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    Why Doesn’t Size Matter…for The Brain?
    By Mark Changizi | November 16th 2009 01:57 PM | 164 comments | Print | E-mail | Track Comments
    About Mark

    Mark Changizi is Director of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella 2009) and Harnessed: How...

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    No one draws pictures of heads with little gears or hydraulics inside any more. The modern conceptualization of the brain is firmly computational. The brain may be wet, squooshy, and easy to serve with an ice cream scooper, but it is nevertheless a computer. 


    However, there is a rather blaring difficulty with this view, and it is encapsulated in the following question: If our brains are computers, why doesn’t size matter? In the real world of computers, bigger tends to mean smarter. But this is not the case for animals: bigger brains are not generally smarter. Most of the brain size differences across mammals seem to make no behavioral difference at all to the animal.

    Instead, the greatest driver of brain size is not how smart the animal is, but how big the animal is. Brain size doesn’t much matter – instead, it is body size that matters. That is not what one would expect of a computer in the head. Brain scientists have long known this. For example, take a look at the plot below showing how brain mass varies with body mass. You can see how tightly correlated they are. If one didn’t know that the brain was the thinking organ and consequently lobbed it into the same pile as the liver, heart and spleen (FYI, I keep my pile of organs in the crawl space), then one would not find it unusual that it increases so much with body size. Organs do that.



    But the brain is supposed to be a computer of some strange kind. And yet it is acting just like a lowly organ. It gets bigger merely because the animal’s body is bigger, even though the animal may be no smarter. The plot below, from a 2007 article of mine (in Kaas JH (ed.) Evolution of Nervous Systems. Oxford, Elsevier) shows how behavioral complexity varies with brain mass. There is no correlation. Bigger and bigger brains, and seemingly doing nothing for the animal!



    It has long been clear to neuroscientists that what does correlate nicely with animal intellgence is how high above the best-fit line a point is in the brain-versus-body plot we saw earlier. This is called the encephalization quotient, or EQ. It is simply a measure of how big the brain is once one has controlled for body size. EQ matches our intuitive ranking of mammalian intelligence, and in a 2003 paper (in the Journal of Theoretical Biology) I showed that it also matches quantitative measures of their intelligence (namely, the number of items in ethograms as measured by ethologists). The plot is shown below, where you can see that the number of behaviors in each of the mammalian orders rises strongly with EQ.



    But although this is well known by neurobiologists, there is still no accepted answer to why brains get bigger with body size. Why should a cow have a brain 200 times larger than a roughly equally smart rat, or 10 times larger than a clearly-smarter house cat? One of my older research areas, in fact, aimed to explain why brains change in the ways they do as they grow in size from mouse to whale (http://www.changizi.com/changizi_lab.html#neocortex), and yet, embarrassingly, I have no idea why these brains are increasing with body size at all. If a dull-witted cow could just stick a tiny rat brain into its head and get all the behavioral complexity it needs, then brains would come in just one size, and I would have had no research to work on concerning the manner in which brains scale up in size.

    So, here’s a plan. I would like to hear your hypotheses for why brains increase so quickly with body mass (namely as the 3/4 power). I will let you know if the idea is new, and I will see if I can give your idea a good thrashing. What’s at stake here is our very framework for conceptualizing what the brain is. Perhaps you can say why it is a computer, and that greater body size brings in certain subtle computational demands that explain why brain volume should increase as it does with body mass. Or, more exciting, perhaps you can propose an altogether novel framework for thinking about the brain, one that makes the enigmatic “size matters” issue totally obvious.

    To the comments!...

    Comments

    It seems to me that total brain mass vs. Body size doesn't account for different parts of the brain.
    Intellegence seems to me to be more related to the percentage of brain mass dedicated to the the Frontal cortex vs the total brain mass. Larger Animals may have need for more brain mass to process more nerve receptors in the larger amount of skin for example, or dedicated to processing Smell. But the part of the brain dedicated to higher level functions may be smaller by some measure (either total mass, or percentage of the rest of the brain mass, etc.)

    Mark Changizi
    Hi Chuck

    "to process more nerve receptors in the larger amount of skin"
    Nice. That's one common hypothesis. And not only more skin and thus more sensory receptors, but more musculature, and so on. But *that* would seem to imply that bigger mammals should have disproportionately larger somatosensory and motor areas, but they don't.

    "dedicated to processing Smell"
    But why should larger animals need bigger olfactory neural tissue?
    The motor processing functions of an animals brain may be proportionate, but the brain as a whole has to take the total motor processing input and output into account; when you are large and have a complex environment to deal with, you need a concordantly larger brain to deal with it.

    3 alternatives for you to debunk :)

    There is no brain function related reason that it gets bigger, and it's just a developmental effect of scaling up everything else. One of those fixed ratio things. More advanced behaviour is related to the development of extra or improved modules rather than size per se.

    Some brain interfacing organs in the body need extra bandwidth the bigger they get. Eyes, Ears, Skin, Tongue, etc are on average all producing more data in larger animals, and so the animals need correspondingly larger brains to process it all.

    In order to send signals all the way across it's large body, an animal needs a large brain to power those signals. Some sort of Inverse square law probably applies. A smaller animal has a correspondingly smaller distance to send it's signals.

    Mark Changizi

    Hi.

    "developmental effect of scaling up everything else"
    That hypothesis is out there, but I don't buy it one bit. Neural tissue is metabolically expensive, and evolution would surely select against brains bigger than needed -- especially 10 or 100 times bigger than needed! Also, there's a lot of research (some of mine, too) showing how finely evolution selects for "minimal wiring" solutions to neuroanatomy.

    "More advanced behaviour is related to the development of extra or improved modules"
    Although "smarter" animals have more cortical areas, the greatest driver of the number of cortical areas is brain size, which, in turn, is driven most by body size. My work (http://www.changizi.com/area.pdf) has shown that the number of cortical areas scales roughly as the 1/3 power of brain volume, and seems to be for wire-optimization reasons, like in VLSI electronic design the right compartmentalization is crucial to efficient wiring. That is, it seems as if bigger bodies force bigger brains, which, in turn, can force evolution to compartmentalize the brain into more areas in order to keep wiring costs efficient. ...all without any gain in behavioral aptitude.

    "Eyes, Ears, Skin, Tongue, etc are on average all producing more data in larger animals"
    I can see the argument for skin (and tongue), except that it would seem to predict disproportionately larger somato-motor regions in larger brains, something that does not appear to be the case. As for eyes, why should larger animals need to see better? A large or small animal with the same eye style -- e.g., both sideways-facing like a rabbit -- have just as much visual field to deal with. And similar point for audition.

    "In order to send signals all the way across it's large body, an animal needs a large brain to power those signals."
    This looks rather novel to me. But not yet clear how one would flesh out the argument.


     

    Just on the eyes comment.
    The greater the size of the animal, the greater the size of the eye (on average, I'm sure there are exceptions)
    the greater the size of the eye, the greater the resolution (number of pixels/sensors) in the eye due to increased surface area.
    The greater the resolution, the greater the bandwidth needed to process the image
    The greater the bandwidth needed, the bigger the brain.

    Mark Changizi
    Fair enough. You're right that bigger animals do have generally greater resolution. But why do they need more resolution?
    More resolution would be useful to identify threats earlier. The larger the animal, generally, the less agile they are, and it is more difficult to defend against predators. If we use the Cow vs Rabbit example.

    A rabbit does not need to identify threats until the threat is much closer to the animal. Just because of their size, it is harder to spot them and identify them as prey. (This can be inferred by a rabbit becoming still when it detects a threat. Also, rabbits are very fast and extremely agile.)

    A cow on the other hand has to identify a threat while it is much father away. Because the animal has less ability to react to a threat. (The herd all has to react to the threat as a unit, using their size to trample the predator.)

    In addition a cow point of view is quite a few feet higher than a rabbit, and most of the time, the rabbit is looking at close features of the terrain. While a cow, because of it's height advantage, looks at much more area than a rabbit does.

    Does that mean that a cow's brain has more "image processing" than a rabbit's? I don't know. But I imagine that while a rabbit might have to quickly process all of the information being captured by the eye, especially while running from a threat. A cow, for the most part, never has to process all of the information the eyes are presenting, and can instead focus on specific items in the field of vision as cues for the next step.

    Source? My working with Rabbits and Cows while growing up.

    Mark Changizi

    I love it. Just the kinds of ideas I like to think of. Whether it suffices to explain why brain mass scales so tightly as the 3/4 power of body mass...probably not, but surely they are ecologically important drivers. -Mark
    Gerhard Adam
    To sort of piggy-back on the previous post. 

    Suppose that there is nothing related to brain function, but strictly anatomy.  In other words, what structural adaptations would have to occur if there wasn't enough brain mass to take up the space it does?

    If you placed a rat brain inside a cow the most obvious problem is that the skull would be far to big to safely contain the brain.  That much additional fluid becomes heavy and may create balancing problems and the brain is more difficult to "fasten" in place to avoid jostling.

    In a nutshell, part of the question is really oriented towards how much we understand of brain usage based on the mass itself.  If we forget humans for a moment, do we find that a cow's brain is just as active as a human's or does it simply consist of more "filler"?

    To refer to your original point about computers ... how much of the space is filled with the "computer" versus peripheral devices versus empty space.
    Mark Changizi
    Hi Gerhard:

    "does it simply consist of more "filler"?"
    That view is out there, but I don't buy it. FMRI on animal brains shows it to be just as "all active" as our own. And I discussed in an earlier response how we have reasons to believe that natural selection has given us no larger meat inside our head than needed. (And certainly not one or two orders of magnitude more than needed!) And if a cow only needed a rat brain to function, then it would have a very different head shape, and not need filler.
    I would not knock out the "filler" idea just yet. How do you know there are not relevant stereowhatever issues?

    everybody knocked out the "ether" idea (me included) and now they came up with it again! if you don't believe me, just try to get some theoretical physicist to tell you about "dark energy" and/or "particle formation out of the vacum"
    so...give the filler idea a few neurons...maybe...

    I suspect Anonymous (of the 3 alternatives) and Gerhard are onto something. My metaphor for the human brain has long been: an enormous hotel, with lights burning in every window—but all the rooms are empty … & way down in front, a lonely clerk sits the front desk, reading a Playboy.

    It's not just a joke; for all the use to which we put it, the cerebral cortex has the appearance of a mushroom that grew, unattended, in the corner of evolution, as the eons passed. That we assume big size = greater power is a mistake committed too often in human affairs to be neglected as an explanation here.

    Mark Changizi
    That describes me all too well: see http://www.scientificblogging.com/mark_changizi/hue_hefner_how_color_made_empire_possible

    But as for a hugely expensive mushroom in our heads that evolution somehow failed to notice, what would the evidence for that possibly be? Our brains are busy doing stuff, and are costly, and evidence suggests they are highly optimized to save on wire. 
    I can't defend it, except to recall all the crazy experiments natural selection has produced, in its blind grope. The crazy variations I've seen on themes in the fossil record have often led me to imagine that anything that can grow on earth—given the available materials—has, or will soon (if we don't poison the well permanently). I've always been skeptical of implications that evolutionary pressure is, in the long view, necessarily efficient or even produces beneficial results. The process is entirely unguided.

    In the absence of a better theory, it seems possible to me that brains may simply tend to swell 'til they fill skulls. Of course, that's like the Big Bang theory—it just knocks the question back a step: why would animals grow so that they need such big noddy heads? As you say, "if a cow only needed a rat brain to function, then it would have a very different head shape, and not need filler." But ca we be certain of that? How many instances of just such absurd, doomed experimentation have there been, down through the eons, that we don't know about? No one would call the fossil record "complete." Maybe there's a feedback loop between environmental conditions and body plans … & the brains are tagging along for the ride.

    Have we got a truly reliable metric, yet, of the ratio of brain volume to efficient use of its physical contents? We know so little about the subtler interwirings of mammal brains (at least). I can't begin to imagine how one would judge the "efficiency" of a brain. How else, then, to judge the likelihood of its size as a proportion of body-mass? I just love this post, BTW.

    Mark Changizi
    Hi John S.,

    I can't claim to fully understand how evolution does it, but my view is that it although "blind", it ends up with masterpieces in most cases, not kluges. The best evidence for this is to look at the huge number of cases of convergent evolution, where, despite not "communicating" with one another, disparate lineages found the same engineering solution to the same ecological problem. (http://en.wikipedia.org/wiki/List_of_examples_of_convergent_evolution) E.g., four or more independent "evolutions" of the "anteater" design. At least three independent "dolphin" designs. The Tasmanian wolf, a marsupial that effectively evolved to the same solution found by wolves. And many many more. How could evolution have this power if it lets mushrooms grow orders of magnitude larger than needed in our skulls?

