This somehow makes things even funnier. If he had any understanding of modern math, he would know that representing a set of things as points in some geometric space is one of the most common techniques in math. (A basic example: a pair of numbers can be represented by a point in 2D space.) Also, a manifold is an extremely broad geometric concept: knowing that two things are manifolds does not meant that they are the same or even remotely similar, without checking the details. There are tons of things you can model as a manifold if you try hard enough.
From what I see, Scoot read a paper modeling LLM inference with manifolds and thought "wow, cool!" Then he fished for neuroscience papers until he found one that modeled neurons using manifolds. Both of the papers have blah blah blah something something manifolds so there must be a deep connection!
(Maybe there is a deep connection! But the burden of proof is on him, and he needs to do a little more work than noticing that both papers use the word manifold.)
I decided to take a look at the bitcoin white paper.
Usually, the introduction of a technical paper is fluff and people quickly move on to the technical parts. However, the casual claims made in the first paragraph of this paper have aged extremely poorly, to say the least. In a better world, Bitcoin would have remained as an obscure academic toy, and this introduction would have remained fluff.
What weaknesses are there in the trust based model? Let's find out!
It seems like this guy really loves non-reversible transactions! But as we've seen with the history of crypto, non-reversible transactions sound really good until you fall victim to a crypto scam and there is no way to appeal to the bank to reverse the charges. Reversibility actually increases trust because you no longer need to be absolutely certain that you're dealing with an honest person.
Almost like that is a problem of human nature. And it's not like cryptocurrency has a spotless record when dealing with fraud! The problem with fraud is not the third party (the bank), but with the second party (the merchant or customer you're dealing with).
The introduction is not long, and most of the paper concerns the technical details of the construction of Bitcoin. By itself, there really is no way to complain about a pile of definitions. But there are still dumb comments that have aged poorly in retrospect.
But why would you want a block header with no transactions? If you wanted to, I don't know, replace the world's financial system, you would need to handle millions of transactions every 10 minutes. How big would the blocks be then? And remember that many copies of the same blockchain would need to be stored (certainly, every miner would need to store a copy). How many thousands or millions of times would that multiply things?
Turns out it was a bold assumption to think that businesses would just run their own bitcoin miners.
The proof of security (Section 11) is extremely sketchy by modern standards. (They're assuming that all attackers would follow a certain format to attack and not try something different. I get it, proper proofs of security in cryptography are very subtle and difficult.) There is also a page of fluff making random calculations with the Poisson distribution. In any case, the security of Bitcoin requires that the collective computational power of the defenders exceeds the power of any attacker (so the defenders can make new blocks faster).
Bitcoin is very strange as a cryptographic system in that the defender must have more resources than any possible attacker. In most cryptographic systems, the system should be secure even if the attacker has vastly more resources than the defender. Your phone's cryptography should be secure even if some government agency dedicated their supercomputers to try and break it. This means that Bitcoin must waste tons of energy, since that is required to maintain security. Any more energy dumped into it will only increase security and not make the actual transactions faster, which makes Bitcoin horrendously inefficient.
As a purely academic idea in cryptography, it is an interesting curiosity, but the arguments for why it's useful are sketchy. There are other such curiosities that are much more interesting, like homomorphic encryption or secure multiparty computation. It would be a nice line on a CV, but not "incredible".
The true significance of Bitcoin was the terrible libertarian economic argument for it, and the chain of events that would transform it into nothing more than a speculative fashion trend. It has nothing to do with the technical details of Bitcoin. The technical and economic arguments for Bitcoin turned out to be so weak that nowadays, the only real support for Bitcoin is that maybe you can sell it for a higher price to a greater fool.