Physics as a Way of Thinking (1936) [pdf] | Hacker News Reader

Physics as a Way of Thinking (1936) [pdf]

kb.osu.edu

181 points7alman12 comments

Professor Smith was, at the time of the publication of this essay (in the Ohio State University's law journal), midway through a 20-year span as chairman of the Ohio State physics department.

He basically works his way through history to demonstrate the development of the modern experimental method and extrapolates that society would be best served by extending the scientific method to many more aspects of society (social and cultural issues, etc).

Prof. Smith describes how social sciences could benefit from the modern, coordinate-free approach in physics. He also wishes for a tighter coupling in social sciences as we've seen historically with physics (theory) and engineering (practice).

Interesting article.

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 of this article, the history of the Technocracy movement may be relevant to those who find these ideas appealing.

> 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.

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 approaches in social sciences could be fruitful.

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 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.

The focus is on the subtle impact of using some framework for analysis rather than the gross impact of individual bias (obviously that's an issue every scientist should be and probably is aware of).

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.

Nope, not that.

https://en.wikipedia.org/wiki/Manifold

The mature formulation of classical (pre-relativistic) physics circa Hamilton and Poincaré was already coordinate-free in this sense.

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. Their consequences must agree with nature. They are working hypotheses which are to be discarded whenever they cease to be effective or helpful.

Progress means bringing new sets of observations with the system in a way to give a complete mathematical description of physical phenomena in terms of the fewest principles or entities, that is to find in a variety of physical phenomena essential relations from which future phenomena can be predicted.

Physics is thus a result of our quest for order and harmony among physical phenomena. It is man's best attempt to think vigorously whatever permits of vigorous thinking. It is not fixed but is subject to change and evolution. Whatever comes out must go back to enrich the soil from which it came

I think it's worth the full read, 20 pages of pretty good physics history

Thank you.

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