    As for some ways of rigorously trying to approach optimization...
    http://www.changizi.com/globalNeuron.pdf
    http://terpconnect.umd.edu/~cherniak/JNeuro94.pdf
    http://www.changizi.com/dictionary.pdf
    http://www.changizi.com/vishierarchy.pdf
    http://research.janelia.org/Chklovskii/KoulakovChklovskii01.pdf
    http://www.changizi.com/ChangiziBrain25000Chapter1.pdf (1st chapter of my 1st book, each section relevant, first on brain, second on networks generally, third on animal number of limbs and optimal wiring).
    Hmm, very skeptical that your examples are numerous enough (given the dumbfounding variety of speciation we can estimate has occurred on earth) to demonstrate anything more than happy accidents. If I were using my overdeveloped cerebellum, I'd defer to your expertise here … & possibly we're caught in an eddy of semantics ("masterpieces" of evolution? Really? Would you call a coastline a masterpiece, or just remark on its raggedness?).

    "How could evolution have this power if it lets mushrooms grow orders of magnitude larger than needed in our skulls?" They may only appear larger-than-needed to us because we judge brains mainly for their processing power—understandable, given info-processing's primacy in our happiness—rather than their mechanical functions … e.g., filling up skulls. You're doubtless right to call brains metabolically costly structures, but that doesn't obviate their fulfilling other needs, no matter how mundane they may seem. It only makes the other needs less likely to get fulfilled. How often, then, over the chasms of evolutionary time, must "less likely" evolve to become a tried-&-true method? Not very often, I suspect, as a percentage.

    In any case, my comments here have been mostly negative—I haven't contributed any insight, so I'm bowing out, but will lurk, as this subject fascinates me. And your links will occupy the rest of my evening; thank you.

    Mark Changizi

    Hi John S. (lurker),

    On the many cases of convergent evolution as happy accidents, I'm not sure how to quantify it (!), but any way I can imagine slicing it, these would appear to be super-astronomically improbable accidents.  Morphology space must have a LOT of dimensions, and is big enough for animals to have their own universe of real estate with no other animal anywhere close to its morphology.

    As for masterpieces, coastlines are indeed pretty, but they don't DO anything. Animals are incredible machines that do stuff, by any engineering standard.

    And on filling up skulls, wouldn't one predict, then, that the skull gets filled up with something cheaper?

    Thank you!

    Mark
    What about the dinosaurs? pea brained behemots no? no extra skull...why did they die? a meteorite? who knows...but they lived for a long time....no brain-mass to body-mass relationship here no? Maybe cows, specially BIG cows are more intelligent than we think! maybe they will survive while humans will be the "dead end" cow generally get along with other cows, humans ...not generally.

    Johannes Koelman
    I'd guess that most (higher?) organisms spend most of their brain power on processing sensory input. If that is the case, it is perhaps not too far off to define as measure of intelligence an encephalization density (ED): the brain mass divided by the total surface area of the organism.
     
    An adult male human typically has brain mass = 1.5 kg, and surface area = 2 m2. This renders ED = 0.75 kg/m2 for humans. I bet no other animal has a higher ED.
    Gerhard Adam
    Does that mean that I get smarter if I gain weight?  :))
    Johannes Koelman
    No, on the contrary, you get smarter if you reduce your waistline... ;)
    Gerhard Adam
    Just goes to show that I need to lose weight.  I did the calculation backwards :)
    Mark Changizi
    "the brain mass divided by the total surface area of the organism."
    That idea used to be the main one in the 1970s or so, and back then it appeared that brain mass scaled more like the 2/3 power of body mass, consistent with what your hypothesis would predict. But the exponent is now fairly agreed to be 3/4 (like the metabolic constant), too high for the surface hypothesis. Also, conceptually, the surface hypothesis would seem to predict that the somatosensory and motor areas should be the regions that disproportionately expand in larger brains, but they don't.
    kerrjac
    Good question.

    I recently started a nice theoretical book about how computers work, just from the ground-up. It sort of de-mystifies the wide-spread use of computers as analogy. It's rather fascinating in fact how *different* the brain is from a computer.

    To take a stab at it, I'd guess it's b/c there's more for the brain to regulate. Input is likely part of it, but most of its size is probably directed towards output. Consider an emotion and the input involved: external and internal sensory. Consider then all the different physiological effects it then has, on organs, muscles, immunity, etc.

    A computer is basically a platform for isomorphisms. Raw data comes in, and most of the work lies in transforming it in a manner useful to the user. Likewise for the brain, I would guess that it's busy transforming data in a manner useful for the user. But the latter requires lots of transformations in coordinating all of the different organs, particularly as the body grows in size and complexity. On the individual organ level, output that's useful for one organ isn't useful for the next. Furthermore, coordinating across organs compounds the difficulty.

    It's similar to the need to increase internal management dep'ts as a company grows. After reaching a certain size, it's not unfeasible for more resources to be going to management (eg, brain) than to lower level employees (eg, organs). This particularly holds if there are a diverse array of expected outcomes (eg, different types of organs).

    Across companies of all sorts of sizes, input is likely pretty similar - cash, material resources, manpower. But if you want to expand output you have to utilize the input in novel ways, such as by collecting DVDs and renting them out through the mail. There's a sort of myth that companies can just keep growing by doing more of the same thing. But this doesn't hold true as per the principle of diminishing returns, which I think holds true in biology.

    A completely different guess - actually from Sagan - is that brain size relates to whatever could fit in child birth.

    Or causation might be reversed, where larger brains allow for larger bodies.
    Mark Changizi

    You say, "...as the body grows in size and complexity," but it is not clear whether larger mammals are any more complex in their internal anatomy.  Same heart, lungs, spleen, etc.  But I totally agree that larger and more complex structures must compartmentalize more, like you say. (http://www.changizi.com/changizi_lab.html#genComplexity)

    What about the correlation between # of neurons v. cells in the body, as opposed to v. body size.

    Mark Changizi

    "correlation between # of neurons v. cells in the body, as opposed to v. body size."
    Most cells in the body don't change size with body size, so total # body cells scales the same as body size. But, on a similar tack, neurons DO change in size with brain size: they get bigger. The number of neurons scales up more slowly than brain mass, namely about as the 2/3 power of brain mass. That means that although brain mass scales as the 3/4 power of body mass, the number of neurons in the brain scales as the 1/2 power of body mass.
    Dave Deamer

    Hi Marc -- I notice that your post and all of the comments that follow focus on the number of neurons as a primary factor. However, there is a very powerful multiplier of nervous complexity that is related to the number of connections between neurons, which was alluded to in my column of November 5. The number of neurons might increase on some linear scale as a power of body mass, but connections between neurons can lead to exponential increments in complexity of a given system. Furthermore, brains might be expensive in terms of metabolic energy, but connections should be relatively cheap I would think. I know that the number of of connections between neurons are at best order of magnitude estimates at present, but in attempting to answer your original question I would want to incorporate this parameter, along with neuron number.

    Mark Changizi
    Hi Dave,

    Connections I'd say are expensive. There's a lot of research pointing toward the conclusion that nervous system organization is often organized to minimize the total wire length required to make all the connections. Connections must be made by wires, long wires, and that's a cost that adds up quickly. For example, I have argued that the rate at which brains compartmentalize is in order to minimize wire length costs.

    On how many "wires" in the brain, there's several ways of talking about it. First would be just the total mass of the white matter, which scales up faster than the mass of the gray matter. (As the 4/3 power of gray matter.) Second would be the number of white matter axons, which probably scales roughly proportionally with the number of (pyramidal) neurons. And third would be the total number of synapses: larger brains have larger neurons with more synapses per neuron -- # syn per neuron scales as the 1/2 power of the number of neurons, and so total number of synapse connections in the brain scales as the 3/2 power of the number of neurons, not as the square (which would be the highest exponent possible).

    Hope that's fodder...
    There are likely to be a number of other variables correlated with brain size and body size that are relevant to this discussion. Maximum life span is one. Larger animals tend to live longer. The brain never gets a chance to reboot, so it just has to keep processing more and more memories and experiences layered on top of one another. Not only would it require more neurons to store these memories, but managing all this data and utilizing it to make optimal decisions requires more processing power.

    "Reboot?" "processing power?" Am I saying that the brain is like an old computer and that every year you have to buy a bigger hard disk to store your extra photos, and more RAM to run the latest operating system? No. The computer metaphor is a powerful one and will never go away. Whether the brain is a computer is not the point. We use metaphors to thinks about our complex world all the time. For example, we use sports metaphors to discuss business (i.e. John really scored with his proposal). This doesn't mean that business is only a sport, it just means that they share a lot in common. Similarly, the issue is not whether the brain is a computer. Clearly it is not, yet they do share a lot in common. It is the active comparing and contrasting of the two that deepens our understanding of them both.

    Mark Changizi
    Agreed on the latter.

    And on the former, that's a great idea. Larger animals (can) probably live longer for some very fundamental metabolic scaling considerations, and as a consequence, perhaps they're stuck having to deal with more "baggage". I love it. Not sure exactly what it should predict yet, but worth thinking seriously about it, and pushing it.
    Johannes Koelman
    Take 2. Combining Mark's hint "the number of neurons in the brain scales as the 1/2 power of body mass" with Dave calling our attention towards "the number of of connections between neurons" rather than the number of neurons itself, one can't fail to notice that the number of potential connections between the neurons in an organism tends to scale with the total mass (or total number of cells) of the organism.

    Before computers became popular, the brain often got compared to a telephone switchboard, right?
    Mark Changizi

    Nice. And thinking like a physicist (my former self).  It would be nicer, though, if the actual number of neural connections were closer to the square of the number of neurons, but it is actually more like 3/2. That is, total number of neuron-neuron connections goes as the 3/2 power of the total number of neurons (or, the degree of each neuron-node scales as the square root of the number of neurons). Not sure how the *potential* number of connections could still be the right quantity to theorize about...
    Johannes Koelman
    Interesting stuff.
    Perhaps the brain economizes on wiring. Having N neurons with N1/2 connections per neuron still allows each neuron to be connected to every other neuron, albeit via an intermediate ('hidden') neuron.
    Mark Changizi


    Right. A characteristic path length potentially as low as two (i.e., two axons must be traversed, on average, to get from any one neuron to any other). I have been able to show that mammalian brains satisfy two kinds of connection invariance. The first concerns connectivity *within* areas: the number of synapses per neuron scales proportionally with the number of neurons per cortical area (intuitively, "full" connectivity within areas).  The second concerns connectivity *between" areas: the number of area-links per area scales proportionally with the total number of areas. These two invariants, along with a "save wire" desideratum, allows one to explain the manner in which a dozen or so micro- and macro-anatomical features scale with brain size. The low path length of two follows from the two constraints, but I don't actually have any further explanation for why these two invariants "should" hold.  It is an elegant two-tiered design -- "full" (i.e., up to a constant factor) connectivity within areas and across areas, but not for the entire brain as a whole. But why two tiers and not more? What's so special about two tiers, or, equivalently, what's so special about having just one intermediate neuron (as you say)? I dunno.

    If anyone's interested in my brain scaling work, see links at
    http://www.changizi.com/changizi_lab.html#neocortex and also
    http://www.changizi.com/ChangiziBrain25000Chapter1.pdf

    Mark

    Johannes Koelman
    what's so special about having just one intermediate neuron (as you say)? I dunno.
    I dunno either... but the universal approximation theorem might provide a hint.
    Johannes Koelman
    Okay, so the picture that seems to emerge is roughly as follows:

    To have the ability of 'universal learning' (i.e. no restrictions in the type of perceptions that can be processed and memorized) the brain needs a multi-tiered architecture of connections. Amongst the multi-tiered architectures, the two-tiered design is optimal. Reason being that for the brain to be able to process signals from an n-dimensional configuration space (i.e. signals characterized by n independent variables), a total of the order of N ~ n2 neurons with ~ n5/2 connections are needed in a 2-tiered architecture. In an k-tiered brain architecture, this would scale as N ~ nk and ~ nk+1/k.
     
    Mark Changizi
    Johannes,

    Seems like you're potentially on to something.  But you'll need  to go slower for me.

    - Why is N ~ n2?

    - And why is # connections E ~ n5/2? (This would mean E ~ N5/4, when its really E ~ N3/2. That is, for neocortex, the number of synapses per neuron, d ~ N1/2, and so the total number of synapses, E ~ Nd ~ N3/2.) (Or did you mean E ~ n3/2, consistent with the "k" formula? But if so, that leads to E ~ N3/4.)

