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Conscious Philadelphia

Conscious Philadelphia by Brian Edwards and Greg Dunn.  Video by Will Drinker.

What:

Neurons are the basic building block of the human brain.  However, individual neurons possess neither consciousness nor intelligence.  It is only through the emergent behavior that is born out of the relationships between these neurons that allows us to think, feel, and experience the world around us.

A city's infrastructure is made of concrete and steel, but its soul is made of the relationship between people.  Similar to the exchange of neurotransmitters between neurons, each of us have thousands of interactions with each other every day.  This begs the question, what is born of the relationships between people? What are we a part of without ever realizing it?

In this piece, Greg Dunn and I visualize the city of Philadelphia by imagining the relationships within Philadelphia's populations as neurons.  Each neuron consists of an axon, soma, and dendrites.  The locations of soma, axon tips, and dendrite tips are chosen randomly by treating Philadelphia's population density as a probability density function.  Each neighborhood is treated as a separate functional region of the brain.  For instance, North Philadelphia is imagined as the Prefrontal Cortex.

Networks find ways of organizing themselves to optimize efficiency while respecting physical constraints.  In the case of the brain, the majority of the intricate interneural relationships happen in the gray-matter at the brain's periphery while long range connections are achieved efficiently though high-speed bundles known as white-matter.  Observing a city, we find traffic uses a similar strategy.  Philadelphia is known as the "City of Neighborhoods."  Each neighborhood consists of a rich culture built on the relationships between its residents within walking distance of each other.  In contrast, Philadelphia also has a network multilane highways that allow you to get from one neighborhood to another quickly.

Since different regions of the brains are responsible for different aspects of human thought, it follows that a sensory input (burning one's finger) will elicit a pattern neural activations as one first pulls the finger away and then contemplates how it happened second later.  We can represent similar regional neurological patterns by routing different neighborhoods, each representing a different brain region, into each other in a sequence.  Given the similarity between traffic architecture and neural architecture, it shouldn't be a surprise that when two neighbors are imagined to interact, we see similar structures appear in a city and in the human brain.

As one walks past Conscious Philadelphia, one can see different neighborhoods of Philadelphia routing neural activity.  Several neural pathways are depicted.  The axons and dendrites make use of Philadelphia's streets as guides, but are drawn in a style that is far more indicative of stochastic processes that were involved in neural growth.

HOW:

In the field of artificial neural networks, each neuron would be considered a single node onto which edges from a previous neural layer would map and which would map onto the following neural layer.  Images like the one the one to the right are very common.  There might be more or less "neuron" and more "layers", but the concept is basically the same.  The workings of this network is governed by the mathematical weight of each connection.

While mathematically convenient, this model doesn't give much indication of its biological underpinnings.  First, in an actual neural network, every node from one layer is not connected to the next.  Rather each node might map to only a handful of nodes in the next layer.  Second, while the dendritic branching is well depicted in this model, the axons are missing.  If each one the depicted nodes represents the somas and beginning of the axons, we can imagine inserting an intermediate layers of nodes that represent the axon terminations.

In the drawing above, these nodes exist in a neat orderly lines.  However, in biological systems they are dispersed randomly throughout the neural tissue.  What is the metaphoric equivalent for a city?   I decided to use the population density of Philadelphia a proxy for the probability for finding either a soma or axon termination at a location.   First, if each network edge represents an interpersonal relationship, it follows that there should be more relationships within the most populous areas of the city.  Second, looking ahead, it follows that the most populous regions will be the best connected through the road system and this is will be vital for routing.

If we consider each step of a neural pathway as consisting of a layers of neurons, then each neural pathway can be envisioned as a series of network edges between point clouds wherein the location of each point is chosen stochastically based on the population density.  The edges are similarly chosen stochastically.  However, they could be informed from an aesthetic point of view based on distances.  Neighbors tend to be friends.

Of course we do not travel "as the crow flies," but rather make use of our network or roads.  These edges are not straight lines, but rather paths through our transportation system.  To find these thousands of paths, I installed a local copy of the GraphHopper routing engine.  (At first I was utilizing Google Maps through their web API, but they got tired of my endless number route requests and blocked my IP.  It was justified.)  Each of the thousands of network edges (ie axons and dendritic arms) are now represented by sequences of points of the form {x,y,t} representing the path between pairs of nodes in the network.  Note that this path not only denotes the "where" but also the "when."

In contrast to a traditional medium such as paint, microetchings allow us to encode an extra dimension of data.  In this case, we choose to encode time.  A neuron will fire when there is a sufficient action potential generated by other neurons and so the firing of the neurons is causal.  To represent this all of the paths must be aligned in time so that the axons will trigger their connected dendrites simultaneously.  This is actually a bit tricky because each path has a duration.  Once multiple layers are combined the network ceases to be acyclic and we need multiple path through the network between the same two nodes to occur in the same time.  This might require that the paths need to be traversed more quickly or more slowly than originally calculated.  This can be formulated as a least squares minimization wherein the "relaxed" duration between the nodes is that calculated by GraphHopper.  This provides an time dilation adjustment factor for each each edge.

When an axon grows it must work its way through all of the other neurons.  When something blocks its path, it might go left on occassion and right on the next.  This process is captured well using a "random walk" which essentially adds stochastic noise onto the route.  Biologically, the long range white matter tends to be smoother and more direct than short range connections.  Within this piece, the long range connections tend to be routed through Philadelphia's highway system while short range connections are done through local roads.  If we tie the stochastic noise to the inverse of the velocity, this will naturally fall out to give a nice blending of a road map with neurological morphology.  The cell somas are added in as well.