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    Calculating Animal Intelligence
    By Dave Deamer | November 5th 2009 09:27 PM | 27 comments | Print | E-mail | Track Comments
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    My research focuses on a variety of topics related to membrane biophysics, including the origin of cell membranes and the use of transmembrane


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        In a column posted a few days ago (November 1) I mentioned that my friend John Evans, a Cambridge (England) mathematician, has developed a general formula for estimating biocomplexity. It is quite simple, using only two variables: the number of units in a system, and the number of connections (interactions) each unit has with other units in the system. Today, in fact, biologists publish ‘interactomes” with furry ball figures that illustrate the number of proteins in a given cell and the number of interactions each protein has with other proteins. The concept of complex interactomes has become embedded in systems biology. 

        John’s formula is simple: C (complexity) = logN * (1 + 2logZ) where N is the number of units and Z is the average number of interactions. (If you would like to see his logic, you can read the paper cited below.) In the paper, we tested the formula by calculating C for the nervous systems of animals ranging from nematodes (N = 302 neurons, Z ~ 10) through insects and frogs and finally a series of mammalian brains. 

        What I proposed is that it might be an interesting exercise to see how well the complexity calculation predicts our perception of animal intelligence, so I challenged readers to use their intuition to put a set of mammalian species into order from most to least intelligent. Ten readers immediately replied, which was sufficient for our purposes. (If you would like to see all ten lists, they are in the Comments at the end of the earlier column.)    I put together a consensus list simply by adding up the value of the placements, then putting the animals in order from lowest to highest totals. For instance, if all ten readers put humans first, the total would be 10, if chimps were number 2 in everyone’s lists, their total would be 20, and so on. Here is the consensus list and totals for each animal:

    1. Human 10

    2. Chimpanzee         24

    3. Dolphin 33

    4. Gorilla 34

    5. Elephant 51

    6. Horse 62

    7. Dog 69

    8. Cat 75

    9. Rat 92

    10. Opossum 100

    11. Mouse 107

        Now I will present several other rankings that are based on the variables we need to use in the calculation. This is followed by a ranked list calculated from the complexity formula itself, and finally a list which was normalized to take into account a third variable called encephalization quotient which I will explain later. We will compare that list to the consensus list to see how well the formula fits our expectations, and then pose a question for discussion. 

        One thing to make clear is that we will take Z to be a constant for all the mammalian species. It is estimated that each cortical neuron connects with around 1000 other neurons, so the second term in the formula is 1 + 2log1000) or 7. (In simpler organisms Z is much smaller. For instance, in nematodes Z ~ 10.)

        The first list is ranked according to brain weight, and of course the elephant comes out on top, with humans and dolphins tied for second. (This list includes a rhesus monkey which I forget to include in my earlier column):

    Brain weight (grams)

    Elephant 4200
    Dolphin 1350
    Human 1350
    Horse 510
    Gorilla 480
    Chimpanzee     380
    Rhesus 88
    Dog 64
    Cat 25
    Opossum     7.6
    Rat 2
    Mouse 0.3

    The next list ranks the animals according to the number of cortical neurons estimated to be present in the brain of each species. In this list, humans and elephants are in a virtual tie for first place, with ~11 billion cortical neurons, followed by chimps, dolphins and gorillas:

    Cortical neurons (millions)

    Human 11500

    Elephant 11000
    Chimpanzee     6200
    Dolphin 5800
    Gorilla 4300
    Horse 1200
    Rhesus 480
    Dog 610
    Cat 300
    Opossum         27
    Rat 15
    Mouse 4

    The next list shows the order given by John’s formula. Again, humans and elephants are close due to the fact that they have the same number of neurons:

    Ranking according to calculated complexity

    Human 70

    Elephant 70
    Chimp/dolphin     68 (tied)
    Gorilla 68
    Horse 64
    Monkey 61
    Cat 58
    Dog 57
    Opossum 52
    Rat 50
    Mouse 46

    It doesn’t seem reasonable that humans and elephants are so close in the rankings, and in fact in the consensus list elephants are ranked fifth, below gorillas. Are we missing something? Maybe we can do better by incorporating the encephalization quotient (EQ). When the amount of brain tissue in a series of animals is plotted against size, from mice to elephants, there is a roughly linear relationship.  However, the value for some animals lies significantly above the line, while others are well below the line. Humans come out on top of the EQ ranking, followed by dolphins, chimps and gorillas. Here is our list according to EQ:

    Ranked by EQ

    Human 7.6

    Dolphin 5.3
    Chimpanzee 2.4
    Monkey 2.1
    Gorilla 1.6
    Elephant 1.3
    Dog 1.2
    Cat 1.0
    Horse 0.9
    Mouse 0.5
    Rat 0.4
    Opossum 0.2 

    The way I think about EQ is that an animal like an elephant, with an EQ of 1.3, needs a greater absolute number of neurons to serve the much larger number of cells in their bodies, but these neurons are not necessarily given over to intelligence. Humans, with the highest EQ of all (7.6) have developed larger brains in relation to body size because our evolutionary pathway happened to select for whatever it is that we call intelligence, which apparently requires more brain tissue devoted to that function. 

