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Again, you miss the point, there will be a paradigm shift. Yes, symbolic maths still exists, but nobody is looking up a special function to solve an equation. T
by js8 3y ago
Again, you miss the point, there will be a paradigm shift. Yes, symbolic maths still exists, but nobody is looking up a special function to solve an equation. They just plug the numbers (and the state machine approximation of the numerical operations) in the computer and numerically, the result comes out.
Symbolic/numeric is just analogy of the paradigm shift that will come to all (applied) math. Another example is in statistics, shift from parametric to non-parametric.
Cryptography.. relies on unproven belief in ETH or P/=NP or some such (in fact, cryptography has, since Caesar, relied on unproven beliefs about cryptosystems). But that's just a belief, we don't really understand how hard any of these specific problems are. Which is actually a great example of the new paradigm I am talking about, because it shows we don't need proofs (of statements about infinitely many things). We can just quantize things directly (into a state machine that actually does the crypto stuff) and be happy.
We haven't even scratched the surface of what is possible in P vs NP. In particular, CNF representation of SAT instances might be a really crappy one.
- Tainnor 3y agoYou should look up provable security. And also, while security proofs typically rely on unproven assumptions, correctness proofs in cryptography are "regular" proofs for all intents and purposes. You can't even do RSA etc. without understanding prime numbers which is impossible if you limit yourself to propositional calculus ("SAT"). > Again, you miss the point, there will be a paradigm shift. Yes, symbolic maths still exists, but nobody is looking up a special function to solve an equation. They just plug the numbers (and the state machine approximation of the numerical operations) in the computer and numerically, the result comes out. This is false.