You may be correct, but with his reputation amongst other mathematicians one wonders why he would be worried by that. Gauss was actually secretive in many ways.

It's actually an interesting read about Kant and Gauss - but way off this thread or even this forum. I can give links but it's more philosophy than science. For example the great Poincare had different views again - he believe it or not was more along the lines of Wittgenstein - ie its just convention - amazing

As a scientist, I have learned to indicate the source when quoting some text. In case you have problems with the quote’s content, please mention your arguments.

Its not that - its just we prefer reputable textbooks, peer reviewed journals etc. Popularisations, even written by highly reputable scientists, can be rather variable and the mentors, correctly IMHO, keep an eye on such to see if they meet usual science standards. I note you have a PhD, and would undoubtedly have had papers passed to you for peer review. I think the criteria is would you accept it as a reputable scientific source. If yes - then its possibly OK - but we may not always agree with you. BTW since I became a mentor I can assure you of something I didn't know before - before such decisions are made, to for example delete a post as its not from a reputable source, just like peer review, significant discussion goes into it - its not taken lightly.

The issue with your quote is 'no good answers to these questions'. That may be true (I don't agree but that means precisely diddly squat scientifically), or not, depending on what you think a good answer is. Is that science or is it philosophy? Already this thread has degenerated into things rather philosophical instead of scientific.

Well, as usual great mathematicians are often not very good physicists; Poincare is among them. Although he for sure knew everything about what we call special-relativstic spacetime concerning the math, even more than Einstein at the time, he didn't draw the logical conclusions from a physicist's point of view. This was done by Einstein, who appreciated the formal math only 10 years later after struggling for almost the same amount of time with general relativity. I guess it took him so long, because of his aversion against formal mathematics. A theoretical physicist must keep a good balance between mathematical formalism and physical intuition.

Another example is von Neumann, who was for sure superior in the math of QT, bringing the non-relativistic theory quickly in a rigorous mathematical form, including the comlicated eigenvalue problem for unbound operators, but he did more harm than good concerning the physical interpretation, inventing the infamous Princeton Interpretation.

Then there is also Weyl, who better than nearly all physicists of his time new the use of group theory and their representations for mathematical physics, and he also wrote a brillant textbook on GR early on (Raum, Zeit, Materie; I think the 1st edition was already in 1918, i.e., very quick after Einstein's and Hilbert's final breakthrough in formulating GR), but his intuition totally failed him concerning his unfortunate try to combine GR and electromagnetism by geometrizing electromagnetism by gauging the scale invariance of the free gravitational field, as we would call it. Ironically this theory, which is physically "not even wrong" (as Pauli acidly put it, and Einstein with one glance disproved it by the simple argument that obviously the length of a yardstick doesn't depend on its electromagnetic history, which is very fortunate for our everyday use of them), gave the name "gauge theory" to (Q)FTs with a local symmetry group.

Yes, great Polymaths like Poincare and Von-Neumann are really interesting when looked at from the vantage of the specialty they are venturing into. Maybe it's the fact they are Polymaths and try to take a view wider than they really should. Poincare was like that - he also wrote widely on the philosophy of science, but was also a practical and professionally qualified mining engineer of some note. These guys are simply enigmas. But at least they cant be accused of, in writing about the Philosophy Of Science, of not knowing what they were writing about - its just they reached strange views. Wittgenstein was also like that - before being a philosopher he was an aeronautical scientist of some note. As a scientist you would expect him to side with Turing - but he didn't. Even Russell found him an enigma - but later came to think he was correct. It goes without saying I think his and Poincare's views utter balderdash - but such are not what we worry about here.

They believed geometry for example had no objective reality - it was simply a convention we have - just a construct we adhere to. Turing countered, since it is used in deigning bridges etc it must have some kind of objective truth or bridges could fall down etc. Wittgenstein, and I presume Poincare, simply said - so what. If they fall down, they fall down and we adjust our conventions.

Its just Pauli's well known acid tongue. He even said to Einstein - you know what Prof Einstein says isn't totally silly or something like that. He did similar put-downs of many great scientists eg Landau, who while one of my heroes basically treated everyone else like a fool. He was well-known to be utterly merciless with colleagues that he considered to be lesser intellects than himself. The only person, who supposedly matched him in arrogance was Wolfgang Pauli. After explaining his work to a skeptical Pauli, he angrily asked whether Pauli thought that his ideas were nonsense. ‘Not at all, not at all,’ came the reply. ‘Your ideas are so confused I cannot tell whether they are nonsense or not’.

I think Landau would have greatly benefited from meeting Feynman - but that never happened. Feynman, like Pauli would have put him in his place. Feynman did meet Pauli, but as far as I know, wisely IMHO, kept his put-downs in check. Feynman was known to mostly be pretty tolerant, argumentative yes - telling greats like Bohr etc you are crazy and what not, but I have heard of only a few occasions where he was into the actual put-down. He hated arrogance of any type - it is said his mask was that of a kid from the boondocks who saw through the ways of city slickers. Pauli or Landau in put-down mode would have really made him mad.

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Kaluza-Klein models go the other way; they reinterpret forces (electromagnetism, in the original model) as being due to geometry. So maybe even if geometry is not completely conventional, we may not be able to empirically distinguish geometrical explanations from other types of explanations. So our observations may not uniquely determine the geometry

That's true. But a conversationalist would counter something, gravitions maybe, simply makes flat space-time act as if its curved - it isn't really - its flat. I asked Steve Carlip about this and he said there is no way to tell the difference. Its just the way it is. Its simply convention based on simplicity that we choose curved space-time. But an actual quantum theory of gravity below the Plank scale may change that - who knows.

The same with LET and SR. Both are equally valid scientifically - we just choose SR because its simpler, more beautiful and elegant, generalizes more easily to QFT - all sorts of reasons. But LET may be true. However IMHO you would need rocks in your head to choose it - all our current knowledge supports SR over LET. I think it's rubbish, personally, to consider theories that are simply contrived for the purpose of demonstrating some philosophical position. As Einstein said - nature is subtle, but never malicious. Can I prove it - of course not.

I think, in this case both views are right but in different senses. Geometry, as a mathematical axiomatic system, is of course convention. You can invent any system of axioms you like to define a geometry. As long as you don't run into some contradictions, it's each a valid mathematical theory. As a description of physical observation it's subject to experimental/observational testing, and one has to verify how accurate the description coincides with observations, and there indeed Euclidean geometry has been found to be only a good approximation, neglecting gravity. Gravity is a very weak interaction, and thus the approximation in our everyday world is very good, because we are surrounded only by quite tiny amounts of matter (the Earth and even the Sun are pretty small masses, and it's hard to find the deviations from Euclidean geometries, like the classical tests of GR, i.e., perihelion shift of Mercury and the deflection of light by the Sun). In this sense, as a physical model of Nature geometry is not pure convention but an empirical finding.

The trouble is we have theories like LET that are experimentally indistinguishable from SR. Why would anyone but 'cranks' choose LET? Conventional scientists know it just fits better with our other knowledge like QFT. It isn't experiment that chose's it - it's some sense we have of right and wrong - maybe what Gell-Mann was getting at.

This is really my last comment. We are getting way off its purpose. Please can we simply stick to its purpose. Really - if we don't it will be shut down.