Judging Idealizations

The combination of talking to practicing physicists and reading the literature on the foundations of statistical mechanics has led me to wonder if those of us who are worried by foundational problems are particularly autistic, in the sense that we take literally things that we ‘should not’ be taking literally. Many foundational problems stem from ‘problematic’ idealizations such as the infinite time limit in non-equilibrium statistical mechanics and assuming quasi-ergodicity to be ‘like’ ergodicity. But clearly there are some idealizations which are implicitly taken to be less problematic. For example, even people who are foundations-oriented don’t tend to raise a big fuss over the use of point masses in classical physics, despite the fact that point masses aren’t supposed to exist. The rigid elastic spheres model in statistical mechanics doesn’t bother people as much as the infinite time limit ‘approximation’ does.

The questions I’m interested in are:
1) What kinds of idealizations bother physicists?
2) What kinds of idealizations bother philosophers (or ‘philosophical’ physicists)?
3) What kinds of idealizations should we be bothered by? (Why should we — if you think we should — be more bothered by the infinite time limit idealization than by the point masses idealization?)

1 and 2 are empirical questions; 3 is normative.

The analogy to autistic behaviour is as follows: Throwing a fit over the fact that people don’t mean ‘How are you?’ literally, versus accepting it as a social signal and reserving your indignation for ‘real’ acts of dishonesty.

2D:4D ratio

Autistic people have been found to have lower 2D:4D ratios compared to non-autistics. Now some research suggests that a low 2D:4D ratio is predictive of higher sporting ability in females. This is uncorrelated with the level of testosterone in the womb, which leads to researchers to conclude that it’s likely a genetic trait. Baron-Cohen’s studies, however, put forth prenatal testosterone as a possible cause of autism and low 2D:4D ratio. So while this new study might seem to support Baron-Cohen’s “male brain” hypothesis for autism, it might actually be a blow against it.

Of interest to me, I suppose, because I have some autistic traits and have always been much better at sports than most other females. And my ring finger is significantly longer than my index finger.

The Tritone Paradox

An applet demonstrating the Tritone Paradox. I unambiguously perceive the first tone as lower than the second at both frequencies. Most people perceive the first tone as higher than the second when both are played at 110 Hz, but the second as higher than the first (which is correct) at 160 Hz. I poked around Diana Deutsch’s website a bit hoping she had something on whether people with perfect pitch are susceptible to the paradox. It would seem that they would have to be unsusceptible to it, by the definition of perfect pitch. And it would also explain why I was not fooled by it. But then I was fooled by the Shepard’s Tones illusion. Evidently if the transitions are finely-grained enough, my pitch-discerning abilities fail as well. When I hear the next octave and try to recall the previous octave, I can hear that there’s something fishy; that it doesn’t sound as high as it should be. But I cannot help but hear the transition from one note to the next as increasing in pitch. I wonder if people who have never been exposed to music (much less trained to recognise relative pitches) are susceptible to the Shepard’s Tones illusion. Is there a chance that they will hear the frequency rather than the musical note?

More thoughts: if, as Deutsch postulates, people’s interpretations of the Tritone Paradox are dependent on their native languages, what bearing does this have on the disproportionate occurrence of perfect pitch amongst autistic people? Keep in mind that one of the symptoms of autism is an impairment of verbal ability. Not all autistic people are impaired in that respect, but certainly there exist musical savants with perfect pitch who are impaired thus. Perhaps language “interferes” with one’s absolute pitch recognition abilities? But that would not explain why speakers of more tonal languages like Chinese are also more likely to have perfect pitch. Here we have the situation where perfect pitch, which is surmised to be linked to language somehow, occurs disproportionately in a group of people who mostly have impaired verbal abilities, and in another group of people who have had special training in recognising pitches in verbal interaction.

Abstract, metaphorical, or both?

One small thing that’s always bugged me about the association of autism with an inability to think abstractly is that plenty of so-called high-funtioning autists are high-functioning in fields that demand abstract thinking, such as maths, physics, computer science and music.

I have no quibbles with the idea that autistic people have problems thinking metaphorically, though. Especially given my own unfortunate tendency to take everything people say literally. So I wonder if there is a misleading dichotomy drawn here between “concrete” and “abstract” thinking, when the real deficiency of autistic people is the inability to understand conventional stories. For all metaphors are really little stories in themselves. And metaphors need not be abstract.

But it would also seem that one would need abstract thinking to relate a metaphor to the general case it is meant to indicate. And it would seem that this is precisely where autists fail — they often take the metaphor to mean something real happening rather than as an analogy, so they evidently can grasp what is happening in the story. So perhaps I’m wrong again. But I reiterate: you cannot be a mathematical or musical savant if you can’t think abstractly!

I’m sure there’s tonnes of literature on this issue, possibly making exceptions for savants in the fields mentioned above, but it seems that I’d rather sulk and recite “I hate you” to myself rather than Google for it, so.