Tuesday, January 13, 2015

Analogies between Analogies

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.”


Cornelius said...

Whenever I encounter models in other fields, I always build analogies back to physics.This is usually helpful and often reveals entire strands of thought that researchers in other fields have barely considered.

However, whenever I encounter anything resembling a market, I find that asset pricing theory provides the best framework. Marriage, dating, drug dealing, etc. Asset pricing theory accurately predicts the trends in these other markets.

BobSykes said...

The real puzzle is what all the DNA that doesn't code protein (90% or so) does. This is rapidly being worked out, and no doubt the whole control system will be known in detail in a few decades. However, the prediction problem is, How does this system interact with the environment? Even well-constrained algorithms like the number of fingers and toes is environment independent, apparently ranging from 3 to 8 depending on species and exposure to something or other during development. Evo/devo is the overarching problem.

BobSykes said...

PS. I firmly believe there is no such thing as junk DNA. We just don't know what it does. It's similar to the claim (now a movie with the gorgeous Scarlet Johannsen) that we only use 10% of our brain (note the same numerology in both cases). Obviously, an organ as expensive as a brain is utilized 100%. Even the sleep/dream time has a use.

steve hsu said...


steve hsu said...

For many traits additive heritability is > 0.5 and broad sense h2 > 0.7 or so. Therefore you can build good quantitative predictors just treating environment as noise. The problem is to extract the parameters in the models (see Turing quote).

David Coughlin said...

One hopes that the cipher is not one-way.

Endre Bakken Stovner said...

While there isn't a good correlation between organism complexity and nb of genes, there is a very good correlation between nb of non-coding RNAs and organism complexity. Much of what is considered junk DNA is probably ncRNAs - we are discovering new classes of them all the time.

I wouldn't be confident that there is no such thing as junk DNA though. The DNA is littered with fragments that seem to do nothing but trying to copy themselves to other places in the DNA, veritable freeloaders. In one of his books Dawkins reported that a Lizardy creature of some sort had had its genome doubled in a short timeframe. Can't remember the details, but that would probably be an example of junk DNA.

Polynices said...

Cf. http://xkcd.com/793/

steve jones said...

yet more evidence that steve cannot understand that there are as many codes as there are environments, that the genetic architecture changes with the environment. it's amazing how dumb a theoretical physicist can be.

steve jones said...

just treating environment as noise

no steve. not at all. from one environment to another h^2 may be the same, but for different reasons.

your lack of subtlety on this point is mindboggling.

MUltan said...

The idea of physics as cryptography makes me think of all the scrambled information inherent in thermal motion and radiation, and what might be decrypted from them.

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