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I think we're on the same page, just different paragraphs. I think I get the gist of your line of reasoning.

Let me try an analogy for the if True case. Gravity (P=NP) exists, and always has. But we didn't understand it a few hundreds of years ago. Before we understood it, we didn't have interplanetary rockets (Efficient Markets). But we do now, and they were never outright impossible before our understanding of delta-v and other aspects. But before we had that understanding, we just straight up didn't have rockets.

Meanwhile if hypothetically gravity was, perhaps stronger or more pervasive over longer distances (P!=NP), it could have stopped interplanetary travel altogether and we would have never have achieved it.

We are just in an equivalent time period to that time in the 1600s before we understood, one way or another, what was ahead of us. If markets can be efficient in the future, they could always have been now and in the past. We just didn't have the tools to figure it out.



Analogy seems roughly right, if it was a statement like "P=NP -> Markets could possibly be efficient" then I'd buy it.

But I think what's more interesting is that

"Markets (present-day) are efficient -> P=NP" could plausibly be true, suggesting that the contrapositive is true: "P!=NP -> Markets (present-day) aren't efficient." Given current state of thought around plausibility of P=NP, that seems pretty powerful nonetheless.

With the slightly stronger statement "Nobody currently possess a polynomial time algorithm to solve a problem in NP -> Markets (present-day) aren't efficient" it starts to become quite likely markets aren't fully efficient.




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