It started with a simple equation. In 1980,
a mathematician named Benoit
Mandelbrot working for IBM plotted the behavior
of points on a plane using a computer. When the plane was
colored by the results, a whimsical world emerged: infinitely
branching scepters and spirals, never ending chasms, endless
tentacles growing from heart-shaped bulbs. It appears as
something from the final trippy minutes of
Kubrick’s 2001: A Space Odyssey, only much
stranger, like a tie-dye painted by insane space aliens.
The
Mandelbrot set shows complexity no matter how far we zoom in.
Source: Wikimedia Commons.
Almost none of the complexity of the eponymous Mandelbrot set
is readily obvious from the equation Benoit Mandelbrot plotted.
Pick a pair of numbers, one real and one imaginary. Now
multiply this pair by itself, many many times, and count the
number of iterations it takes to exceed a certain magnitude, or
distance from zero. Color each coordinate pair on the plane
according to the number of iterations that point took to grow
above the threshold. And viola! Complexity is born.
The shocking depth of complexity found in the Mandelbrot set
may teach neuroscientists a lesson about emergent
properties. Emergent properties are crucial
to understanding complexity and the brain. Unlike
simple phenomena, like the swinging of a pendulum, emergent
properties such
as intelligence and consciousness cannot
be understood by merely studying simple parts of a system. Even
holding the rulebook, in the case of Mandelbrot, may not
readily show how the rules result in complexity. Why does
squaring each number and adding back the result create such a
beautifully complex pattern? Why does a particular pattern of
neural connections allow for language and intelligence? To be
sure, mapping cells and their synaptic connections to other
cells in the brain has value. If nothing else, such maps
outline which communication routes are possible. But this alone
is not enough.
Closely related to emergent properties is the concept
of self-organization. This is the idea
that new phenomena can result from interactions between parts,
with no one part leading or controlling the system. Consider
the tiny worm C. elegans. Mapping all 302 neurons and synapses
in the adult hermaphrodite worm should, by the opposing
logic of reductionism, turn the scientist
into a prescient wizard who can foresee how the worm responds
to every possible stimulus. And yet, such knowledge has lead to
only modest insights into C. elegans‘ behavior.
Does this suggest that we still don’t fully know the rules
for how these neurons interact? Or is the simulation still not
detailed enough?
The roundworm C. elegans. Adult hermaphrodites have
exactly 302 neurons.
Source: Wikimedia Commons/Dan Dickinson, Goldstein lab,
UNC Chapel Hill
Sometimes we need more firepower. If we have enough powerful
computers, this reasoning goes, a simulation will show us how
every wiggle and breath results from each poke and prod. Such
is the justification for the Human Brain
Project (HBP), an undertaking co-funded by the
European Union that has inherited goals from
Switzerland’s Blue Brain project. Lead by
neuroscientist Henry Markham at the
Swiss Federal Institute of Technology in Lausanne, HBP aspires
to run a massive simulation of a human brain using the vast
firepower of supercomputers across Europe. Not the least
of these is an IBM blue gene supercomputer performing
nearly six quadrillion floating point operations per second!
In the case of the Mandelbrot set, computers were the key to
unlocking complexity—without their laborious firepower, it is
likely that no human would ever see the haunting patterns that
emerge from a simple equation. But for an emergent property to
be simulated by a computer, the complete rulebook must be
known. As we discover new molecules and developmental
trends in the brain, our humility grows with our knowledge. Are
we actually ready to build a computer model of the human brain
when, as recently as several years ago, a widely accepted model of neural
connections in the adult brain known as
the tripartite synapse was found to
be wrong? And there is still some disagreement among neuroscientists on
questions as basic as how and where memories are
stored in the brain. Other gaps in our
knowledge—such “orphan”
receptors whose
neurotransmitter parents have not yet been
discovered—underscore the possible hubris of such a moonshot
level undertaking.
It’s important to emphasize that even small discoveries of this
sort matter. Small causes may have big effects. This concept,
known as nonlinearity, underlies complex
systems. In Mandelbrot’s case, changing the position of a point
on the plane by a hair may completely alter its color or
magnitude. In the brain’s case, slightly adjusting the resting
voltage of neurons may completely alter their collective
activity. Nonlinear interaction between parts is
central to self-organization.
In the Mandelbrot set, patterns on all scales exist, even if the observer
zooms in for infinity. While the brain does not exhibit a truly
infinite range of complexity, it does exhibit structure and
activity over a vast range of different scales of space and
time. Complex connectivity patterns are observed from
microscopic synapses to the whole-brain scale. This facet of
brain complexity urges us not to build our understanding of the
brain only on cells, but all relevant scales. Indeed, the
“functional unit” of the nervous system is sometimes identified
as the neuron, but also as larger structures known as cell
assemblies and neocortical columns.
Markham has closed a TED talk by suggesting his model
brain might one day speak to humans through a hologram.
Herculean goals of simulating consciousness or otherwise
biting off more than the project can
chew have been criticisms of HBP. But if we cannot
understand emergent properties through vast computer
simulations like HBP, how can we understand the brain? Is
reverse engineering the brain possible?
Henry Markram
Source: Flickr user cea+
A true reverse engineering approach requires understanding the
brain on its most abstract level. Such holistic understanding
transcends knowing that a gene or brain region is needed for
memory or cognition—it explains how and why. A paper
published in the journal Neuron in February calls for neuroscientists to consider how a
circuit in the brain could or should work before dissecting it
with a plethora of tools, just as one needs to understand such
concepts as aerodynamics and lift before studying a bird’s
wing. This idea, which originated with the late
neuroscientist David Marr, implies that
HBP first needs a theory for how language or consciousness
could emerge from neurons and synapses before blindly
simulating billions of them.
Until we know how and why a certain pattern of activity or
piece of brain tissue is needed for behavior, we can’t really
claim that we understand the brain. In the meantime, there will
always be room for theoreticians outside the lab to ponder our
behaviors and ask what biological machinery could beget such
complexity. The foundation of neuroscience need not
be merely single cells, but also great ideas.
