Posts Tagged ‘Evolution’

I’ve argued there’s no imminent singularity, and I’ve thrown water on the idea that the web will become smart or self-aware. But am I just a wet blanket, or do I have a positive vision of our human future?

I have just written up a short “manifesto” of sorts about where we humans are headed, and it appeared in Seed Magazine. It serves not only as guidepost to our long-term future, but also one for how to create better technologies for our brains (part of the aim of the research institute, 2ai, I co-direct with colleague Tim Barber).


Mark Changizi is Director of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella Books, 2009) and the upcoming book Harnessed: How Language and Music Mimicked Nature and Transformed Ape to Man (Benbella Books, 2011).

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In How Many Limbs Should Humans Have? I described my Limb Law, an empirical law I discovered which relates how long an animal’s limbs are to how many limbs it has. This law is explained by virtue of animals having evolved a limb design that minimizes the amount of needed materials to reach out into the world (see links to my academic work in the previous piece).

To see the Limb Law in action, go to my web site where you can play with an animal’s limb length and watch how the optimal number of limbs changes. Roughly speaking, the animal designs you can create in this program are the ones we find on Earth (…among radially-directed-limbed animals).

The Limb Law applies to more than just animal legs. By “limbs” I refer to any appendages that reach out, and so the hypothesis applies to hands as well, but where a hand’s “limbs” are its digits.

The only thing we must keep in mind in order to apply the Limb Law to hands is that hands are not free-range animals, but are, rather, connected to an animal. Hands have digits pointing away from the arm that connects to the hand, and so have only about half of the digits one would expect if the hand were roaming the world on its own.

In light of this fingers-are-the-hand’s-limbs observation, in this piece I’d like to ask…

Why do we have ten fingers?

In addition to being fundamentally interesting, this question also has deep implications for why we use a base-10 number system (rather than a base-2 or base-8 system, each which would arguably be better).

How can the Limb Law tell us how many fingers we should have, given that it only tells us the relationship between limb length and number of limbs?

Because hands like ours have plausible constraints on how long their fingers should be. Hands must close, i.e., their fingers must be able to reach back over the palm and cover it up. And that simple requirement is enough to enable us to predict roughly how many fingers we should have.

Recall that the Limb Law was that the number of limbs, N≈2π/k, where k was the “limb ratio,” k = L/(L+R), where L is limb length and R the radius of the body.

The demand that finger length be approximately the diameter of the palm means that the finger length should be about twice the palm’s “radius”. So, L≈2R. It follows that k ≈L/[L + (L/2)] = 2/3. And, plugging in k=2/3 into the equation for the number of limbs, N, we have N≈2π/ (2/3) = 3*π ≈ 9.42.

That is, given that fingers must be roughly as long as the diameter of one’s palm, then there should be about 9.42 fingers poking out from the circumference of the palm.

But remember that palms aren’t animals living freely on their own, but are attached to arms, and thus we expect palms to have digits on only about one half of their circumference. So, 9.42 is twice what we should expect for the number of fingers. Divide 9.42 by 2 and we have 4.78 fingers per hand. Or, about five.

Could it be that your run-of-the-mill alien would also have ten fingers, and thus get saddled with base-10?


There was a healthy discussion when this was posted at Science20.com, and it is worth repeating one exchange here. Here is the comment, followed by my reply…

We have a maximum of 5 digits per limb, because ancient ancestors of all subsequent quadrupeds settled on 5 digits per limb, after initially starting out with a higher number (7 or 8 digits per limb – see for example, http://www.dinosaurjungle.com/prehistoric_animals_acanthostega.php ).

My reply…

The fact that number of digits has tended to only fall among tetrapods (from polydactylous to pentadactylous and lower in many cases) could mean there is some kind of (genetic or developmental) difficulty in adding digits, as you suggest. But abnormal polydactyly is fairly common in vertebrates (including humans), and often has a hereditary component. On this basis it would seem that adding a digit is possible. And, evolution can take more creative approaches as well, like the Giant Panda extra pseudo-digit you mentioned.

Rather than supposing that there is some kind of difficulty in adding digits, or some kind of upper limit of five, an alternative hypothesis is that the original polydactylous tetrapod had simply “too many” digits for most hand designs relevant for terrestrial environments, and that tetrapods ever since have been disproportionately losing digits to fill in vacant spots in design space, with only the occasional added digit. That is, the tendency for digit loss over time may be due to adaptive selection pressures, not a no-adding-digits constraint.

So, I’m not convinced that developmental / genetic constraints force a five digit maximum.

Also, I’m of course not suggesting that prior “evolutionary stages are planning ahead for the number of fingers humans would need in millions of years time.”

