Kaj_Sotala comments on Boredom vs. Scope Insensitivity - Less Wrong

37 Post author: Wei_Dai 24 September 2009 11:45AM

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Comment author: Kaj_Sotala 24 September 2009 01:17:53PM *  5 points [-]

(Eliezer sometimes treats scope insensitivity as a simple arithmetical error that the brain commits, like in this quote: “the brain can't successfully multiply by eight and get a larger quantity than it started with”. Considering that the brain has little trouble multiplying by eight in other contexts and the fact that scope insensitivity starts with numbers as low as 2, it seems more likely that it’s not an error but an adaptation, just like boredom.)

Arithmetic is a relatively late cognitive technology that doesn't appear by its own (1). We can to a certain degree train ourselves to use exact numbers instead of approximate magnitudes in our reasoning, but that remains an imperfect art - witness the difficulty people have truly grasping numbers that are at all higher. An imprecise analog magnitude representation is the brain's native way for representing numbers (2 3), and while there is evidence about that analog system indeed being capable of multiplication (4), I'd be careful about making claims concerning what low-level systems we have no introspective access to can or cannot multiply.

(Especially since we do know plenty of cases where a particular system in the brain doesn't share the capabilities other systems do - we might intuitively solve differential equations in order to predict a baseball's flight path, but that doesn't mean we can natively solve abstract equations in our head.)

Comment author: SilasBarta 24 September 2009 05:08:33PM *  9 points [-]

we do know plenty of cases where a particular system in the brain doesn't share the capabilities other systems do - we might intuitively solve differential equations in order to predict a baseball's flight path, but that doesn't mean we can natively solve abstract equations in our head.

Good point, but I'd go even further: we are not even solving differential equations in predicting a baseball's flight path, but rather, pattern-matching it to typical falling objects. Though I frequently criticize RichardKennaway's points about control systems, he is right that you actually need to know very little about the ball's dynamics in order to catch it. You just need to maintain a few constant angles with the ball, which is how humans actually do it.

To the extent that "you" are solving a differential equation, the solution is represented in the motions of your body, not in any inference by your brain.

Comment author: CronoDAS 25 September 2009 03:04:09AM 2 points [-]

Consider a related problem - how much dynamics do you have to know in order to make a 3-point shot in basketball?

Comment author: kpreid 24 September 2009 05:15:45PM *  4 points [-]

Your link syntax (2) is broken; to fix it put backslashes before parentheses inside the URL, like this:

[2](http://www.duke.edu/web/mind/level2/faculty/liz/Publications/Brannon%20\(2006\).pdf)
Comment author: Kaj_Sotala 24 September 2009 06:47:05PM 0 points [-]

Thanks! Fixed.