email of the month: grids on the brain

An intriguing email from Kenny Easwaran:

I was very struck by this post in which you try to generalize the geometric issues to show that some of these features of transit are really universal.  [JW: I also wrote this on the underlying power of grids in public transit.]

At the time, I was thinking of the various transportation systems we know of that aren’t designed by humans.  The main examples I could think of were things within the human body, and I noticed that things like the circulatory systems of animals and plants, and the digestive system of animals, seem to follow somewhat different trajectories from grids.  In particular, they either have a branching tree structure, or something more like an extended linear structure.  

Of course, in these cases, it may have more to do with the drive system – the circulatory system is driven by a single central pump, and I don’t know if it has any sort of intelligent routing, which may make a grid system hard to operate.  It also seems to primarily ferry resources from two centers (the lungs and digestive tract) to all the rest of the body, so a tree structure may be the most efficient way to do this (like an old hub and spoke rail network centered on downtown).  

At any rate, the reason I’m writing this e-mail now is that I just saw an article suggesting that the human body *does* actually use a grid system!

Monkey-connectome-640x442From the article:

It’s rather weird: If you’ve ever seen a computer ribbon cable — a flat, 2D ribbon of wires stuck together, such as an IDE hard drive cable — the brain is basically just a huge collection of these ribbons, traveling parallel or perpendicular to each other. There are almost zero diagonals, nor single neurons that stray from the neuronal highways. The human brain is just one big grid of neurons — a lot like the streets of Manhattan, minus Broadway, and then projected into three dimensions.

Kenny goes on:

It seems plausible that the information transport network of the brain is a better comparison for human transportation needs than the resource transport network of the bloodstream … !

Looking at the diagram in that article a little more closely, it seems that there’s a two dimensional grid structure, even though the brain is three dimensional.  There appear to be axes going from front toback, and other axes going radially from the “suburbs” through the central axis through to the “suburbs” on the other side, but no grid elements going around the periphery from left to right.  I guess there’s an interesting sense in which a three dimensional transport structure can be gridlike in two dimensions but not the third?

At any rate, I’d be very interested to hear your thoughts on any of these analogies!  (It might also be interesting to look at structures in ant colonies and prairie dog towns, to see how they approximate thevarious geometries of transportation that you think might be worth looking at, though they are probably more analogous to purely pedestrian cities, rather than ones with long transport tubes.)

I’d be interested in hearing everyone’s thoughts on this!  (Apologies for the new comment monitoring; it’s purely to combat spam!)

Image from the article.

15 Responses to email of the month: grids on the brain

  1. Tim August 6, 2012 at 10:04 pm #

    A fascinating parallel–this is brain candy for my inner planner and inner psychology!
    As for Kenny’s information/resource transport analogy, I think he’s right on the money. Global commerce routes goods through a branching tree, with ports and rail hubs and producers connected along major arteries and then branching out to smaller, lower-capacity routes to send goods to their final destinations. Cities are more like massively parallel processors, with countless scattered hubs that need to interact with many neighbors. I’m no neuroscientist, but I’d venture to guess that the scaling relationships of goods movement to passenger travel in cities are similar to those of blood flow to neural activity in the brain.

  2. EN57 August 6, 2012 at 10:55 pm #

    Anyone interested in networks and network science should see “How Kevin Bacon Cured Cancer” – trailer at
    This has been shown on Australian TV a couple of times – and is totally fascinating in terms of the potential power of network thinking in many human endeavours including transport planning.

  3. Brendan August 7, 2012 at 3:55 am #

    I don’t necessarily think many of these analogies work for transit because these networks have different purposes. A grid works well because you can fairly efficiently go from any destination to another by following grid lines. Radial symmetry and branches have problems because it’s not easy to go from one branch to another.
    With blood in veins, it doesn’t always matter which blood cell is where, it only matters that any blood is getting to that area. With humans and transit, the object of transit isn’t to flood every space with humans but to transport specific humans to specific destinations.
    Ant analogies don’t work either for very obvious reasons. If you’ve seen a trail of ants, you’ll realize they all have the same jobs and they’re headed to just about the same locations and doing the same thing. There are certain specialty ants with different purposes, but it’s still nothing like humans.
    Also, ants have to build their routes in certain shapes for more than just ‘efficiency,’ they also build them a certain way for safety and mitigating potential damage to their nest.
    We can learn *some* things from looking at other non-human networks, but none of the ones suggested feel like they have even remotely similar functions.

