[Comp-neuro] Re: Attractors, variability and noise

Dan Goodman dg.comp-neuro at thesamovar.net
Wed Aug 20 14:39:36 CEST 2008

(I sent this email a little while ago, and Jim Bower replied on the 
list, but it was rejected because I sent it from the wrong email 
address. Apologies for it being slightly out of sync with the discussion.)

As a recent convert to neuroscience from pure mathematics, I'd like to
say something about the use of intuition. Pure mathematics, if anything,
would surely be considered the ultimate expression of "formal systems
freed from a reliance on human intuition". This is partly true as a
description of a completed mathematical proof (although not entirely,
but I won't go into that here), but it's a really bad description of the
process of discovery and investigation in mathematics, which is strongly
guided by intuitive notions. Indeed, I don't think it can be any other
way, because we humans are really bad at thinking directly formally, we
have to think using metaphors and analogies. This is the lesson of the
Wason Card Problem which almost nobody gets right when it is stated in
formal terms (cards with A, B, 1, 2 on them), but everyone gets right
when an exactly equivalent problem is stated in familiar terms (a
bouncer at a bar).

Why is this important? Because even though our intuitions are often
wrong, they are just about all we can use to come up with creative new
ideas. It's a practical necessity to develop intuitive understandings of
concepts in order to get anywhere, even though we know our intuitions
will mislead us and that most attempts to generate good intuitive
concepts won't work out. These intuitive concepts help us to find our
way in the unimaginably immense space of possible ideas. Without them,
we're just stumbling about in the dark, and although we might find our
way it could take a very, very long time.

I could give you any number of developments in pure mathematics which
are all about transforming one theory into an equivalent theory that is
intuitively easier to understand. These helped mathematics to progress,
because although a formal proof in the original theory was theoretically
possible, nobody would have been able to imagine it without the
transformation to the more intuitive theory. In my own PhD thesis, the
key to finding the main result was realising that there was a loose
analogy between a particular type of hyperbolic geometry and a concept
from number theory (continued fractions). This loose analogy allowed me
to create a new intuition, a mental picture of that hyperbolic geometry
(yes, it is possible to visualise these things in some sense!), and use
that picture to find a proof of the result. Without that picture, even
though in some strict sense it was inaccurate, I would never have been
able to find that proof.

In Popperian terms, it's worth making the distinction between the
context of justification (testing a theory against evidence) and the
context of discovery (coming up with the theory to test). I would say
that 'understanding' is not necessary in the context of justification,
but that anything goes in the context of discovery - we shouldn't
discard anything that helps us to generate new ideas. This is perhaps
particularly important for theoretical neuroscience because there aren't
many reliable intuitive concepts yet (by reliable, I mean ones that can
be relied on to generate good insights in many cases).

Jim asks "Who cares if single individuals understand?". Even if
individuals aren't going to understand everything, if there is going to
be any understanding, it will have to be somehow at the individual or
group level, and if it's going to be at the group level that
understanding will have to be communicable (in part even if not as a
whole), and I'd argue that to be communicable it will have to use
intuitive elements that are comprehensible at an individual level.

That said, none of this says you shouldn't be striving for simulations
that are more and more detailed, but it does say that people should also
be looking at less detailed more concept driven work as well.


