[Comp-neuro] Re: Attractors, variability and noise
Robert Cannon
robert.c.cannon at gmail.com
Wed Aug 13 20:23:02 CEST 2008
>
> As I understand the other end of the spectrum, we construct
> increasingly realistic models and end up with a simulated brain without
> a real understanding of how it works, which makes no sense to me.
> Understanding is what we're after, and that understanding can only
> reside in the brains of the population of scientists, not in their models.
>
Brad's point is fascinating - not least because I couldn't disagree more. :)
I do like the notion of understanding, but I suspect it is also somewhat
self-indulgent, because there may not be a level on which it can be shared
above that of working models.
To help explain why, when I was working in astronomy there was a
feeling among many of my colleagues that there should be a moratorium
on publication of papers purporting to explain a particular classical
phenomenon because the type of explanations being sought couldn't
actually exist. The problem is a fairly basic bit of astrophysics -
the transition of many stars from dwarfs to giants for the last tenth
of their active lives. There is no mystery here: there are
half a dozen equations and a bucket-full of well known physical data.
You implement them on a computer and you get something that behaves pretty
much like a real star. Then you've got your "prodable brain"
equivalent and it is natural to seek higher level,
intuitive, easily communicated, mathematically elegant explanations
of what's going on. Quite a few (mutually incompatible) explanations
were published.
The whole game unraveled however when people began addressing
"what-if" questions with these models. By definition, the explanations
are insensitive to quantitative details (like the opacity or
pressure-density relationship for stellar material) but it turns out
that if you compute what would happen with slightly different physics
(bigger gravitational constant, different opacities etc) then stars
don't necessarily turn into giants. So they are not actually insensitive
to the quantitative details. In effect the parameter
space is lumpy and we're in a particular patch (of course, you can
theorize about why we have to be in that patch but that's another
question entirely). Elegant explanations assume smoothness but
the space isn't smooth, so no such explanations can be correct.
Another observation was that when you ask people to predict
the outcomes of these what-if questions (about the only type of
experimental intervention that is possible in astronomy) then the people
who write and run the programs often do better than the theorists.
So, like most areas of expertise, you can develop an intuitive
understanding and internal model of the domain by years of
application, but there's no short cut - you can't get it from a
book. Other people who want the same abilities will have to get
there in the same way by internalizing the same mass of data.
My point is that for this particular problem, high-level theory is
not much use. Some of it is epiphenomenal, and the rest is just plain
wrong. The models work fine but they are too complicated to run in
your head. The simpler things that you can run in your head or on
paper are too coarse to be any use.
My personal guess, which I realize is deeply unpopular, is that this
also applies to much of neuroscience. If we do have a simulated brain,
then it will have been built using a vary large volume of data, a few
equations and a lot of extremely sophisticated software
engineering. I'm not sure there will be any point in looking for
theories at a higher level than the design documents and software
architecture that went into making it. If such complexity reduction
were possible, then you'd hope the engineers have got there by then.
The issue of whether, when you have a 64 bit floating point unit at
your disposal instead of a mass of synapses and ion channels, you can
make an equivalent but more mathematical and easily computed version
of a purkinje cell seems like a case of premature optimization
(or perhaps of engineering expediency) driven by todays prevalent
technology, not a question of durable scientific relevance.
As I see it, the area that needs the most attention, (both funding
and education) but receives practically none, is not maths, but how on
earth we develop the software engineering and data management
concepts, languages and technologies that will enable us to build the
next n generations of models.
Robert
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