Big brains

A little while ago now, I read some adverse comment about one Dr Markram, about his claims for his team’s work on the European big brain project, websited at reference 3. I think the comments came from someone who thought that these claims were a bit overdone and who resented the amount of funding that the good doctor had managed to tuck under his belt. See, for example, reference 1.

I now read at reference 2, in much greater, if not altogether comprehensible detail, of the some of the work that Dr Markram and his large team of neurologists and others have done on the brains of rats. Assuming that I have read it right, this includes building a bit – maybe a third of a cubic millimetre – of rat brain on a computer. This bit of brain is called a microcircuit and I think the story is that it includes all the right sorts of neurons, getting on for 150,000 of them, depending which experiment you are looking at, of the right sort of size and shape, in the right sort of places and with the right sort of connections between them, but which has not yet been actively programmed to actually do anything in particular.

The bit of brain so defined was simulated using the NEURON simulation package of reference 8, augmented for execution on a supercomputer, together with additional tools to handle this particular model, this microcircuit.

All in all, a feat of big science which required a computer which at the time, a couple of years ago now, rated around 100 in the worldwide league of big computers. I quote: ‘… The systems used included an IBM Blue Gene/L (until 2009), a CADMOS 4-rack IBM Blue Gene/P (until 2013), a CADMOS 1-rack IBM Blue Gene/Q (until 2014), and the Blue Brain IV operated by the Swiss National Supercomputing Center (CSCS)…’.

It struck me that it was all rather bizarre that we should we spending so much time and treasure on something so little. Maybe more than a touch of hubris about it all. But then, maybe it will all come good. But then also, what about that other endeavour of big science, the quest for the quark at the large hadron collider at CERN and other such places? They are looking for a theory of everything which will explain the physical world, while here we are looking for a theory of everything which will explain the spiritual. Two big branches on the tree of knowledge, two sides of two not so very different coins, at least from a spiritual point of view. I don’t think that the God of the Garden of Eden would approve of either.

I then thought about the matter some more, the matter of one computer inside another, but with the one inside without a program. A formulation which is not entirely fair, as the model, the one inside, does exhibit interesting behaviour when it is poked. For example, if you twiddle with calcium levels, one of the parameters of the model, sometimes the neurons all jump up and down in a synchronised way, sometimes they just jump up and down.

So what we have is a chunk of rat brain, built on the basis of very general information, on the basis of vital statistics, but which manages to exhibit interesting behaviour.

This includes a lot of information about biological neurons, very complicated objects, objects which come in more than 57 varieties. They might all share the property of being electrically active and being able to generate electrical spikes, but they come in all different shapes and sizes, this being the morphological variation. And then there are all the different ways of responding to electrical stimulation, this being the electrical variation. And then some more.

Then there is a lot of statistical information out there about the numbers of all these different varieties and their distribution in space, through the six layers of a column through a small patch of cortex (the aforementioned deity having just missed the magic seven on this occasion). About the densities of the synapses of various sorts on those neurons.

A modified version of the Nobel prize winning equations which describe the behaviour of just one such neuron is illustrated (and which was taken from reference 4). By comparison, the neurons which computer people have been using for years to build neural network applications are very simple indeed, even those used to beat the Chinese at ‘Go’. So computer modelling of the joint behaviour of lots of these more realistic ones is a very considerable achievement.

All this has been done and the resultant model exhibits interesting behaviour when you poke it – but without the team having had to say anything about what the model is supposed to do. Rather as if we had built a general purpose computer, and then given it a poke to see what happens – and finding to our surprise that it does indeed do something of interest.

Maybe it not that big a step to using such a model to make predictions about how the real thing might respond if we give it a poke? About how, in certain circumstances, the real thing might go wrong in various kinds of way?

