A Theorist’s Apology
August 29, 2014 26 Comments
Almost four months have snuck by in silence, a drastic change from the weekly updates earlier in the year. However, dear reader, I have not abandoned TheEGG; I have just fallen off the metaphorical horse and it has taken some time to get back on my feet. While I was in the mud, I thought about what it is that I do and how to label it. I decided the best label is “theorist”, not a critical theorist, nor theoretical cognitive scientist, nor theoretical biologist, not even a theoretical computer scientist. Just a theorist. No domain necessary.
The problem with a non-standard label is that it requires justification, hence this post. I want to use the next two thousand words to return to writing and help unify my vision for TheEGG. In the process, I will comment on the relevance of philosophy to science, and the theorist’s integration of scientific domains with mathematics and the philosophy of science. The post will be a bit more personal and ramble more than usual, and I am sorry for that. I need this moment to recall how to ride the blogging horse.
In his Apology, Plato’s Socrates compares himself to a gadfly biting at the lazy horse that is Athens and agitating the polis toward questioning the soundness of their understanding of Virtue, Knowledge, and the Good. Although most of the Socratic dialogues end at an impasse where neither Socrates nor his interlocutor arrive at an answer to the question of discourse, the discussion is not in vain. At the very least the activity exposes to the interlocutor the limits of their understanding. More importantly, the act of discussion — even when inconclusive — helps us learn more about the question. We don’t always need an affirmative answer to discover something, it is possible to learn from failure. The stated and ideal goal of these dialectics is, of course, Truth, but the willingness to discuss and frequent lack of decisive conclusion (as well as Plato’s literary qualities) remind us of the importance of perspective. Finally, through dialogue Socrates not only interprets the world in various ways, he acts to change it by engaging directly with the polis. It is hard for me to understand how Marx could have arrived at his 11th thesis, given that one of the founders of western philosophy serves as such a tempting counter-example.
A theorist is the gadfly of science. A theorist, in the sense I am trying to justify here, aims to engage with large swaths of science, uncover their assumptions, limits of understanding, and encourage the sharing of theoretical tools between different domains of inquiry. In some ways, this is similar to the goals of a philosopher of science and probably why posts on the philosophy of science appear so often on TheEGG. There is a distinction, though, in that a theorist is less concerned with describing (and definitely not prescribing) how science progresses or what broad methods it uses, than engaging directly with scientists on technical matters in venues and a language familiar to them. Maybe a theorist is part applied philosopher of science and part applied mathematician with a short attention span; the distinctions can get blurry sometimes.
Of course, no one is without philosophical baggage, and a theorist is no different. In this case, a certain neo-Kantian view of science is useful for justifying why the theorists expects certain models to be applicable in different domains. Everything, including “facts” and “observations”, is theory laden (in the Popper sense of the word), and these theories are shaped not only by the domain that they seek to describe, but also by our cognitive milieu. Thus, I expect to see similar models appear in different domains not (just) because the domains share something in common, but because there are limits and regularities in how we think about and describe things. We are all relying on models, but for many these are vague and intuitive mental models. Although our natural aversion to cognitive dissonance encourages us to prefer holding onto logically compatible models, sometimes paradox is hard to spot. Extracting, expliciting, and explicating these mental models allows us to bear the power of logical analysis and mathematics on our search for paradox and to clarify our underlying assumptions.
This elucidation of assumptions and search for contradiction might seem derivative-of and secondary-to the building of new models and conducting of experiments. At times, it can even seem pedantic and destructive. Although I sometimes embrace the label of professional troll (a modern variant on the gadfly, and maybe a more fitting title for Socrates given the descriptions of his appearance), I think these common prejudices are misplaced. The most striking advances in science, and Thought more generally, have come from identifying hidden and implicit assumptions. Assumptions that when questioned transformed not only our theories but the very nature of the relevant domain’s critical discourse. For me, the most salient examples are non-Euclidian geometry, evolution, Cantor’s theory of the infinite, special relativity, incompleteness and computability, and foundations of quantum mechanics.
The expliciting and formalization of mental models helps us to communicate better. Science has never been, and is most definitely not today, an isolationist, individual endeavour; it is a social process and demands scientists to be able to share their ideas with their peers. In such communicative settings, Zipf pointed out that ambiguity arises from the conflict in energy investment between the speaker and listener (note that there are some important assumptions buried here, too). The speaker wishes for a totally ambiguity — one sound to mean everything — and leave the difficulty of disambiguation for the listener. The listener, on the other hand, wishes for a totally unambiguous language, so that the speaker is left with the difficulty of words. In this regard, theorists are a listener’s friend, a theorist helps disambiguate the meaning of our private mental models. It also means that a theorist has to communicate in ways that bridge domains while maintaining mutual intelligibility with as many thinkers involved.
One of the best parts of mathematics, or — to avoid the “is math a language?” discussion — the mathematicians’ approach to discourse, is the clarity with which it recreates the ideas of your mind in the minds of others. Its effectiveness is so great that mathematicians can ponder together such highly complicated ideas that they start to feel the ideas as external to themselves. This is why a popular imagery among mathematicians is not that we are creating arbitrary mathematical models in our minds but discovering and exploring Platonic vistas. This high fidelity makes the formalization of mental models that theorists undertake an essential part of serving as connectors. By expressing ideas in a precise and highly communicable language, we can recruit more minds to work together instead of in isolated silos. However, mathematics can also be dangerous in its alienation. As Fawcett & Higginson (2012) pointed out, every equation in a biological paper drops your citations by a third. This means that a theorist must resist the urge to intimidate or self-gratify through math and instead stick to the simplest tools (and clearest accompanying prose) that will get the job done. Sometimes this might mean simply simplifying the work of others.
