Posts Tagged ‘Complexity’

Humans are hive enthusiasts. We love social insects like ants and bees, and we pay extra attention to Star Trek episodes when the you-will-be-assimilated Borg are featured. But what exactly is so interesting about hives? They’re interesting to us because, en masse, they amount to a superorganism, with analogs to organisms at the genetic level, reproductive level, and the behavior level. Also, just as larger, more complex, organisms tend to have a greater number of specialized cell types, larger ant colonies tend to have a greater number of “ant types” (see the figure).

And in new research this week in the Proceedings of the National Academy of Science, Chen Hou from Arizona State University found that the metabolic rates of ant colonies follow the same law – Kleiber’s Law – that solitary-living insects follow concerning how metabolism scales with body mass. Metabolically, colonies act like superorganisms rather than just big groups of organisms. Ant colonies really are organisms.

Why, though, should we find that fascinating? If ant colonies are organisms, then they should get imbued with the same level of interest we find in the average organism. To understand what makes social insects especially exciting, we must get inside our own heads, and the perceptions we evolved to possess.

In addition to the perceptions you may have heard about – like color, motion and form – we have intrinsically much more complicated perceptions. Face recognition is one example, but relevant to our purposes here is the perception of “animacy”. Certain stimuli elicit perceptions in us of there being a living, animal-like, thing. Even a simple square moving about can elicit this kind of perception, so long as it moves in a sufficiently animal-like fashion.

But there is one thing our “animal perception” requires that ant colonies and the Borg violate: Animals must be solid objects. To be an animal, our perceptual system demands that the constituent cells must be physically connected, not merely be informationally connected. Hives do all the requisite information interconnectivity without having to be physically touching, and although that is a difference that makes no computational difference, it makes all the difference in the world to our perception.

Our perceptions of animacy lead us to the conclusion that the ant drones are the animals, not the colony itself. That is what makes social insects so interesting: social insects are cases of animals that don’t fit our evolved perceptual expectations for animals. What makes social insects and the Borg so interesting is, then, more about our perceptual apparatus than it is about the intrinsic coolness of ants or assimilation.

And if hives can be exhilarating to our brains for perceptuo-cognitive reasons, then we can exhilarate in the other direction. Rather than concentrating on the animal-hood of colonies, let’s ask about the colony-hood of animals. Animals are, after all, massive colonies of cells. The problem with thinking of animals as cell colonies is that even if we could see individual cells, cells don’t have the animal-like properties ants do, and thus cannot tap into our animal perceptions.

Or can they? Cells do often behave in an ant-like animal fashion, but just move too slowly for you to perceive their animal-likeness. When one views videos of cells in a a growing animal, and the video allows us to see the individual cells moving, animals begin to look instead like colonies of cells. Take a look at the second and third video here — http://pr.caltech.edu:16080/events/kulesa/ — showing cell movements in the developing chick embryo from the laboratory of Paul Kulesa. (In fact, download the videos to your computer first, and then play, so that you can make the video larger.) You will see, especially in the third movie, individual cells poking about, and at this spatio-temporal scale your animal perceptions are activated, and the chick is no longer an animal, but is perceived instead as a colony of single-celled animals.

This first appeared on January 24, 2010, as a feature at the Telegraph.

Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

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There is an apocryphal story about a graduate mathematics student at the University of Virginia studying the properties of certain mathematical objects. In his fifth year some killjoy bastard elsewhere published a paper proving that there are no such mathematical objects. He dropped out of the program, and I never did hear where he is today. He’s probably making my cappuccino right now.

This week, a professor named Peter Sheridan Dodds published a new paper in Physical Review Letters further fleshing out a theory concerning why a 2/3 power law may apply for metabolic rate. The 2/3 law says that metabolic rate in animals rises as the 2/3 power of body mass.  It was in a 2001 Journal of Theoretical Biology paper that he first argued that perhaps a 2/3 law applies, and that paper — along with others such as the one that just appeared — is what has put him in the Killjoy Hall of Fame.  The University of Virginia’s killjoy was a mere amateur.

Peter Sheridan Dodds, Buzzkill

The 2/3 scaling law, you see, is intuitively obvious (even if not intuitively obvious to truly defend in detail). The surface area of animals scales as the 2/3 power of their body mass, and so the rate of heat loss scales as the 2/3 power. If metabolic rate scaled as the 2/3 power, few theorists would probably have bothered taking the problem on.