  4. Matt Caywood August 7, 2012 at 6:13 am #

    Hi Jarrett — I’m a neuroscientist with some familiarity with transit geometry.
    Unfortunately this example isn’t a good analogy for transit. The wires aren’t making any connections with each other! They’re “fibers of passage” going from one suburban area on the outside of the brain (cortex) to another suburban area, and only connecting at the terminals.
    There is one major connected grid system in the brain. It’s in the cerebellum, the convoluted area at the back of the brain that’s specialized for learning movement. There, parallel fibers and Purkinje cell dendrites connect at each intersection point, as shown in this schematic:

    Note that the two axes of the grid don’t have the same dimension — it’s roughly like a city where west-east routes are all 10 miles long, but north-south routes are only a mile long.
    Overall, I think resource transport (blood vessels) and information transport both have some analogies to transit — but which one is appropriate depends on geometry of the city, features of the network, and the physics of the vehicles.

  5. Tom West August 7, 2012 at 9:50 am #

    To me, it looks like it’s based around a cylinder, not a cube. You have radial lines from the axis of the cylinder, lines parallel to the axis, and then circles (“orbital lines”) centred on the axis.
    (It’s like a radial/orbital system plus vertical lines)

  6. Kenny August 7, 2012 at 9:59 am #

    Thanks for hosting a discussion about this! I’m definitely interested to hear what things make the analogies and what things break them. That’s exactly what we need to know to figure out if some specialized transportation application ought to be structured differently from others.
    One thing I was realizing last night thinking about hub-and-spoke systems is that they make a lot more sense when a single transit line doesn’t want to stop everywhere along the way. A grid will only make sense if it’s very easy for the transportation method to stop and exchange passengers everywhere along the way – airplanes really wouldn’t work very effectively that way, so instead it just makes more sense for each airport to have a flight to a couple major hubs nearby. (Although it would be funny to imagine Southwest running a “grid system” of east-west and north-south short hop flights.)

  7. Steve Munro August 7, 2012 at 3:23 pm #

    I think a central point has been omitted in much of this, namely that transportation networks in cities come very much after the fact, after the child is born, so to speak. Moreover, there are competing visions of what that system should accomplish. There are even overlapping uses of the same network. Networks are “optimized” for whatever problem consumes a city at the moment with little thought for how it might work in 50 years because demolition is always an option.
    By contrast, the circulatory and neural systems have evolved over millenia and species to optimize for what they do, and to provide their services for the lifetime of the organism.
    There are no environmental assessment hearings, no carpet-bagging developers who care little for the effect of their schemes on existing cities, no technology gurus trying to find an excuse for their latest gadget, no councillors looking to line their pockets with campaign contributions.
    If the demand on the circulation network grows beyond its capacity, the luckless patient dies. If it’s a city, we build an expressway and call it progress.

  8. Jeffrey Bridgman August 7, 2012 at 6:09 pm #

    I wonder if things like ant colonies, blood, etc., really work more as an analogy of automobile transportation systems? There’s no grouping: each ant and each blood cell is like a car, each with its own path and destination
    In that sense, they better models road hierarchy (local street, collecter, arterial, etc).