    Mark
    Johannes Koelman
    Hi Mark -- there is indeed an issue with these estimated power laws. In fact, it appears the universal approximation theorem alone is not sufficient to work out such a scaling law. What seems to be missing is the scaling of the number of hidden neurons with the total number of neurons.

    I need to give this more thought.

    But before doing so, I would like to better understand the scaling of the number of connections between neurons.

    Here I read that the human brain has about N = 1011 neurons and some E = 1014 synapses. How does this fit with a E ~ N3/2 scaling law?
    Mark Changizi

    Hi Johannes,

    One needs data from across mammals of varying size to get this. Neuron density has long been known to scale as the -1/3 power of brain mass, and thus the number of neurons scales as the 2/3 power of brain mass. But evidence also suggests that synapse density is approximately invariant across brain size. Because every synapse belongs to a neuron, it follows that the number of synapses per neuron scales as the 1/3 power of brain volume.  ...or as the 1/2 power of the total number of neurons. Or, the total number of synapses in the brain scales as the 3/2 power of the total number of neurons. (And I'm presuming that the total number of neuron-neuron edges scales proportionally with the total number of synapses.) My papers on this stuff are...

    http://www.changizi.com/diameter.pdf
    http://www.changizi.com/connectchapter.pdf
    http://www.changizi.com/brainencyc.pdf
    http://www.changizi.com/ChangiziBrain25000Chapter1.pdf

    Mark
    Johannes Koelman
    Mark --  the stuff you are investigating is fascinating. However, something seems not right to me.

    Now, I am not familiar with all the neuroscience jargon, and I might be drawing the wrong conclusions. So would like to check with you if I got some things mixed up.
    If I understand you correctly the number of neurons N and the number of connections E are related as E/C = (N/C)3/2, with C roughly equal to 105. Right?

    So, whilst a human has about 1011 neurons with 1014 interconnections, a small organism with 107 neurons would have only 108 connections. [As an aside: a relationship like this would seem to place a lower limit on viable brain sizes (E > N > C = 105).]

    Now, the whole two-tier concept does not seem to fit in this scaling behavior. Point being that, the two-tier concept requires C to be close to unity. In other words: C >> 1 will yield network diameters much larger than 2.
    Mark Changizi

    My argument went like this...

    Network diameter = (log N)/(log d), where N = tot # neurons, d = # synapses per neuron. (Assumes neocortex is small world.)

    For neocortex, have roughly N = cd2, where c is a proportionality constant.

    So, net diam = log(cd2)/log(d) = [2log(d) + log(c)]/log(d) = 2 + log(c)/log(d).

    For sufficiently large brains (and thus sufficiently large # syn per neuron d), net diam approaches 2.

    As back-of-the-envelope estimates of c = N/(d2), for mouse c = (2e7)/(8e3)2 = 0.3. For human it is c = (10e10)/(5e4)2 = 4. That is, the constant c is bouncing vaguely around 1, and so log(c) < log(d), and so network diameter may *actually* be near 2, rather than just some day in the far huge-brain future.

    That was my reasoning, at least.

    Mark


    Johannes Koelman
    OK, fair enough. The equation you are using for the network diameter (log N)/(log d) gives (for large enough networks) a lower bound. In fact, the bound is realized for a specific class of networks only: the so-called Kautz graphs. (See here for an explanation and a neat way to construct these minimum-diameter graphs.) There are many reasons why the diameter can be larger than indicated by the (log N)/(log d) bound. One reason is that the neural network will generally deviate from the Kautz architecture, another reason (as remarked by someone else in this thread) is that usually only a fraction of all synapses outgoing from a given neuron will be connected to different neurons. 

    Using Kautz graphs, it can be shown that to connect N = d(d + 1) nodes in a network with diameter 2, you need S >= d2(d+1) links. I was hoping (based on the false impression that the constant C above would effectively be unity) that it would be possible to demonstrate that evolution results in neural networks optimized to reach diameter 2 using as few connections as possible. Based on the values for N and S listed above for humans and other species, that hope seems idle.
    Mark Changizi

    Interesting.  I didn't realize it is a lower bound only.  And I need to read about Kautz graphs...

    On the fraction of synapses that actually connect to distinct neurons, typical estimates suggest that the fraction is very high, near-ish 1.

    And the constant C would not be about 105, but closer to unity.  You earlier had said, "So, whilst a human has about 1011 neurons with 1014 interconnections, a small organism with 107 neurons would have only 108 connections."  That underestimates the interconnections.  If nearly all the synapses amount to distinct connections, then the total number of interconnections for human may be more like 5x1015. And for mouse there might be 1011 interconnections.

    Mark
    Mark -- I agree that there is some sort of selection for minimal length of "wiring" but I can think of factors other than metabolic energy why this might have selective value. I also have a question about the meaning of "connections". One number would be how many other neurons a typical cortical neuron might connect to, and a second number would be how many synaptic junctions a typical neuron has. The estimates I have seen for mammalian neurons are 1000 connections to other neurons and 10,000 synapses per neuron, and I'm sure there is a lot of variation around these averages. So we are already talking about some pretty big numbers, but on a microscopic scale. When I guessed that it would not be very expensive (in terms of metabolic energy) to add increasing numbers of connections, I had these numbers in mind. If these numbers increased to 1100 and 11,000, for instance, there would be no difference in the number of neurons, but because of the power law, it might make a huge difference in potential computing power.

    Mark Changizi

    If neurons are to get more synapses, then like all tree-like things in nature, they have to have thicker trunks. The entire volume of the arbor becomes greater. For neurons, trunk diameter scales approximately as the 1/3 power of the total number of synapses on the neuron (consistent with something called Murray's Law). Although the diameter of the neuron's trunk (i.e., its cell body diameter, or the caliber of a white matter axon) scales slowly (1/3 power is slow) with the number of synapes per neuron, the total volume of the neuron scales faster, because it depends on the entire length, which "feels" a disproportionate effect of the diameter increase. Connections are costly. ...and they are scaled up as slowly as possible, but still just barely fast enough to maintain the two-tiered invariant connectivity (invariant connectivity within, and between, cortical areas) I talk about in comment above.
    I'm not sure I have a good argument for any brain size debate, especially since there are no invertebrates on your scale :-)
    But the computer analogy only goes so far. As you point out, brains are "always active" (you cite fMRI data (see 'default-mode network' and Marcus Raichle). Indeed, not only brains are always active, all animals with brains are almost constantly producing behavior, as long as they're awake. Point in case, a common theme for neuronal principles of behavior activation is disinhibition - basically, brains always want to do something, but there is a layer of inhibition over this activity. Only behaviors where this inhibition is blocked will get generated.
    In other words, brains are active organs and don't just passively wait for stimulation. The "stimulus-response" concept comes from the experimental approach of neuroscience, but covers only a small fraction of what general brain function entails. As long as computers are passive, they're a poor analogy to brains.
    In fact, defects in the networks which are constantly active in the resting state in humans (default-network), are associated with most major psychiatric disorders. At the same time, brain size correlates with behavioral flexibility, for instance in birds (migratory vs. stationary) and predators catch primarily smaller-brained prey. Obviously, trying out things makes you more flexible. 'Trying out' is something computers don't do. Maybe the brain size correlation comes from more active brains needing to be larger in order to try out more things and be more flexible? The computer-like rest of the brain may not really need to scale all that much?

    Mark Changizi
    Hi Bjorn!

    On computers, when I am wondering whether the computer metaphor holds, I have a much looser notion of computation. It need not remotely be desktop computer-like. Just an information-processing computation device of some kind. ...and for any such device, it is strange to see it vary so much in size with no obvious behavioral difference.

    On "brain size correlates with behavioral flexibility", yes and no. My own data across mammals does not find this, although I wasn't measuring "flexibility" so much as behavioral repertoire size. It seems clear, though, that a cow is not more -- much less ten or more times more -- behaviorally complex than a smaller-brained cat.
    Hi Marc,
    I don't know of any computer that is constantly doing something without instructions. Of course this:
    10 print "hello world"
    20 goto 10
    doesn't count as "constantly active". We don't even know enough about the default-mode to be able to guess what is going on in order to give a computer appropriate instructions. Maybe, if we knew, we would understand why it scales with size and then whatever it is that makes our future computers do it (hard- or software) will also scale? My current understanding of computers or software is not sufficient to even come close to serve as a brain analogy - and I do some programming and neuronal modelling. Computers and brains are like a knife and a Leatherman multi-tool: sure there are some similarities, but the versatility is just orders of magnitudes off.

    Here's the data on mammalian prey brain size:
    Shultz S, Dunbar R (2006) Chimpanzee and felid diet composition is influenced by prey brain size. Biology Letters 2: 505-508.
    This study shows a correlation of brain size with monogamy in primates:
    Schillaci MA (2006) Sexual Selection and the Evolution of Brain Size in Primates. PLoS One 1: e62.
    Of course, the cause-effect relation in both studies is not straightforward, but confirmation bias made it all fit so nicely for my argument. Go ahead, tear it apart :-)

    Here's a nice paper on insect brain size, aptly titled "are bigger brain better?":
    http://www.cell.com/current-biology/fulltext/S0960-9822%2809%2901597-8
    It's a great review, the only thing bad I can say about it is that Lars didn't cite me, lol :-)

    Mark Changizi

    My computer metaphor is meant to refer to computation of any kind: Turing computability. I certainly (still) believe that our brains are capable of doing only the Turing computable.

    Thanks for the paper links. I got to meet Lars when he contacted me about his paper.
    I wonder if birds are different from mammals in this sense of behavioral flexibility and brain size. If you think about the constraints to brain size being more extreme in birds than in mammals this makes sense. For birds, weight is a major issue. Too heavy and you might be too slow moving to avoid being caught by a cat. So, in birds smaller brains are better. To counter the negative consequences of the larger brain, they had better be more "flexible" behaviorally.

    I'm still thinking as I read here... this is a fascinating topic, and one I've thought about from time to time as I've peered at the little brains of my birds.

    Mark Changizi

    Hi Dr. Kiki!

    Although that sounds logical, the 3/4 power scaling law applies just as well to birds as to mammals. So, even if there was some overall constant factor difference, the scaling exponent is the same, suggesting the same fundamental principle driving brain size. Furthermore, not only do birds have the same scaling exponent, but also have the same proportionality constant, so that they lie pretty much directly on top of the mammal plot. ...meaning birds of the same body size as a mammal have about the same brain size as that of the mammal.

    One could wonder whether birds would be selected to have smaller bodies in order to keep brain size in check, for flying sake. But the expectation would go the other way: larger bird bodies would lead to relatively smaller brains (because brains scale up more slowly than bodies) -- although to really make this argument I would need to work out the lift as a function of body weight too.
    Thank you, dr. Kiki, for ushering in the birds. Mark, do you think, or have any numbers, of the validity of the 3/4 power scaling for dinosaurs? Mammals started as small animals in evolution, getting bigger on the average. We now think that dinosaurs weren't really smart, but if the 3/4 power rule stands, they must have had pretty big brains. These, in the course of evolution, shrunk to the size of bird-brains, without giving up much complexity. On the contrary, I can hardly beleive a dinosaur that was as smart as a crow, or could sing like a skylark.

    Mark Changizi
    A taxon conforming to the 3/4 law doesn't mean they must have pretty big brains. The formula is brain mass = constant * bodyMass^{3/4}. If the constant out front is small, then the taxon will have lower brain mass compared to similarly sized other taxa. Dinosaurs are like this, a lower constant. -Mark
    Stellare
    I have a huge head so I tend to think that size matters. I am very, very smart. :-) On the down side, when I'm full of myself I am also very, very full of myself. :-)

    Jokes aside, I have the deepest respect for the complexity of our brains - and I do not believe we are anywhere near understanding how it works. We can observe the physics of it, be it the size of it or the 'electronics' or wiring. To me both statistical methods and the assumptions that more activity in the form of particles (of various sizes) moving around can be used to prove intelligence for instance are insufficient and does not give valid results.

    I wonder if the size approach to the issue of intelligence of the different species may not lead to further understanding at all. Unfortunately, I cannot offer the solution. Even though my brain is enormous and placed on the top of a body with a typical female waistline. :-)
    Bente Lilja Bye is the author of Lilja - A bouquet of stories about the Earth
    Mark Changizi

    On a related (or not) note, I've often wondered whether high status human males actually DO get larger heads. One finds larger face padding in orangutans and alpha male apes. Do CEOs of companies, say, need larger thumbnails than copy boys?

    I think there are bigger evolutionary pressure fore smaller brains in small animals.
    And there can be more evolutionary explanations where the brain size equilibrium is, smaller animals often have larger population and shorter life spans.
    I really think that if you “only” change brain size it needs to be much bigger to be a little smarter. Then I am to stupid to analyse the dynamic system, need more brain…..

