Linguistic Ambiguity and Paradox

Have twenty minutes? Read this essay by Margaret Wertheim; it's the most interesting this I've read in weeks. Don't have time? Stay up twenty minutes later or something. It's worth it.

Summary (for those who didn't read it)

Wertheim has extensive experience in both the sciences and in the arts and brings both fields to bear. She describes the Platonist assumptions that underlie much of modern physics: that physics is a way of objectively describing "the way things are". During the Scientific Revolution nature was thought of as a "book" written by God in the language of mathematics which we, by the discovery of scientific "laws", are able to know. Though the explicit linkage between physics and theology has since dried up, the metaphor of delving into the "mind of God" continues. Current tensions in physics like the wave-particle duality--the tendency of photons, electrons, etc. to behave like waves and particles simultaneously--or the seeming incompatibility between the branches of physics pertaining to very large scales (general relativity) and very small ones (quantum mechanics) are seen as thorns in the side of the quest for an all-encompassing "theory of everything", tantamount to Galileo's "cosmic book", and many religious physicists continue to see a strong linkage between their faith and their work.

Wertheim contrasts her experiences serving on two panels: one with a cosmologist who saw physics in this way, as "a progression towards an ever more accurate and encompassing Truth", and another with a Lewis Carroll scholar who viewed mathematics as playful storytelling and mythmaking with little connection to reality. She here highlights a divide in academics' thinking about mathematics: scientists tend to see the correspondence between equation and reality as so reliable that the mathematics is allowed to proceed ahead of experience and intuition as our tool for finding "the way things are", leading us to counterintuitive (and impossible-to-test) theories to make sense of the math like the many-worlds hypothesis. She says, "what is so epistemologically daring here is that the equations are taken to be the fundamental reality. The fact that the mathematics allows for gazillions of variations is seen to be evidence for gazillions of actual worlds." Meanwhile, humanities scholars see this thinking as naive and disconnected from what is truly "real".

Duck or rabbit?

She ties this in intriguingly with a book called Purity and Danger by Mary Douglas, which ends with some theory about language, noting that all languages parse the world into discrete categories. For example, we categorize animals between categories like "mammals", "reptiles", "birds", "arthropods", and so on. But then we run into animals that refuse to follow these categories, like the pangolin, echidna, or platypus. Or consider the above optical illusion: is it a duck or a rabbit? Our brains flip between categorizing the same image in two different ways, trying to resolve the ambiguity because it's easier to just pick one than not categorize the image at all.

Wertheim notes the parallels between these linguistic paradoxes and issues in physics like the wave-particle duality:

As Douglas sees it, cultures themselves can be categorised in terms of how well they deal with linguistic ambiguity. Some cultures accept the limits of their own language, and of language itself, by understanding that there will always be things that cannot be cleanly parsed. Others become obsessed with ever-finer levels of categorisation as they try to rid their system of every pangolin-like ‘duck-rabbit’ anomaly. For such societies, Douglas argues, a kind of neurosis ensues, as the project of categorisation takes ever more energy and mental effort. If we take this analysis seriously, then, in Douglas’ terms, might it be that particle-waves are our pangolins? Perhaps what we are encountering here is not so much the edge of reality, but the limits of the physicists’ category system.

She is suggesting another possible approach to paradoxes in physics: rather than attempting to resolve the apparent contradiction between quantum mechanics and relativity, or between light being a wave or a particle, Wertheim wonders if the categories dictated by the language of physics we have, combined with the rejection of contradiction as unacceptable in the "mind of God", might be leading us to ask the wrong questions. Perhaps by trying to cram photons into the wave-particle spectrum we are missing something. "To put this into Douglas’s terms, the powers that have been attributed to physicists’ structure of ideas have been overreaching. ‘Attempts to force experience into logical categories of non-contradiction’ have, she would say, inevitably failed. From the contemplation of wave-particle pangolins we have been led to the limits of the linguistic system of physicists."

Commentary

The comments on the Reddit thread by which I found this essay criticize it for being overly dismissive and pessimistic about scientific progress. I agree in that Wertheim doesn't really try to offer a constructive solution, but simply thinks scientific inquiry has reached a barrier: "Will we accept, at some point, that there are limits to the quantification project, just as there are to all taxonomic schemes?" What Wertheim misses is that this ambiguity is an artifact only of our language, not of our minds, which are not bound to the symbol-concept mapping of any one language or even, necessarily, by the need to fit everything into a single clear-cut category. If our current classification scheme is inadequate, we can find a better one. The conclusion I would tentatively draw from the wave-particle duality is not that it is an ambiguity impossible to resolve conclusively, but that our categories of "wave" and "particle" themselves may need to be rethought into something stranger. (I'll leave how to do this and keep the results meaningful and applicable to the physicists)

Of course, I can't help but try to relate this subject to theology. Like with physicists, theologians' thinking can easily become caught on simplistic dualities, categories, and spectra that don't fully describe the more complex "way things are". These things can be useful mental stepping stones for trying to wrap our brains around a complex subject (and there is no more complex subject than God), but allowing them to define theological reality to our thinking leads to dead ends, endless debates, and wondering why-can't-they-just-see-it-my-way. I'm sure you can provide your own examples of this, but a few that readily come to my mind would be Calvinism and Arminianism, asking whether salvation is by faith or by works (usually before affirming that it's by faith alone), and asking whether it's a sin to do ____. I call this allowing of one perspective to crowd out others that aren't necessarily incompatible "totalization".

Because theology is the study of an infinite, transcendent Subject, it will always be incomplete. I think this is why I find it so much more exciting than my field of undergraduate study, which being a manmade subject has relatively little in the way of unanswered, weighty questions besides ones that intersect with mathematics like whether P equals NP. This continual incompleteness means recognizing that no theory of atonement, of salvation, of Trinity, etc. can ever totally describe these weighty subjects or definitively box up our discussion of them (and that's a good thing!). Let that be a reminder to keep your mind open to truth and always learning.