And, at any rate, all this is beside the point. Let’s suppose that some kind of historical accident were to force exactly five digits on all progeny of an animal, and that some of those progeny became primates with our hand design. Is it true that it is a historical accident that we have five fingers, in this thought experiment? Not quite. Being stuck with five digits would have constrained the kinds of hand (and body) designs possible for this animal’s progeny. Some hand designs, and animal designs, would then be out of reach to this lineage. The hand designs within reach for such a lineage would be ones which work really well with five digits. …and one such hand design is the “grasper” one where the digit length is of similar length to the palm diameter, very roughly our hand. The question is whether our hand/digit design is optimal in some hypothesized sense. My suggestion is that our 5 digits and our digit-length-to-palm ratio are “designed for one another” (because that relationship is consistent with cheap reaching-out wiring costs). My suggestion is an engineering hypothesis, not a historical hypothesis. If five-ness was historically fixed, then what historically evolved was the length of the digits to become a proper grasping hand. To put it another way, if our long ago ancestors had, say, three fingers, and could not add new ones, then primates would probably not have evolved in the first place, because the hand would have led the lineage down new design paths.


This first appeared on May 17, 2010, as a feature at Science 2.0


Mark Changizi is Professor of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella Books) and the upcoming book Harnessed (Benbella Books).

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Please get Tom Cruise first, please get Tom Cruise first, please get ...

In War of the Worlds, giant alien robots emerge out of the ground and begin vaporizing large numbers of actors. There’s a lot to like in those scenes, but there are three things I could not stand.

Like those three legs they walked around on.   Not their fragile-appearing spindly-ness, but their actual three-ness.

There should be more legs. Around six of them, in particular.

“Look,” you might reply, “it’s an alien ship, and who knows what kinds of principles they’ve uncovered.”

Of course, that’s possible. But another way to look at it is that we Earthlings come in a large variety of body and limb plans, and yet we don’t find the three-limb design anywhere. Perhaps that’s a good argument that aliens wouldn’t build a ship with three legs.

What do we Earthlings do for limb design?

We tend to follow a law, one that may cut across all animal phyla, a law I first published in the Journal of Theoretical Biology in 2001 [ http://www.changizi.com/limb.zip ], and elaborated upon in my first book The Brain from 25,000 Feet [ see final section in http://www.changizi.com/ChangiziBrain25000Chapter1.pdf ].

This “limb law” relates an animal’s number of limbs to the length of those limbs (relative to the body’s size).

When an animal’s limbs are very long relative to its body size, I argued that the optimal reaching-out solution (that uses the least amount of “wire,” or limb material) is to have about six limbs. (This applies to animals with limbs that are approximately radially directed around a perimeter. For animals whose limbs directions are uniformly spread over a spherical surface, the expected number of limbs in this case would be about 12.)

As the animal’s limbs shorten relative to body size, the expected number of limbs rises, with tremendous numbers of limbs when the limbs are very short. (By the way, a snake is consistent with infinitely many infinitely-short limbs – i.e., no limbs.)

More generally, the law predicts that an animal’s number of limbs is inversely proportional to relative limb length. And, more specifically, the law predicts a particular proportionality constant, so that “six” is the solution in the case of really long limbs.

Letting L be the limb length and R the radius of the animal’s body, then k = L / (L + R) is the relative limb length, or “limb ratio”.

The number of limbs, N, is expected to vary approximately as
N ≈ 2π/k 6.28 k-1

The figure below (from my first book) shows how the number of limbs in fact relates to limb ratio, for 190 species across seven animal phyla (Annelida, Arthropoda, Cnidaria, Echinodermata, Mollusca, Vertebrata, and Tardigrada).

The predicted trend is shown with the solid line, consistent with the N ≈ 6.28k-1 equation we saw just above.

The actual trend is shown with the dotted line, leading to an empirical equation of N ≈6.24k-1.17 … or very close to the prediction.

To get a better impression of the Limb Law that Earthlings appear to follow, check out this little dynamic visual program by Eric Bolz, allowing you to vary limb length and watch how the number of limbs varies: http://www.changizi.com/limb.html . The right vertical axis allows you to modulate the limb ratio and watch the number of limbs change. The bottom axis allows you to make longer or shorter creatures. The left vertical axis just allows you to resize the creature on the page.

The alien ships from War of the Worlds should have – given their long limb length and assuming they should be treated as approximately pointing around a perimeter – around six limbs. Not three.

That’s why they look so silly. They’re outside of the sweet spot in design space for limbs.

In my next piece, I’ll discuss how this limb idea tells us why we have 10 fingers, and perhaps, therefore, why we have a base-10 number system.

