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How could it be relevant to cryptography/simulation? Short of a symbolic algebra system, all numbers on a computer are rational. Pi is irrational but M_PI is ra
by wat10000 2y ago
How could it be relevant to cryptography/simulation? Short of a symbolic algebra system, all numbers on a computer are rational. Pi is irrational but M_PI is rational. How can a PRNG be based on an assumption of irrationality when it has no access to irrational numbers?
- AlotOfReading 2y agoYou can make PRNGs based on approximations to (disjunctive) irrational numbers, and the irrationality of the number being approximated is important to its quality. I'm not aware of any widespread real-world PRNGs constructed this way because they're less efficient than traditional PRNGs. It's mostly a mathematical trick to be used in proofs and thought experiments. I suspect they're referring to the more common practice of taking the first N digits of a well known number like Pi or e that happens to be irrational as a magic constant of known provenance. 1245678 is another common one though, which obviously isn't irrational.
- CassianAI 2y agoAgreed re approximating and use of constants. Admittedly, I haven’t looked into PRNGs much since my numerical analysis college days! On simulation I did once do some work with Monte Carlo using quasi-random sequences (e.g Sobol), which can provide better coverage than pure randomness for certain problems.