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Marr (1982) identified three levels at which we can describe information processing systems, including the human mind: the computational level, the algorithmic/representation level, and the implementation level.

Now I'm wondering which level is depicted by this situation: A theory that baseball players estimate how quickly to run to catch a ball by fixating on the ball, beginning to run, and adjusting their running speed so that the angle of their gaze remains constant.

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  • $\begingroup$ From a computer science perspective of the terms it seems that they are implementing a greedy algorithm. (run, adapt if needed). I know nothing about Marr though. The computation is the estimation of the angle. $\endgroup$ – skymningen Dec 14 '16 at 8:41
  • $\begingroup$ Here are some scientific papers that describe how baseball players look at and catch a ball. I have no time to give a summary, but it may give you a nice start: scholar.google.nl/… $\endgroup$ – Robin Kramer Dec 14 '16 at 18:54
  • $\begingroup$ that is an algorithmic explanation. the computation is "estimating how quickly to run to catch a ball". the implementation is how what you describe is instantiated in neurons $\endgroup$ – honi Dec 14 '16 at 19:17
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The computational level is about available information and in-principle what can be derived from that information. For catching a ball, this would be, for example, an analysis of what information is available to a fielder using a particular perceptual device, and what possible inferences could be drawn from that information. From the flux of light projected on a stationary 2D retina, is it possible to derive where the ball will be when? What if the 2D retina can move in response to the light, then is it possible? What if there are two eyes (i.e., stereo vision)? Your description of the procedure for catching a ball assumes that the information used by procedure is sufficient, but does not explicitly analyze and prove it, so your description is probably not best thought of as the computational level.

The algorithmic level is about the particular representation and process for computing an inference and making a response. There are usually many different ways to compute an answer. For example, adding two numbers can be done with Roman numerals and a difficult process, or with binary numerals using a power-of-2 place system and a simple process. Your description of a procedure for catching the ball seems closest to the algorithmic level, but the description would have to specify more details to be a fully fleshed-out algorithm.

The implementational level is about "hardware". How do the optical tracts of the brain encode and process the signal, and how does the body implement the motions requested by the brain? Your description of a process for catching the ball does not rely upon or mention these details, so is probably not best thought of as the implementational level.

(At least, that's my take on it. I think that the levels were intended as a useful framework for organizing and thinking about theories and how they interconnect. Marr suggested --if I recall correctly-- that it was valuable to do a computational analysis before diving into algorithmic particulars. But discussants sometimes devolve into heated philosophical debates about the "correct" interpretation of this or that. I hope this answer does not generate too much heat.)

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