But in the 1930s one Max Kleiber accumulated data that suggested to him that metabolic rate scales as the 3/4 power of body mass. It came to be known as Kleiber’s Law. 3/4 is fun. …to a theorist. 2/3, however, is boring. 3/4 is so fun that theorists had a field day trying to explain it, and there was an especially gigantic spike in the fun starting from 1997, especially from a series of papers by West, Brown and Enquist, and also by Banavar and Maritan.

And that’s when buzzkill Dodds came along with his 2001 paper. He re-examined the data, and suggested that a 2/3 law could not be rejected. There may be no 3/4 law to explain after all. Nothing to see here, move along everyone. That paper further put salt in the wound by pointing out that one of the theories deriving the 3/4 law had an error.

Although Dodds is still at it with his current paper, to compensate for his party-downer laurels, he’s accumulated some of the most interesting research out there, from rivers to bodies to disease to the happiness of songs over time. (Thanks, Peter, for being a good sport.)

Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

This first appeared on February 9, 2010, as a feature at ScientificBlogging.com.

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This first appeared on December 14, 2009, as a feature at ScientificBlogging.com.

Daniel Tammet is an autistic savant and author of the recent book Embracing the Wide Sky: A Tour Across the Horizons of the Mind (Free Press). You may have heard of him. For example, most people first became aware of the existence of Iceland upon hearing that Tammet learned Icelandic in a week.

This is also the fellow that rattled off the first 22,514 digits of pi in five hours, enough for even the most exacting civil engineer, and far more accurate than the 19th century Texas town that passed an ordinance that pi would be approximated as 4. If ever there were a real human with superpowers, then Tammet fits the bill. Although stricken with adversity, his brain nevertheless is in certain respects blessed with something extra, smarter, almost magical.

But I don’t believe that the moral of extraordinary people like Tammet is that they are extraordinary. No doubt they ARE extraordinary – doing *anything* 22,514 times is amazing, especially when a transcendental number is involved. The moral of Daniel Tammet is not that he’s extraordinary, but that it follows that we must ALL be extraordinary. In fact, it follows that we must all have powers even greater than the ones in the savant repertoire.

You might be responding, “Extraordinary powers! Me? No, you must be mistaken.” And that does seem like a reasonable response, because if we really had mind-boggling powers, wouldn’t we be the first to know? The answer is, “No.” Your own powers are perhaps the most difficult for you to notice. Your capabilities were selected over evolutionary time to work effortlessly as intended, but there was no selection pressure to brag to your consciousness about how exceptionally cool your hardware is.

You have employed your natural capabilities your whole life, and you have seen them in action in everyone you know; that leads to a “nothing to see here, folks, please go home” mentality about your own capabilities. The only time you are likely to notice your capabilities is when something goes wrong with them. But that still falls quite short of appreciating just how powerful the mechanisms are when they are up and running.

And this is where Daniel Tammet’s brain, and that of other savants, becomes useful . (I knew there was a reason for your brain, Daniel!) His brain allows us to begin to appreciate the true extent of our own non-savant capabilities. The savant brain is just like our brain, but with a twist. And because giving a (metaphorical) twist to neural tissue can only hinder its workings, the powers of savants are an underestimate to the power we have inside us.

Why? Consider what cannot be underlying the talents of savants. It is NOT the case that their brain possesses mechanisms, or algorithms, fundamentally different from those found in our brains. That’s the impression one might get by watching television shows or movies about savants: their brains are endowed with some altogether fancy qualitatively new design enabling them to implement their power. But savants are savants because of a disorder; their brains do not end up as they “should” be.

Their brains have undergone a “twist”. And when mistakes happen in the construction of any machine – biological or otherwise – the chances of getting efficiently designed and altogether new functionality is essential zero. Evolution gets fancy new functionality by virtue of countless generations of tiny changes. Evolution does not design new gadgets in one go.

What must, then, be going on is that one of the fancy gadgets that is inside all of us is being directed, in savants, in a manner in which it wasn’t selected for. For example, Tammet describes his internal experience of what it’s like to determine the digits of pi as something like visualizing a complex landscape. His brain ended up with a “twist” that gave him the ability to harness the computational power of his visual system for calculating the digits of pi, something his visual system was not designed to do. (As an aside, see my own attempt to harness our visual system for computation)

The beauty of savant cases is that once the power of the brain is redirected in an utterly unusual direction, then we who observe these savant powers in action have a much better ability to judge the true extent of their power. Whereas we are nearly incapable of gauging how superbly capable the mechanisms are when directed as evolution intended, we see clear-as-day the brawny power of our mechanisms when twisted to point in a strange direction.

