4 ms·

>> This is no different from mathematics where each "X theory" is essentially its own language Nice connection between models and languages. The maths/physics

>> This is no different from mathematics where each "X theory" is essentially its own language Nice connection between models and languages. The maths/physics discoveries achieved by using a new representation of a problem don't change the problem, they just present the issue at hand simply enough to be tractable. Each representation moves complexity trade-offs to a different category of problem. I guess that does say something in favour of automatic syntax conversions but it seems too low level. Maybe conversions between the mode of abstraction being used is where it gets interesting.

logicrook 11y ago
In mathematics, there are fairly few such 'meta-results', and each one is duly celebrated as impressive; the one that comes to mind is Curry-Howard correspondence... but in more 'traditional' maths, it's very hard to find general high-level translations. There are many cases where automatic syntactic low-level constructions can bring huge improvements, in compiler design, etc, it's more that they are less susceptible to be directly useful to laymen.