Also see Relationship between Mathematics and Physics - https://en.wikipedia.org/wiki/Relationship_between_mathemati...

There's a quote Atiyah has about spin geometry which he heard from his advisor Hodge, who had an office next to Dirac at Cambridge.

Only two people understand spinors: God, and Dirac. And Dirac's dead.

Yes, vaguely related. Dirac is not wondering why measurement itself works, but why mathematical reasoning applies so effectively to the measurement results.

I think it's valid to be surprised that all observations of a physical phenomena up until this point have obeyed a beautiful and (relatively) simple mathematical relationship, without even thinking about predicting the future.

Measurement works because universe moves in a simple way. As Hume indicates, you need very complex motion for irregularity, maybe even sentient, but sentient universe is fairy tale.

Math, Science, ..., certainly not God

Pretty much everyone worships some sort of God. (The exceptions are non-self-aware people living moment-to-moment.)

What people argue about is the degree of personality and autonomy that God possesses.

There is no logical reason why the second method should be possible at all,

One reason I can think of is if we consider that some regularity in the physical behavior is required for consciousness to evolve and so consciousness only forms in such worlds.

Later down in the essay, Dirac himself answers this;

With this kind of cosmological picture one is led to suppose that there was a beginning of time, and that it is meaningless to inquire into what happened before then. One can get a rough idea of the geometrical relationships this involves by imagining the present to be the surface of a sphere, going into the past to be going in towards the centre of the sphere, and going into the future to be going outwards. There is then no limit to how far one may go into the future, but there is a limit to how far one can go into the past, corresponding to when one has reached the centre of the sphere. The beginning of time provides a natural origin from which to measure the time of any event. The result is usually called the epoch of that event. Thus the present epoch is 2 x 109 years [actually 2x10^9].

One further point in connection with the new cosmology is worthy of note. At the beginning of time the laws of Nature were probably very different from what they are now. Thus we should consider the laws of Nature as continually changing with the epoch, instead of as holding uniformly throughout space-time. This idea was first put forward by Milne, who worked it out on the assumptions that the universe at a given epoch is roughly everywhere uniform and spherically symmetrical. I find these assumptions not very satisfying, because the local departures from uniformity are so great and are of such essential importance for our world of life that it seems unlikely there should be a principle of uniformity overlying them. Further, as we already have the laws of Nature depending on the epoch, we should expect them also to depend on position in space, in order to preserve the beautiful idea of the theory of relativity there is fundamental similarity between space and time. This goes more drastically against Milne's assumptions than a mere lack of uniformity in the distribution of matter.

Show respect to Mathematicians/Physicists/etc. many of whom had studied Philosophy and i dare say had a better understanding/insight of it than mere academic Philosophers. Why? Because they don't go off into la-la land but try very hard to have both observed evidence and a mathematical model of it match cleanly via a Theory.

For your edification, read first "Meditations on First Philosophy by Rene Descartes" followed by "Physics and Philosophy by Werner Heisenberg".

unwritten rules

  Kaffee: Corporal, would you turn to the page in this book that says where the mess hall is, please?
  Barnes: Lieutenant Kaffee, that’s not in the book, sir.
  Kaffee: You mean to say in all your time at Gitmo you’ve never had a meal?

If an article is a few years old then it could be out-of-date. But if an article is almost 100 years old then its classic.

I think this passage is more about the fact that mathematics is a form of symbolic computation people create and it is weirdly congruent to the physical measurements and models of reality. Not that mathematicians see certain models and objects used in physical models in a favorable way. What favor even means here?

It is quantifiable: several mathematical objects and categories people invented to do symbolic computation in letters and published papers are somehow very useful to model and understand data from physical measurements of reality.

I highly recommend reading the "Unreasonable effectiveness of mathematics" essay by Wigner:

https://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableE...

Dirac was talking about the fundamental laws. In favour of his point, and not known at the time he gave the talk, the standard model of particle physics is based on the symmetry groups U(1), SU(2), and SU(3), so Lie groups (which mathematicians find interesting) appear to have been chosen by nature.

Well there are counting arguments to say that a higher level intelligence that somehow achieves say, 100000× brain efficiency of humans, still can't do that much more work than humans, if humans found the "best abstraction". Think about computability for example - that means you could feasibly solve problem instances of n+20 relative to what a human can solve.

Of course, I think putting numbers to wishy washy meta-quantities like "how efficiently does a certain conceptual scheme help you" are super loaded and hard to properly talk about (incommensurability). I've been toying with trying to make a repository of all the possible "moves" one can make in this kind of abstract analysis - constrain the problem statement, argue something like "the system is what it does", dissolving, etc. but even that seems hard

Related;

From Heisenberg to Goedel via Chaitin - https://arxiv.org/abs/quant-ph/0402197

Right. Added the wikipedia link to Dirac's LNH above.

Also found this; The fundamental constants and their variation: observational status and theoretical motivations - https://arxiv.org/abs/hep-ph/0205340

The dominating idea in this application of mathematics to physics is that the equations representing the laws of motion should be of a simple form. The whole success of the scheme is due to the fact that equations of simple form do seem to work. The physicist is thus provided with a principle of simplicity, which he can use as an instrument of research.

https://arxiv.org/abs/math-ph/0009007

Occam's Razor as a Formal Basis for a Physical Theory

We introduce the principle of Occam's Razor in a form which can be used as a basis for economical formulations of physics. This allows us to explain the general structure of the Lagrangian for a composite physical system, as well as some other artificial postulates behind the variational formulations of physical laws. As an example, we derive Hamilton's principle of stationary action together with the Lagrangians for the cases of Newtonian mechanics, relativistic mechanics and a relativistic particle in an external gravitational field.

Quite independently of the Mathematics, Bohm's ideas of "Implicate and Explicate Order" are very interesting and comprehensible by the layman at a high-level - https://en.wikipedia.org/wiki/Implicate_and_explicate_order

In particular, students of Hindu Philosophical Schools will find lots of parallels here. Bohm was heavily influenced by Jiddu Krishnamurti which inspired his take on quantum theory.

Bohm also wrote a great book, "Quantum Theory" based on the Copenhagen Interpretation which contains separate parts on "Physical Formulation" and "Mathematical Formulation" of quantum theory.

Dirac comments that he thinks a potential path to the discovery of new physics is to start with a mathematical domain and work outwards from there, guided by mathematical beauty. This is what I took OP's comment to be about - of course setting aside questions on an LLM's ability to recognize beauty

There's this little pet project of mine, the Functional Universe [0]. It explores a direction suggested by Dirac: treating mathematical structure and transformation not merely as a language for describing physical reality, but as potentially constitutive of it. FU models physical reality in terms of functional state evolution, with an emphasis on composition, aggregation, and transitions. In that sense, I think there's an interesting point of contact with Dirac's emphasis on transformations: Dirac points toward transformations as fundamental mathematical structures from which physics might be derived; FU asks what happens if physical reality itself is formulated in terms of transitions and their composition.

[0] https://voxleone.github.io/FunctionalUniverse/