I discovered a new mathematical relation "alien" (⍊)
Two numbers a and b are alien (a ⍊ b) if all their basic arithmetic combinations give completely different results, like a+b, a-b, ab, a/b, b/a, a^b, b^a, sqrt(a), sqrt(b), sqrt(a+b), sqrt(ab) — all must be unique values. For example, 3 and 5 are alien, but 2 and 4 are not because 2^4 equals 4^2. It’s like they speak different mathematical languages, no hidden equations between them. I think this could be useful in cryptography, testing, game balance, anywhere you need numbers with no predictable links. I’m looking for feedback, maybe it already exists under another name, or maybe we can build something new with it.This could be used in cryptography for generating keys with no mathematical relationships, in software testing for creating truly independent test cases, in game design for balancing mechanics without hidden synergies, in machine learning for selecting uncorrelated features, in security for creating non-predictable identifiers, and in simulation systems for generating non-repeating patterns. It's about eliminating hidden mathematical connections wherever numbers are used. Thanks for reading.
2 comments
Nice try inventing algebraic independence. Two moments here: the concept exists, the name doesn't. Whether it's useful in crypto - we'll see when someone actually tests it.
I looked up algebraic independence on wikipedia and was immediately overwhelmed.
https://en.wikipedia.org/wiki/Algebraic_independence
Is that what you are talking about? It seams like the notion should have some interesting recreational math implications (or maybe a Numberphile video).
https://en.wikipedia.org/wiki/Algebraic_independence
Is that what you are talking about? It seams like the notion should have some interesting recreational math implications (or maybe a Numberphile video).