Thinking like a pile of sand

It sometimes seems to me that managing my thoughts (and memories) resembles
trying to control a pile of sand grains as they sift through my fingers. Now,
new neuroscience research suggests that the analogy is not far off the mark. As
reported recently in the New
Scientist, it appears that the way in which our brain’s neurons connect
to each other and communicate is very much like the way a pile of sand behaves,
and it is this that bestows on our brain some of its “remarkable powers.”

Ten years ago, a Danish physicist, Per Bak, published How Nature Works:
The Science of Self-Organized Criticality, a book that I devoured and still
refer to (the paperback cover has an image of sand ripples; it’s now, sadly, out
of print and used editions seem to be going for either $130 or £130!). Bak used
sand pile avalanches as an illustration of the ubiquity of scaling  or
power laws in nature: the frequency (or its logarithm) of occurrence of
something is proportional to a measure (often size) of that something
multiplied by itself a specific number of times (raised to a certain
power, mathematically speaking). Newton’s law of gravity is a power law; the
pull of gravity on an object decreases with distance to the object squared.Since it decreases, Newton’s law is an inverse power law—and so is
that of sand avalanches: the bigger the event, the more rare it is. But what
about the “real world”? Scaling laws show up everywhere—in earthquake magnitudes
(each successively larger magnitude on the scale is a multiple of the previous),
population distributions, city sizes, the brightness of the Sun, and music (the
structure of rock music, classical music, and the spoken word all obey scaling
laws). Systems displaying this behaviour exist on the boundary between stability
and instability, order and chaos, and Bak coined the term self-organized
criticality (SOC)to describe this condition. It would now seem
that the brain operates in this apparently precarious realm, but generally
manages it rather well - and powerfully.

SOC is definitely notcharacterised by randomness, and, thankfully,
neither are our brains (contrary to occasional appearances). If the connections
between the neurons in the brain were random and structureless, then the organ
would be instantly overwhelmed by the sheer numbers of useless but
energy-sapping events. Nor are the neuronal connections simple - the new work
makes the comparison with “small-world” networks, more flexible and powerful
than simple networks, but perfectly manageable compared to randomness.

Such a
network of connections allows powerful “avalanches” of neuron communication
across relevant regions of the brain, often with synchronised “phase-locking” of
large groups of neurons firing at the same frequency; these groups operate
effectively but independently of other groups. These episodes of phase-locking
alternate with periods of much greater disorder, “blizzards” of activity in
which significant reorganisation seems to take place. The durations of these
phases and the avalanches of firing neurons at different frequencies all seem to
fit with the characteristics of SOC, apparently providing the brain with its
amazing capacity to process information and with its adaptability. And also a
great new excuse - “sorry, that part of my brain’s phase-locked right now.”

It’s worth noting that power laws and SOC are compelling phenomena, but often
easier to hypothesise than conclusively demonstrate. Phillip Ball has an
excellent discussion of the phenomena and the problem in his new book Flow,
one of his new trilogy on nature’s patterns (plus lots of other good stuff about
granular materials).

This fascinating topic has also been discussed on the Neuronarrativeblog which includes a link to a piece on which I can’t possibly comment, Why a Woman’s Brain is Like an Avalanche, a Landslide, an Earthquake, or a Hurricane.

Oh, and there’s also real “brain sand” - small quantities of grit often found
in the pineal gland, composed of various calcium minerals, referred to as
corpora arenacea, and believed by some swamis to carry holographic
rhythms of the body’s spatial and temporal existence. SIGNATURE

Comments

Silver Fox (2009-07-09):

Very nice! I wonder how often the “blizzards” occur, and how they might seem to those of us experiencing them. And I’ll have to remember that phase-locking excuse, sounds much more sophisticated than anything else I’ve heard!

Sandglass (2009-07-09):

Speaking for myself, the blizzards seem to occur quite frequently and they come with a sort of blurry sensation. And I had a phase-lock at the end of the post - a couple of links now added that you might enjoy.
Ah - was that a snow flake or just a floater?

Silver Fox (2009-07-12):

Thanks, maybe that’s why Stevie Nicks sings about landslides! :)

Originally published at: https://throughthesandglass.typepad.com/through_the_sandglass/2009/07/thinking-like-a-pile-of-sand.html