    Mark Changizi
    NissE: "think there are bigger evolutionary pressure fore smaller brains in small animals."
    It is a good point to remember: that brains don't just "get large". They "get small" too. When animals are selected to become smaller, their brains must also reduce in size. And the brains must change their organization in order to remain efficiently organized -- this includes reducing the number of compartments, for example.

    "Then I am to stupid to analyse the dynamic system, need more brain…"
    If you dig that kind of thing, you may like to read up on Godel's Incompleteness Theorem, and philosophy arguments about its implications for the brain.
    Gerhard Adam
    Mark

    I realize that you've mentioned mammalian brains on several occasions, so this raises the question of whether there is a different architecture for non-mammals.  We certainly know that the scaling being discussed didn't apply to dinosaurs since their bodies were significantly larger than their brains, so there is no direct correlation between being large, longer-lived and brain processing requirements (at least not for these animals).

    Secondly, it seems that we have a fundamental problem of assumptions that are difficult to fill in.  In particular, we understand something about human intelligence but can only surmise what we mean by other intelligences.  We may have some insight, but we truly have no sense of how they experience their world or even what their requirements are for survival under normal circumstances.  As a result, we are assuming that the relationship between human intelligence and others is based on our own sense of what it means to be intelligent.

    However, I think this can be misleading, since natural selection did not choose brains to work on quantum physics or mathematics.  That's an incidental development for human beings, so perhaps we need to consider what the human brain is used for under evolutionary conditions, rather than just the way we see it being applied today.
    Mark Changizi
    Hi Gerhard,

    On dinosaurs and "no direct correlation between being large...and brain processing requirements", dinosaurs show the same 3/4 style brain-body scaling law. So do birds, fish, and all vertebrates. But, each of these vertebrate classes has a different y-intercept in the first plot I showed, or proportionality constant in the equation relating brain mass to body mass. So, among dinosaurs only, the plot would look like the brain-body one, but shifted lower on the page.

    I *certainly* agree with the point that "we need to consider what the human brain is used for under evolutionary conditions" -- much of my research is exactly along those lines. And I agree we must be careful in gauging the "intelligence" of other animals. My estimates were from ethograms from ethologists who become "bathed" in the behavior of one animal, spending thousands of hours learning the ins and outs, and eventually coming to a classification of the behavior categories.  Has many potential problems as a measure, but better than many other measures.
    Hi Mark
    Interesting challenge! Here are three ideas for you to tear apart:

    Perhaps larger animals have larger brains simply because they can. In terms of both space and metabolic constraints, a 20g animal simply cannot have a 20 g brain. For a 2 kg animal, 20 g of brain tissue are not such a problem. Sure, this hypothesis is a bit silly, but I think permissive factors probably have played a major role in brain size evolution.

    I think (but cannot prove) that encephalization quotients have increased most often in lineages that also went through significant increases in body size. If this is true, and if brains generally scale with negative allometry (let’s posit this even though I recognize you’re trying to explain this as well), then the animals with larger bodies would have more room in their heads for expanded brains. A small animal would not be able to increase its brain size without growing quite an ungainly head!

    I also think that, within a group of closely related animals, the larger bodied animals, with their larger brains, tend to be smarter. I know this is fiendishly hard to prove. I doubt we have good ethogram data for testing this hypothesis, and I’m not sure ethograms really capture the flexibility that many believe to be the hallmark of “intelligence”. Anyway, from my personal experience with many different animals, I think there is something to the idea that bigger brains (of the same general design) tend to be “better”. Of course, the human species is a bit befuddling in this respect.

    Just thought I’d share my thoughts. I’ve been asking myself these sorts of questions for years; nice to know I’m not alone.

    Mark Changizi
    Thanks Georg,

    "Perhaps larger animals have larger brains simply because they can."
    But brain tissue is very costly, and it would be greatly selected against.

    On your third paragraph, I think that's a good point. Perhaps bigger body animals *do* tend to be smarter, counter both to intuitive judgements and to quantitative measurements I made. I'm certainly open to this, because, as I've written elsewhere, we don't know jack about the kinds of capabilities we have.  And, as an earlier comment suggested (brilliant idea, I think), perhaps all that bigger brain is for more memories given the longer life, and, if so, surely that would be *used*, even if the basic behavioral repertoire is pretty much the same.
    Is there any evidence of brain sizes increases when energy is unlimited? If brain tissue is energetically costly, and limited as a result of limited resources. Wouldn't it follow that a species having unlimited access to resources might see larger neural development?

    Do we see this in humans in developed countries? Aren't we seeing an increase in C-sections because babies heads are becoming larger? OR, do I have it wrong and it's the pelvises that are shrinking...

    Mark Changizi

    I don't know.  I'm not aware of people trying to look at EQ, say, as a function of "habitat cut-throatness". But that would be nice, although tricky to measure. For humans, I wonder if there's been enough time to hope to see a signal through the noise (if there's any signal at all).
    Bente Lilja -- From your post above, it strikes me that you are a perfect example of the advice that, "If you've got it, flaunt it!" I'll bet your encephalization quotient is way up there around 8.

    Jokes aside, I agree with your expressed sentiments. To paraphrase Haldane (or was it Bernal) "Not only is the brain more complex than we imagine, it may be more complex than we can imagine."

    Stellare
    Well, thank you, Dave! (I think...:-))
     
    Haldane or Bernal or both or someone else entirely, was perfectly right I think. "...can imagine..." is what Mark here is trying to overcome. An optimist he must be! :-)
    Bente Lilja Bye is the author of Lilja - A bouquet of stories about the Earth
    Johannes Koelman
    So my suggestion that the brain volume should scale with the cross-sectional area of the waistline didn't meet a lot of support. Strange. yet, I have to admit that the brain:waistline ratio of Bente seems to provide a counter example to the scaling law proposed.

    So let me offer an alternative scaling law:

    1) The amount of processing needed to have the body function properly scales with the metabolic rate
    2) This processing takes place predominantly in the brain
    3) The processing capacity of the brain scales with its mass
    Ergo:
    4) Brain mass scales with metabolic rate.
    Mark Changizi

    I like the general strategy. (1) and (3) would need some theoretical fleshing out.  It's hard to see how to interpret (1), but I can imagine that, with the right theoretical abstraction, something like that might fall out. And for (3), because the number of synapses scales proportionally with brain mass, I've often imagined that it is the synapse that ought to be thought of as the principle furniture in the brain, not the neurons at all.  But I've never been able to follow that up.

    The "bigger brains are for memory" a commenter mentioned here also roughly fits the framework.

    Mark
    Stellare
    I can't even begin to tell you how thrilled I am to be a part of a scientific theory! However small.

    Unfortunately, I have to give you some more counter intel. My large brain work on high steam most of the time, burning a hell of a lot of calories, I'm sure. However, my personal metabolism is first and foremost inspired by a whole body activity. Even though I sometimes loose my head, it is connected to the rest of the body as a rule. Thus maybe there is something to this theory after all...

    An excellent demonstration of elegant modal logic, it is, regardless. :-) Johannes!
    Bente Lilja Bye is the author of Lilja - A bouquet of stories about the Earth
    In regards to the earlier comments on the idea that the brain needs to be larger because the head is larger and since dinosaurs have already been mentioned, as you correctly point out, dinosaurs had much smaller brains than mammals, given the same body weight. That did not imply that their "walnut sized" (to use the traditional metaphor) brain bounced around in a cow brain-sized cavity, instead that cavity was just the right size for that brain. And while some taxons of dinosaurs (Pachycephalosauria and Ceratopsia comes to mind) did fill out most of the rest of their skulls with loads of bone tissue, most did not, they simply had smaller skulls. The point is, the skull grows to accommodate the larger brain, the brain does not grow to fill a larger head. This still leaves the original question unanswered though; Why does the brain grow?

    An interesting point was touched on briefly in the earlier discussion of dinosaurs; All major groups of animals show the same brain size to body size ratio but the different groups are shifted around in the plot, i.e. they have the same slope but in different places. This gives us two important things to consider; First, absolute brain size is not determined by absolute body size. A cow-sized (to continue with our main example) dinosaur would have a much smaller brain (and thus, skull) while still fully functional. We don't know (nor can we investigate) the range of behaviours of that dinosaur but it certainly could function enough to survive. This point also gives us a way to test the Memory-theory mentioned above, did similar sized dinosaurs live roughly to the same age as a mammal? (I don't have any references on dinosaur lifespans available so I don't know.) If so, then the storage needs are apparently not a factor. On the other hand, if their lives where shorter and this shortening could be correlated to the difference in absolute size (by some factor), then we would have some basis for that theory. It is, of course, also possible that neither of these cases are true.

    The other point that comes from an aggregated plot of brain size to body size is that despite the segregate groupings of different animals, all of them show the same slope. This is pretty interesting and not something that would be expected. Without knowing the data, one might have assumed that, for instance, dinosaurs had a lower slope than, say, mammals, but they don't. This probably shows that there is something very fundamental about this ratio as it is consistent across very different animal "architectures" (mammals, fish, reptiles, etc.) Unfortunately, this still does not bring us closer to what that factor really is. If the "Control system"-theory of the last few comments is true, then that would mean that it takes a much more advanced control system to regulate a mammalian body architecture than it takes to regulate a dinosaur (keep in mind that there is strong evidence that most Dinsaurs were endotherms as well).

    A very interesting topic.

    Mark Changizi
    Dear Paul,

    "First, absolute brain size is not determined by absolute body size. A cow-sized (to continue with our main example) dinosaur would have a much smaller brain (and thus, skull) while still fully functional."

    Good point to keep in the fore. The whole "why do bigger bodies demand bigger brains?" question only makes sense *within* a class of animals (e.g., mammals, birds, reptiles, etc.), not when one combines them all in one pot.  The implicit presumption is that, within a class, there is some single fundamental brain design / template, one that gets mucked around as body size changes. But if you move from mammals to fish, then you've altogether started with a different fundamental brain design / template. 

    As for the memory storage, and dinosaurs versus mammals, dinosaur age follows a similar power law with body size.  It could just be that dinosaurs get by on much less memory-mass per year.

    Mark
    First let me say I don't really like the computer metaphor for brains to much anymore. Maybe its because my primary training is in CS... I prefer to think of the brain as transducer of the "forces" of the "world" its is situated. I suppose one can think of a transduction as computation, but I digress...

    Here is a thought on the relationship of body size to brain size.

    one consistent behavior among the cognitive agents you are discussion seems to be that they all have a good understanding of how their body "fits" into the world. In other words, I don't generally bump my head into things. I don't reach for things that are beyond the length of my arms, etc. Lets then assume this "understanding" emerges during the development stages of the agent via some sort of self-organizing "brain" structure similar to a self-organizing map (i.e. Kohonen map). Maybe a 2 dimensional representation of the 3 dimensional body. Probably not a single "map" but a number of maps which aggregate to "represent" the whole body. Of course the key feature of a Kohonen map is that the input topological information is maintained in the resulting map. So there would be some relationship between the size of the resulting lower dimensional map and the higher dimensional input. More input (i.e. bigger body) would result in a bigger map (bigger brain structure).

    Anyhow just a thought...

    Jeff

    Mark Changizi

    Hi Jeff,

    If I'm following, wouldn't such a map refer to the somato-motor areas? ...and perhaps also the visual areas (if one considers the retina)?  If so, it seems like one would expect somato-motor areas to disproportionately enlarge in bigger brains, but they don't. 

    Mark
    Not necessarily, there are theories which states that more or less all higher functions of the brain can also be described by self-organizing-maps. It is just that they map more abstract features (the output from somatosensoric areas or vision for instance) to even more abstract ones, thus making it very difficult to build a convincing case for such a theory (or even figure out how such maps would look).

    Some of these proposed maps will eventually map to physical output, actions (anything from very minor responses to advanced coordinated movement).

    Anyway, I'm not saying that this is the case, only that such a model is not limited to sensor-areas.

    Mark Changizi

    I see. Perhaps all brain maps ultimately map to the outside world; it is just that they become more and more abstruse mappings.  I like it.  And no good having internal maps map to abstract space, per se, unless that abstract space, in turn, maps to the real world or behavior in some way.   ...one might argue.
    Hi Mark,

    So yes it certainly seems logical that what I described before would "exist" in the sensor-areas. I would also assume a disproportionate size in those areas of larger brains if we assume a modularized brain. (At this point let me interject that my knowledge of a mammal brain is actually quite limited, so please excuse me ignorance. I come at cogsci from a computer science background). Maybe modularized is the wrong way to say it, but I am meaning regions that are significantly independent. However, I would assume instead that most of a brain would be highly coupled. My thinking being that evolution is a sloppy programmer, it does what works and is easiest at the time. From a programming perspective such a philosophy results in spaghetti code. Everything connected to everything else... Not the best analogy, but I am certainly no brain scientist so please feel free to let me know where it is flawed... :)

    That being said what I would expect (and what I think both you and Paul are eluding to in the two most recent posts) i that the rest of a brain would increase in size relative to an increase in size in the sensor/motor areas. Is that plausible? If a child suffers some sort of brain size reduction (maybe some sort of head injury) do/can they still develop normally?