    We can use relative EQ to correct for the effect of body size by normalizing against the human EQ. The complexity equation then becomes:

    C = log(N*EQa/EQh) * (1 + 2logZ), where EQa is the animal EQ and EQh is the human EQ, taken to be 7.6.

    Normalized complexity compared to the consensus list

    Human                70    Human

    Dolphin                 67    Chimpanzee

    Chimp                 65    Dolphin

    Elephant              64    Gorilla

    Gorilla                 63     Elephant

    Monkey/Horse    57 (tied)    Horse

    Cat                       53    Dog

    Dog                     52    Cat

    Opossum/rat        41 (tied)    Rat

    Mouse                 38    Opossum


    Well, that’s pretty amazing! The consensus list and the calculated list are very similar, with no animal farther away than a single rank inversion between the two lists. 

    What does it all mean? I have a couple of suggestions. The first is that a certain level of complexity is required for higher nervous functions, just as my Mac iBook is much more complex than the Apple IIe I purchased back in 1981. It is interesting that all five animals with complexity values of 63 and above are self-aware, at least according to the following test. If you glue a round red dot to the forehead of a chimpanzee (or a dolphin, as demonstrated by Lori Marino) and let the animal see itself in a mirror, it will react to the presence of the dot. All animals with complexity of 57 and below are unable to understand that the image in the mirror is in fact themselves, and they pay no attention to the dot. 

    The second point is that a chimpanzee, although self-aware, cannot come close to what we recognize as human intelligence. It seems that a complexity value of 70 or above is essential, that is, 11 billion neurons, each with 1000 connections to other neurons, and an EQ of 7.6.

    A caveat: I am not a neurobiologist, and am uncritically taking all of the parameters used in the calculation out of the literature.  If you read the literature, you can probably find more sophisticated theories of the relationship between neuroanatomy and self-awareness, intelligence and the conscious state. 

    Now, for those readers who enjoy Scientific Blogging, here is the question: Is there a minimal complexity required for the phenomena of self-awareness and consciousness? If so, how can we arrive at a quantitative estimate of that complexity?

    Reference: Deamer DW, Evans J. 2006. Numerical analysis of biocomplexity. In Life As We Know It. J Seckbach, ed. p 201 - 12. New York: Springer.


    Mark Changizi
    Thanks. But the more complex formula, with EQ incorporated, does not seem to do any better than just EQ alone. No?  Mark
    The mirror test was done in Elephants and it apperad they passed it, with all the usual caveats.

    Gerhard Adam
    Well, it seems that there are several factors that one needs to consider in evaluating animals against each other.  It seems clear that humans are unique in that they possess almost no physical capabilities for either hunting, or escape when compared to other animals.  Therefore, it would appear that the brain fulfilled that role and negated such external physical tools.  So, on one level we would expect human intellectual behavior to be radically different from other animals.

    On the other hand, as I've mentioned elsewhere, self-awareness is a fundamental property of life that exists at all levels, so the only real issue is at what point an animal achieves "conscious self-awareness".

    It would seem that consciousness becomes a requirement when decisions need to be made based on historical information or extrapolation into the future.  In other words, when confronted with a choice a simple decision process can occur, however when longer-term thinking is required then the consciousness provides a vehicle to be able to see oneself in the third-person in evaluating a decision. 

    However, I would also argue that 99% of intellectual activity doesn't require any real sense of consciousness beyond the fact that we are simply aware of it as background information. 

    Mundus vult decipi
    >> Q: Is there a minimal complexity required for the phenomena of self-awareness and consciousness? If so, how can we arrive at a quantitative estimate of that complexity?

    A: Consciousness and intelligence are different categories not necessarily related, depending on definition. For instance in the Quantum Theory of Consciousness of Penrose & Hameroff consciousness exists at the cellular level. And in David Bohm’s description of the soma-significance problem in Quantum Mechanics consciousness and meaning exist even in elementary particles, although supposedly not of self-aware type. The assumption that consciousness is a quality that “emerges” at a certain level of the biological scale may not be right after all. It may well be that Consciousness is a fundamental attribute in nature and the differences that we know are just a matter of organization levels and qualitative complexity.

