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April 22, 2009

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Cell b(iii) looks suspicious. How much noise does their procedure introduce so that someone with 50 interpolation points can end up coloring in the opposite corners of the graph? Or were they wasted? I need to read the paper, that's just a reaction to the plot. The other cells all seem plausible. Maybe the experiment just measured how much people suck at estimating the length of a horizontal bar?

It seems a weak link can be clearly identified in each row. It's not so much gradual decay but the eventual intervention of a moron

b-iii is a dumbass... or there's an error in the protocol
c-iii and c-iv share the blame
d-v is a moron

50 corrected and 100 blind guesses for each function seems like an awful lot of work. What incentive did the subjects have to do this diligently? Fascinating study though.

On each trial, the value of the stimulus was presented as a visual magnitude, being the width of a horizontal bar on a computer screen. Participants responded by adjusting the height of a vertical bar and then received corrective feedback

To me, this seems like a pretty strong cue that the respective magnitudes should correspond. That cue alone might explain why everything tends towards x=y

That's a hilarious result. non-mathematicians (I assume) plausibly believe that all functions are positive, smoothly monotonic, and roughly 1:1.

Though of course, as Arthur B. points out, each of the rows in the summary shows a gradual decoherence interrupted by someone who believes that the best guess when you don't understand the data is f(x) = x. And that one turns out to be easy to recognize, remember, and transmit.

Brilliant experiment.

There must be some shared structure in the brain or brain plus visual system that is processing the input.

Does this make x=y a platonic form?

Open loops are unstable! Feedback is crucial to accurate signal measurement.

Fascinating experiment. This is one that I'll remember to bring up in future conversations. However, I see Tom Breton (Tehom)'s point. I'd be very interested to see what happens when the subjects are asked to encode function values in other ways.

People aren't very good at conveying uncertainty - for instance a lot of times they'll say 50-50 to mean "I don't know" even when the correct probability is nowhere near .5 (e.g. footnote 10 of this study implies that over one fifth of respondents said they had a 50% chance of being hurt in a terrorist attack in the next year). As Tom and others have suggested, in this design some people may have felt that the way to express uncertainty is by matching the length of the horizontal bar, and you only need one or two of those people in a chain to converge on y=x.

I'd say that comparing a horizontal bar to a vertical bar is a terrible way to receive a function. We see an obvious pattern in (c) immediately because it is plotted for us. It's easy to remember this plot once you have it and reference it to output.

This would be a good candidate for an online game or mechanical turk implementation.

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