Connectionists: how the brain works?

[Levine, Daniel S]

Jim et al.,

To pioneers who understood more about complexity than we often give them credit for I'd add Warren McCulloch.  McCulloch and Pitts are clearly well known for their theorem about networks of all-or-none neurons.  And yet in about 1969 just before his death I met McCulloch as a graduate student who was just beginning to migrate from pure math into neural modeling.  I asked him what area of math I should study in order to be an effective modeler, and he advised me to read a book by a Russian named Minorsky on nonlinear oscillations.

Best,
Dan Levine

________________________________
From: Connectionists [connectionists-bounces at mailman.srv.cs.cmu.edu] On Behalf Of james bower [bower at uthscsa.edu]
Sent: Wednesday, March 19, 2014 9:33 PM
To: Geoffrey Goodhill
Cc: connectionists at mailman.srv.cs.cmu.edu
Subject: Re: Connectionists: how the brain works?

Geoffrey,

Nice addition to the discussion actually introducing an interesting angle on the question of brain organization (see below)  As you note, reaction diffusion mechanisms and modeling have been quite successful in replicating patterns seen in biology - especially interesting I think is the modeling of patterns in slime molds, but also for very general pattern formation in embryology.  However, more and more detailed analysis of what is diffusing, what is sensing what is diffusing, and what is reacting to substances once sensed — all linked to complex patterns of gene regulation and expression have made it clear that actual embryological development is much much more complex, as Turing himself clearly anticipated, as the quote you cite pretty clearly indicates.   Clearly a smart guy.   But, I don’t actually think that this is an application of Ochham’s razor although it might appear to be after the fact.  Just as Hodgkin and Huxley were not applying it either in their model of the action potential.   Turing apparently guessed (based on a lot of work at the time on pattern formation with reaction diffusion) that such a mechanism might provide the natural basis for what embryos do. Thus, just like for Hodgkin and Huxley, his model resulted from a bio-physical insight, not an explicit attempt to build a stripped down model for its own sake.  I  seriously doubt that Turning would have claimed that he, or his models could more effectively do what biology actually does in forming an embrio, or substitute for the actual process.

However, I think there is another interesting connection here to the discussion on modeling the brain. Almost certainly communication and organizational systems in early living beings were reaction diffusion based.  This is still a dominant effect for many ‘sensing’ in small organisms.  Perhaps, therefore, one can look at nervous systems as structures specifically developed to supersede reaction diffusion mechanisms, thus superseding this very ‘natural’ but complexity limited type of communication and organization.  What this means, I believe, is that a simplified or abstracted physical or mathematical model of the brain explicitly violates the evolutionary pressures responsible for its structure.  Its where the wires go, what the wires do, and what the receiving neuron does with the information that forms the basis for neural computation, multiplied by a very large number.  And that is dependent on the actual physical structure of those elements.

One more point about smart guys,  as a young computational neurobiologist I questioned how insightful John von Neumann actually was because I was constantly hearing about a lecture he wrote (but didn’t give) at Yale suggesting that dendrites and neurons might be digital ( John von Neumann’s The Computer and the Brain. (New Haven/London: Yale Univesity Press, 1958.)  Very clearly a not very insightful idea for a supposedly smart guy.  It wasn’t until a few years later, when I actually read the lecture - that I found out that he ends by stating that this idea is almost certainly wrong, given the likely nonlinearities in neuronal dendrites.  So von Neumann didn’t lack insight, the people who quoted him did.  It is a remarkable fact that more than 60 years later, the majority of models of so called neurons built by engineers AND neurobiologists don’t consider these nonlinearities.  The point being the same point, to the Hopfield, Mead, Feynman list, we can now add Turing and von Neumann as suspecting that for understanding,  biology and the nervous system must be dealt with in their full complexity.

But thanks for the example from Turing - always nice to consider actual examples.   :-)

Jim





On Mar 19, 2014, at 8:30 PM, Geoffrey Goodhill <g.goodhill at uq.edu.au<mailto:g.goodhill at uq.edu.au>> wrote:

Hi All,

A great example of successful Ockham-inspired biology is Alan Turing's model for pattern formation (spots, stripes etc) in embryology (The chemical basis of morphogenesis, Phil Trans Roy Soc, 1953). Turing introduced a physical mechanism for how inhomogeneous spatial patterns can arise in a biological system from a spatially homogeneous starting point,  based on the diffusion of morphogens. The paper begins:

"In this section a mathematical model of the growing embryo will be described. This model will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of greatest importance in the present state of knowledge."

The paper remained virtually uncited for its first 20 years following publication, but since then has amassed 8000 citations (Google Scholar). The subsequent discovery of huge quantities of molecular detail in biological pattern formation have only reinforced the importance of this relatively simple model, not because it explains every system, but because the overarching concepts it introduced have proved to be so fertile.

Cheers,

Geoff


On Mar 20, 2014, at 6:27 AM, Michael Arbib wrote:

Ignoring the gross differences in circuitry between hippocampus and cerebellum, etc., is not erring on the side of simplicity, it is erring, period. Have you actually looked at a Cajal/Sxentagothai-style drawing of their circuitry?

At 01:07 PM 3/19/2014, Brian J Mingus wrote:
Hi Jim,

Focusing too much on the details is risky in and of itself. Optimal compression requires a balance, and we can't compute what that balance is (all models are wrong). One thing we can say for sure is that we should err on the side of simplicity, and adding detail to theories before simpler explanations have failed is not Ockham's heuristic. That said it's still in the space of a Big Data fuzzy science approach, where we throw as much data from as many levels of analysis as we can come up with into a big pot and then construct a theory. The thing to keep in mind is that when we start pruning this model most of the details are going to disappear, because almost all of them are irrelevant. Indeed, the size of the description that includes all the details is almost infinite, whereas the length of the description that explains almost all the variance is extremely short, especially in comparison. This is why Ockham's razor is a good heuristic. It helps prevent us from wasting time on unnecessary details by suggesting that we only inquire as to the details once our existing simpler theory has failed to work.

On 3/14/14 3:40 PM, Michael Arbib wrote:
At 11:17 AM 3/14/2014, Juyang Weng wrote:
The brain uses a single architecture to do all brain functions we are aware of!  It uses the same architecture to do vision, audition, motor, reasoning, decision making, motivation (including pain avoidance and pleasure seeking, novelty seeking, higher emotion, etc.).

Gosh -- and I thought cerebral cortex, hippocampus and cerebellum were very different from each other.


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