    Jeff

    My two bobs worth. It's Sunday night so don't expect much.

    John, crazy Aussie.

    Larger animals engage in more complex behaviors and typically rely on a greater range of sensory faculties. While larger animals may rely predominantly on one sense complex behaviors typically require a range of sensory inputs. Put simply, a larger animal is contending with many more environmental contingencies which demand more complex behaviors. The cerebral complexity arises because the animal must not only contend with these challenges but must also integrate all these sensory inputs. What we hear must in some way be correlated with what we see. There are enormous survival advantages in this cross modal cueing.

    Perhaps paradoxically there is considerable evidence that some forms of frontal lobe damage will increase iq. Even more strangely, while such individuals can demonstrate higher intelligence they are absolutely hopeless in managing their daily lives. There is evidence to suggest that iq may relate to operations in the parietal cortices. IQ is not the whole game in intelligence. In the world at large we are often confronted with ambiguity. No algorithm, no computation, can solve these problems. If it was purely computational Turing Halting Problem would take on a whole new meaning.

    In anthropology it is surmised the driver of encephalisation was not the need to solve problems but the need to understand the most complex things in the known universe: human behavior. Long ago someone counted all the theories on personality. Something over 300. Go find me another area of human endeavour where we have generated so many often contradictory theories that are mostly hokey trash. We still don't understand.

    Lesion studies strongly suggest that those massive frontal lobes are absolutely fundamental to our social behavior. Whereas we typically think of intelligence as being about academia, we tend to forget that a single human being is a helpless creature, it is only through our co-operative efforts that we can get things. So perhaps these enormous frontal lobes evolved to deal with the overwhelming ambiguities that arise in dealing with other people.

    Mark Changizi

    Hi John H.,

    Great ideas.

    "Larger animals engage in more complex behaviors."
    Not sure there's any evidence for this, at least within mammals, say.  People's typical intuitions are that, no matter where -- left or right -- on that brain versus body plot, there's a wide vertical range of stupid to smart. ...which is why encephalization quotient does better.  And my own data suggest this as well.

    I agree that the most intelligent stuff we do tends to be the stuff we have no appreciation for at all.  And we have very little understanding of our brains, indeed.  And EQ does correlate with social group size.

    Mark
    Thanks Mark,

    No time at present but I'll try to have a closer look at your ideas and then see if I can come up with something more substantial. What I was wrote was predicated on material I read years ago. Concerning cerebral organisation there are some questions that have long puzzled me and if I can put together some half coherent words addressing these issues I will present the same here. Eg. One thing that has long puzzled me is that geometric nature of cerebral regions and the implications this has for what brains do.

    Good blog,

    John.

    Gerhard Adam
    Mark

    What differences (if any) do we see between the highest and lowest intelligence humans themselves?  Is there anything appreciable in the size/structure/connections, etc. that would provide a hint just within humans or isn't the separation significant enough to make a measureable difference?

    Gerhard
    Mark Changizi

    You mean, what anatomical differences does one find between my brain and my wife's, for example?  There are literatures that look more into that fine-scale level for differences, but I don't follow it. 

    -Mark
    Gerhard Adam
    Well, I don't know if you're trying to be funny or I didn't make myself clear.  I was suggesting comparing the brain of a genius and the brain of a "slow" person, and perhaps someone with savant syndrome.

    Don't know if that has anything to do with your wife and you, but I wouldn't touch that comment with a 10 foot pole.

    Mark Changizi

    :)

    Seriously, though, people have been very interested in that.  E.g., people have studied Einstein's brain over and over again, finding supposed differences.  But I seriously don't follow that literature much, and don't know whether they're onto anything.
    Gerhard Adam
    The reason I was asking is in thinking about someone like Kim Peek, with a reported IQ of about 73 and yet can recall the content of about 12,000 books.

    Clearly he lacks a creative element that prevents him from advancing that knowledge, but for someone with fairly straightforward computer-like abilities he's a pretty good example.  His ability to read two pages simultaneously (right page-right eye; left page-left eye), suggests that his brain is engaged largely in data transfer operations instead of dealing with comprehension while reading.  Since he has total recall, his eyes can behave like scanners whereas the rest of us tend to combine comprehension with the act of reading.

    It would seem that his abilities are several orders of magnitude different from the average person and yet the implication is that there is no appreciable difference in his brain structure versus anyone else's.

    Mark Changizi

    My own interpretation of such people, and also autistic savants, is that they are windows into just how amazingly complicated our own brain computations are.  When our brains do what they're supposed to, we don't notice its power. But when that power gets deviated in a mistaken direction, like the savant computing the first 10,000 digits of pi, we get to see just how super we all are. I say "we all are" because such savants can't have specialized new powers. That's not what happens with disease or developmental mistakes. Instead, they have your and my power, but being "run" on something it isn't supposed to. In fact, our own power is probably much greater than what we see in the window of these savants, because their brains aren't designed for counting the digits of pi. Our brains are running on the content they're designed for. 

    None of this gets at anatomy / morphology, though...
    Gerhard Adam
    Actually I was getting at the point that the increased "intellect" is actually a brain that is set to recognize more details and process them for the environment.  Humans are somewhat unique in their ability to recognize even irrelevant details from their environment, so perhaps that suggests what is different about our brains.

    In other mammals, as they become larger, they tend to traverse a larger territory which may require greater recognition and navigation skills, especially when this is coupled with being longer-lived then perhaps the need to recall past food/water sources as well as dangerous locales takes up more brain storage.  This may also include increased requirements when the animals are social since additional rules of behavior and response may be needed.

    Perhaps the brain/body size ratios are a function of the animal's caloric requirements, so that the more food the animal needs to maintain it's body, the easier it is to reserve a certain amount for the brain
    Like studies have been done. An old Australian study compared the cerebral activation of gifted children against norms. The gifted children expressed much wider levels of cerebral activation in solving novel problems. The converse of this is that the smarter you are the less cerebral resources you devote to addressing problems with clear logical steps towards a solution. Generally this is true for all of us, as we become more skilled with a task we devote less cerebral resources to the task.

    The studies on Einstein's brain are controversial and as it is an isolated example I don't trust it. It was revealed that Einstein had greater numbers of glial cells and an "extension" over the parietal cortex on the left side(sorry, memory hazy on this). This is interesting because it does appear that mathematical and iq ability appears to stem predominantly from these regions. I add that I don't like modularity ideas. The model died a long time ago but obviouisly there is some form of modularity going on. I suspect that the final picture will be a type of modular function together with Lashley's "mass action" idea.

    Mark Changizi
    "In other mammals, as they become larger, they tend to traverse a larger territory which may require greater recognition and navigation skills, especially when this is coupled with being longer-lived"
    I like this. Similarities to the "bigger brains for more memories" idea earlier.

    Also, on caloric requirements, I had an idea like that. But I don't like it so much. My idea was that, let's suppose that brain mass scales linearly (exponent of 1) with body size, the non-vascular brain mass, that is.  I argued that the vasculature should scale more like the 3/4 of body mass, and that more metabolically costly organs should scale lower and lower from 1, toward 3/4.  See Figure 5 in http://www.changizi.com/diameter.pdf (and the discussion in the Conclusion). I don't like it because I must assume that the non-vascular portion of brain mass scales linearly with body mass, which only worsens the problems we've been discussing here.
    Is there an embryologist in the house?

    Larger animals have larger neural tubes(assumption), this structure serving as the basis for CNS development. It may simply be a matter of embryonic development that larger animals end up with larger brains because of larger neural tubes. It is a physical constraint, that is, selection pressures could not reduce the final CNS size because it is largely predicated on neural tube size. That is, we may be looking in the wrong direction, thinking that brain size must be related to intelligence. Natural selection is not the be all and end all of phenotypes.

    It is well known that human brains at least undergo a rather massive loss of neurons during development and at the onset of puberty. This may serve as a compensatory mechanism, adjusting brain volume and subsequent metabolic demand in anticipation of future CNS demands. Studies on enriched environments clearly indicate that the "use it or lose it" function holds well for muscles and brains.

    It is generally believed that Cro Magnon Man had considerably bigger brains than ours. I assume this is after body size adjustment. Cromagnon was a big dude, large body, larger neural tube???

    Mark Changizi

    Hi John H.,

    Final CNS could always just radically retract.  That kind of "kill off the unneeded organ" happens all the time. In birds their brains change in size *seasonally*. 

    As for Cro Magnon, and other hominids, I have heard they had bigger brains, but haven't looked into how their EQ compares.

    - Mark
    And finally I add this on strategic matters:

    Why are we assuming there is a single cause explanation for this phenomenon? Single causes analyses belong in the lab, in the real world it just aint that simple. I wish it was!

    Mark Changizi

    For a nice empirically simple regularity like the brain-body one, it is so clean that one expects a single explanation. For a multiple-cause explanation, it would seem likely that the relative "weights" of the two causes would vary in some way as a function of body size, and so there wouldn't be a nice power law exponent.

    More generally, my guess is that, although there are often multiple underlying principles shaping the design of organisms, the odds are low that two or more different selection pressures would be roughly equal in their importance. One will, for statistical reasons alone, tend to be bigger than the others. And theorists like me glom onto that one and run with it. We're screwed if there are two or more equally relevant contributors, because there's typically a currency translation problem (i.e., we know the optimal A, and the optimal B, but can't derive the optimal A&B). 

     
    Hi Mark - nice topic to post on - you should revisit it again in a few years - bet you/we all could get some more mileage out of it! I have a number of questions and ideas, which cannot easily be brought into a coherent whole, especially this late in the thread, given all that's been said but here's a couple thoughts...

    1) Two of the early commenters suggested larger brain size to deal with larger sensory inputs (more receptors etc) and you responded by saying sensory cortex is not disproportionally larger in bigger animals. Why the focus on disproportionality? As opposed to larger animals having proportionally larger somatosensory cortices to deal with the greater sensory input? Or would you also say that larger animals do not even have proportionally larger primary sensory cortices to deal with the greater number of skin receptors etc. (if so could you point me to references?)

    2) The discussion raised by others, above, about larger brains needed to store more memories makes sense to me. Without knowing the answer, I would guess that primary sensorimotor cortices would increase proportional to body size (as I reasoned above) and that disproportional increases in association areas would promote higher EQ and greater behavioral complexity. The association areas would be the areas that store the abstract representations and concepts, (maybe corresponding to the "maps" discussed above - e.g. hippocampus as a cognitive map) and maybe are proportionally bigger in primates, who show behavioral complexity but not in cows (whose behavior I really am not familiar with but can guess). Also, it seems to me that behavioral complexity might be better (or additionally) interpreted not as the ability to perform many behaviors, as in the ethogram data, but the ability to perform or not perform different behaviors depending on the circumstance - more of a flexibility thing than a sheer number thing. But then we'd have no data for your graphs, since I'd argue we don't really have useful behavioral complexity data for that many species (e.g. just in the last decade had it been shown that rodents have episodic-like memory, with what-when-where components). But that's ok - we get to revisit it in the future!

    -Jason

    Mark Changizi

    Hi Jason,

    On "disproportionately", I mean compared to the other regions. One would expect somato-motor regions to be larger and larger relative to non-somato-motor regions...if it were the case that the brain's body-driven enlargement is largely due to more musculature and skin. 

    And I completely agree on the importance of "the ability to perform or not perform different behaviors depending on the circumstance". And, in addition, contingent upon having the right memory to initiate the appropriate behavior.  That data will be hard to get. But thinking recently about ways of inferring it from the existing literature...

    - Mark

    Gerhard Adam
    Mark

    In an earlier post the following point was made:
    "In order to send signals all the way across it's large body, an animal needs a large brain to power those signals."
    This looks rather novel to me. But not yet clear how one would flesh out the argument.
    However, let me raise a couple of specific questions that get away from just the scaling and consider some of the functions.  In the case of larger animals and propagating signals over a greater distance, as well as controlling a larger physical anatomy it would seem that two factors would come into play; Signal bandwidth and signal reliability (error correction mechanisms).

