The Dichotomy Dichotomy

Let me just say: it's probably no longer cool to call something a false dichotomy. People in section -- inspired perhaps by late greats of philosophy or by someone they heard say something smart in another section -- are really into replacing dichotomies with continua. Gender, sex, politics, truth, whatever. I can't claim to be innocent here. It's an easy point to make and sometimes appropriate. But I think we need to dig deeper into the general ontological problem posed by the "dichotomy-continuum dichotomy." [That phrasing gives you a big hint about where I'm headed with this post.] Here are some things about that:

The terms "dichotomy" and "continuum" do obtain quite clearly in different situations.

Consider the difference between the operation of a computer at micro and macro scales. Fundamentally, computers use zeros and ones to encode information; one can analytically divide the system into identical units in exactly one of two states. An emergent property of certain computers, the graphical user interface displays colors which it can select out of an open space with continua as axes. (Note: given a consideration of the interface as such, it's irrelevant that one could eventually quantize this color space--find two colors with no third color in between--since the computer can articulate the color space more finely than human vision can apprehend it.)

One can also find examples of this hierarchical relationship reversed--i.e., of the continual loosely underlying the dichotomous. A coin's position as it travels through Newtonian space moves along a straightforward continuum, but when it lands it displays either heads or tails. Or take a chemical reaction requiring a certain activation energy (a threshold) to proceed. Incrementally increasing energy available will change the behavior of individual molecules but not enable the reaction until it crosses the necessary threshold.

But sometimes a situation makes it hard to decide between categorizations.

In the case of sex, scientists have distinguished between body configurations resulting from XX and XY with a high degree of empirical success. Yes, everyone has estrogen and testosterone... but the distribution of these hormones is statistically bimodal, not linear or a bell curve, and the mode to which an individual corresponds can be predicted with high (but not perfect) accuracy from an examination of chromosomes. (Of course, the X and Y chromosomes also possess no essential nature, just a statistical differentiation, but operating in the present and on the timescale of relatively slow biological evolution, we can clearly distinguish them in nearly all instances.) (As far as I know. I'm not a scientist, so I'm open to being corrected.)

We can imagine all sorts of phenomena distributed in statistical distributions somewhere in between the perfect bimodality of the coin flip and the perfect linearity of (a slice of) a computer's color space. These differences can even occur within a conceptual domain, like the distribution of resources in different societies or of grades in a class.

Does this create a self-referential paradox?

No, thank god (Hofstadter?). We've broken down the meta-dichotomy between dichotomies and continua... in favor of what might be a meta-continuum. But this doesn't contradict. The original argument doesn't reject these concepts entirely, it just contextualizes them and makes them more meaningful. Given a potentially infinite sample space (remember, we're talking about the sample space of sample spaces), it makes sense to call the distribution of models from dichotomy to continuum continual:

(a) We can continually provide examples of arrangements anywhere between the two extremes.
(b) There's no way to link two types of arrangements and demonstrate an inequality between their infinite extensions (the way there is for, say, rational vs. whole numbers).
(c) Therefore each division of the continuum (no matter how thinly you want to slice) could be said to contain an equal infinity.
(d) Therefore... perfect continuum. QED. (But then again, I'm not a mathematician either, so I could well be wrong about this stuff, too.)

This doesn't necessarily mean that you couldn't, by strategically limiting the sample space, generate a useful distribution of distributions. I'll hint at what that would look like for psychology at the end of the post.

Why do I care?

Implications for the rhizome: (1) Never forget that "there are knots of arborescence in rhizomes, and rhizomatic offshoots in roots" (Deleuze and Guattari, ATP, 20). The pure rhizome, if it exists, lies at the end of a continuum of concepts (and a continuum of things). (2) Recognize that perhaps sometimes arborescent ontology works better than rhizomatics; make it rhizomatic not by forcing the real situation into a bad framework, but by putting the tracing on the map and by plugging the tree into other apparatuses. If it's true that models operate on a continua, any tree formation will inevitably be interacting with (more) rhizomatic assemblages that lie proximate to it. This implies a non-arborescent (though not necessarily completely rhizomatic) plane of consistency. It might imply a relativisation of the extent to which situations map onto dynamical systems.

Implications for psychology: we need to think more carefully (or I need to read more about) the interactions between root structures (Gestalt principles and decision trees) and probabilistic networks of influence. Abstractly, it seems that aspects of conscious experience will result from large-scale statistical patterns in the brain... but there are dichotomous (and trichotomous, etc.) phenomena produced at the level of consciousness which must result from neural activity crossing a certain type of threshold. For example, the "faces/vases" optical illusion causes the brain to shift back and forth, but doesn't allow you to see 75% face, 25% vase. You recognize a face or you don't. Face recognition generally "clicks" at some point, after which an entity goes from being a human in the abstract to a human you know, in turn brining to bear a cascade of new information from your memory. It seems like it might be possible to examine salient psychological phenomena to determine generally how dichotomous and how continuous they were... Although you probably could do in the abstract what I did in the previous section, limiting the sample spaces to variables psychologists agreed were important might provide some predictive results. For example, if the distribution of distributions is strongly bimodal, this would provide the basis for a useful classificatory scheme of psychological phenomena based on a split into those two types. Yet another thing I'm not qualified to do!

Implications for section: think before you say "the reading really dichotomized this thing, but actually it seems like more of a continuum." You might be obfuscating more than you reveal.