X-Message-Number: 15353 References: <> Date: Tue, 16 Jan 2001 09:44:23 +0000 From: "Joseph Kehoe" <> Subject: Turing >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. don't know enough about brain biology to comment on this. >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). But once you set the bound at that the problem is no longer exponential. A new neuron can have at most k connections when it is added, where k is some constant. This is not exponential growth but linear growth. It can only be exponential if you have an unbounded number of connections possible for each new neuron. It may still be computationally hard but the growth of brain is not exponential. From a theoretic point of view you need to prove that simulating the brain is an NP-complete problem before speed becomes an issue. If it is NP complete then you can say with reasonable assurance we will never be able to simulate a brain fast enough. Without that you cannot say so. So NP complete implies we have problems - not NP complete means there is no reason why we will not get there someday. To show that computers can never simulate brains show that brain functioning is isomorphic to the Halting problem. [sniped stuff] > 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? We don't know at this time but it is starting to look more likely that turing machines can imitate our brains. Until someone can show some sound theoretical barrier to this I would assume they can. Proposed barriers incl. Quantum tunneling (Penrose, I believe) and God. Also on slashdot.... A reknowned computer scientist punctures some of the arrogance and hype surrounding computing and details some of the many computational and other problems computers can't solve. After years of rising expectations, the public expects computers to reverse aging, solve the most complex problems, and restore the ozone layer. So do many computer scientists, says the author of "Computers LTD., what they really can't do." It's a good question. What can't computers do? Jump in. http://slashdot.org/article.pl?sid=00/12/16/1549258 Joseph. Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=15353