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Comment by Hermel | Hacker News Reader

Intuitively, I think "proof of stake" could violate Gödel's incompleteness theorems. These basically state that no complete system can proof its own correctness. And that's exactly what "proof of stake" tries to do: proof its correctness without external anchor of truth.

Of course, Vitalik Buterin knows that so he resorted to "weak subjectivity", basically saying that if you are not online often enough, you need to trust someone with providing you check points to decide which fork is the "true" one.

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Be careful about how you interpret the word "prove" there. Are you sure that the sense of "prove" that applies to that theorem of Gödel corresponds to the sense of "prove" when you are talking about proof of stake?

The proofs of Gödel's theorems work by encoding the axioms and inference rules of the system in a way that can be dealt with within the system, and using that to encode statements like "this statement cannot be proven within the system" within the system.

I am not sure what the analogous thing would be if you were to attempt to carry the proof over. I am not even sure what it would mean to try to do that.

To prove that, there is no proof that can be carried out within proof of stake, that there is no proof of Falsum that can be carried out within proof of stake?

What would that even mean? What would it even mean for proof of stake to prove Falsum?

I am not asserting that proof of stake can work well, but I am not convinced by the line of reasoning that you lay out, with its current level of detail. Perhaps if you went into the details I would find it more convincing.

Just a quick handwavy idea: from falsity you can derive anything, so maybe in this context Falsum would be something that could be used to "prove" the validity of any transaction you want? That said, I'm not an ETH enthusiast and I don't know how you'd express this in that system or if their notion of proof is comparable to "proof" in logic.

Isn't that equivocation on the word "proof"? In the case of "proof of stake," I don't think it's referring to a formal proof of the correctness of the system. It's intended to be a consensus mechanic that the users of the blockchain consider "good enough" to trust. Of course there can always be collusion among parties in a blockchain or other attacks on the blockchain, but "proof of work" (and every "proof of x" mechanic I know of) is intended to be "good enough."

"Proof of stake" does not appear to have anything to do with "proof" in the logical sense. I really, really do not think the incompleteness theorems are at all relevant here. Apologies, but this reads just like every other nonsensical attempt to invoke the incompleteness theorems without a good understanding of what they actually say. (Like, how are you possibly going to get proof of stake to simulate arithmetic?)

Proof of stake is just another way to achieve distributed consensus. Not sure how that’s impossible or violates the laws of physics.

While Hermel certainly appears to have no idea what he's talking about, that doesn't make this reply of yours correct either. In particular, the incompleteness theorems are not physics.

I never made the assertion that Godel’s incomplete theorems are physics. My comment was to point out that if one makes the claim “X is impossible”, the burden of proof lies upon the person making the claim or assertion. Simply making an assertion or premise does not prove nor disprove it.

I do not find your explanation of the objective of PoS convincing. Maybe you are talking about their protocol that is true by construction?

Proof of Stake strategy is to make it where attacks on the blockchain are impossible in the economic sense. Proof of work strategy is making the attack infeasible by making the work required impossibly large.

Now is PoS possible? No idea. That possible fork attack seems like an impossible barrier to overcome. But we will see.

History has shown us that humans don't always act economically or rationally. So nothing is impossible.

In PoS, it is a known assumption that if the majority of nodes act rationally, then so be it. This is an issue that is out of scope.

Humans can be rational or irrational. That is how they are born. So far, we can only make tools and books to prevent irrationality.

Do you think PoS is as safe as PoW when dealing with irrationality?

Yes, there are principled ways to model these things. You can compare the byzantine fault tolerance threshold across PoW and PoS. You can compare the cost of deviating from the Nash equilibrium, and calculate how much an attacker needs to spend to deviate in return for every dollar of damage he causes.

Sorry, but you seem really confused about Godel's theorems. You're going to need to explain why you think it's related to proof of stake at all, besides the use of the word "proof".

To me the logic behind Proof of Stake is more like "so much money is bet on the answer being correct, that we'll assume it is. If the majority is wrong then feel free to permanently leave this chain and start your own". I consider it to be a superior system to Proof of Work in nearly every way.

> "so much money is bet on the answer being correct, that we'll assume it is"

Good luck with that https://en.wikipedia.org/wiki/Too_big_to_fail

The one you link is entirely different. zzz

How?

Corporations is controlled by those who own the shares. 1 share 1 vote. But usually only a very very few individuals own majority of the shares. So they have all power what a "too big too fail corporation" can do.

With Ethereum PoS. It is dependent on ETH being distributed to many individuals. If only a few individuals own most of the ETH, then they will then have the power dictate what is the "truth" in the blockchain. Right now, ETH is very well distributed around the whole planet.

As you can see, one is oligarchic, the other is very democratic.

Ethereum is not a Corporation that is designed to make profits. It is non-profit, it's not even a company, it's simply a protocol implemented in Free Software.

The problem with that is that you only know that 'so much money' is being bet because you know who owns the money. But you only know who owns the money because that same money was bet earlier by people that you know owned the money because the same money was bet earlier by...

It's completely circular. It's like the Bible trying to proof itself. With no anchor to the physical world, you can't actually ever know

It's not completely circular. For example in casper-ffg if you as a full node log in every 4 months starting from ethereum's genesis block (about 3 years ago), the chain of logic you outlined terminates at the genesis allocation and PoW rewards.

I'm not saying that requiring clients to log in every 4 months is a reasonable security assumption, just showing that hand-waving it as "completely circular" is incorrect. It's more nuanced than that.

How did the node get started in the first place though? Unless you were part of the genesis block yourself, you only believe the history at all because someone told you it was the right place to start.

In full PoS in the model I described you'd need social consensus to determine the allocations in the genesis block. In PoW you need social consensus on the genesis block as well - the PoW algorithm, the initial difficulty and block reward, the difficulty adjustment algorithm, the block reward schedule

Allow me to hyperbole this a bit. If we go back to 2008, this is like saying - "there is so much money bet on subprime loan being correct, that we'll assume it is". And it worked for sometime before it dint.

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