Vehicle 5: Logic

In this chapter, Braitenberg's design innovation will be to analogous to introducing hidden units in a connectionist network. These units are threshold devices with the value of the threshold preset, excitatory or inhibitory connections, and in which memory can be achieved via recurrent signalling (feedback loops).

More important, though, is that Braitenberg is now in a position to make explicit one of the key themes of his book, and (perhaps) the most important lesson that we can learn from him:

"It is pleasurable and easy to create little machines that do certain tricks. It is also quite easy to observe the full repertoire of behavior of these machines -- even it it goes beyond what we had originally planned, as it often does. But it is much more difficult to start from the outside and try to guess internal structure just form the observation of the data. [...] Analysis is more difficult than invention in the sense in which, generally, induction takes more time to perform than deduction: in induction one has to search for the way, whereas in deduction one follows a straightforward path. A psychological consequence of this is the following: when we analyze a mechanisms, we tend to overestimate its complexity."

This is Braitenberg's law of uphill analysis and downhill invention. It is very much akin to Simon's observation about the complexity of the path taken by an ant [Get Simon's quote for here!!]. It is also a central point to this book.

What consequences might the law of uphill analysis and downhill invention have for the practice of cognitive psychology?

Braitenberg now moves to his innovations for Vehicle 5. His goal is to build simple "brains" for his machines. This is done by introducing threshold devices that stand between sensors and motors. (NB: The direct analog to this in cognitive science is the creation of more sophisticated artificial neural networks via the introduction of hidden units.) These threshold devices have fixed thresholds, but the designer can decide what the threshold will be. As well, some threshold units will fire only when the signal is above threshold, while others will only stop firing when threshold is exceeded. As an additional nice wrinkle, some notion of time is added -- the response of a threshold unit is not instantaneous, as it first must perform some computations to determine what kind of response to emit.

In addition to all of this, Braitenberg adds excitatory and inhibitory connections between threshold units. As no learning is described at this point, all of this circuitry looks very much like the McCulloch-Pitts neurons that were proposed in the early 1940s. In 1943, McCulloch and Pitts were able to prove that a Universal Turing Machine could be constructed from such units. (NB: Now why is that an important demonstration??) No wonder that Braitenberg writes "You realize what I am driving at: with enough threshold devices it can do anything a computer can do, and computers can be made to do almost anything." This reminds me, too, of the claims made in the 1986 PDP volumes about the power to be gleaned from exploiting hidden units -- permitting arbitrary I/O mappings.

Circuits of these threshold units, hooked into a feedback loop, can be used to instantiate memory. A similar approach was used by Dawson and Schopflocher in their autonomous pattern association network.

Such memory circuits, though, are finite in size, and therefore doom the machine to limited capacity memory. Is there any way that this problem can be overcome? Sure -- let the vehicle have the ability to read and write the external world, so that the environment of the vehicle can serve as a storage device. Braitenberg imagines the vehicle moving from water to sand, being able to trace patterns in the sand, and to read these patterns at a later time. Please note that it the use of external memory was exactly the strategy required by McCulloch and Pitts to prove that one of their networks could be used to build a UTM!

Indeed, if you know how a Turing machine works, thinking of one is unavoidable given Braitenberg's description of the "sand vehicle." "The vehicle can crawl on the beach, leaving marks in the sand indicating the succession of digits in the large numbers that emerge from its calculations. Then it can crawl back, following its own track, to read off the digits and put them back into the calculation." If the vehicle is viewed as a tape head, and the sand track is viewed as the tape upon which symbols can be written, then the parallel is exact.

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