This first appeared on May 10, 2010, as a feature at Science 2.0


Mark Changizi is Professor of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella Books) and the upcoming book Harnessed (Benbella Books).

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I have yet to be bored watching the 27-and-a-half-hour extended versions of the Lord of the Rings movie trilogy with the kids. It is truly an awe-inspiring cinematic masterpiece.

There is, however, one persistently annoying aspect of the trilogy that I am petitioning the studio to change on the next release and for the prequels that will appear soon. What’s that one annoying thing about the Lord of the Rings? You know what it is…


I know, I know, hobbits are fairly integral to the plot, and especially so for the upcoming prequels (titled “The Hobbit,” Parts 1 and 2). We’re stuck with hobbits in these stories, and so the question is how they can be fixed.

In order to fix the hobbits, though, we must diagnose what exactly it is about them that makes us wish the Ringwraiths had finished them off in a bloody spectacle in the first part of the Lord of the Rings when they were foolishly cooking on that promontory.

The problem with the hobbits is not merely that the music shifts to weepy-give-me-a-hug music whenever Frodo and Sam get within two meters of one another. The main objection to the hobbits is, instead, a biological one…

Hobbits are lame. The hobbits in the movies are given the physical prowess of a regular human four-year-old with furry feet.

And that’s the problem.

Hobbits are small, yes. But that doesn’t mean that their only way of garnering respect from the other Middle Earth races is by cooking second breakfasts or getting completely wrecked and dancing on tables.

Small animals are not merely smaller, weaker, and slower versions of their larger-animal counterparts. Instead, small animals are more energetically active, sleep more, and possess many other consequences of scaling due to their smaller size. Small animals live their lives at a faster pace – they are quick, and practically impossible for much larger creatures to catch. In addition to being quick, small animals tend to be feisty, exhibiting morphological and behavioral specializations likely to rip, tear or stab something of importance on a larger animal’s body.

Have you ever tried to catch a tiny monkey? It’s practically impossible! Even chimpanzees can only do so with great tribal effort. And pity on you if you ever do manage to catch one; you’re likely to be licking your wounds a fraction of a second later. I’ll not even get into the inclination for smaller animals to defecate on bigger animals, something very relevant when trying to catch a monkey.

To illustrate the “quick and fierce” side of the small, take a look at the following two videos, the first showing a squirrel going for a deer’s jugular, and the second showing a bear deciding against tangling with a house cat.

We see, then, that small animals tend to be quick and feisty, and – unlike hobbits – decidedly NOT lame.

Imagine how much fun it would be to watch the Lord of the Rings movies, but with fleet, ferocious and blood-thirsty little hobbits replacing the plodding, pleading, thirsty little hobbits we have gotten to know and grudgingly love. (Please forward this to Peter Jackson.)

This first appeared on March 23, 2010, as a feature at ScientificBlogging.com.


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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Scientists are prone to going on and on about how strikingly early in life we are able to comprehend speech. Our children’s aptitude for reading, however, doesn’t cause much excitement. At first glance this seems sensible: children comprehend speech fairly well by two, whereas they typically can’t read until about five. This is because, the standard story goes, we evolved to comprehend speech but did not evolve to read. And while one might debate whether we have evolved to comprehend speech, no one believes we evolved to read. Writing is only several thousand years old, far too short a time to have crafted reading mechanisms in our brain. And for many of us, our ancestors only started reading one or several generations back.

But are children really so clunky at learning to read? At five years old, most children can’t be trusted to pour a pint of beer without spilling it, and most can’t even do stereotypical ape behaviors like somersaults and the monkey bars. And yet these same wee ones are reading. That’s quite an accomplishment for an ape, especially one who gets read to so infrequently compared to getting talked to.

Picture 2

Children are, in fact, quick learners of reading, and our brains become fantastically capable readers. How can we come to be so good at reading if we don’t have a brain for it? Is it because our visual system can handle any writing one may throw at it? No. Our children would be hopeless if writing looked like bar codes or fractal patterns. How, then, did apes like us come to read?

Gifted neuroscientist Stanislas Dehaene argues in his new book, Reading in the Brain (Viking), that we read not because we have a reading instinct, and also not because our visual brain is a particularly pliable learner. Rather, we read because culture “neuronally recycles” our visual system. Culture over time has seen to it that the letter shapes of our writing systems have the shapes our visual system is good at processing. In particular, the brain is competent at processing the contour combinations that occur in natural scenes, and writing systems have come to disproportionately use these shapes.

For example, below are four configurations each having three contours and two Ts. Three of the four can happen in natural scenes, but one of these cannot, and it turns out that only this oddball is rare across human writing systems. It is not so much that the brain has a reading instinct, but that writing has a brain instinct. In fact, to the extent that writing has come to be shaped like nature (in order to get into the brain), writing has a nature instinct.

