The Oscillating Truth

If we were to graph statements (on the y axis) according to their truth value with true being 1, and false being zero, it might look something like this:

But what do we do with this statement: “Everything I say is a lie.” Plainly if this too is a lie, then the statement is true, but if it’s true, then not everything he says is a lie, which makes it false, but if it’s false, then it is, in fact, a lie, which makes it true… ad infinitum. How would that look?

It would oscillate back and forth, kind of like a sine wave, (though sine waves go from -1 to 1, rather than zero to 1.) So while there are statements that are definitely true, and others that are definitely false, there’s a third class that oscillate true/false over time.

Perhaps some of the confusion and conflict we encounter in our discourse is due to miscategorizing this third class as one of the other two. A simple example is the efficient market hypothesis:

The efficient market hypothesis (EMH), alternatively known as the efficient market theory, is a hypothesis that states that share prices reflect all information and consistent alpha generation is impossible.

According to the EMH, stocks always trade at their fair value on exchanges, making it impossible for investors to purchase undervalued stocks or sell stocks for inflated prices.1 Therefore, it should be impossible to outperform the overall market through expert stock selection or market timing, and the only way an investor can obtain higher returns is by purchasing riskier investments.

In other words, some people take it as true that no one can outperform the market over time except via extra risk (and luck that you don’t get wiped out.) Is the EMH actually true?

I would argue it falls into Class 3. That when almost everyone thinks he can beat the market and is making his own buy/sell decisions independently, the signal in the market price of each heavily-traded stock should be robust, i.e., there is a ton of information in it, and it would be very difficult (nearly impossible even) to beat it over time without getting lucky.

Conversely, when everyone believes the EMH and therefore stops trying to beat the market via individual buy/sell decisions, but simply piles into passive index funds for which a relatively small number of managers make all the decisions, the signal is weak — there’s not nearly as much information contained therein. Instead of the inputs of millions, you have the inputs of a few thousand.

Hence, I’d expect the EMH to oscillate between being true and false, based on whether people believe in it. Ironically, the fewer people who believe in it, the more likely it is to be true, and the more who believe in it, the more likely it is to be false.

While the EMH might spawn impassioned debate in certain niches, there are other more emotionally charged versions of a similar genre. Take the highly politicized environment around “trust the experts” vs “do your own research,” for example. Some people believe you should trust credentialed experts when it comes to matters of health, while others believe you should find out for yourself. (In 2022, I’ll be up front about my strong bias toward the latter camp.)

But what if this debate is also a Class 3 masquerading as Class 1/2? Perhaps doctors and scientists, operating independently, with minimal social and professional pressure to come out on a certain “side,” would produce information and recommendations that are reliable and trustworthy. But when they have been captured by powerful financial incentives (and more importantly disincentives), they are unreliable and not to be trusted.

An important question before deciding whether to be more or less trusting generally in experts is where on the oscillating sine wave are we? Are we in a place where doctors and scientists are free to offer dissenting opinions with minimal consequences to them personally and professionally, or is it worse than ever? Maybe it’s a fool’s errand to seek resolution on the question of trusting “experts” generally, and instead we should narrowly tailor the presumption of trust to the specific environment in which we find ourselves.

(Of course, in any environment there will always be exceptions, so even if one is leery of captured experts in an environment of stifling conformity, that should only go to one’s presumption, not be a blanket policy impervious to contraversion via evidence. Likewise, no matter how reliable experts are in an environment of intellectual tolerance and freedom, one should always verify for oneself to the extent one is capable.)

There are likely many other examples of Class 3 propositions that are mistaken for ones of the simpler Class 1 and 2 variety, and maybe by being aware of the distinction, we can avoid some rhetorical dead ends.

I’ll end by noting we even have common sayings, viewed as truisms, that completely contradict each another like:

Absence makes the heart grow fonder. Out of sight, out of mind.

Birds of a feather flock together. Opposites attract.

When it comes to these kinds of propositions, what is true is such only insofar as certain conditions hold. While human nature is ever the same, particular conditions come and go as we find ourselves at difference places along the recurring sine wave, infinite fractals of oscillating truth — all the way down.