X-Message-Number: 15332 Date: Sat, 13 Jan 2001 07:41:34 -0500 From: Thomas Donaldson <> Subject: and more on computers and brains Hi again! More on just how many connections become possible between neurons. This note will take a little different approach. Suppose we have a set of N neurons. As I mentioned, the neurites may extend quite far, while dendrites tend to lie more close to their neuron. This means that a neuron will generally send messages much farther than its dendrites extend. On the other hand, its dendrites can RECEIVE messages from more than one neuron. The role of exponentiality in the working of our brain therefore needs more than superficial comment. First, the average length of an axon isn't a good parameter, since that length varies a good deal. It's more appropriate to consider the distribution of axons of different lengths among neurons, a figure which I do not have and is likely to differ with the exact kind of neurons. Pyramidal neurons are likely to have longer axons, other kinds (except possibly the Purkinje cells in our cerebellum). Other kinds of interneurons may be quite short in the length of their axons. The exponentiality of increase caused by generation of one new neuron would depend on just how far its axon and its neurites might extend. To limit our thinking to simple cases, I shall suppose that its axon extends over (say) 1/10th of the entire brain. This gives the number of possible connections it may form in our brain... smaller than that of the total brain, but a large number still. It also suggests taht if we had a brain with N neurons, then the possible connections come to (0.1) * (N!). (Please understand that this is VERY approximate; it is an attempt to estimate behavior based almost on theory alone). The main point to remember here is that such a figure, even multiplied by a relatively small restriction (1/10, 1/100, etc) remains extremely large. The factorial of a large number is very very large. The importance of this comes from one simple truth, believed by almost all neuroscientists: our memories consist of connections between many neurons. The number of POSSIBLE connections gives the possible memories we may have. To the extent that our connections belong to us alone, we may think of them as our own special memories. (In reality, we're likely to find that an individual neuron is limited by the connections it can form, so that "unique" connections are again limited; for the purpose of this discussion, I am ASSUMING that those limits can be ignored in a rough estimate). Moreover, a NEW neuron will form new connections, again with a wide range of possibilities. The discussion by others, as I understand it, looks at the connections of one particular brain. Clearly if we knew them beforehand we could predict the behavior of that particular brain, and even make a machine to imitate it, at least for a short while. (As the brain learned, those connections would change). In that sense, someone at some particular time might well be imitatable by a computer. However unless the computer ALSO had similar features those of brains, it could not continue this imitation for long. Does the possession of those similar notion of attributes to brains mean that a Turing machine, EVEN FORGETTING THE ISSUE OF TIME, could imitate the behavior of such a machine? Best wishes and long long life for all, Thomas Donaldson Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=15332