Scientists know that a crucial test of whether you've understood a phenomenon is whether your understanding helps you accurately predict new information. (Some people argue that refining our predictions about the world is in fact all science actually does, but that's a topic for another day.) So it occurred to me that a good test of whether you've understood a postmodernist text -- as opposed to merely thinking you've understood it -- might be whether your alleged understanding of a string of pomo text helps you predict the next word in that string.
That's where information theory enters the picture. The information-theoretic definition of entropy is a measure of the uncertainty associated with a random variable, or how reliably you can predict its value based on the information you already know. In 1950, the father of information theory Claude Shannon measured the entropy rate of English-language texts by how predictable each successive letter was, based on the letters preceding it. The less predictable each letter is, the higher the entropy rate of the entire sequence of letters. As you might guess, English has a lot of unpredictability (if I say "This letter is an e, what comes next?" it's hard to guess with much confidence) but also some predictability (If I say "This letter is a q, what comes next?" you can probably make a pretty confident guess).
Measuring a text's entropy rate at the letter-level the way Shannon did probably wouldn't tell you much about whether it contains any coherent ideas. But what about entropy at the word-level? The unpredictability of a word based on the preceding words is a measure of the information content of a text and also of its meaning. Too predictable (entropy too low) and you've essentially got repeated mantras; too unpredictable (entropy too high) and the words have literally no relation to each other. Somewhere in between those two extremes is a range of entropy rates in which meaningful fields fall, and I'd be willing to bet that pomo would be a high-entropy outlier.
Let's return to the quote from Deleuze I used in my previous post:
“In the first place, singularities-events correspond to heterogeneous series which are organized into a system which is neither stable nor unstable, but rather ‘metastable,’ endowed with a potential energy wherein the differences between series are distributed ... In the second place, singularities possess a process of auto-unification, always mobile and displaced to the extent that a paradoxical element traverses the series and makes them resonate, enveloping the corresponding singular points in a single aleatory point and all the emissions, all dice throws, in a single cast.”
This text obeys the rules of the English language, but so does the sentence "Colorless green ideas sleep furiously," linguist Noam Chomsky's quintessential example of a grammatically correct but meaningless statement. In meaningful writing, there is more logic to the placement of words than just the logic of grammar, and that's the difference which I think an entropy rate calculation would capture. So when Deleuze talks about singularities that "possess a process" and of "differences" being "distributed" in an "energy," those are arrangements of words which you would not normally see in coherent English writing. Phrases like these are a large part of what makes pomo writing incoherent, and I suspect they would also make its entropy rate very high relative to other expository writing.
Finally, before I stop picking on the poor postmodernists, I want to mention a great, intuitive test proposed by Tony Lloyd in the comment thread of the previous post. Pick a statement in a pomo text and ask an expert, "What evidence could conceivably falsify this claim (or at least cast doubt on its veracity)?" If no evidence which could ever be obtained, even in principle, has any bearing on the claim's veracity, then the claim is consistent with literally all conceivable states of the world and therefore meaningless. So, Deleuze: How would we know if singularities do NOT possess a process of auto-unification?
The vagueness of pomo writing also makes it very difficult to falsify (conveniently, some might add). What conceivable evidence could falsify Deleuze's description of a system being "neither stable nor unstable"? It’s the same trick that astrologers, and other people who make pseudoscientific or mystical predictions, use to inoculate themselves from disproof. If your horoscope predicts that you are "extroverted but can also be withdrawn," or that you will experience "financial success but watch out for setbacks," it will never be wrong. But that doesn’t make it right.