Necker Cubism

Don Geddis wrote:

... I want a computer program that
can effectively substitute for my receptionist, ...

Pero que chulada, la muneca!

Ahem, Mr. Geddis will see you now.

... or my stockbroker (with
interaction only by email, say), then surely it is apparent that I don't
_necessarily_ need to care about every last detail of human cognitive
performance, such as visual interpretations of Necker cubes.

Funny you should mention that. This is a particularly interesting case of an
optimal response to an ambiguous signal - one instance among many where two
(or N) interpretations of the data are equally likely, a case where the
probability distribution over the consequences of a response, given the
stimulus, is not only bimodal, but each mode is of equal magnitude.The cube
flips flops at "random". Your broker is in a "buy, buy, buy, sell, sell,
sell" dilema, and your receptionist flits between "come here, come here,
come here, go away, go away go away".

What I find interesting is that here you have a constant signal, a high
signal to noise ratio, and yet the "optimal" response (given some plausible
assumptions) is to vacilate: random switching between two alternatives.
Further, the statstics of switching times (e.g. mean and variance) can be
derived. We can ask "what would Bayes do", calculate the answer (flip flop,
with flips and flops quantified as a stochastic process) and find that this
is a close match to what people report:

/*
[56.] Random switching and optimal processing in the perception of ambiguous
signals. W Bialek & M DeWeese, Phys Rev Lett 74, 3077-3080 (1995).

In the case of motion estimation [53] there is nothing deep about the
statistical mechanics problems that we have to solve, but here we found
that in cases where stimuli have ambiguous interpretations (as in the
Necker cube) the estimation problem maps to a random field model. The
nontrivial statistical mechanics of the random field problem really does
seem to correlate with the phenomenology of multistable percepts. This is
interesting as a very clear example of how the idea of optimal performance
can generate striking and even counterintuitive predictions, in this case
predicting fluctuations in perception even when inputs are constant and the
signal to noise ratios are high.

http://www.princeton.edu/~wbialek/optimization_links.html
*/

So, while Robobroker may not need a spatial vision module, it will encounter
the Necker Scenario. As to the FemmeFatalatron in your digital anteroom, I
can only guess at the ambiguities resolved.

-- Michael

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