Axiomatic Realism III: The Secret of Light

Forthcoming in Ars Scientia journal

Links to all five parts of this piece — not all of which are out yet, but will be available at these links if not already ::: Part 1 ::: Part 2 ::: Part 3 ::: Part 4 ::: Part 5

As a reminder, I said this in earlier posts, where I was signposting the few weeks’ worth of material that are surfacing on these pages. Feedback, comments are extremely welcome!

…I want to briefly introduce the next few posts. Last autumn, after many months of stewing ideas and/or wildly procrastinating, I finally sat down to write a dirty first draft of a lengthy new article taking a critical look at the epistemological arc of the sciences (my original home territory) through the memoiristic lens of autotheory. It’s going to be included in the second issue of the wonderful Ars Scientia, a new journal of scientific arts, which takes as its second theme “axiomatics”. Since the article is a weird mix of history and philosophy of science, historical recollections, and post-disciplinary meaning-making, and also because it still needs a little something extra according to some critical feedback I received and agree with, I thought it might be a good place for us to start. It’s pretty long — first draft was over 10k words, and the journal editors originally asked for 3-5k — so I’ll be splitting it into 3 or 4 digests and saving a final one for some additional rumination and riffing.

I also wanted to include an excerpt of the great motivational text that the editors of Ars Scientia posted on their website, to give a sense of where my piece is coming from.

Ars Scientia Issue 2 on Axioms
“It had been tactless of me to prove something on the topic of man – mathematically!”
Stanislaw Lem, His Master’s Voice, 1968

Axioms are “self-evidently true without proof.” In axiomatic systems, truth is preserved throughout the system as statements derive directly from the axioms. While the axiomatic approach can seem like a top-down monolith, in 1931 Gödel famously challenged the claims of metaphysical access through axiomaticity by demonstrating that within any such system there are true statements that cannot be proved. In addition to Gödel’s challenge, the history of axiomatic thinking also presents a multitude of traditions, concepts and crises.

For instance, automated theorem proving is a field of mathematics which attempts to automatize mathematical proof-writing with computing. Confirming the validity of this method and achieving automatization beyond first-order logic has been greatly challenging, where-as the methods of writing proofs by hand or with computerized (but not automated) proof assistants do not face the same scrutiny of “viability.” How does this history of mathematics relate to other interests more broadly?

In the first issue of Ars Scientia, we took the lead from Goethe's Metamorphosis of Plants as a study in the systematization of the relation between observer and phenomena, a relation that makes up a blueprint of the simultaneity of aesthetic practice and scientific inquiry. In the upcoming second issue of Ars Scientia, we are interested in what happens when, as Thomas Moynihan writes, “this plenty [of the organic world] and progressivism becomes divorced, decoupled from, devoid of purpose? What happens when the artisan recedes from the picture—as the century following Goethe witnessed unfold?” (2021, Philosophical Life of Plants). We want to extend this conflict beyond the discipline of mathematics or the illustration of nature and towards synthetic practices between the artistic and the scientific.

Are our axioms so silent as they might appear? What is formalization, systematization when devoid of purpose? What does it mean to reintroduce such a purpose? What are the possible axiomatics that speak from below and beyond the mathematical impetus of abstract proof? Where is the hand? Can the silent speak for the quivering?

---

Axiomatic Realism III: The Secret of Light

“Information long ago broke through the truth barrier and moved into the hyperspace where things are neither true nor false, since everything in the realm of information depends on instantaneous credibility. Or, to put it more accurately, information is truer than true since it is true in real time — this is why it is fundamentally uncertain. Or again, to draw on Mandelbrot’s recent theory we can say that things in the information space or the historical space, like those in fractal space, are no longer one-, two- or three-dimensional: they float in some intermediate dimension. We no longer have any standards of truth or objectivity, but a scale of probability.”

J. Baudrillard (translated by Chris Turner), Information at the Meteorological Stage, in Screened Out, Verso Books, 2002.

Publish or Perish

After Pople’s epistemic bombshell, I carried on with the early stages of my research, which was mostly rooted in understanding the field that I was operating within — photophysics and spectroscopy of metal-organic complexes — despite having already made a start as an undergraduate (paper links 2003). Chemistry always seemed like such a messy enterprise, in both theory and practice, and I’m sure that is most students’ experience of school and undergraduate levels of the subject. In comparison, physics and mathematics seemed ordered, and elegant. It wasn't until the late stages of my undergraduate degree that the interconnections between seemingly disparate domains of the natural sciences became apparent — to me, at least — and the previously discussed realisation that a few quantum numbers could give rise to the seemingly arbitrary complexity of the elements, and in turn their combination into molecules, polymers, crystals, and yet more complex materials led me closer to the boundary between physics and chemistry as a place to look for ‘answers’. This interdisciplinary boundary was referred to as either chemical physics or physical chemistry depending upon which vantage point one was approaching the epistemic borderlands from.

Year after year, progressing through school education and the academy, the limits of knowledge and our models of scientific phenomena became ever clearer. Almost like clockwork — appropriately, since photophysics is necessarily rooted in the temporal — we would arrive in a ‘more advanced’ theoretical class than the prior year, to be met with the same message, which went something like this:

“So, the things we taught you last year, well, sorry, but those were naïve and reductive. Here's the way things really are.”

This continued until one was in charge of one’s own research program as a doctoral student, after which the refrain become more like:

“Actually, we don't know what the hell is going on here. Can you figure it out please?”

All of that serves to say that, all my ideals of objectivity and faith in scientific axiomaticity¹ in my formative years had completely washed away within a few months of doctoral research. I saw experiments which gave uncertain or contradictory results ignored as ‘bad’, whilst the ones which delivered outcomes which suited our hypotheses — the stories we tell ourselves out the way things really are — lionised, spotlighted, and elaborated upon. Researchers who could not achieve a set outcome, for example to synthesise a particular target molecule, or to crystallise a protein, often left the university without doctorates. The blame for an outcome that could not be achieved was seemingly the fault of the student, rather than shortcomings in the apparatus or approach, or simply that it was infeasible or impossible. What made this much worse, was the ‘publish or perish’ culture of UK STEM academe, already suffocating by the early 2000’s but so much worse now. No reputable² journal would publish a negative result — Popper must be turning in his grave at velocities approaching the speed of light — so there was no way of knowing if the improbable task a researcher was struggling to achieve had already been found to be a dead end by others. In STEM, failure has never been an option.