it's more like math hasn't got to the stage where it can describe complex systems, i.e. chaotic systems, e.g. weather, turbulence, market behaviour. That's not a 'human element', it's a 'chaotic element'. Cryptography's purpose is to obscure information for the purpose of un-obscuring it later. Which is essential for underpinnings of mechanics of crypto currency. But when you want to start to lose information like you do with anonymity, (in my opinion) it's not the best suited way. Because it's essentially reversible with the right tools (because the information is confined in one place, it security relies on your ability to decode it). Trying to lose information in a complex system, i don't think that approach is a good idea. You need to abstract the problem and use the system itself, in DRK's case, disparate location of the information, combining information to create ambiguity, across a chaotic network, is used to help 'lose' it - a cryptographic function can't do that; it's an alternative method. So just because there is not a mathematical proof to describe it doesn't matter, current math fails to describe most complex systems, forward brances are trying to like chaos theory. it's the application that counts and the efficacy of it's application which distils down to a statistic result, same as cryptography does IMO.
Hi BlockaFett,
I'm not sure what you mean by "math hasn't got to the stage where it can describe complex systems". I have a math degree and several published papers in mathematics and I can't for the life of me square this claim with actual work in the field. Mathematics, though the power of clever abstractions, is able to describe extremely complex systems with inhuman precision and correctness. The breakdown in modeling real systems comes from the fact that real systems have many independent moving parts which we are unable to measure precisely and which are infeasible to compute with anyway. So the problem is not complexity per se, nor is it somehow a failure of mathematics that things are this way. The breakdown in modeling software is that there often is no much-simpler description of a software program than the program itself (which can span many millions of bits). Oh -- and we can define "simpler description" precisely and actually prove that this is true for almost all programs.
"Chaotic systems" can be modeled as stochastic processes, and this field is much better developed than I think you realize. And anyway this is about situations where there is no physical way to obtain complete information, not about systems which are humanly defined and whose components are purely mathematical in nature anyway. It sounds like you're trying to justify the standard altcoin practice of responding to criticism by piling on so much complexity that experts won't bother looking at it anymore. But there is no mathematical or scientific result or practice that justifies this. It's just charlatanism.
Next, cryptography's purpose is not "to obscure information for the purpose of un-obscuring it later". If you define "obscure" as "computationally indistinguishable from the encryption of a random element" I suppose it might be the purpose of encryption, but that is a much stronger definition of obscure than is usually meant by the word. Lots of cryptography is designed specifically to remove information: zero-knowledge proofs, ring signatures, preimage-resistant hash functions and pseudorandom functions are some examples (and there are many others ... this is just the longest list I could form without slowing typing to think). So this notion that cryptography is inappropriate for these kind of applications is just not true. In fact the only way to do these things
without cryptography is to physically control the flow of information, which is at odds with trust-minimization and public verifiability, not to mention really difficult in a world where people routinely communicate over long distances.
I hope this helps clarify some things.
Andrew