Comments on: What’s so metaphorical about the computer metaphor?

By: Max Greene

Max Greene — Fri, 29 Jun 2007 09:03:56 +0000

Surely the brain has evolved from a simple type nucleus for the multicelled species with a motivational centre (hypothalamus). It creates the survival and reproductive behaviour. The highly socialized human, evolved memory banks (frontal lobe memria) to store the vast amount of info to cope with social conditions. Our primitive memory (memrium) being only capable of a limited quantity of datam required shutting down (sleep) to transfer material to the main memria, otherwise it overloaded and acted neurotically, like a computer running out of storage space. (My website, trinology.co.uk details this hypothesis)

By: Paul Patton

Paul Patton — Sat, 23 Jun 2007 00:19:47 +0000

Individual neurons lack a capacity for language. The capacity for language arises as an emergent property of an appropriately organized network of neurons within an embodied brain. Before such a network evolved, linguistic understanding did not exist and thus language could not exist. I maintain that our mathematical cognitive faculty is likewise is an emergent property of an appropriately organized neural network, and that literal computation likewise does not exist at the level of single neurons. Before the evolution of such a network, mathematical understanding did not exist and thus literal computation could not exist. The key feature of our mathematical cognitive faculty is not that it can perform literal mathematical computations but that it can *formulate* them and interpret them based on mathematical understanding. In fact, our mathematical cognitive faculty isn’t actually very good at literal computing, which is why we need computing tools. This is where engineering enters the picture. I’m changing my position a bit, in that I now claim that the key feature of literal computation is that it is formulated based on mathematical understanding. Once formulated it can be implemented either “in the head” or with the assistance of engineered tools.

The position I’m trying to take about neural computation of the McCulloch/Pitts sort is similar to that staked out by Patricia Churchland and Terry Sejnowski in Chapter 2 of The Computational Brain. They maintain that just as a gardener can choose whether to designate a plant as a weed, an investigator can choose whether or not it is useful to treat a given system as computational. Computation is not an inherent property of brains, just as weedness is not an inherent attribute of plants.
Computational neuroscience simply adopts an often useful strategy for understanding how nervous systems work.

By: Pete Mandik

Pete Mandik — Fri, 22 Jun 2007 12:47:54 +0000

Paul,

Your putting “engineered” in scare-quotes looks a lot like a concession that the literal computation wasn’t literally engineered.

The mathematical cognitive faculty is a neural system which itself, the neural system, is neither engineered nor derived from the mathematical cognitive faculty. The mathematical cognitive neural system cannot be derived from itself. So, it itself is an exception to your rule that all literal computation derives from the mathematical cognitive faculty.

It looks to me that you are stuck with having to admit that at least one neural system constitutes a literal computer. Further, since it isn’t a general rule that all literal computation is literally engineered, it remains open (insofar as you have not successfully demonstrated otherwise) that other neural systems, including the nervous systems of electric fish and the simple circuits described by McCulloch and Pitts, are literally computing.

By: Paul Patton

Paul Patton — Fri, 22 Jun 2007 03:58:50 +0000

Pete-
When I add two numbers in my head this literal computation was devised or “engineered” by me. Human beings have a faculty for mathematical cognition which allows them to understand and formulate computations, to understand mathematical concepts and to devise new ones. Although we don’t know how this cognitive faculty works, there is no reason to assume it is anything other than an emergent property of the behavior of vast numbers of appropriately interacting neurons (Although the mathematician Roger Penrose thinks that the capacity for mathematical insight requires special non-computable quantum processes). I claim that all literal computations derive from such a mathematical cognitive faculty. Literal computations performed “in the head”, using neurons are not special exceptions to this rule.

By: Pete Mandik

Pete Mandik — Thu, 21 Jun 2007 11:33:42 +0000

Paul,

It strikes me as totally irrelevant to the question of whether brains are literal computers that they were not designed by engineers. If one grants the point I made in my previous comment, namely that at least sometimes nervous systems literally compute, and that they do so even though those nervous systems were not the products of engineering, then it follows that the fact that something was not engineered doesn’t block it from literally computing.

