Even before relativity was discovered, Peirce was already proposing experiments to check if space was always necessarily flat, or had just evolved towards this generalised Euclidean geometry. — apokrisis

Do you remember the uproar when Rupert Sheldrake said in a TED talk that the speed of light may not be constant? Led to a 12-month-long Wikipedia editing war and the video of Sheldrake's lecture being removed from the TED website.

Do you remember the uproar when Rupert Sheldrake said in a TED talk that the speed of light may not be constant? Led to a 12-month-long Wikipedia editing war and the video of Sheldrake's lecture being removed from the TED website. — Wayfarer

I didn't pay the story any attention being too familiar with Sheldrake and his shenanigans. But a quick check shows he was talking about variation in efforts to measure the speed of light as those became more precise from the 1920s to the 1940s.

I'm not sure how - perhaps it was morphic resonant clairvoyance - but Peirce himself, as a world authority on precisely this issue, made the most cutting comment on that TEDx talk then.

The non-scientific mind has the most ridiculous ideas of the precision of laboratory work, and would be much surprised to learn that, excepting electrical measurements, the bulk of it does not exceed the precision of an upholsterer who comes to measure a window for a pair of curtains.
—Charles S. Peirce (1908)

Actually this article is a good general account of how Peirce viewed the whole speed of light physical constant issue himself as he worked with Rutherford to use the assumption of light speed constancy to ground an international definition of a standard metre of length. And how that then inspired Michelson and Morley in their interferometer measurements that demonstrated a constancy that meant there was no dragging ether. Which in turn gives us Einstein and relativity, so building in that constancy as a brute fact ... until someone can step outside both the Newtonian and relativistic framework of cosmology to see how that constant got baked into the observable boundary conditions of the Big Bang.

So this is what a scientist might mean by an evolution of c as a universal constant. First, it is acknowledged that constancy is an axiomatic assumption of the theory being conjectured.

Peirce’s proposal was that “the standard length may be compared with that of a wave of light identified by a line in the solar spectrum.”

The proposal was not without problems. It involved “the assumption that the wave-lengths of light are of a constant value,” Peirce wrote in 1879.

That was shortly before the Michelson-Morley experiments, and he was worried about possible ether effects: “[T]here may be a variation in wavelengths if the ether of space, through which the solar system is travelling, has different degrees of density.”

Astutely he added, “As yet we are not informed of such variation.”

And likewise, Peirce made the crucial epistemic point that our uncertainty can only be constrained by acts of measurement. The opposite attitude of course is taken by charlatans like Sheldrake who find their "smoking gun" in scientific failures to completely exclude theoretical claims like morphic resonance, or as here, variable c.

He realized that there is no such thing as absolute precision. “Dealing as they do with matters of measurement, [physicists] hardly conceive it possible that the absolute truth should ever be reached, and therefore instead of asking whether a proposition is true or false, they ask how great its error is.”

And then, as I say, with the interferometer, science could make measurements sufficiently precise to be justified in excluding the possibility of a dragging ether as the material medium conducting lightwaves. The Newtonian expectation born of standard wave mechanics of a variable c was disproved by experiment! So the assumption of constancy could be taken to a new level of theory - a post-Newtonian one that did away the redundant materialism.

To now show that c ain't a constant demands someone coming along with a post-relativistic theory that posits some new kind of measurement - one that produces observable change as some condition or other is changed. That would be science doing what it does. Provide measurable counterfactuals that will - within acceptable error - give a thumbs up or thumbs down.

And that is the kind of interesting challenge that Sheldrake failed to supply. As usual.

The Physics Today article is well worth the read for its biography of Peirce as well as his pragmatic philosophy.

https://physicstoday.scitation.org/doi/full/10.1063/1.3273015

thanks! Great read, that article.