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> Sure seems like the universe doesn't seem to care much about our math. Well, some mathematical truths are so universal even the universe can't escape them. t

> Sure seems like the universe doesn't seem to care much about our math. Well, some mathematical truths are so universal even the universe can't escape them. the incompleteness theorems [0] come to mind. Regarding the article, I think most physicists consider the continuous models they use to attack the problems at hand a hack to make the mathematics consumable. I don't think they consider the universe itself to be non-discrete. [0] https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...

tromp 8y ago
Perhaps those who expect quantum computers to scale to millions of qubits do. The amplitudes involved seem to defy discreteness...
- krastanov 8y ago
  There are workarounds for that: for instance, do not use such a poorly conditioned basis to describe the system. In particular, problems in physics that appear only in one particular basis are probably human-created notation issues, not something fundamental, as physics should be basis independent.
j7ake 8y ago
Could you give examples on how the incompleteness theorem explains physical phenomena? I would be curious.
- krastanov 8y ago
  I would suggest Aaronson's "NP-complete problems and physical reality" for this type of thinking (public PDF on his academic page). It is short and has a ton of examples. I really like the style, but it is not a common view among working physicists (yet? It is just not particularly practical for the moment).
krastanov 8y ago
I am a physics in academia and no, most physicists do not think that (especially given that most physicists are not quantum foundations physicists, and even then). It is an interesting question, and if I am forced to guess on its answer I would even agree with you, but good science would be to not speculate the way you imply.

tromp 8y ago

Perhaps those who expect quantum computers to scale to millions of qubits do. The amplitudes involved seem to defy discreteness...

krastanov 8y ago
There are workarounds for that: for instance, do not use such a poorly conditioned basis to describe the system. In particular, problems in physics that appear only in one particular basis are probably human-created notation issues, not something fundamental, as physics should be basis independent.

j7ake 8y ago

Could you give examples on how the incompleteness theorem explains physical phenomena? I would be curious.

krastanov 8y ago
I would suggest Aaronson's "NP-complete problems and physical reality" for this type of thinking (public PDF on his academic page). It is short and has a ton of examples. I really like the style, but it is not a common view among working physicists (yet? It is just not particularly practical for the moment).

krastanov 8y ago

I am a physics in academia and no, most physicists do not think that (especially given that most physicists are not quantum foundations physicists, and even then). It is an interesting question, and if I am forced to guess on its answer I would even agree with you, but good science would be to not speculate the way you imply.