When we see Daniel Tammet reaching the 22,500th digit of pi, and we’re reeling with wonder, we should pause and realize that what Tammet has done is provide a lens through which you can see the superpower hidden inside your own brain.

In fact, because Tammet’s pi-calculating machinery wasn’t designed for that, the machinery is probably nowhere near as sophisticated as a pi-calculating biological machine would be were pi-calculation to have been selected for.

The machinery Tammet harnesses for pi-calculation – machinery you have as well, but without the “twist” you can’t harness it as he does – is much more well designed for what it is supposed to do (something having to do with seeing) than for pi-calculating, so the power of Tammet’s superpower pales in comparison to what’s going inside of all of us (including Tammet when he uses his visual system as “intended”).

Daniel, thanks for illustrating to the world the amazing power of our brains! And thanks for being a good sport!

Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

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This first appeared on November 23, 2009, as a feature at ScientificBlogging.com, coincidentally aligning with the 150th anniversary of The Origin of Species.

“Come on into the hot tub,” I told my three year old boy. But he wouldn’t budge. No way was he joining his older sister in there. “It’s warm, and it feels nice!” I urged, “There’s nothing to be afraid of.” But it was only when I turned off the jets that I could eventually coax him in.

“Why would my boy be so afraid of a hot tub?” I wondered. But as I reflected upon my panty-waist boy, I decided that perhaps I wasn’t being fair to him. In fact, in hindsight, I think he was behaving rationally. Hot tubs are frightening. They violently churn and bubble, as if they are actually boiling. I have spent so much time in hot tubs over the years that I now hardly notice the foam, the burning temperature, the Pseudomonas bacteria and the skin-ripping, high-pressure jets.

We get used to things, and not just to jacuzzis. My jacuzzification also happens for intellectual matters (a topic of an earlier piece, The Value of Being Aloof: Or, How Not to Get Absorbed in Someone Else’s Abdomen). One generation’s jacuzzi is another generation’s maelstrom.

In particular, we get used to evolution. We scientists, especially. We’re so accustomed to evolution that when we find skeptics of evolution, we think of them as poor, blind, close-minded saps who can’t see the most obvious truths.

Darwin's jacuzzi

But how obvious is evolution, really? And how close-minded are those who don’t yet accept evolution?

Let’s start with the obviousness of evolution. First and foremost…evolution ain’t obvious! Evolution is perhaps the craziest true theory ever!   “Let me get this straight: Add a teaspoon of heritable variation, a ton of eating one another, and epochs of time…get yourself a superzoo of fantastically engineered creatures. Yeah, that’s not crazy!”

The only reason most of us scientists don’t find evolution crazy is that we’re jacuzzified to a wrinkley pulp. And this level of comfort with the bizarre theory of evolution can be counterproductive when trying to explain evolution to the uninitiated. You won’t convince my three-year-old to get into the hot tub by suggesting that there is no bubbling or churning – he can see the bubbling and churning with his own eyes. (BTW, no intent to analogize evolution skeptics with three-year-olds! Just a useful analogy that popped up.) If you’re so jacuzzified that you fail to see the churning, you will be incapable of addressing the real worry: that the churning might hurt.

Similarly, if you’re so used to evolution that you fail to see how weird it is, you’ll be in a poor position to explain why it isn’t as crazy as it at first sounds. Better to say, “Yes, evolution is crazy, but there’s overwhelming evidence that it is, indeed, the mechanism underlying the emergence of life in all its glory.” (And you should also admit that, although we have mountains of evidence that evolution is the mechanism, we are very far from understanding how exactly it does it, just as we’re sure the brain underlies our thoughts but do not comprehend how the brain works. This was the topic of an earlier ScientificBlogging.com piece titled Is Evolution Fast Enough?’ How I Responded.

The fact that evolution wins the prize for “non-obviousishness” should already begin to change one’s view about the supposed close-mindedness of evolution’s skeptics. Evolution is extraordinary, and extraordinary theories take extraordinary evidence. Extraordinary evidence indeed exists, but you can’t communicate the evidence in a simple one-liner. (Much less in a one-liner addressing the other as a “close-minded sap”.)

Religious folk surely have their hang-ups (whereas I am utterly hang-up-less), but religious doctrine has come a long way over the centuries. Few still believe the Earth is at the center of the universe, for example, something that was once perhaps just as central to the religious world view as creation. But the evidence for the Earth not being at the center is overwhelming. And more important than being overwhelming, the idea that the Earth is not at the center of the universe is not nearly as crazy as evolution.

