BoundedRationality_TheAdaptiveToolbox.pdf

76 Peter Hammerstein
a' =a + 5/(^+1).
In other words, rescale the angle measuring the change of direction by the
distance from home and calculate the new estimate of the home direction by
adding the rescaled change of direction to the previous home direction.
In the experiments, the ants behave as if they did this kind of calculation,
rather than using trigonometry, to solve their problems. I must admit, however,
that we do not really know the complete information-processing sequence
that is going on in their minds.
Economist: If the algorithm cannot be described fully in terms of neural circuitry,
how did Wehner then come up with this picture of the algorithm?
Biologist: The method is to expose Cataglyphis to various situations in which its
navigational system makes serious errors. From these errors one can learn
about the way in which the ant processes information. To put it in your language,
we should be happy that Cataglyphis is boundedly rational and
makes mistakes. If it didn't make so many mistakes, it would probably be
much harder to understand its navigational system.
Economist: Okay, but let's return to the major thread of our discussion. I can see
that mistakes help to identify the ant' s algorithms. However, the fact that serious
mistakes are made does not exactly look to me like evidence in favor
of the maximizing tendencies of the evolutionary process. I take it that these
ants have been around for many generations and had a good chance, genetically
speaking, to become perfect navigators.
Biologist: I don't like where you are going with this. You are pushing me into a
position as if I had defended the idea of full rationality. Let us adopt the
more down-to-earth view of an evolutionary biologist. There is, first of all,
the problem of how the compass may have arisen. The compound eye of an
insect can be seen as a preadaptation because it does, in some sense, represent
the sky. After the compass had been invented, the new problem was
how to deal with its errors. Instead of creating several internal templates of
polarization patterns for various positions of the sun, evolution has maintained
the simple compass but generated ways of coping with the error.
Within a short time span, the error is systematic and can be corrected by
some sort of initial calibration of the system. This is precisely what
Cataglyphis seems to do.
Economist: Well, perhaps the ant is not quite as bad as I thought. But don't go
too fast. The error correction by initial calibration is doomed to fail when
the ant takes off on a long excursion and the sky pattern changes during the
excursion. Thus, you still have failed to convince me of the power of evolutionary
adaptation.