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But one way can be vastly easier to get results than another other way. Even easy but wrong ways can be useful, such as Newtonian mechanics. (It's computational

by tlb 8y ago

But one way can be vastly easier to get results than another other way. Even easy but wrong ways can be useful, such as Newtonian mechanics. (It's computationally infeasible to predict, eg, robot movements with quantum mechanics.)

whatshisface 8y ago
Newtonian and quantum mechanics deliver different answers, which means that without approximation they are different theories - not different schools of thought. With approximation (in a certain limit), quantum and Newtonian mechanics are the same, and take the same amount of work to find answers - quantum mechanics yields Newtonian mechanics in that limit, doing "room temperature large scale" quantum mechanics means writing down Newton's laws. In this sense it's most accurate to say that Newtonian mechanics is a particular approximation to quantum mechanics that holds under certain circumstances. This other school-of-thought business (Bayesians vs. frequentists, pilot waves vs many worlds vs Copenhagen, everything like them) means choosing between different sets of words to describe the same thing. You are left with one of two cases: either they can be shown equivalent (in which case people are prone to keep on arguing over which one is better), or they are different (in which case one is wrong.)
- Retra 8y ago
  There is no upper or lower bound on the minimum length of a proof when you are free to choose the language in which it is expressed. This means that there almost certainly are things can only be communicated in one language but not another, even if the languages are equivalent in some vague limiting sense. So as a practical matter, you have to work in a better language, because the difference between spending 30 years to learn something and 30,000 years is quite significant.
- billfruit 8y ago
  Just to throw in a metaphor, rather that Newtionian and Quantum mechanics, perhaps the schools of thought are like the differing formulations of classical mechanics like Newton Vs Hamiltonian Vs Lagrangian formulations.

by tlb 8y ago

whatshisface 8y ago

Newtonian and quantum mechanics deliver different answers, which means that without approximation they are different theories - not different schools of thought. With approximation (in a certain limit), quantum and Newtonian mechanics are the same, and take the same amount of work to find answers - quantum mechanics yields Newtonian mechanics in that limit, doing "room temperature large scale" quantum mechanics means writing down Newton's laws. In this sense it's most accurate to say that Newtonian mechanics is a particular approximation to quantum mechanics that holds under certain circumstances. This other school-of-thought business (Bayesians vs. frequentists, pilot waves vs many worlds vs Copenhagen, everything like them) means choosing between different sets of words to describe the same thing. You are left with one of two cases: either they can be shown equivalent (in which case people are prone to keep on arguing over which one is better), or they are different (in which case one is wrong.)

Retra 8y ago
There is no upper or lower bound on the minimum length of a proof when you are free to choose the language in which it is expressed. This means that there almost certainly are things can only be communicated in one language but not another, even if the languages are equivalent in some vague limiting sense. So as a practical matter, you have to work in a better language, because the difference between spending 30 years to learn something and 30,000 years is quite significant.
billfruit 8y ago
Just to throw in a metaphor, rather that Newtionian and Quantum mechanics, perhaps the schools of thought are like the differing formulations of classical mechanics like Newton Vs Hamiltonian Vs Lagrangian formulations.