Learning to accept unknowability

Conspiracy theories and superstitions have the same origin. They are both attempts to deny the pervasiveness of randomness in life. People who become overly invested in a low-noise worldview are prone to late-life conversions to superstition because they are so invested in the idea that the world is predictable that they would rather switch hypotheses on the basis of noise (and hence overfit) than admit that the signal-to-noise ratio is that low.

Admitting Unknowability is much more terrifying than admitting Unknownness.

1 comment
Tim

I love that a post on dealing with file encodings is followed by one on unknowability. Apropos

Wittgenstein's ladder

Austrian Philosopher Wittgenstein once described the structure of his expositions as such:

My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)
He must transcend these propositions, and then he will see the world aright.

This concept is known as Wittgenstein's Ladder (wikipedia: do read this)

A lot of the finesse in designing a modern syllabus lies in understanding how to construct this ladder, such that

  1. The first rung is reachable from where the student is right now
  2. Each following rung is reachable from the previous rung
  3. The final rung is where you want it to be, and goes far enough

Knowing where you want the final rung to be may not tell you very much about the first rung at all, because the first rung could be completely fictional relative to the last - what's important isn't consistency per se, but the ability to conceive of a continuous path of rungs in between them. The presented facts can outright contradict each other, even, if that helps promote faster ladder-climbing.

Lagged asset correlations, a thought experiment

Suppose I start a fund that imposes a 1-day withdrawal lead time, and takes your money and invests it in the S&P 500 on day 0, but then reports the day 0 return as the day 1 return, the day 1 return as the day 2 return, and so on, reporting the return on day 0 as 0. This fund has a return which is a tiny bit less than the S&P, but is completely uncorrelated on a daily basis. It would, however, have an almost perfect correlation on an annual basis, and that's why you wouldn't invest in such a thing. If you only used daily correlations when deciding whether to put this asset into your portfolio, you would have been greatly mislead!

If you optimized for track record Sharpe ratio you would actually invest in this stupid fund. That TYPE of smoothing is worthless though!