One catch is that according to the work of Dr Herculano-Houzel at reference 5, a  rat brain might contain some 10 billion neurons altogether, compared with the hundred thousand or so on show here. And a human brain might contain about 100 billion. So getting from a fraction of a cubic millimetre of a rat brain to the whole of a human brain might need an improbably large computer.

Another catch is that the model appears to have a large but fixed population of neurons and synapses. The synapses do not come and go, they do not wax and wane. To use the jargon, there is no synaptic plasticity. The model is not adapting, is not attempting to include learning, which goes on in a real brain all the time, from time scales of tens of milliseconds upwards. That said, the model does appear to be fully for up adaption, it has all the information needed.

On the plus side, the more recent work reported at reference 8 suggests that the behaviour of this model is correlated with its structure, from the point of view of algebraic topology, the topologies derived from the various directed graphs that can be derived from its chemical synapses. That some topological/statistical measure varies in time in a significant way as the model responds to stimulation. Another step forward.

This linking of neurons to topologies and measures reminds me of the IIT theory, being driven forward by Messrs. Tononi and Koch, from which they too extract a mathematically defined measure, called PHI, first noticed by me at reference 12, with the idea being that this measure is, in effect, a measure of consciousness. See reference 10 for a more useful introduction.

In the meantime, my own very modest efforts at brain science are from the top down rather than from the bottom up, involve neither fancy science nor fancy computers and with my LWS describing the data and process content of a small, conscious sheet of cortex at a level of abstraction in which the all-important neurons are barely visible. Never mind synaptic plasticity, supposed not to be an issue for the duration of what I am calling a frame of consciousness, although it certainly is for the compilation of that frame. See, for example, references 6 and 7. Very small science by comparison, barely science at all. But I do think that there is a place for it, just as there is room in the world for both experimental and theoretical physicists. 

Furthermore, it so happens that I once took an interest in algebra and topology separately and, as a result, someone had the bright idea that I might take an interest in them taken together, that is to say the algebraic topology mentioned above. This did not work out, with my failing to get properly started, but leaving me with a souvenir in the form of the well known book on the subject written by Eilenberg and Steenrod back in 1952. But now, forty years later, prompted by the topological appendix of the paper at reference 8, I am now motivated to try again. Eilenberg and Steenrod is still difficult and Wikipedia is a tool for reference rather than a textbook for the student, but somewhere along the line I came across the book by Hatcher (at reference 11) which has the advantages of being fifty years newer, open-access as a pdf and available secondhand for £20 or so. The case has been reopened, rather late in the day.

Maybe I will morph LWS from something like a large Excel workbook to something that an algebraic topologist would recognise. Maybe I too will find a use for mathematical measures, something which, in effect tests whether an instance of LWS contains enough for it to amount to consciousness, to a subjective experience. Or whether it is incoherent, the subjective equivalent of white noise.

References

Reference 1: https://www.scientificamerican.com/article/why-the-human-brain-project-went-wrong-and-how-to-fix-it/.

Reference 2: Reconstruction and Simulation of Neocortical Microcircuitry - Henry Markram, Eilif Muller, Srikanth Ramaswamy and others – 2015.

Reference 3: https://www.humanbrainproject.eu/en/.

Reference 4: Mixed-mode dynamics and the canard phenomenon: towards a classification – N Popović – 2008.

Reference 5: The human brain in numbers: a linearly scaled-up primate brain – Suzana Herculano-Houzel – 2009.

Reference 6: http://psmv3.blogspot.co.uk/2017/02/restatement-of-hypothesis.html.

Reference 7: http://psmv3.blogspot.co.uk/2017/05/in-praise-of-homunculus.html.

Reference 8: http://www.neuron.yale.edu/neuron/.

Reference 9: Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function – Michael W. Reimann, Henry Markram and others – 2017.

Reference 10: https://en.wikipedia.org/wiki/Integrated_information_theory.

Reference 11: Algebraic topology – Allen Hatcher – 2001.

Reference 12: http://psmv2.blogspot.co.uk/2013/04/phi.html.