IdeaStorming: underdetermination and information theory

[gusl]

uncritically philosophizing:

* Physics is hard to learn.
* Therefore, the collection of physics theories contains a lot of information.
* Therefore, there must a lot of experimental data to account for, otherwise such complex theories would not be warranted. (What's the relationship between the information content of data observed (theory-relevant information, excluding noise) and the information content of the theory)


criticism:

Problems: physics could be hard to learn due to a priori knowledge (mathematics contains very little information, and yet it is hard)

Is physics hard in the same way that math is hard?

Comments

What's physics?

[fare.livejournal.com]

What is physics? i.e. what makes an assertion more or less physical than another one?

The difference between Mathematics (the study of formal tautologies?) and Physics (the study of regularities in the "physical world"?) could tell what makes physics harder or not than mathematics. Determining what makes a meaningful and relevant physical statement depends on interaction with the physical world, independently from other people. Mathematics in contrast has meaning or lack thereof in abstracto, and relevance by application to physics as well as mere discussion with other mathematicians. (Which makes it better than leftist "social sciences" that have no meaning whatsoever, and only relevance through interaction with other people -- to manipulate their minds.)

So physics will be less hard than math in the way that math is hard, but harder in a way that is foreign to math. If you want to put these incommensurable on a same scale, well, you can, in infinitely many ways. And in practice, the only relevance of that "hardship" is for a student to choose between two topics -- and then the answer will depend on his own psycho-epistemology.

[jbouwens.livejournal.com]

Therefore, there must a lot of experimental data to account for, otherwise such complex theories would not be warranted.

Is that a valid implication? The inverse is not always true: A swarm displays very complex behaviour (lots of experimental data), yet the theory describing this behaviour consists of only a few rules.

Also, data != information. There can be little experimental data that nevertheless contains a lot of information, requiring complex theories.

[gustavolacerda.livejournal.com]

There can be little experimental data that nevertheless contains a lot of information, requiring complex theories.

Please give me an example.

[jbouwens.livejournal.com]

Schrodinger's cat deals with only 1 bit of experimental data, yet it requires quantum mechanics to properly describe.

[turingtest.livejournal.com]

I think it's likely that they're both difficult for the same reason: their modern forms tend to contradict the evolved inference systems that we already have hard-wired in our brains (see Domain Specificity and Intuitive Ontology (http://www.anthro.ucla.edu/faculty/barrett/BoyerBarrett.pdf) by Boyer and Barrett).

Since these internal structures also represent a great deal of information, the problem is therefore not directly a matter of the information quantity but of its deviation from what we already have and use. With effort and proper training we overcome these system limitations to some extent, but it's unlikely that we ever bypass them completely when processing our environment.