11–15 of 15 posts
a tldr would be welcome
c+p of 252-253: "The world of physics is then," as Planck says, "a deliberate hypothesis put forth by a finite mind in an attempt to reduce the facts of observation to a system based on certain physical principles such that known phenomena are necessary consequences of the system." The basic principles are chosen on experimental grounds. Whether they are true or false in the absolute sense is not a pertinent question…
Earlier quoted context omitted.
I only skimmed the article but I didn't see the word "coordinate" mentioned. When you say "coordinate-free" do you mean "independent of any fixed frame of reference"? Because AIUI coordinate-free actually means something else, it's really just a mathematical detail: the choice to work with vectors as first-class objects rather than arrays of coordinates. It's a question of elegance rather that meaning. Given the date…
> When you say "coordinate-free" do you mean "independent of any fixed frame of reference"? Yes. Einstein's field equation can be derived using differential geometry, e.g. a coordinate-free approach. Prof. Smith discusses the evolution from egocentric (early Greek) to absolute fixed-frame (Newtonian) to coordinate-free (relativistic).
Earlier quoted context omitted.
> When you say "coordinate-free" do you mean "independent of any fixed frame of reference"? Yes. Einstein's field equation can be derived using differential geometry, e.g. a coordinate-free approach. Prof. Smith discusses the evolution from egocentric (early Greek) to absolute fixed-frame (Newtonian) to coordinate-free (relativistic).
As thanatropism said, "coordinate-free" is not synonymous with (Einsteinian) relativity. It's a general mathematical approach, and it doesn't have any philosophical consequences that I'm aware of. Just because spacetime is a curved manifold doesn't mean it can't be dealt with using coordinates in a higher space in which it is embedded.
Earlier quoted context omitted.
As thanatropism said, "coordinate-free" is not synonymous with (Einsteinian) relativity. It's a general mathematical approach, and it doesn't have any philosophical consequences that I'm aware of. Just because spacetime is a curved manifold doesn't mean it can't be dealt with using coordinates in a higher space in which it is embedded.
Sometimes, symmetry reductions become easier using a coordinate-free approach. This means that you could better determine invariances in the system without having a bias towards a particular coordinate system. Philosophically, finding commonality in systems is powerful and any bias (coordinates) distorts those commonalities making them harder to perceive. From the article, I inferred that finding coordinate-free appr…
There's always, in discourse, an origin--a speaker. We can't escape that (see e.g. the linguistic notion of deixis) I think the article risked patronizing the non-hard sciences by assuming that they couldn't see that, being somehow blind to objectivity. Pretty dangerous territory.
Earlier quoted context omitted.
Sometimes, symmetry reductions become easier using a coordinate-free approach. This means that you could better determine invariances in the system without having a bias towards a particular coordinate system. Philosophically, finding commonality in systems is powerful and any bias (coordinates) distorts those commonalities making them harder to perceive. From the article, I inferred that finding coordinate-free appr…
I'm not a mathematician or physicist, but (after a bit of googling) I do find some material that advances coordinate-free approaches as a kind of ethical discipline. Relations, understood as ordered pairs, for example, don't have a "natural order", we should mentally maintain the symmetry and absence of priority between statements like "the cat sat on the mat" and "the mat was sat on by the cat". There's always, in d…
For example, statistical causal models are widely used in the social sciences. After searching within the field, I looked for a problem associated with explanation ambiguity due to how the models were framed (or could be equivalently framed leading to alternate explanations) and found this paper:
MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L. R. (1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114(1), 185-199. doi:10.1037/0033-2909.114.1.185
I'm not sure if they could extend their approach using manifold theory and an equivalence class for the set of models, but I wouldn't be surprised if someone did something similar. It could then be an example of a coordinate-free approach to data analysis in psychology.