I don’t understand how Uspensky’s definition is different from Eliezer’s. Is there some minimum number of people a proof has to convince? Does it have to convince everyone? If I’m the only person in the world, is writing a proof impossible, or trivial? It seems that both definitions are saying that a proof will be considered valid by those people who find it absolutely convincing. And those people who do not find it absolutely convincing will not consider it valid. More importantly, it seems that this is all those two definitions are saying, which is why neither of them is very helpful if we want something more concrete than the colloquial sense of proof.
As I understand Eliezer’s definition: “Your text is proof if it can convince me that the conclusion is true”
As I understand Uspenskiy’s definition: “Your text is proof if it can convince me that the conclusion is true and is I am willing to reuse this text to convince other people”.
The difference is whether the mere text convinces me that I myself can also use it succesfully. Of course this has to rely on social norms for convincing arguments in some way.
Disclosure: I have heard the second definition from Uspenskiy first-person, and I have never seen Eliezer in person.
Does Uspenskiy have an opinion on Zero-knowledge proofs? They differ from standard proofs in that they have a probability of being wrong (which can be as small as you want), and the key property which is that if I use one to convince you of something, you aren’t able to use it to convince anyone else.
Does anyone consider them the proofs in the ordinary sense?
I could ask him, but given that experience of verification of ZKP is an example personal/non-transferrable evidence, I see no question here.
And in some sense, ZKP proofs are usualy proofs of knowledge. If you represent ZK prover as a black box with secret information inside that uses random number generation log and communication log as sources to calculate its next message, access to this blackbox in such form is enough to extract some piece of data. This piece of data makes the proven statement trivial to verify or to prove conventionally—or even to play prover in ZKP. So all the efforts in ZKP are about showing you know some secret without letting me know the secret.
I don’t understand how Uspensky’s definition is different from Eliezer’s. Is there some minimum number of people a proof has to convince? Does it have to convince everyone? If I’m the only person in the world, is writing a proof impossible, or trivial? It seems that both definitions are saying that a proof will be considered valid by those people who find it absolutely convincing. And those people who do not find it absolutely convincing will not consider it valid. More importantly, it seems that this is all those two definitions are saying, which is why neither of them is very helpful if we want something more concrete than the colloquial sense of proof.
As I understand Eliezer’s definition: “Your text is proof if it can convince me that the conclusion is true”
As I understand Uspenskiy’s definition: “Your text is proof if it can convince me that the conclusion is true and is I am willing to reuse this text to convince other people”.
The difference is whether the mere text convinces me that I myself can also use it succesfully. Of course this has to rely on social norms for convincing arguments in some way.
Disclosure: I have heard the second definition from Uspenskiy first-person, and I have never seen Eliezer in person.
Does Uspenskiy have an opinion on Zero-knowledge proofs? They differ from standard proofs in that they have a probability of being wrong (which can be as small as you want), and the key property which is that if I use one to convince you of something, you aren’t able to use it to convince anyone else.
Does anyone consider them the proofs in the ordinary sense?
I could ask him, but given that experience of verification of ZKP is an example personal/non-transferrable evidence, I see no question here.
And in some sense, ZKP proofs are usualy proofs of knowledge. If you represent ZK prover as a black box with secret information inside that uses random number generation log and communication log as sources to calculate its next message, access to this blackbox in such form is enough to extract some piece of data. This piece of data makes the proven statement trivial to verify or to prove conventionally—or even to play prover in ZKP. So all the efforts in ZKP are about showing you know some secret without letting me know the secret.