Picture 3

More generally, Dehaene’s line of thinking suggests that much of what makes humans stand so far apart from the other apes is a result of neuronal recyclling – not a result of natural selection at all.

Other pieces about the origins of writing are here, and also play prominently in my book, The Vision Revolution.

This first appeared on January 12, 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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Several weeks back I wrote a piece for the Telegraph about how too few of us scientists stop to remind ourselves of the wonder of Darwin’s theory. “It should blow your mind,” I said. But it would be a shame if Darwin’s skeptics take comfort in scientists exhibiting awe for the complexity of nature. And it would also be a shame if Darwinists like me are deterred from communicating this awe with the worry that skeptics will somehow take comfort.

To see why no comfort should be taken, let’s step away from natural selection for a moment and consider the most complicated object in the known universe: your brain. Any neuroscientist will be happy to admit that we are still woefully ignorant about how the brain works. Our understanding of the brain’s mechanisms is moving forward quickly, and accelerating, but we have a very long way to go. And the idea that computationally meager neurons can, in large numbers and larger interconnectivity, underlie the mental life we cherish is, well, mind boggling.

But as boggled as neuroscientists might be about the brain’s mechanisms, consider what no neuroscientist is in the least confused about: that the brain is the mechanism underlying our mental life. The evidence that the brain, and not some other thing, is the mechanism underlying our thoughts is so overwhelming it is hardly worth discussing.

The difference here is one of “how” versus “that”. Discovering how the brain instantiates our minds is orders and orders of magnitude more difficult than discovering that the brain instantiates our minds. While this distinction is obvious for the brain, the point can often be overlooked for evolution. Comprehending exactly how the mechanism of natural selection underlies the diversity and complexity of life on Earth is an astronomically more difficult science problem than showing that natural selection is the mechanism. The “how” of natural selection is as difficult as the “how” for the brain, perhaps moreso. But the “that” of natural selection is another story, and is teeming with evidence.

Skeptics of evolution often aim at the “how”, and seem to believe that if scientists cannot fully answer the “how” question, then Darwin is all wet. But by that standard, neuroscientists should begin doubting that the brain underlies thoughts every time someone asks a difficult question about how the brain works.

[See also https://changizi.wordpress.com/category/evolution/ ]

Mark Changizi is the author of The Vision Revolution, and is a professor in the Department of Cognitive Science at Rensselaer Polytechnic Institute.

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Darwin and Evolution

Darwin’s 200th anniversary has come and gone, and thousands of news stories have reflected upon it. One of the largest issues we still grapple with is why so many people still don’t believe in evolution, by which I mean, they don’t believe that natural selection suffices to explain all the wonderful life we find here on Earth. And that issue is, accordingly, one of the most commonly recurring issues in last year’s Darwin pieces. There is, however, a potentially more troubling issue lurking about, also related to understanding Darwin, and this issue emanates from within scientific circles, from among Darwinists themselves (and I’m one of them).

And the problem is this: Many proponents of evolution, having grown up with natural selection, have lost their ability to see just how amazingly counter-intuitive the idea is. As a professor of mine used to say, “One generation’s maelstrom is the next generation’s jacuzzi.”

It is not that “evolution” is counter-intuitive. There is no mystery in the idea that organisms can change, and can even do so in small steps in response to selection pressure, like moths changing color or bird beaks changing shape over generations. What is mind-boggling, and what many Darwinists forget is mind-boggling, is how these small changes can add up over millions of generations to create complex fancy machines. What is mind boggling is that this kind of local, short-term evolution that we can wrap our minds around can possibly explain the life on Earth.

Let me try to reconvey the wonder of natural selection by an example. Consider the Grand Canyon. We can comprehend how it got formed. We see the local, short-term erosive properties, and we can fairly well  fathom how, with enough erosion, the canyon gets deeper and deeper and wider and wider and branchier and branchier and so on. 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 can do amazing things.  That’s what it should mentally feel like when one contemplates that, with a little selection pressure and extraordinarily long periods of time, one can get elm trees, octopus and humans out of goo. It should blow your mind. That’s why Darwin is worthy of remembering for 200 years, or for 200,000 years. Not because he pointed out that organisms can slowly change over time in response to selection forces, but that he suggested that that is enough to explain all the complexity of life.

This problem I am pointing out among scientists like me is also relevant for better convincing creationists. If a creationist has not been steeped in natural selection, they may actually have a better grip on how mind-boggling it is. If one hopes to unboggle the creationist’s mind, one must first recognize the reasons for it having become boggled.

[See these pieces for more about evolution.]

This first appeared on January 4, 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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