Religion can, then, be convinced of scientific discoveries it is initially opposed to. And, it is reasonable to expect that the more intrinsically implausible a theory sounds, the longer it will take for religion to become convinced. Evolution is the king of the implausible, and perhaps that’s why it is one of the last major scientific truths not having infiltrated all the corners of religion.

But evolution won’t infiltrate religion if we scientists can’t address the skeptic’s worries. And we won’t be able to address the worries if we’re so overcooked in evolution that we are incapable of seeing just how preposterous it seems.


There were some interesting comments at ScientificBlogging.com, which can be read here. One quote worth repeating here is a response of clarification of mine:

“For the Grand Canyon, I can see how more and more erosion, with self-organizing drainage networks, leads to deeper and deeper and wider and wider etc., etc., etc.

But imagine that I told you that, after all that erosion, the result wasn’t the Grand Canyon, but a modern football stadium, with seats, bathrooms, flat field, fake grass, box seats — the works.  That is, imagine after more and more blind activity, one gets a highly engineered complex structure that *does* amazing stuff.”

That’s what makes the hypothesis of natural selection so crazy. I’d go so far as saying that if you don’t appreciate how crazy it is, you don’t really get it.


Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

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Jay Ingram’s Daily Planet television show on Discovery Channel has a  piece on my cities-are-shaped-like-brains research (the paper which recently appeared in the journal Complexity, with co-author Marc Destefano). The clip begins about half way through the segment (7 minutes and 30 seconds.)

See these posts at my blog (and also one at ScienceDaily) for more information about the research.

Mark Changizi is Professor of Cognitive Science at RPI, the author of The Vision Revolution (Benbella, 2009) and The Brain from 25,000 Feet (Kluwer, 2003).

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For The Quarterly Review of Biology

Review of Melanie Mitchell (2009) Complexity: A Guided Tour (Oxford University Press, Oxford).

Complexity – what is it, and does it matter? Melanie Mitchell, a denizen of the community of complexity researchers provides an engaging introduction to the many interdisciplinary issues surrounding attempts at understanding how fantastic holistic attributes  can arise from teems of underwhelming components. …how minds arise from simple neurons, and cagey ant colonies from embarrassingly thick-headed individual ants. The book is primarily aimed for the undergraduate or high school student, covering nearly all the first-order facets of complexity within dynamics, information, computation, evolution, and networks. But even researchers familiar with the traditional stomping grounds may enjoy many of her meta-discussions on where the field of complexity stands today, and whether it is progressing or dying. Melanie Mitchell’s book may itself exemplify a very good reason for maintaining “complexity” as a monicker for the suite of disciplines it unites: books like hers may be pegogically useful for the growth of young scientists. First, the topics taken up in her book are exciting to newcomers, tapping into the romance of science many of us researchers once had (and now struggle to recall). Second, the issues in complexity require interdisciplinary training, which may serve to motivate students to get interdisciplinary training, something they will never regret wherever they end up in science (and odds are they won’t end up in “complexity” proper). Third, an introduction to the problems under the heading of complexity helps put students in a non-reductionist mindset, so that when such complexity-fed students land in traditional scientific disciplines, they push their fields toward the development and testing of large-scale, unifying theories. If Melanie Mitchell’s book were required reading for undergraduate freshmen, I would anticipate a large surge in the number of students interested not only in complexity, but interested in science more generally. And not just more students, but students more exercised about what may lie ahead as they attempt come to grips with nature.

Mark Changizi is Professor of Cognitive Science at RPI, and the author of The Vision Revolution (Benbella, 2009) and The Brain from 25000 Feet (Kluwer, 2003).

[A related story in ScienceDaily: cities shaped like brains]

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RPI’s press release on my and Marc Destefano’s city-brain paper just came out, written by science-writer Michael Mullaney. I have included a copy of it here as well…

Ego City: Cities Organized Like Human Brains

Credit: Rensselaer/Mark Changizi

New study shows striking similarity in the evolution of brains, cities

Cities are organized like brains, and the evolution of cities mirrors the evolution of human and animal brains, according to a new study by researchers at Rensselaer Polytechnic Institute.

Just as advanced mammalian brains require a robust neural network to achieve richer and more complex thought, large cities require advanced highways and transportation systems to allow larger and more productive populations. The new study unearthed a striking similarity in how larger brains and cities deal with the difficult problem of maintaining sufficient interconnectedness.

