General relativity, quantum computing, some parts of thermodynamics/information theory/statistical physics, some parts of quantum field theory, some parts of condensed matter physics are all things that started as purely mathematical statements. I am not trying to diminish the monumental importance of empirical measurements, but please do not diminish the importance of logical consistency and mathematical constraints. We can say a lot about our universe with great certainty even though in same cases making direct measurements is orders of magnitude beyond our technology.
GR was amazing, but it wasn’t well known and accepted until the first measurements confirmed it. Quantum Computing is still very much up in the air, but it’s also weird to bring it up in this context, because QM is one of the most tested theories of all time. QED In particular is tested to the most decimal places of any prediction, ever. It’s also weird to act as though GR and QM started out in a vacuum, instead of what they really were, which was based on centuries of math, theory, and experiment.
Edit: Unrelated, but I see you’re a fellow Greg Egan fan, good to meet you! Planck Dive has to be one of my all time favorites.
We are talking past each other: It is a bit contradictory to say "quantum computing is up in the air" and "QM is one of the most tested theories" as an argument against what I am saying. Yes, both are statements are true, but they are in no ways counterpoints to what I am saying, if anything they support it. QM is a well established and empirically tested theory. Quantum Computing is a purely mathematical construct that emerged from that well established theory without any experimental evidence for it, and only now, 30 years later, we are starting to have a chance to employ this purely mathematical construct in practice.
Same with GR: it was a purely mathematical construct for a while until we could test it, but there were too many theory clues that it must be right.
And this is not selection/survival bias: it is extremely rare for humanity to find a robust mathematical construct for which we can have a high degree of certainty that it describes the universe well. In the few cases where we have had that certainty, due to mathematical proofs in seemingly disjoint fields, we ended up being right.
To push it to stuff like super strings and quantum gravity: few respected scientists would claim that their pet mathematical construct is correct, but many of them will say "the vague commonalities between all these diverse and seemingly unrelated mathematical constructs definitely point to an underlying fundamental construct".
Everything you list was formulated in response to measurements that didn't fit with existing theory, with the possible exception of quantum computing. I'm not diminishing the value of theory, merely correcting what I think was an overstatement of its importance on your part.
