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A Neuromorphic Model: The Cerebellum 
A question I examined in 
The Age of Spiritual Machines
is: how does a ten-year-old manage to catch a fly ball?
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All 
that a child can see is the ball's trajectory from his position in the outfield. To actually infer the path of the ball in 
three-dimensional space would require solving difficult simultaneous differential equations. Additional equations 
would need to be solved to predict the future course of the ball, and more equations to translate these results into what 
was required of the player's own movements. How does a young outfielder accomplish all of this in a few seconds with 
no computer and no training in differential equations? Clearly, he is not solving equations consciously, but how does 
his brain solve the problem? 
Since ASM was published, we have advanced considerably in understanding this basic process of skill formation. 
As I had hypothesized, the problem is not solved by building a mental model of three-dimensional motion. Rather, the 
problem is collapsed by directly translating the observed movements of the ball into the appropriate movement of the 
player and changes in the configuration of his arms and legs. Alexandre Pouget of the University of Rochester and 
Lawrence H. Snyder of Washington University have described mathematical "basis functions" that can represent this 
direct transformation of perceived movement in the visual field to required movements of the muscles.
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Furthermore, 
analysis of recently developed models of the functioning of the cerebellum demonstrate that our cerebellar neural 
circuits are indeed capable of learning and then applying the requisite basis functions to implement these sensorimotor 
transformations. When we engage in the trial-and-error process of learning to perform a sensorimotor task, such as 
catching a fly ball, we are training the synaptic potentials of the cerebellar synapses to learn the appropriate basis 
functions. The cerebellum performs two types of transformations with these basis functions: going from a desired 
result to an action (called "inverse internal models") and going from a possible set of actions to an anticipated result 
("forward internal models"). Tomaso Poggio has pointed out that the idea of basis functions may describe learning 
processes in the brain that go beyond motor control.
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The gray and white, baseball-sized, bean-shaped brain region called the cerebellum sits on the brain stem and 
comprises more than half of the brain's neurons. It provides a wide range of critical functions, including sensorimotor 
coordination, balance, control of movement tasks, and the ability to anticipate the results of actions (our own as well as 
those of other objects and persons).
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Despite its diversity of functions and tasks, its synaptic and cell organization is 

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extremely consistent, involving only several types of neurons. There appears to be a specific type of computation that 
it accomplishes.
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Despite the uniformity of the cerebellum's information processing, the broad range of its functions can be 
understood in terms of the variety of inputs it receives from the cerebral cortex (via the brain-stem nuclei and then 
through the cerebellum's mossy fiber cells) and from other regions (particularly the "inferior olive" region of the brain 
via the cerebellum's climbing fiber cells). The cerebellum is responsible for our understanding of the timing and 
sequencing of sensory inputs as well as controlling our physical movements . 
The cerebellum is also an example of how the brain's considerable capacity greatly exceeds its compact genome. 
Most of the genome that is devoted to the brain describes the detailed structure of each type of neural cell (including 
its dendrites, spines, and synapses) and how these structures respond to stimulation and change. Relatively little 
genomic code is responsible for the actual "wiring." In the cerebellum, the basic wiring method is repeated billions of 
times. It is clear that the genome does not provide specific information about each repetition of this cerebellar structure 
but rather specifies certain constraints as to how this structure is repeated (just as the genome does not specify the 
exact location of cells in other organs). 

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Some of the outputs of the cerebellum go to about two hundred thousand alpha motor neurons, which determine 
the final signals to the body's approximately six hundred muscles. Inputs to the alpha motor neurons do not directly 

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specify the movements of each of these muscles but are coded in a more compact, as yet poorly understood, fashion. 
The final signals to the muscles are determined at lower levels of the nervous system, specifically in the brain stem and 
spinal cord.
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Interestingly, this organization is taken to an extreme in the octopus, the central nervous system of which 
apparently sends very high-level commands to each of its arms (such as "grasp that object and bring it closer"), leaving 
it up to an independent peripheral nervous system in each arm to carry out the mission.
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A great deal has been learned in recent years about the role of the cerebellum's three principal nerve types. 
Neurons called "climbing fibers" appear to provide signals to train the cerebellum. Most of the output of the 
cerebellum comes from the large Purkinje cells (named for Johannes Purkinje, who identified the cell in 1837), each of 
which receives about two hundred thousand inputs (synapses), compared to the average of about one thousand for a 
typical neuron. The inputs come largely from the granule cells, which are the smallest neurons, packed about six 
million per square millimeter. Studies of the role of the cerebellum during the learning of handwriting movements by 
children show that the Purkinje cells actually sample the sequence of movements, with each one sensitive to a specific 
sample.
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Obviously, the cerebellum requires continual perceptual guidance from the visual cortex. The researchers 
were able to link the structure of cerebellum cells to the observation that there is an inverse relationship between 
curvature and speed when doing handwriting that is, you can write faster by drawing straight lines instead of detailed 
curves for each letter. 
Detailed cell studies and animal studies have provided us with impressive mathematical descriptions of the 
physiology and organization of the synapses of the cerebellurn,
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as well as of the coding of information in its inputs 
and outputs, and of the transformations perforrned.
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Gathering data from multiple studies, Javier F. Medina, Michael 
D. Mauk, and their colleagues at the University of Texas Medical School devised a detailed bottom-up simulation of 
the cerebellum. It features more than ten thousand simulated neurons and three hundred thousand synapses, and it 
includes all of the principal types of cerebellum cells.
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The connections of the cells and synapses are determined by a 
computer, which "wires" the simulated cerebellar region by following constraints and rules, similar to the stochastic 
(random within restrictions) method used to wire the actual human brain from its genetic code.
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It would not be 
difficult to expand the University of Texas cerebellar simulation to a larger number of synapses and cells. 

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The Texas researchers applied a classical learning experiment to their simulation and compared the results to 
many similar experiments on actual human conditioning. In the human studies, the task involved associating an 
auditory tone with a puff of air applied to the eyelid, which causes the eyelid to close. If the puff of air and the tone are 
presented together for one hundred to two hundred trials, the subject will learn the association and close the subject's 
eye upon merely hearing the tone. If the tone is then presented many times without the air puff, the subject ultimately 
learns to disassociate the two stimuli (to "extinguish" the response), so the learning is bidirectional. After tuning a 
variety of parameters, the simulation provided a reasonable match to experimental results on human and animal 
cerebellar conditioning. Interestingly, the researchers found that if they created simulated cerebellar lesions (by 
removing portions of the simulated cerebellar network), they got results similar to those obtained in experiments on 
rabbits that had received actual cerebellar lesions.
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On account of the uniformity of this large region of the brain and the relative simplicity of its interneuronal 
wiring, its input-output transformations are relatively well understood, compared to those of other brain regions. 
Although the relevant equations still require refinement, this bottom-up simulation has proved quite impressive.