“Natural selection has passively guided the evolution of mammalian brains throughout time, just as politicians and entrepreneurs have indirectly shaped the organization of cities large and small,” said Mark Changizi, a neurobiology expert and assistant professor in the Department of Cognitive Science at Rensselaer, who led the study. “It seems both of these invisible hands have arrived at a similar conclusion: brains and cities, as they grow larger, have to be similarly densely interconnected to function optimally.”

As brains grow more complex from one species to the next, they change in structure and organization in order to achieve the right level of interconnectedness. One couldn’t simply grow a double-sized dog brain, for example, and expect it to have the same capabilities as a human brain. This is because, among other things, a human brain doesn’t merely have more “dog neurons,” but, instead, has neurons with a greater number of synapses than that of a dog – something crucial in helping to keep the human brain well connected.

As with brains, interconnectedness is also a critical component of the overall function of cities, Changizi said. One couldn’t put together three copies of Seattle (surface area of 83.9 sq. miles) and expect the result to have the same interconnectedness and efficiency as Chicago (surface area of 227.1 sq. miles). There would be too many highways with too few exits and lanes that are too narrow.

In exploring this topic, Changizi discovered evidence linking the size of a city or a brain to the number and size of its supporting infrastructure. He investigated and documented how the infrastructures scale up as the surface area of brains and cities increase.

As cities and the neocortex grow in surface area, the number of connectors – highways in cities and pyramidal neurons in brains – increases more slowly, as surface area to the 3/4 power, Changizi found. This means the number of connectors increases in both brains and cities as S3/4, where S = surface area. Similarly, as cities and brains grow, the total number of highway exits and synapses — which share a similar function as terminal points along highways and neurons — increases with an exponent of about 9/8. The number of exits per highway and synapses per neuron were also closely aligned, with an exponent of approximately 3/8.

These and other findings are detailed in the paper “Common Scaling Laws for City Highway Systems and the Mammalian Neocortex,” published this week in the journal Complexity. The complete paper may be viewed online at the Complexity Web site.

“When scaling up in size and function, both cities and brains seem to follow similar empirical laws,” Changizi said. “They have to efficiently maintain a fixed level of connectedness, independent of the physical size of the brain or city, in order to work properly.”

Marc Destefano, clinical assistant professor in the Department of Cognitive Science at Rensselaer, co-authored the paper.

Earlier this summer, Changizi’s new eye-opening book, The Vision Revolution: How the Latest Research Overturns Everything We Thought We Knew About Human Vision, hit store shelves. Published by BenBella Books, The Vision Revolution investigates why vision has evolved as it has over millions of years, and challenges theories that have dominated the scientific literature for decades.

For more information on Changizi’s research, visit Changizi’s Web site and read a recent magazine story on his work. See Rensselaer’s recent news release for more information on The Vision Revolution.

Published September 3, 2009

Contact: Michael Mullaney
Phone: (518) 276-6161
E-mail: mullam@rpi.edu

[See it in ScienceDaily.]

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The following piece was written for ScientificBlogging.com on my new paper on the brain-like organization of cities…

The brain-like organization of cities. (Or, is it, the city-like organization of brains?)

Mark Changizi

You may recall the “China Brain” thought experiment about consciousness, which goes something like this: if each person in China were to mimic the activity of a neuron using cell phones to communicate with one another, would this China-sized brain like Chinese food? I may be missing some of the philosophical nuances in the question, but as a one-time philosopher, I know enough about consciousness to know I have nothing remotely worthwhile to say about it.

So let me set consciousness aside. Here’s a different kind of “China Brain” question more up my alley: Are the people of China actually organized in a brain-like fashion? This is not a thought experiment, but a genuine question. A silly question, you might say. But countries do tend to be cohesive complex systems that function via the movement of people, goods and information.  In fact, cities are more cohesively organized than countries, and the same question can be asked of them: Are cities organized like brains?

Cities shaped like brains.

Cities shaped like brains.

Although most cities don’t at first glance look much like brains, there are some initial similarities.

First, unless you buy a thousand acres of land and have your own city built to order, cities get their shapes via (political and economic) selection forces over many decades. Like brains, cities evolve: ones that are not well organized wilt (people move away over time) or modify themselves to become more efficient.

Second, cities interconnect themselves with highways, and are under selection pressure to connect themselves efficiently. Highways break out of the two dimensional street grid, and “pull” the city’s edges closer to one another. Brains, too, have highways: white matter axons. The pyramidal neurons in the cortex send their axons out of the gray matter to faraway parts of the cortex.