james bower wrote:
 > Is this how string theory or cosmology works in Physics?
 > Isn't the big lesson of non-euclidian geometry (as historically the
 > first example) and physics as a whole, that formal systems free you from
 > reliance on human intuition?
 > Can you really 'visualize' a world in which parallel lines always cross?
 > Who cares if single individuals understand?  Single individuals don't
 > understand much of anything these days -- really --  Further, who says
 > that everyone should understand or can understand?  Why does biology and
 > neuroscience have to live by some egalitarian - one for all all for one
 > standard for explanation.  Hate to say, but one of the reasons that many
 > experimental neurobiologists don't like theory, is that it bothers them
 > that they don't have the skills to participate (thus the need to
 > completely change how biologists are educated).  Of course, there are
 > also abstract modelers that don't like detailed compartmental models for
 > much the same reason (too much biological detail -- inelegant, etc).
 >  Then there are those who intentionally make their models so complex
 > (and hide their base code) to reinforce the idea that they and they
 > alone are smart enough to figure these things out.  Seems to me that one
 > way or another, as in physics to a remarkable extent, we have to get to
 > the point that these ego driven human frailties don't matter -- But by
 > embracing them, and taking them as a standard for what is useful
 > explanation, we are all just agreeing to dance around the camp fire
 > (ppt) and tell interesting stories.  That's not science, and won't work.
 > Yes, this is an issue of the nature of explanation, and the nature of
 > the tools that lead to that explanation.
 > Ironically enough, although it annoys me at times, most of the funding
 > for neuroscience research in the US comes from the National Institutes
 > of Health.  They could not care less (in principle) about grand theories
 > of brain function , because their focus is (again in principle) on
 > understanding and improving human health.  Wouldn't a complete physical
 > model of the brain -- be a useful device to understand the mechanics of
 > disease?
 > Personally, I also study brains for more etherial reasons (the chase,
 > they are beautiful, get to hang out with smart graduate students,  etc),
 > but, it just seems bizare to me to justify models of brains that may
 > have nothing to do with brains because it is relatively easy to tell
 > lots of people about them.
 > The planets would still circle the earth if that were the standard
 > applied to physics, and we would know nothing about gravity.
 > It is very unlikely that the brain will ever be understood by 'the
 > people' -- but accurate models of the brain will be very useful for
 > people anyway, and lots of fun to build.
 > The core point remains, however, in a system as complex as the brain,
 > how can you possibly ignore its machinery if we are trying to understand
 > how that machinery works?  It is simply too easy for unrecognized biases
 > and assumptions to sneak into other levels of explanation, justified by
 > selective reference to simple ideas about the machinary.  In the end,
 > 'the neurons represent the truth" and probably will make fools of us all.
 > Jim
 > On Aug 15, 2008, at 12:23 PM, Brad Wyble wrote:
 >> On Wed, Aug 13, 2008 at 7:23 PM, Robert Cannon
 >> <robert.c.cannon at gmail.com <mailto:robert.c.cannon at gmail.com>> wrote:
 >>         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.
 >> But It is still the people, and not the models, that possess the
 >> understanding.   If I were to email you my theory, encapsulated in a
 >> functioning model of the hippocampus using millions of 500 compartment
 >> neurons, you would still need to execute the model and build an
 >> understanding of its function in your head, in order to have any
 >> useful thoughts about it.    To do that, I would have to tell you my
 >> theory in verbal form, and how to find evidence of it within the
 >> model's behavior.
 >> For complex behavior, that verbal formulation has to be high enough
 >> level to capture the dynamics of interest in the behavior.   I mean,
 >> do channel dynamics have much to say about language production?  And
 >> if not, why use a supercomputer to simulate them?
 >> [snipping Astronomy analogy]
 >>     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 
 >>     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.
 >> I agree with you completely.  One cannot run the model in one's head
 >> because even a simple equation can have surprising dynamics.  But
 >> abstract modelling does not involve thinking in one's head, it just
 >> involves a level of simulation that averages over low level details,
 >> much as you already average over  Brownian motion.
 >> But one does need to *have* a high level theory to understand
 >> behavior.  The back and forth between the scientist and the model is
 >> what generates progress, not the mere existence of the model.
 > ==================================
 > Dr. James M. Bower Ph.D.
 > Professor of Computational Neuroscience
 > Research Imaging Center
 > University of Texas Health Science Center -
 > -  San Antonio
 > 8403 Floyd Curl Drive
 > San Antonio Texas  78284-6240
 > Main Number:  210- 567-8100
 > Fax: 210 567-8152
 > Mobile:  210-382-0553
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