Frustrated by how physics is generally explained/taught

[burakumin]

Structures are in terms of sets and numbers with things synthesized from those quantities.

So what? Sure, if we're speaking about sets as defined by the usual set theory (ZFC) almost all usual mathematical objects, including numbers, can be described as sets. So your statement is trivially true.

Forget all the high level stuff for the moment and get this stuff sorted first.

Who decided that this stuff was higher level than set theory, number theory or real/complex analysis? You did?

Don't bother about buzz-words at the moment - use the language in mathematics as it exists and allow us to combine it so that we get an idea of what you are trying to say so that we can differentiate it from what already exists and then comment on the difference.

Buzz-words... mathematics as it exists... incredible ! If we take for example measure theory, its started in the late 19th century. It is a well established domain of mathematics and the foundation of the modern definition of integration.

In physics things are organized with continuity and geometry because that is how humans sense this information in the real world.

Well... affine space (that belongs to "high level stuff" I presume) is nothing more than the formal concept for the most usual geometric spaces ones considers when she informally speak about "line", "plane" or "3D space". You want geometry and continuity? Fine, read the definition of affine spaces. It's a good place to start.

The states will always be the same regardless of the approach since they map to exactly the same things - but the organization will be different and from what you are saying the thing you disagree with is how the information is organized and yet you haven't addressed these questions at all in any significant capacity.

Indeed it appears I haven't addressed these questions in a language you, Chiro, seem to understand, I grant you that. Let me make a last attempt: the language I'm expecting is precisely this kind of supposedly "high level buzz-words". Now I would suggest you to update your knowledge in mathematics (I told you: I'm not a teacher) rather than insinuating again and again I don't know what I'm talking about. But I have an idea that you won't be very receptive to such an advice.

That book ("Geometry of Physics") not an introduction to physics, it's an introduction to using algebraic geometry in physics.

I keep the reference. Thanks again.

 

[George Jones]

To take a very simple example, I don't like the identification of the usual physical space with $\mathbb{R}^3$. It should simply be described as a set of points $\mathcal{A}$ ( = positions = places without spatial extensions). Assigning coordinates to positions is a pure computational issue. Now I can try to think about a structure on my set of points $\mathcal{A}$. As the notion of distance between positions seems to make sense I suppose there exist a distance function $d : \mathcal{A} \times \mathcal{A} \rightarrow \mathbb{R}^+$ with the usual axioms. There is obviously no priviledged point in $\mathcal{A}$, so I should not be able to speak about any center or origin. But it seems I can define things like lines and angles. So there must be a structure that can encode these notions

An affine space, with an inner product defined on the associated vector space?

 

[Dale]

Closed for moderation

Edit: a recent slightly heated exchange has been removed and the thread is reopened.