms that say that all information is preciously reflected in profits is a simplifying assumption you can sometimes make to make your life easier. Just like you sometimes neglect friction in physics. But when you want to decide how long your train needs to emergency brake, you kinda need to take friction into account. Similarly, when trying to make money in the market or trying to understand how others like Jane Street make money, the strongest EMH is not a good guide.

Compare https://arxiv.org/abs/1108.1791 and why computational complexity is often more interesting that computability.

Eg you can get complex numbers from matrices.

But if you want to go in your direction: you can say we get fractions and negative numbers this way.

Maybe. But I found it a nice piece of recreational mathematics nevertheless.

Definitions are either a bit fuzzy, or not universally agreed on.

Though interestingly https://en.wikipedia.org/wiki/Elementary_function says "More generally, in modern mathematics, elementary functions comprise the set of [...]". Though at least Wikipedia thinks that 'modern mathematics' has a consensus; of course, there's no guarantee that whoever you are talking to uses the 'modern mathematics' definition that Wikipedia brings up.