    Presumably to control muscle and respond to three-dimensional orientation and movement issues, more data has to be processed from more locations.  Moving my arm involves far more muscular control and feedback than a mouse moving its front paw.  In addition, signals can be corrupted over distance,so I'm wondering if there is any type of error correction mechanism that would require additional data be set to the receiver.

    Within the brain itself, the question comes up regarding how information is looked up.  Is there an addressing scheme that might lend itself to explaining the nature of connections (and potentially why a 2 tier approach?).  In particular, I'm wondering how much would be broadcast requests for data, versus following a more hierarchical structure, versus single-thread/parallel retrieval and consolidation.

    Lots of idle thoughts, but I'm wondering if you have any thoughts or can point me to some papers for this. 
    Thanks
    That kind of "kill off the unneeded organ" happens all the time. In birds their brains change in size *seasonally*.

    Doesn't that question the very idea of a distinct and clear relationship between brain and body size?

    Before I speak about the brain, I'll speak about the eyes!
    If I am not mistaken, one of the sharpest eyes in nature is the eye of eagles. I believe their resolution exceeds any other species' vision.

    So, in theory, a whale could have eyes the size of eagle eyes, and still have better vision... Right?
    To me, it seems to me this is an analogous reasoning to your brain size problem.
    I think your theory is based on functionnality alone: something doesn't need to be bigger if it doesn't function better (whatever "better" might actually be).

    Maybe another perspective should be ensivaged. The eyes, the brain, are just body organs, like fingers, stomach, and so on.
    When body size increases, so do all the organs. Whether this is useful or not may not matter.
    For example a bigger stomach's function is self-obvious. Bigger eyes: not.

    I would think, organs roughly keep their proportions to one another, independently of functionnaliy.

    * A cow would not want to have sex with a cow that had a rat-sized head. Gross! Similarly a cow would not want to have sex with a cow that had a whale-sized head. Gross!

    Hi Mark and every one who joined in so far — thanks for a very stimulating exchange. I haven't gone through all comments yet but briefly checked whether some of the points I would raise have already been brought up and trashed, but here are two that I haven't seen mentioned so far:
    Quantification of behaviour is notoriously difficult, even within species, and applying coherent standards of quantification across the orders listed in your second figure is nearly impossible.
    Even ignoring the previous point, it is perhaps not surprising that the correlation becomes weak if you move away from the species level on the taxonomic hierarchy. How does the figure look like if, e.g., the single dot representing primates were expanded to the family, genus or species level?

    Mark Changizi

    Hi Daniel,

    On the first question, yes, indeed. But the old ethologists were very careful, and had loads of methodological principles helping guide their measurements.

    On the second question, the results look the same if I used the individual species data. The problem is that there are some orders with a lot more data than other orders, so I averaged the behavioral repertoire sizes within an order, and plotted it.  All the behavioral repertoires I compiled (not including ants, where I have another several dozen or more) are in the second section in this chapter...
    http://www.changizi.com/ChangiziBrain25000Chapter1.pdf

    Sincerely,

    Mark
    I now had a closer look at table 1.5 in http://www.changizi.com/ChangiziBrain25000Chapter1.pdf and think that my doubts on the use of ethograms across orders have not been dispersed. Unfortunately, the list of references is not included in that file, but those references that I tracked down (e.g. Lewis 1985 for the Caiman's 188 and Hutt & Hutt 1971 for a kid's 111) were not accessible to me, nor were the papers by Schleidt et al., 1984 and Drummond, 1985 that deal with the standardization of ethograms and that you mention in your 2003 JTB paper. My suspicion thus remains that the ethograms you base your argument on use a granularity that is not consistent across the wide taxonomic ranges that you target, thus blurring any relationships that may exist.

    Of course, this argument does not say anything about why the ethogram size may correlate with EQ, as you show in the third diagram above, and I do think that quantifying basic behavioural types in terms of muscle contraction scenarios has merit. Is it possible for you to make the datasets underlying your ethogram vs. brain size and EQ available for some interactive visualization, preferably at the highest taxonomic resolution (i.e. species level)? I will get back to that after catching up with further background reading. In the meantime, I invite feedback on and participation in a wiki article that I have started on brain size.

    I repeat that I really find this discussion fascinating, and it reminds me of the Polymath project which solved a considerably tricky problem in extreme combinatorics in about six weeks of a mainly blog-based discussion (using a TeX plugin, by the way). Unfortunately, applying this approach to non-mathematical fields is a bit more complicated, since the data cannot readily be derived or computed but require experimentation or deep digs in the literature.

    Gerhard Adam
    Yes, well the problem Mark has presented is that if a brain is bigger, then why doesn't it seem to do anything better for the animal?  After all, if we used the computer analogy we would expect a "bigger" computer to be capable of more processing, yet this simple relationship doesn't seem to hold for animals. 

    Since the brain is energy intensive, it begs the question as to why a larger organ should be required if it doesn't convey corresponding advantage.  The brain/body mass ratio is like saying that a computer will be more powerful based on the box it is housed in.  While true, it doesn't make any sense.
    Brains change sizes together with bodies (as is seen with creatures which get smaller on islands), and i think size does matter, but only to produce new properties of the brains, new subsystems which then become functional over time (there is no evolutional selection against neutral mutations). The relation between size and funcitonality is best seen in the jump of complexity to mamal brain. It's a consequence of centres of smell becoming larger and larger (proportionally) and interacting with other older brain structures, the new appropriates the old inside itself so now we have 2 kinds of vision, reptilian (the old centre) and mammal (the consciouss one), this also explains conscioussness as a functional property of the neo?cortex (old reptilian centre enables vision, but not consciouss vision, subject that have lost the ability of cortical and thus consciouss seeing but retained the ability to move around objects. This is a theory i combined from my knowledge of neurosicence which is pretty low, so please criticise me.
    also my english might be a bit rusty.

    Hi,

    Maybe it's genetic economy. Instead of attempting to decouple the development of the brain and other structures the embryo makes a sacrifice there to make room for other expressions. Nature may favour saving as much variability as possible for leg sizes and shapes rather than for brain sizes and shapes.

    Could it have to do with the brains of relatively sized creatures coping with cranial inertial traumas?

    Have you considered the Thermal properties of the brain? Could it be a cooling organ?

    Larger animals have larger hearts. Artery numero uno goes directly to the brain. Were a cow heart and a rat brain in the same body, how could an organism regulate an even and constant blood flow to the brain under various blood pressure and pulse rate scenarios? Would a larger brain, with more fluid, act as a buffer against the peak high blood pressures during a hearts "pump" causing a stroke?

    SW analogy:
    simple SW can do a job like sending data.
    When it must do data sending reliably, it needs to monitor if connection is working and was the message received.
    When a failure is detected, reboot may often be the simplest way to resolve the problem. If reboot is not allowed, then more failsafes and more complex recovery mechanisms are needed. Maybe smaller creatures do allow for "reboot" == death more often?
    As the SW grows more complex, it gets harder to add new features. If rewrite is not allowed, then a new feature may require very complex changes despite the seemingly simple behavioral change.

    I have two thoughts on the issue:

    Dr Kiki mentioned one of them. At least in mammals incapable of performing C-sections, vaginal size will strongly limit brain size. At some point, there will be an equilibrium reached between the probability that birth will kill the mother and the value of that large brain. Evolutionarily, the cost of a brain is not just energetic, but also a cost to the mother to give birth to the child. I would hypothesize that even a single maternal death in delivery due to the head being so big is pretty strong evidence indicating that none of it is filler, as the early comments were prone to suggest. If the larger brain were not hugely beneficial, delivery complications would surely select it out. I'd be curious to see if separating out mammals from non-mammals, if the correlations are the same or if maybe the egg-layers occupy a different section of the plot from the mammals.

    In addition, if this is the case, and there is a strong selection for larger brains and also for healthy deliveries, will we see larger birth canals in the next few thousand years? Or will C-sections in humans remove that pressure? Or, perhaps, will we see people evolve to be born with smaller brains that are able to grow more neurons post-birth? I know, way too much to discuss in one post.

    My second thought, touched by John H, is that this is a much more complex organ than "the brain." Why are we locked into single cause to single effect, here? Brain size is almost certainly a combination of many effects based on many causes and drivers. What if we did one plot of "the cerebellum" and another for "the cortex" and maybe moved on to smaller substructures. Would we find that the cerebellum would experience greater selection pressure from growth in coordinated tree-hopping or hunting animals while the cortex would experience greater pressure to grow in social animals? And if so, would the addition of multiple terms end up producing the overall ratio you're seeing for the whole brain? If a particular species, homo sapiens, requires a huge cortex to maintain social relationships in order to secure food and sex, but no longer needs much coordination or balance to sit on the couce and cyber-date, the overall ratio of brain-size/body-size is much less relevant than seeing its component parts.

    It is interesting, though, that across all species in your graph, the correlation seems to hold regardless of birth-methods or brain-subsection-usage. Does that observation alone refute my hypotheses? And does it imply that, perhaps, cortical growth comes at the expense of cerebellar growth or vice-versa?

    My impulse is to step back and look at the structure of the body as a whole. What determines the size relationships between the various parts?

    What is the relationship in size between the distal, middle and proximal phalanges of my 2nd digit? How does the size of my first digit compare to the size of my other digits, my hand, my forearm, my upper arm? What determines this? These sorts of ratios are clearly uniform across our species, and respectively across all species. And the brain fits in there somewhere along with all the body systems.

    If there is an underlying mathematical structure present in nature, acting as some sort of scaffolding, it follows that this would in part determine the brain/body size relationship. In other words, biology is forced to accommodate a preeminent mathematical form. Through natural selection adjustments are made within ranges, as long as they aren't maladaptive. Nature has no intent.

    As far as brain function is concerned, the difference between the sensory experience of a human and an elephant seems to be one of quality and the the way in which body structure determines an organism's relationship to itself and its environment. It seems that a human has a much more involved relationship to its organism than an elephant does, with the human organism providing more opportunities for development towards what we would consider a better use of a brain...

    Its not the size that matters, but the connections and ability to make new connections in the brain. Also, the various parts of the brain vary in shape and size. Humans for example have a bigger frontal lobe that most animals, which mean we do more thinking and processing that other animals.

    Let's posit that evolution is an optimization process. For things that move from one generation to the next, e.g., things with brains, there exists a plethora of ever-changing external factors (evolutionary pressures) that are the criteria on which this optimization is based. The process can be seen as a relentless march toward an optimal design for the given the criteria.

    Given this assumption, the “brain facts” of:

    - Brain size and body size being tightly correlated and
    - Brain size and intelligence being loosely correlated

    must be direct consequences of an optimization process. Casting these “brain facts” as outcomes makes determining why they exist an exercise of studying the optimization process that led to their existence.

    The nature of optimization is the production of an outcome that is overall advantageous in some way, given the optimization criteria. Advantageous could mean a minimization of a non-trivial function that involves things like efficiencies, e.g., energy utilization, processing speeds, chemical actions, breeding, etc. Each of these factors carry different weights of importance in the optimization process and all are constrained to limits such that genes always find their way into the next generation.

    Find the factors that tend to be tweaked by optimization across generations and find the range of values for each factor that yield a viable optimization result. Think of the factors whose values are varied by optimization as a set of knobs that can be adjusted from one generation to the next, each with its own range of values. A given optimization results from one set of values for each of the multi-dimensional factors, given a set of environmental influences, each with their own range of values.

    Drop the presupposition that the brain is a computer (just as the supposition that the brain is a set of cogs has been dropped). Make no assumptions about what it is or isn’t. Focus on finding a set of factors that “matter” and a pertinent range of values for each factor. Couple that with evolutionary pressures that “matter” and a range of values for each pressure. Then, you have your answer. For example, you might be able to show that given certain “values” for chemical & thermal environment, availability of food & water, breeding competition, etc., etc., no other such “brain facts” can exist.

    Models can be established and tested in software using a range of algorithms, e.g., genetic algorithms, neural networks, simulated annealing, etc. Adjust the “knobs” on the complex array of factors and observe, over the generations, which result in brains that match the “brain facts” that we know to exist.

    Steve Floyd

    I suggest that the size of the brain of larger animals is simply due to the size of the cavity in which the brain must reside. Why are house cats proportioned so similarly to tigers? Or lizards to dinosaurs? Because proportional scaling is simple, elegant and obvious. Why is the penis of an elephant so large compared to that of a mouse? Are an elephant's sperm cells proportionately larger, requiring a larger delivery system? Is not the entire purpose of either reproductive system to provide the opportunity for a single sperm cell to fertilize a single egg cell? The brain is just another part of the system, and if the rest of the system can be scaled in a (more or less) proportional way, then why should that not apply to the skull, its cranial cavity, and thus brain, regardless of the number of synapses or intelligence?