I long ago stopped my subscription to the Flat Earth Society newsletter, but I still have reason to believe that cities are flat, and this is a third similarity between cities and brains. Even if you live in San Francisco, your city lies on the surface of the Earth, rather than, say, being built in a three-dimensional array below ground, or like the Borg cube. Our cortex is also flat, and if you’re lucky enough to be used in an experiment, researchers will flatten your gray matter onto the nearest cold metal table.

Having noticed these prima facie city / brain similarities, and having long had an interest in understanding why brains are shaped as they are, I thought I would take a closer look. I asked, Given what we know about how brains change when they get larger, do we find that cities change in similar ways as they get larger? So graduate student Marc Destefano and I took data from U.S. cities varying in population from about 10 thousand to about 10 million, and determined how city organization changed as city size increased. Our paper just appeared in the journal Complexity.

We found that cities and brains are quantitatively very similar in how they change their organization as a function of size. For example, the number of highways increases more slowly than does the surface area of a city, something already known to be the case for our brain’s highways (i.e., our white-matter-projecting neurons); in particular, in each case the number increases at about the 3/4 power of surface area. And the total number of highway exits in a city increases faster than the land area of the city, also the case for the total number of synapses in the brain; in fact, in each case the number increases at about the 9/8 power of surface area. Our paper discusses a number of other similarities – and discusses differences – e.g., for the diameter of highways, their propagation velocity (i.e., cross-city travel time), and the number of compartments (akin to cortical areas).

One notable problem with the analogy is people. What does population mean for the cortex? We’re not sure, but we found that the population of cities increases very fast as a function of land area, namely nearly as the 3/2 power of land area. That means population density in cities tends to increase as the 1/2 power, or as the square root, of land area. Bigger cities seem to demand that people really get up close and personal. That’s too bad for your and my kids, because cities are growing ever larger, and I don’t want anyone getting up close and personal to my wee girl.

Why do larger cities demand greater population density? Well, our measurements show that the total surface area of highways in a city also increases approximately as the 3/2 power of land area. Perhaps an efficiently running city highway system requires that each person in the city gets an invariant swathe of highway, so that no matter the size of the city, the total number of people per unit area of highway is a constant.  Our data suggest that this is, indeed, roughly a constant across cities, although whether this is itself one of the evolutionary drivers of city highway organization is unclear.

Given our findings that city highway systems tend to obey certain quantitative scaling laws, and presuming that they obey these scaling laws because they have been selected over time for greater efficiency, then one way to diagnose the health of a city highway system is to see whether a city’s data point is where it should be for its land area. For example, if one plots total number of highway exits versus land area for many cities, and one sees a city that does not fall on the line (e.g., maybe it has too many exits), then one would know how to purposely get a city into line, rather than waiting for selective forces to work over the decades to come.

Cities are a lot smarter than we have thought. And that, I contend, is true about most complex systems that are under selection pressure for considerable periods of time. If we can understand the organization of cities, then we might have a leg up in understanding the brain. And cities make it easy, because relative to the size of these city-brains, we are nano-particles traveling through them like the characters from Fantastic Voyage.

Mark Changizi is Professor of Cognitive Science at RPI, and the author of The Vision Revolution (Benbella, 2009) and The Brain from 25000 Feet (Kluwer, 2003).

[A ScienceDaily piece.]

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Could the organization of our cities be smarter than we think? Here’s the abstract of my and Marc Destefano’s new paper in the journal Complexity…

Cities and the mammalian neocortex may seem to have little in common, but each is approximately a surface with a network of conduits (roads and neurons, respectively) connecting its disparate parts. Because both cities and brains are under selection pressures to make their connections efficiently, we investigate the hypothesis that the organization of city highway networks and the mammalian neocortex may be governed by common principles. Here we measure how city highway networks vary with city size and find that, consistent with the hypothesis, highway networks scale with exponents nearly identical to those found for the analogous quantities in the neocortex. As a function of surface area, the number of conduits scales approximately as the 3/4 power, the number of “leaves” (highway exits and synapses) scales approximately as the 9/8 power, propagation velocity scales approximately as the 1/8 power, and total conduit surface area scales approximately as the 11/8 power. We also find that city population scales as the 1.46 power of surface area, potentially driven by the total surface area of highways. We discuss the extent to which explanations for neocortical scaling can be extended to cities.

The paper is here

Here’s a little piece at ScientificBlogging.com

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Mark Changizi is Professor of Cognitive Science at RPI, and the author of The Vision Revolution (Benbella, 2009) and The Brain from 25000 Feet (Kluwer, 2003).

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