By: Paul Patton

Paul Patton — Thu, 21 Jun 2007 00:12:22 +0000

Peter-
I certainly didn’t mean to imply that I though that literal mathematical computation requires an immaterial soul, or a Cartesian res cogitans or anything like that. I don’t doubt that mathematical computation, in the literal sense, involves some highly specialized activities of the human brain. When I said that nervous systems don’t literally compute anything I had in mind neural computation of the McCullough and Pitts sort. It seems to me that since that brains weren’t designed and built by an engineer for the purpose of performing mathematical computations, it would be misleading to speak of them as literal computers. Human beings invented mathematics and computation in order to deal cognitively with certain orderly regularities and patterns in the world. We formulate laws of physics as provisional, relative, and imperfect attempts to understand these regularities. In a much more general sense, biological systems and processes must function appropriately with respect to world’s orderly regularities. Evolution by natural selection is the process by which this appropriate function comes about. To guide behavior, complex multicellular organisms have evolved cells that are specialized to interact with one another quickly and in highly specific ways, which we call neurons. Patterns of interaction that promote the survival and reproductive success of the organism persist, others don’t. Birds and airplanes look somewhat alike because natural selection had to ’solve many of the same problems’ (speaking metaphorically) to make the bird, that the engineer had to solve (speaking literally) to design and build the airplane. (Notice how hard it is to write about evolution without slipping into metaphors that regard it as an intelligent agent). The activities of neurons seem as if they are performing mathematical computations for much the same reason. However, evolution is not a cognitive system. It knows nothing about math, computation, aerodynamics, or physics, and therefore no literal computation is occurring.

By: Pete Mandik

Pete Mandik — Tue, 19 Jun 2007 10:58:34 +0000

Thanks, Paul. This helps clarify your position. I think I have a better sense of where you are coming from on these issues. I do have some further questions, however.

If, as you admit, someone adding 2 and 2 is literally computing, and, if you’ll grant, this is something that some of us can do with no external assistance - adding sums in the head - it looks like you’d be forced to admit that literal computation takes place, at least sometimes, solely in nervous systems.

This leads me to wonder how best to read your earlier statement that “Nervous systems donâ€™t really compute anything” since, if you grant the above, you’ll need to grant that sometimes nervous systems really do compute.

I like the way you frame these issues towards the end of your last comment in terms of what computation is an objective attribute of. I can grant for the purposes of conversation that computation is not an objective attribute of either digital computers or pencil marks on paper. Even granting that, though, it still looks like computation is an objective attribute of something. More specifically, in cases in which one is doing sums in one’s head, computation is an objective attribute of some serious chunk of one’s nervous system.

By: Paul Patton

Paul Patton — Tue, 19 Jun 2007 00:02:54 +0000

Peter-
Mathematics is a system of symbols and operations invented by human beings to deal with certain perceived abstract regularities in the world. A child literally computes when he adds 2+2, a mathematician literally computes when she uses the rules of linear algebra to take the dot product of two matrices. There are some studies showing that other animals have a limited concept of quantity (Irene Pepperberg’s work in the African Gray Parrot comes to mind), but I don’t know of any work showing that animals can perform mathematical operations such as addition. So, perhaps literal computation is a uniquely human ability. I’m not up on the latest neuroimaging studies of mathematical cognition, nor am I familiar with any literature on the effects of brain lesions on computational abilities in humans. I nevertheless don’t doubt that people use their brains when they compute. However, people aren’t really very good at computation, and must usually use tools (paper and pencil, abacus, slide rule, computer) to help them. Perhaps it’s best to speak of the human brain, arm, hand, pencil, and paper as literally performing the computation as system. Electronic computers are tools designed, built, and programmed by human beings to assist them in computation. I’m not sure it makes sense to speak of computation as an objective attribute of the computer any more than it does to speak of it as an objective attribute of a pencil and paper or of a slide rule. I want to write about the nervous system next, but am out of time for now.

By: Pete Mandik

Pete Mandik — Mon, 18 Jun 2007 11:44:47 +0000

Paul,

Do mathemeticians and scientists compute anything? If so, do they do it without using their nervous systems? If not, when is anything ever literally computed?

By: Dr. Paul Patton

Dr. Paul Patton — Sun, 17 Jun 2007 20:12:21 +0000

It strikes me as a bit odd, then, to say that calling people or their minds â€œcomputationalâ€ is something metaphorical.

Peter-
Consider an electric fish. Physicists must use fairly complex differential equations to describe the electric fields it generates around its body, and the ways in which these fields are distorted by items in the fish’s environment. Further complicated equations are needed to explain what the fish’s nervous system would need to do to reconstruct its surroundings on the basis of the electric stimulus it receives. Yet the fish does not require an advanced degree in physics to use its electric sense to sense and respond to its surroundings. In the literal sense, fish know nothing about mathematical computation. The fish’s nervous system is simply wired up so that it behaves in accordance with the needed relationships, just as if it were computing. The fish’s nervous system wasn’t designed by an Engineer with a knowledge of mathematical computation either. The fish’s nervous system is wired the way it is as a result of learning and natural selection. Natural selection works simply by recurrent cycles of random variation and selective survival. There is no mathematician and no computation anywhere in the picture. Mathematical computation is a tool invented by human beings, which we can use to make sense of what the fish’s nervous system is doing and express the functional relationships it embodies. This is the sense in which speaking of minds or nervous systems as computational is metaphorical. Nervous systems don’t really compute anything. We find it useful to use concepts of representation and computation to help us understand the functional relationships they embody as a result of evolution and learning.