    Mark Changizi

    But, if so, what are these larger mammals doing with such bigger brains? Why aren't they ten or a hundred times smarter?
    Gerhard Adam
    How would you know that they weren't?  We can say that a difference is apparent by looking at human achievements, but I would argue that such achievements are actually human anomalies, because there are still humans alive that would never operate towards those objectives, and yet are arguably as intelligent as any other human (i.e. Australian Aborigines as an example). 

    So it would hard to believe that humans only became intelligent in the last several thousand years, and yet that's what we would have to believe if the previous hundreds of thousands of years didn't count simply because they didn't build cities.
    Mark Changizi
    I agree (I think) that we shouldn't use many of our human achievements as yardsticks for mammals.
    Gerhard Adam
    Mark

    Actually my point is that we can't necessarily use human achievements as yardsticks against other humans.
    Mark Changizi
    I agree.  ...because culture harnesses us, and turns us into something different! ( Some hints about what I'm talking about are here: http://changizi.wordpress.com/category/news-on-my-next-book-harnessed/ )
    Gerhard Adam
    Sounds like it will be an interesting book.  I've often equated human culture (and it's affect on us) in a similar vein (although not identical) to the profound changes that must've occurred in eusocial insects, like ants.  While there are obviously significant differences, I think some of the same questions occur.  Just as language shaped humans and culture, wouldn't the ants use of pheremones follow a similar path?  It wouldn't make sense for an individual ant to have such a trait, but together it binds the colony in terms of recognition and social interaction, just as language does for humans.

    I suspect similar arguments can be made for other such strong social groups, so while there may be significant biological differences, at the "cultural" level, maybe not so much difference.
    Mark Changizi

    Certainly there are social similarities, one (of many) big difference relevant for "Harnessed" is that I'm arguing that language and music are results of cultural evolution, not natural selection. (Language and music culturally evolved to fit the brain by mimicking nature.)  -Mark
    Gerhard Adam
    Doesn't that become sort of a chicken/egg problem?  I've always viewed language as giving rise to culture (and the reverse) because language became necessary to articulate beliefs and values, which would be the basis of those sharing similar views to be considered a cultural entity. 

    Since beliefs would have consequences in terms of natural selection, such groups would congregate together and increase their use of language to bind their culture together.  As a result, language would become important in mate selection and practices since it was a representation of the beliefs that allowed people to successfully survive.

    In that respect I see culture and language as promoting each other until we reach the state of cultural selection where fitness is directly related to one's ability to participate in that culture or be expelled from it.  I don't think it's any coincidence that most tribal societies practice a form of banishment for those individuals that just don't "get it".
    Mark Changizi

    On language and culture, there is a variety of evidence over the last decade of cultural transmission in a variety of primates, and other species. ...where there is no language. Now, it still is a far cry from the dynamic culture we possess. And it may well be that there is a positive feedback, so that once language was invented, it accelerated cultural evolution.

    But I am suggesting that that all is fairly recent, and didn't affect us via natural selection. Speech gets into our our brains via shaping itself to sound like the solid-object events that are at the core of the competencies of our ancient non-language auditory systems. We find a similar story for the origins of writing, where we know we haven't had time to evolve reading mechanisms. In each case, so I am arguing, the cultural artifact "works" well on our brains only because it has shaped itself like nature. To the extent that I have been able to show that these cultural artifacts are shaped like nature, then it means there is no reason to suppose we have specialized speech comprehension or reading mechanisms.
    Gerhard Adam
    I think what you're saying makes a great deal of sense.  In particular, my own view has become that cultural evolution may occur in only a few generations (and perhaps significant modifications can even occur in as few as two). 

    Sounds like it will be a good book to read, so when is it going to hit the streets?
    Mark Changizi

    The editing process at the publishers takes some time, so it won't appear until 2011. Thanks for asking. -Mark
    rychardemanne
    Mark, so how does your theory account for illiteracy? I find illiteracy baffling, in that reading and speaking seem so related for me. For example, have totally failed to learn Thai as have no memory for just listening to language, have to see it written down and then can match symbols to sounds and then to meanings. BTW am bilingual and can cope with another 2 languages on top of that but they are all European languages and hence links are easier to create. However, my two fluent languages operate rather differently in that I think in each language; if I forget a word I will scan the same language and not try to look for synonyms in the other language, although will often mix the two languages togethre in the same sentence if talking to family. If that makes sense.
    crazymodem
    Hi Mark,
    I really enjoy your blogs and articles. Your new book just appeared in my mailbox today as well. Thanks for provoking my thoughts. Your question about brain size is excellent and I made a stab at trying to address it in my own blog in the Psychology section. Basically, I think brains develop the way they do because they are necessary. I also do not think that very much brain or neuronal tissue is wasted. As you correctly point out, neuronal tissue is "expensive." I do not think nature wastes this tissue much at all. I think one of the human-centric fallacies that we might fall prey to is in the manner in which we define (or try to define) intelligence.

    Thanks again for all your wonderful blogging!
    Mark Changizi
    Thanks so much for the kind words! And here, everyone, is James' piece he refers to: http://www.scientificblogging.com/psychologically_speaking/blog/my_my_wh...

    -Mark
    Cows can "afford" a larger brain than rats can, and although "large cow brain < small rat brain", surely "large cow brain > small cow brain". The fact that a large cow brain is wildly inefficient compared to a more optimized smaller brain is irrelevant to natural selection, a process that "search[es] the immediate neighborhood of its present point in the solution space, over and over and over."[1] It's not as if cow evolution is an intelligent being that can go take a peek at rat evolution and copy its processes.

    Still, why don't we see such apparent resource-wasting in other organs? My guess is that the brain is special, in that

    1) As with other organs, it seems plausible that the easiest/fastest "immediate neighbor" adaptation to selective pressure on a large animal to acquire more intelligence is simply to grow a larger brain.

    2) But in contrast with other organs, if a larger brain is very expensive (hard for the rat to fit into tight places, scampers slower, requires much more food), there are other ways to dramatically improve brain performance* - albeit ones that natural selection may be slower to hit upon. Why slower? Presumably because they are more complex, less suited to an "immediate neighbor" search. (I assume the evolution process is even slower in large animals with longer life cycles.) Finally, the pressure on the cow's brain to continue optimizing would also be less than that on a cow-quality rat-sized brain (a truly inferior piece of wetware!).

    It would be as if there are two roads to more intelligence - the fast, expensive, low-quality road and the slow, cheap, high-quality road.

    *This seems to be the linchpin to the recursively self-optimizing "AI go FOOM" argument of I.J. Good and Eliezer Yudkowsky (see link below for Yudkowsky's exposition).

    [1] http://lesswrong.com/lw/we/recursive_selfimprovement/

    Mark didn't make it clear why brain tissue is so 'expensive'. I think he means that brain tissue uses a lot of energy per mass unit. Bone tissue is very cheap, it uses no energy at all (while functioning). The cow species might do an "immediate neighbour search" for evolutionary improvement, and stumble immediately on an easy solution: make a little less brain, and a little more skull, nicely keeping overall body architecture the same. Well, it'll need some more muscle to sway the heavier skull, but it can achieve that by training, no evolution needed, and presto! you got a great evolutionary advantage, especially in the environment of a cow (or bull): better defence against predators and better ram to push sexual competitors aside.

    So the question remains: why make so much expensive neural tissue, instead of cheap bone?

    It may have something to do with Darwin's rules for selection - future generations are favoured by stronger, more nimble, smarter, etc characteristics (i.e. anything which gives advantage)

    Let us theorise there are two types of genetic modification events F1 and F2 - say F1 events cause everything to scale larger uniformly (i.e. bigger limbs, bigger heart, bigger brain) , and F2 causes only specific parts of the body to improve (eg becoming more nimble, or becoming smarter by improving the wiring of the brain).

    Now, we have F1 potentially expanding the size of the brain without any increase in its processing power. I.e. the Darwin selection benefit is to run faster, yet we get a by-product of everything else growing in size, but not necessarily contributing equally to a benefit.

    If there are large enough numbers of F1 events compared to F2 events, then we could theoretically see the significant emergence of large brains with limited processing power.. alongside the emergence of other lines which have smarter brains.

    Mark Changizi
    I suppose the bigger brains in bigger bodies could just be filled with tremendous inefficiencies (and they must be tremendous, because body size induces brain size to increase by a couple orders of magnitude, which one would have to hypothesize in this context is thus a couple orders of magnitude bigger than necessary), but that's not what we generally find in evolution, nor what one finds for neuroanatomy, which tends to be highly optimized to minimize the amount of wire needed.  -Mark
    Mark,

    Maybe the reason we can't fully understand why the brain is the size it is in different animals is because we still don't know everything about how the brain functions or what it's completely there for. Or, and this one is actually a long shot, maybe we're not meant to understand it, but rather play around and experiment with different things dealing with it.

    Mark Changizi
    We certainly don't know everything!  (And as for not being "meant" to understand it, people have played with Godel's incompleteness theorem-like arguments to suggest we'll never understand ourselves.) Thanks for the comment, -Mark
    I think it is a matter of balance. Like a big fat guy can not use tiny keyboards because his big fat fingers would strike two or three keys at once, so he gets himself a big keyboard., so the big cow gets himself a big brain.

    first of all , englisch isnt my motherlanguage so my writhing can be a bit strange sometimes

    My theorie is one that can only be aplied on some animals, namely the large ones that are also prey.
    the hunted animals have a number of abilities to be on guard for attacking animals, one of them is to be able to look around. It is often the cause for large animals that they are easy prey and so they have to be awake most of the time.
    However , the body needs sleep , both for the mind and for the body.This is where the big brain is needed.
    The bigger the brain gets , the less sleep is needed. my gues is that the increased brain alows less sleep because when one part of the brain is in need of sleep , it "shuts down" for a moment and let another part take over. the more spare parts of the brain there are , the longer the animal can stay awake.
    there must also be a upper limit or else animals like the elephant would need no sleep at all , most likely stress related and some rest for the body to maintain its strenght.

    Mark Changizi
    That is a fantastic idea!  Not sure I believe it yet, but it is a new idea, as far as I know.

    It is well known that total daily sleep time scales as roughly the -0.2 power or so of body mass, meaning larger animals sleep less per day. (Exactly why *this* is the case is something I've spent months trying to explain, to no avail.  I figure it is a physico-mathematical consequence in some sense of more general brain scaling, driven by, e.g., the fact that larger brains have larger neurons with thicker "wires".)

    And, one might imagine that, indeed, larger prey animals are essentially really big bags of meat, and are disproportionately tempting to predators.

    So, the idea is that larger prey animals would be selected to have brains that can accommodate staying awake more of their day, for vigilance.

    Even on its own terms, it is unclear what all that extra brain is actually *doing* for the animal, however.  But your idea is a new wrinkle on this that I need to mull over...

    glad that i could help

    Could diet have something to do with this, brains in general are full of cholesterol, larger animals need a larger diet this extra cholesterol would need to go somewhere large animals and large brain size could just be incidental of a large diet

    Mark Changizi
    One can certainly see how a bigger animal *can* have a bigger brain. But given that they do, and it's all *doing* something, how come bigger animals aren't smarter? ...a LOT smarter?
    I was trying to say the brain could be a dumping ground for excess cholesterol that would be inevitable with a larger diet, as long as the increased energy that the brain uses is less disadvantages than having that extra cholesterol in the blood stream. I guess I should have been more clear on the point I was trying to make

    Mark Changizi

    One difficulty with that idea is, Why should a cholesterol dumping ground lead to a bigger brain, rather than just to fixed-sized brain that has a big ball of cholesterol for storage? Why scale up the number of neurons so much? And given that there are more neurons, what are they doing, computationally? (Unless I'm still not following...)

    One thing I haven't really seen mentioned is the effect that the external world has on the growth of the brain- human brains don't have to be as large as they are- look at institutionalised infants' brain sizes for example. Increased stimulation, i.e. enriched environments, leads to greater brain growth. Could larger brains be partially the result of increased sensory stimulation during optimal ('critical') growth periods? For example, I know human infants are effectively ex-utero fetuses for the first year of their post-womb life due to birthing constraints...

    Just a conjecture, as I don't know enough about the gestational and developmental periods of other mammals... But regardless, it would be interesting to discuss the way in which external factors affect brain size

    I also thought the point on the possible need to differentiate between mammals and birds was important- as there are fewer birthing constraints on bird brain size, I would think this could lead to very different evolutionary mechanisms behind brain size differences

    Additionally, much of this discussion has assumed that we need to be considering the brain-body ratio when considering intelligence, but I've come across a recent article that suggests that absolute brain size is a better predictor of behavioural repertoire than bodysize-adjusted figures. http://www.ncbi.nlm.nih.gov/pubmed/17510549 Any thoughts on that?

