Good luck telling in advance which math is pointless guessing and which math is the groundwork for the next revolution in our understanding.

Which neither means that beautiful math is necessarily describing the world inaccurately.

Taken to the extreme, the best description of the world is a long list of all events and facts. No beauty in that. Now science tries to compress this list of events to a simple model that explains it best. Like in statistics, one should aim for the simplest model predicting most of the data.

I'd argue that if you think of science as an attempt to compress all the data in the world, then OP's statement is obvious, and at the same time there's good reason to value beautiful (i.e. short & simple) explanations higher provided they generalize well.

You say "best", except a long list of events and facts has no predictive power, no way to infer what the future will be, only describes what the present is. The whole point of a model is to be able to predict the future. So in that sense, a long list of all events and facts is the worst description.

Not sure why you’re being downvoted; what you’re saying is true. A model whose length is the same as the data it is describing has no predictive power. A perfect model what be the size of the minimum program that prints out all of the events in the universe (that is, the program whose size matches the Kolmogorov complexity of the universe).

> 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_...

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.

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

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.

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

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).

> Just because the math is pretty doesn't mean the universe actually works that way.

Interesting thought ... is mathematics really orthogonal to the universe or does it "result from" or fall out as a result of the universe within which it was described?

Getting philosophical, I know, but if you follow, then perhaps the degree to which you don't have to twist mathematics to describe the universe might suggest you are in fact on the right path....

Are we not looking at a mathematical result that constraints what the universe "can do"?

Agreed. Easy and intuitive as Euclidean geometry it is not right. It is not easy ask anyone doing proof in that paradigm.

Getting more mtr complicate not meaning they are right.

Reminds me of a haiku i wrote a long while ago:

—-

Movement and measure

How to discern life through time

Everything is change

—-

Time and the inherent math of the universe is amazing to think upon, especially when you look back upon the wisdom of ancient humans who were able to perceive cycles of the stars that were many thousands of years long whilst human conscious life is so fleetingly short.

Its interesting that we do not try to ask HOW civilizations past could have been aware of cycles that last for tens of thousands of years.

And now humans are so myopic on what is in front of them, we hardly look up.

> Its interesting that we do not try to ask HOW civilizations past could have been aware of cycles that last for tens of thousands of years.

That’s probably because they weren’t. What “cycles of the stars that were many thousands of years long“ were ancient peoples aware of?

Precession of the equinoxes? For Earth, this is circa 25,000 years, although I don't believe there's a reasonably accurate measurement of this value in Antiquity.

I'm not sure that meets the criteria for a "cycle of the stars" since it's a planetary change, but I guess for Hipparchus it probably did look like a celestial change. It definitely doesn't match the claim that "we do not try to ask HOW civilizations past could have been aware", though. We know exactly how Hipparchus recognized this. Nonetheless, this is a reasonable response to my question.

Noting a long-term cycle of equinox precession is impressive but also not terribly surprising. If you can note the change, you can reasonably assume it's cyclical (because the alternative is that it's going to suddenly stop moving at some point in the future).

The Mayan Long Count calendar? If I remember right, it's method of counting leap years is more accurate than the modern Gregorian calendar.

The Mayan calendrical system uses a "year" of 360 days without attempting to account for leap days. Essentially, the long count (the classic 13.0.5.7.6 style system) is a base-20 count of the number of days from the epoch, with one of the digits being base 18 instead. The other components are the 260-day year of 20 "months" of 13 days, the 365-day year of 18 months of 20 days (with 5 extracalendrical days), (and together these two things create a 52-year cycle that's the "Short Count" calendar), a week-ish system (of 9 days), a lunar cycle count, a correction to the lunar cycle because it's annoyingly 29.5 days long, and a 819-day cycle we don't understand yet.

Their calendrical system did not attempt to correct for leap years, but we do know that they knew the length of the year to roughly the same precision as the Gregorian approximation.

“The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. He to whom the emotion is a stranger, who can no longer pause to wonder and stand wrapped in awe, is as good as dead —his eyes are closed. The insight into the mystery of life, coupled though it be with fear, has also given rise to religion. To know what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty, which our dull faculties can comprehend only in their most primitive forms—this knowledge, this feeling is at the center of true religiousness.” -- Albert Einstein

I find it abhorrent that people cannot place into the same realm physics with 'poetic reflections'

Tiring is the limiting of mind and creativity such that one thinks that science and reflection are not, intrinsically, the same thing.

If they are the same thing, why prefer Einstein to Chopra? Why quote Einstein's fluff, rather than his science? Why shouldn't we give samstave a Nobel Prize for his poem?