Again, this might seem secondary to the “real” work of experimentalists and domain experts creating mental models, and applied mathematicians solving formal models. But this view would miss half of mathematics, mathematics is not just about proving theorems but it is also about coming up with good definitions. Good definitions can often allow you to give intuitive and simple solutions to the hardest problems. The art of definitions is seldom taught, but I would argue that it is often the more creative of the two sides of mathematics. Coming up with good definitions and formalization requires having a foot in both the highly informal world of domain experts and the more formal world of applied mathematics. I think that a theorist is a definitions expert.
As the intuitive and philosophical roots of new fields ossify and a preferred terminology and formalization sets in, it becomes easier to forget the importance of translating between the intuitive and the formal. Theoretical computer science faces this problem. Computer science students — or maybe programmers more specifically — are among the few that are explicitly taught — instead of hoping that they pick it up on their own — how to translate the intuitive into the formal. After all, what is programming other than translating our intuitive goals and desires, or thoughts on procedure into the most formal and portable of languages? Yet the theoretical branch of the field has established its preferred interface of tools and terminology so well that many great theorist start to forget the central role of modeling the intuitive. In the early days of the cstheory StackExchange, we even had a discussion on if how-to-model-this questions should be allowed or not. Thankfully, Scott Aaronson reminded us of the importance of modeling:
A huge part of our job description as theoretical computer scientists is finding formal ways to model informally-specified notions! (What is it that Turing did when he defined Turing machines in the first place?) For that reason, I don’t think it’s possible to define “modeling questions” as outside the scope of TCS, without more-or-less eviscerating the subject.
Aaronson is a theoretical computer scientist that holds on to the philosophical roots of the field. He recognizes the importance of formalizing the intuitive not just for technological ends but also to gain insight into many of the timeless problems of philosophy. Although he works primarily at the intersection of computational complexity and quantum computing, he has also published insightful thoughts on economics, chemistry, classic problems of philosophy, ‘complexity’ or ‘interestingness’ of physical systems, and free will. He supports philosophy more than one expects now from personalities close to physics, but I don’t think he goes far enough to be my ideal theorist. The deal breaker for me is his endorsement of an exclusive focus on ‘ground truth’ and dismissal of hermeneutics and dialectic.
In some fields, most notably physics, the formalization of the domain’s mental models all share a single ontology and are expressed in a common language so well that it becomes easy to mistake the map for the territory. This lets us forget how our prescientific prejudices can blind us to our assumptions. In particular, it becomes easy to forget the problem of underdetermination and assume that your field’s ontology is unique and applicable far outside its original domain. The working ontology gets mistaken for the ‘ground truth’ and philosophically interesting positions are dismissed out-of-hand. This often stops a discourse before it starts, or devolves to two sides talking past each other. I like to call the condition: interdisciplinitis. When this is combined with direct condescension of the alternative views, it can become scientism.
I can see the roots of this in my own education; my technical background spanned numerous courses in computer science, physics, and math. During that time I was not taught or encouraged to dig into another thinker’s ontology, grant them as much of their system as possible simply for the sake of argument, and then critique from within their framework — on common ground. Even during the brief allusions to formalism in mathematics, we never went as far as working in obviously arbitrary or mutually inconsistent axiomatic systems. The closest I came to that was when I played around with building my own axiomatization of set theory, but even then — in my arrogant naivety — I thought I was searching for a Platonic ground truth, and that somehow I would do better in that quest than Frege, Russell-Whitehead, von Neumann–Bernays–Gödel, or Zermelo–Fraenkel. To some extent an education in the hard sciences felt like being initiated into a sacred cult with privileged access to the Ground Truth, and it felt great; I felt that I could proclaim, in agreement with Sheldon Cooper: “I’m a physicist. I have a working knowledge of the entire universe and everything it contains”.
Only in my philosophy electives, was I forced to assess the strength of people’s arguments from within their own frameworks. Even when I strongly disagreed with the basic premises of their ontology (as I often did in the case of philosophy of mind, for example), it was often enlightening to engage with their argument on common ground. I could learn some subtle aspects of the question under discussion by examining it from these different perspectives. Some of the lessons could then be reapplied through analogy from within frameworks that I was more comfortable with or believed to be closer to the ‘ground truth’. It was my only real experience at dialectic and the aporia in which it often ends.
I think that a theorist has to strive for a generous dialectic when entering a new domain. A theorist has to go through the hermeneutics of learning the standard approach and frameworks, relevant history, preferred terminology, and arbitrary quirks of domain specific discourse. A theorist should not try to overhaul these foundations completely, but just critique from common ground or introduce one new element within the framework. Only if there are multiple perspectives in play, should you use your intuition for ‘ground truth’ to pick the one that seems most likely. Even in these cases, though, it might be better to pick a framework that is not the most comfortable for you, since it will teach you more and have more space for your flavor of ideas. Of course, uncovering the foundation and structure of certain framework of thought, and exploring their history and interconnections with other frameworks is also rewarding outside the context of individual problems. It is beautiful to see the unity and contrast of different perspectives on the world.
Although this post has given you no reason for my extended absence, I hope it has let you see a bit more order in the mess of topics that TheEGG meanders through. I also promise to resume regular blogging, and assure you that I will try my best to not indulge as much in the naval-gazing that saturated this article. However, concerns over length have cut me a bit short, so I will still have to save explicing the obvious allusion to G.H. Hardy for next time.