Written by: Stephen Hsu

Primary Source: Information Processing

As reported by Stan Ulam in Adventures of a Mathematician:

“A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.” –Stefan Banach

See also Analogies between Analogies: The Mathematical Reports of S.M. Ulam and His Los Alamos Collaborators; esp. article 20 On the Notion of Analogy and Complexity in Some Constructive Mathematical Schemata.

I’ll add my own comment:

The central problem of modern genomics is essentially cryptographic. The encryption scheme is the model relating phenotype to genotype, and the ciphertext–plaintext pairs are the genotypes and phenotypes. We will recover the schemes — models which can predict phenotype from genotype — once enough ciphertext and plaintext (data) is available for analysis.

We have programs (DNA code) and their outputs (organisms) to study; from this we deduce the programming language.

See also Alan Turing:

“There is a remarkably close parallel between the problems of the physicist and those of the cryptographer. The system on which a message is enciphered corresponds to the laws of the universe, the intercepted messages to the evidence available, the keys for a day or a message to important constants which have to be determined. The correspondence is very close, but the subject matter of cryptography is very easily dealt with by discrete machinery, physics not so easily.”

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