Comment by apathy
9 years ago
The fundamental result behind the gambler's ruin is the human tendency to perceive patterns in genuine randomness. Rorschach blots, lotteries, slot machines, most betting endeavors all work because some humans will always find patterns in randomness. The result is easy enough as are the experiments (generate random noise from Uniform(0,1), project it onto a suitable manifold, hire some undergrads or local homeless people to look at them). That's not at all what I claimed Konrad originated. If you want an origin for this type of thing, de Finetti or Laplace or Descartes might be some candidates.
Konrad did give the phenomenon a catchy name and proposed that an increase in this tendency is an initial step in developing schizophrenia. If someone could actually establish this at a neurogenetic level that would be impressive and fundamental; I'm not aware of anyone doing so. I'd expect it to show up in a CNS journal and NIMH or WT to make a big deal if someone did.
The contrast between epiphany and apopheny is so striking, though, and so relevant to this topic, that it annoys me to no end when it is ignored. At the base of all of statistics is a desire to quantify how much of each is present in an observation, experiment, or cyclic series.
As you probably guessed, I am an applied statistician, not a neuroscientist. (I have serious issues with the way statistics are misused in neuroscience, for whatever that's worth). I do not, and cannot, claim that Konrad's theory is fundamental to that field. I do claim that anyone attempting to explain statistical reasoning to a lay public ought to internalize the contrast he proposed. Its setting as a proposed turn towards insanity is just a happy historical note.
>The fundamental result behind the gambler's ruin is the human tendency to perceive patterns in genuine randomness.
I don't think pattern recognition drives most gamblers. There are all kinds of other benefits, perceived or real, that are not accounted for in a purely monetary payoff grid.
I don't know how you can generate random noise. I assume you are using a standard, pixelated display to read this message. Even if a random process was choosing what to display on that screen, there are only a finite number of configurations. Exactly what you are viewing now could be recreated by such a random process.
The problem that hasn't been addressed yet is that "pattern" is not well-defined. If a random display shows a horizontal line pattern, it is still a pattern by some definition (and you would have no way to distinguish it from a "intentionally patterned" display that has the same configuration).
Of course you could have an intersection between recognizable images and random noise. The odds of this occurring with any regularity are infinitesimal, hence the design of experiments. (Recall that there is nothing like a mathematical proof in the physical world -- at a molecular level, some water molecules are moving upstream at any given moment, but by reaching into a stream or tossing some objects into the flow you are taking a large enough sample to determine where most of them are going).
Since you're not going to get proof one way or another, all a well designed and experiment can do is give you evidence. This happens to be more valuable than just about anything else that science has come up with, but it isn't proof.
Which is why the gold standard for a result is replication in a large sample. I could have this very page generated by convolving couple of high entropy random streams. Is it likely to happen repeatedly? Not if the generator is any good. Same principle for randomized trials. You can end up with unbalanced arms (I'm proofing a manuscript where we had exactly this problem). But it's unlikely that they'll be consistently unbalanced across trials with sufficient sample sizes.