  9. EN57 August 7, 2012 at 6:18 pm #

    I don’t accept the general assumption here that grid networks are the only applicable network structure for urban transit in all known universes. There’s a lot of redundancy in grid networks that can make them financially unviable and unsustainable in many urban environments – something that’s not tolerated in the natural world. Readers here need to be mindful of the sheer cost of frequent grid networks and be able to discern when and where grid networks are viably applicable and where they aren’t. Why do grid systems seem to attract lots of passengers in Canadian cities and not the US? The questions also go beyond network structures.
    In the cut-throat airline world, hub and spoke networks make sense under the given circumstances, but no seriously competitive airline would ever make the mistake of chaining themselves to a fixed idealised network structure when markets start going in a different direction. Airlines must know when and where network bypass (eg providing direct service) is necessary as market circumstances and opportunities change. I’m not advocating continually changing transit networks in urban areas, but rather knowing what structures best fit the needs of a particular city given its unique characteristics. Radial, trunk and feeder, hub and spoke networks are all perfectly legitimate transit network structures too. There may be much yet we can learn from natural network systems in this regard.

  10. Daniel N August 8, 2012 at 6:15 am #

    These kinds of threads are what comments are made for. I appreciate the intriguing suggestion.
    Steve Munro is right on. The major disconnect in the analogy I see is that the brain functions to optimize performance of a single organism, while a city has many competing interests. The brain doesn’t have to worry about neurons complaining about the traffic in front of their own house, or businesses lobbying for more access than their competitors. The city gets developed piece-meal through many political struggles.

  11. August 8, 2012 at 3:57 pm #

    I really like the idea. I am a big proponent of using concepts from natural systems in structural engineering design and I could see it working well for transportation as well. I also like the analysis of having two distinct locations like in blood cells vs a whole grid like in the brain – to me that seems like a fundamental question in planning a public transportation system.

  12. Alex B. August 12, 2012 at 2:01 pm #

    Interesting stuff. I recently read a book that put this in terms of the laws of physics, arguing that the properties of flow determine the form of the network we see. I wrote up some brief thoughts here.

  13. Eric O August 12, 2012 at 6:03 pm #

    Delightful to think of these analogies because the contrast they make with the grid network is instructive. I don’t know anything about neural networks (they might have “grid” properties), but in the case of the branching networks, such as the circulatory system and the bronchial tree, these are clearly simple point to area branch networks. They move things in and out from the single point (the heart/lungs, the nostrils) to an area (the cells of your body, the individual alveoli). They are systems maximized to transfer things from a point to individual destinations in a large area (and vice versa). The suburban street network is similarly organized with the same branching logic -a branching, hierarchical pattern organized around arterial trunks, collector branches, leading to individual cul-de-sac homes. I really, really like Jarrett’s term for these patterns: “DENDRITIC”. These patterns are organized to move things from individual homes spread out in a large surface area to the central large hubs of commerce and offices. Each link of the branching system serves similar purposes. Someone’s local street is much like someone else’s local street, tying in to collector streets that lead to faster/wider arterials, which lead to limited access even faster arterials and so on. So you have your primary, secondary, tertiary elements – a hierarchical system of progressively sized functional pieces.
    In fact this is the way we must all move. A grid serves the SAME pattern movements through space. We all must begin in a point in space and somehow navigate through a network to another point in space. Most pattern movements typically look “dendritic”, if we mapped them out individually in space. We begin with walking to catch the bus from our residence (one scale), we ride the bus to a hub (another scale), transfer to a subway, and so on, then reverse the process.
    But the wonderful thing about a grid is that everybody else’s dendritic patterns are able to share links regardless of function. They can be “superimposed”. The primary, secondary, teriary elements can be mixed and shared with others. Someone else’s “local” movement can be someone else’s “arterial” movement, conceptually speaking. The connective grid layers everybody’s diverse movements in an elegant unified net that, yes, is redundant. That redundancy actually represents an advantage for diversity, the diversity of different kinds of movements, a diversity of trip types. There is a subtle density of utilization built out of similar elements requiring less infrastructure here, which is the advantage of cities (see Geoffrey West’s TED talks on these allometric relationships evinced in cities). Basically, the grid is a configuration that “layers” dendritic patterns, densifying the geography of movement. You can say it superimposes the dendritic point to area patterns over one another.

  14. Nathanael August 20, 2012 at 6:35 am #

    If you’re curious about different network shapes, you’ll also want to look up “scale-free networks”.

  15. Carla Kenyon September 25, 2012 at 4:42 pm #

    Speaking of bodily maps…