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How can you communicate the axioms of Peano arithmetic to intelligent extra-terrestrials, in a way that they would recognize it?
by rrwo 4y ago
How can you communicate the axioms of Peano arithmetic to intelligent extra-terrestrials, in a way that they would recognize it?
- Koshkin 4y agoWell, first we could send a series of integers, each being a sequence of pulses, to convey the fact that we are talking about integers. Then express each axiom by a series of concrete examples. And repeat. Intelligent species should be good at recognizing patterns.
- PuppyTailWags 4y agoWhy would we identify a sequence of pulses as integers if, for example, the passage of time is perceived differently by aliens? Or if mathematics within alien life is based on atomic units of group like set logic, and so the sequence of pulses itself is seen as "1".
- rrwo 4y agoThe ancient Egyptians expressed axioms by a series of concrete examples. Stating them as actual axioms or theorems with proofs (by Greeks, Indians and Chinese, among others) was an improvement. How can we communicate actual axioms to extra-terrestrials? Presumably we can create a kind of Rosetta Stone with different representations of logical and algebraic expressions, and maybe they can decode that if they can figure out how to decode whatever "broadcast" representation of this we come up with. And that assumes that they recognize such a broadcast as something from intelligent life.
- authpor 4y agowhy would you do that? maybe what you really want is to show them that you can count too? peano arithmetic (an axiomatiazation of counting) isn't how we count. It is how we make other things count for us.