    Finally, just a note on the estimated neuron number in humans- I believe a recent study (the only one of its kind) found that the figure is closer to 86 billion, and that glia (non-neuronal matter) was about 1:1 with neuronal matter

    Jill

    Mark Changizi
    Definitely experience (from the external world) contributes to brain development, although I don't know how and whether it affects brain size. And if brain size does get enhanced from this, then it would be because that's what the animal's body/brain was selected to do. That is, I'm not sure if it would help explain what all the big brain is for.

    On birds, surely that might matter, but the brain-body plots for birds and mammals are pretty similar. ...that is, not just in the rate at which brain size increases with body size, but in the actual brain size for any given body size.

    The article you refer to applies to primates, where absolute brain size did a little better than relative brain size. Generally, across mammals, this isn't the case.

    Best -Mark
    Here's the answer: Because mammals don't evolve to optimum parameters. Each evolutionary step has to evolve from what's evolved in the past, and only those steps that result in a 'birth defect' that can survive are those evolutionary steps that persist. That means that evolutionary steps that result in less brain material in general do not work very well for mammals. A species does not evolve to optimum configurations, but rather they evolve inside an ecosystem that demands they evolve to survive -- they not evolve to optimize.

    Mark Changizi
    But that doesn't help explain why brain size should be increasing with body size. By your argument, evolutionary steps that result in more brain material also wouldn't in general work very well. Change is harder than non-change, so why don't larger mammals have a constant brain size?
    Given all the evolutionary steps it took to get to where mammals are today, less brain matter for larger mammals must not work very well in terms of survival. Change is not harder than non-change -- it is less likely in the short term -- but given the vast expanse of time all the likely and unlikely converge to being equally likely, so really on a evolutionary scale change is as likely as no change. A species evolves due to pressures or opportunities in an ecosystem to survive, but they do not evolve to optimize. Survival is the result of successful evolution. The best solution for mammals must be for the brain to grow in some proportion to body mass. After I thought about it a while, I'd like to suggest it has to do with a trade-off between the cost of growing brain mass, and the chemical equilibrium that must be maintained in a mammal's body mass -- a larger mammal must intake greater quantities of water and food, with each meal and (especially) water presenting a mammal with a fairly quick change in body chemistry that must be compensated for quickly. This mechanism for land-based mammals has had to transition from tiny rodent size mammals to 12 ton elephants -- brain mass in proportion to body mass might be a necessary component to make this mechanism work.

    Mark Changizi
    Interesting direction to think in...
    EQ is more related to the number /depth of grooves and surface area of the brain - to body weight ratio; than, it is to mass ("size") of the brain.

    Mark Changizi
    Right that EQ is about brain-body ratio. (Although, btw, convolutedness increases with brain mass, not just with EQ.) The question is why brain size should increase so fast with body size? And why only EQ seems to predict how "smart" the animal is, not brain size.
    Actually I think its clear that the bottom line is that meat is expensive. Computationally. All those internal organs have the ability to wreck each other by the results of all their selfish activity. Like individual societies they use up each others resources and poison the environment they are in. That environment is us. Each of us, true even for guppies and insects. My cells and yours don't really play well with the neighbors. They need constant high-level regulation. Like Enron.

    That is why brain size closely follows body mass, and EQ positively explodes as you exceed that curve. Especially for larger, long lived mammals, that neural-meat needs to be even more complex to keep the peace ever longer. Most importantly cells remain more or less the same size even as bodies grow. Therefore when the EQ of some organism (like us) ticks just a little higher than necessary, there is an especially large number of neurons freed up. If a nematode acquired 5% more neurons, that might be 5 extra neurons. If a large mammal does the same then that 5% could be an extra 5 billion neurons. And then comes the invention writing...

    If true, the implications of this for the brain/computer comparison are a little worrying. Such comparisons have lead people to expect that a new desktop computer might match the human brain by about 2040. Supercomputers maybe a decade sooner. Those are raw power estimates of course. And I think I've just explained why the raw power of the human brain in particular, as well as all others, is a poor predictor of behavioral complexity. I guess that means a "Skynet" could be working reality before the end of this decade. If I turn out to be right, I'll be the oddly smug SOB hiding in the monkey house at the zoo...See you there.

    My hypothesis:
    Larger mammals require their eyes to be further apart for better depth perception/stereo vision, hence they need a larger brain-case, and a larger brain to fill it.

    Mark Changizi
    Even if so (and I've argued in the literature that forward-facing eyes isn't actually for stereo vision, but that's not really relevant to your point), why couldn't the animal just have a more hammer-head like shape? Or just fill the head up with dumb meat, or bone, or fat. Instead, it's filled up with thinking brain. What's all that new brain thinking about, if it's not needed?
    Bonny Bonobo alias Brat
    ‘Instead, the greatest driver of brain size is not how smart the animal is, but how big the animal is. Brain size doesn’t much matter – instead, it is body size that matters. That is not what one would expect of a computer in the head.’
    Couldn’t this be simply to do with the fact that the large animal has a large spine which requires a large amount of clear cerebrospinal fluid (CSF) to keep the spine and the brain buoyant, protected, chemically stable and free from ischaemia? There is a sac inside the brain full of CSF which circulates flows a bit like ocean currents and tides. This picture from Wikipedia shows that the brain could also be working a bit like the pump on the top of a turkey baster keeping the CSF flowing.


    MRI showing pulsation of CSF from Wikipedia.
    See http://en.wikipedia.org/wiki/Cerebrospinal_fluid
    Make love not war
    Mark Changizi
    I can see how that might force larger CSF sizes, but why more brain? What's it all for?
    Bonny Bonobo alias Brat
    Well the brain includes the CSF within and around it doesn't it? More fluid then more brain.
    Make love not war
    Bonny Bonobo alias Brat
    If you were weighing a brain you would include the blood vessels and cerebrospinal fluid wouldn’t you?

    The larger an organism is, the more brain weight is required for basic survival tasks, such as breathing, thermoregulation, senses, motor skill, etc. The brain controls the other organ systems of the body, either by activating muscles or by causing secretion of chemicals such as hormones and neurotransmitters.This centralized control allows rapid and coordinated responses to changes in the environment. The brain is supplied with nutrients by the blood vessels and toxins are removed via the cerebrospinal fluid which is generated and serviced by the blood vessels. So surely the bigger the animal the bigger the brain required to keep this system functioning? How else could it work?
    Make love not war
    I don't think the CSF pump hypothesis holds up, otherwise, dinosaurs would have had huge brains.

    Bonny Bonobo alias Brat
    Surely that's what this blog is about, why do bigger animals have bigger brains? Are you saying that all bigger animals except for dinosaurs have bigger brains? Maybe that's another reason why they became extinct? Apparently ‘dinosaurs generally have a smaller encephalization quotient (EQ), partly due to lower thermoregulation and/or motor control demands compared to mammals’ See http://en.wikipedia.org/wiki/Brain-to-body_mass_ratio#cite_note-10

    Make love not war
    Mark Changizi

    Bigger dinosaur bodies had bigger brains, and thus have the same explanatory difficulty as mammals. (It's just that dinosaurs, overall, have lower brain size than mammals and birds.)

    On motor control, Helen, indeed, something along those lines probably is where the explanation is to be found. But it would seem that one would thus predict that bigger bodies should have brains with disproportionately large somatosensory and motor areas, and they don't.
    When you compare such dissimilar animals as dinosaurs and humans it is not so easy to see the differences in intelligence as relating to only a single factor, as so many factors differ between giant extinct reptilian dinosaurs and our hominid selves. Surely the relationship between size and intelligence could be more clearly compared in more similar species, as in comparing us to chimps, and other great apes. on down to marmosets and other small primates, and comparing dinosaurs to living relatives, such as crocodilians with relatively small brains. I am trying to find information comparing the intelligences of different species of felines, from Tigers and Lions, Leopards, Jaguars, Snow Leopards, Cheetahs, and Cougars, on down to Lynxes, Bobcats, and house cats. Do you have any information on comparative feline intelligences in your calculations and research?
    What about how convoluted the brain is as a measure of intelligence? Humans, Great Apes, and Cetaceans are often cited as being the most intelligent based on the high number of convolutions in their brains, which does not necessarily correlate directly with size. More convolutions would mean more connections between the neurons, but don't you have the number of connections between neurons as a constant in your formula?
    As far as why did evolution develop bigger brains? I think evolution invariably leads to bigger and bigger everything, until something comes along, (like a giant meteor and Ice Age did for the dinosaurs, and human hunters did for the Mammoths, Giant Sloths, and flightless Moa birds), and wipes out the biggest, and mother nature has to start over again with the small survivors, who were smart enough to hide from danger, and in turn evolve to become bigger and bigger. The brain just develops in proportion to the body, until or unless it has some reason or mutation which causes it to specialize, like unusually large eyes in cows, and nocturnal animals, the specialized areas of the brain in cetaceans and microchiroptera which allows for the processing of echolocation signals, or the need to process scents from the specialized Jacobson's organ in order for carnivores to identify the smell of prey and rotten meat. I think the bigger brain is like a bigger canvas, a small painting may be already painted in one corner, but it has lots of room to paint new material on. Evolutionarily, it would be an advantage to have that extra space in which to "paint" new adaptations as needed.

    Cosmas
    Hey Mark, nice try, but the brain is not a computer, nor did it develop as such. As for allometric scaling and metabolic rate, whether of brains or muscles or whole bodies, the exponents 2/3 and 3/4 are deliriously off the mark. I direct your attention to a discussion of this very thing in the paper "The terrestrial evolution of metabolism and life - by the numbers," in the journal Theoretical Biology and Medical Modeling. Nerves and the nervous system resulted from energetic pressures, not from a need for problem solving, with nervous tissue developing to distribute energy captured from digestion. This is true for coral (which has nerves) to all multi-cellular organisms that have motor ability (and a central nervous system). Encephalization was a prerequisite for increased mammalian size and life span, because it made possible greater metabolic rates (measured in watts and directly related to lifespan). Dinosaur size, in its extreme form, was not a result of increased brain size (unlike in mammals), but instead was the result of the organization of its cells such that it could survive by eating less. For this reason rodents, and similarly-sized birds (the residual dinosaurs) have life spans differing by an order of magnitude. Those same rodents live longer if given less food, something the birds' bodies will not tolerate.

    One must get away from the complexity issue when considering the brain, as its origins and evolution are related to life's essentials - water, energy, organic molecules, and how they bear upon metabolic rate.
    Hi Mark, I’ve been wondering the same thing for a long time so I’m glad it’s not just me who doesn’t find the answer obvious. A couple of thoughts though about larger animals having more sensory input. Firstly is this true or do bigger animals deal with bigger things and therefore need only a coarser sensory resolution? Does a whale’s skin have the touch sensor density of my dog, if I stroke a blue whales flank will it notice? Does an elephant’s eye have that many more ‘pixels’ than a horse and does its cochlea have a lot more hairs than mine? I am not a biologist so I genuinely do not know the answers to these questions but unless the sensors scale up proportionally the logic doesn’t seem to work.

    My second thought (as an ex programmer) is that if I had a system, say an improbably sophisticated robot, with tens of thousands of sensor I would not feed them all directly to my processor chip. I would probably take groups of sensors (say those on a mechanical ‘finger’) and take them to an “interrupt controller” type of chip. I’d do the same for all the other digits, limbs, internal ‘organs’ and so on. Those chips would feed to more chips further up the hierarchy. This structure eventually leads to just few top level inputs. If a sensor on a toe changes state its controller chip may decide to action the chip above it and so on till my processor is finally made aware that something has happened. Only then will it give some attention to finding the location, cause and severity of the event that caused the input and take an appropriate action (including ignoring it). My point being that this tree structure allows sensors to be added exponentially without needing a similar increase in processing power. Of course if all (or many) of the sensors all go off at once we could have a problem but this is usually solved by some low level prioritising. Have you noticed that if you stub your toe you temporarily forget how hungry you were?

    Hope you find the answer soon,

    Dave

    to be able to generate enough electrical current to move those fat muscles.

    Hi Mark. Not sure if you're still tracking this post three years later. I stumbled upon it searching for something else entirely.

    I would say that size "doesn't matter" (relatively speaking) because it's the morphological structure of the animal - as situated within its environment - that leads to the "use" of the brain (or the degree of expression of brain-capabilities).

    The body/brain removed from ecologico-spatio-temporal context looks merely like any other 'body'.

    As an evolving process situated within a specific habitat, the brain finds unique outlets for capacity.