    Dave Deamer
    Here are my responses to comments:
    To Mark, yes, EQ has been considered one of the main anatomical markers for intelligence in mammals. However, the Evans equation was originally applied to organisms all the way down to C. elegans, some of which don't have the kind of nervous system to which EQ can be applied.

    To Coturnix -- Thanks! I also ran across that reference last night, and was happy to add the elephant to the list in the edited version now posted.

    To Gerhard, I think it makes sense to distinguish between awareness and self-awareness. Granted that even an E. coli is "aware" and responds to sensory input, but to be self-aware is a much higher nervous function. Only certain primates, dolphins and elephants can see their image in a mirror and know that there is a red dot attached to their body that shouldn't be there.

    To Ulysses, I like to be as precise as possible in word usage, and extending "consciousness" to cells and elementary particles blurs the definition too much for my taste. 
    Gerhard Adam

    The distinction I make between self-awareness and conscious self-awareness is based on the fact that it is the latter that I think you're describing.  The reason for this particular distinction is that the E. coli example is more than simply "aware", but it must be minimally capable of recognizing that it belongs to a particular group.  This is a necessary condition to avoid eating your own kind and determining who eligible mates are in sexual animals.  When this is coupled with distinctive bacterial behavior where cannibalism is a specific exception and occurs under stress, I am concluding that these bacteria are aware of themselves and capable of recognizing others of their own kind.  This certainly isn't consciousness, but it is self-awareness.

    I think you're saying essentially the same thing, so this may well simply be about terminology.  The red dot example implies conscious self-awareness (i.e. being able to recognize yourself as a specific entity), rather than simple self-awareness.
    Mundus vult decipi
    Gerhard -- You propose that bacteria are self-aware, using the logic that they recognize themselves as members of a group, use sensory input and appropriate responses to find mates, avoid cannibalism etc. You reserve conscious self-awareness to define the mirror test. I guess I’m not so sure that this is a useful distinction. How, then, would you use the word aware? I would guess that most biologists would reserve this word for a fairly high level of nervous function, and certainly would not apply it to bacteria. I view bacteria as essentially little robots that have a programmed set of responses to specific environmental conditions.

    Speaking of robots, would you use the phrase self-awareness to describe the behavior of one of those little robots that has a programmed ability to search and find “food” in the form of an electrical outlet to recharge its batteries? I kinda doubt it, but I don’t think a motile bacterium is much more complicated than that.

    Gerhard Adam
    How, then, would you use the word aware?
    I'm not sure what you're asking here, but "awareness" as a general state is a forgone conclusion.  It would make no sense to suggest that any living thing is capable of interacting in the world and not be aware of it.
    I view bacteria as essentially little robots that have a programmed set of responses to specific environmental conditions.
    I think you have to be wary of sensory bias.  After all what would you call it when you visually recognize someone, or recognize a familiar smell?  It is every bit as unconscious and automatic as the bacteria.  You aren't conscious of a single element in the operation of those senses.  What separates us from the bacteria is that we have a conscious element that allows us to associate those sensations with a memory from which we can construct a virtual scenario of recollection.
    Speaking of robots, would you use the phrase self-awareness to describe the behavior of one of those little robots that has a programmed ability to search and find “food” in the form of an electrical outlet to recharge its batteries?
    Since they aren't alive they can't represent a valid comparison to biological organisms.  However, it would be reasonable to say that they have been programmed to behave according to the rules of self-awareness for their engineering.  Admittedly when you get into robotics, we're essentially talking about a device that is designed to emulate living organisms.  So it invariably creates a problem in terminology when describing the behavior of the organism itself and the emulated behavior of the device.  Is one more real than the other?
    Mundus vult decipi
    Steve Davis
    Gerhard, I think the fact that bacteria exchange information supports your position nicely.
    Dave Deamer

    Gerhard -- Perhaps the way to clarify word usage is to perform what I, as a chemist, would call a titration. The specific meaning of the word titration is the addition of increasing amounts of something to something else until there is an observable change in the properties of the system. For instance, crystals will not form until enough solute is titrated into a solution to become super saturated, and a basic solution becomes acidic as we titrate it with acid. (Agreed that the analogy is inexact, but I wanted to explain the specific meaning of the word titration so that my general use is understood.) In the thought experiment, I want to titrate complexity, something that is not easy to define, but like beauty, we know it when we see it. I will also make use of an organic chemical that inhibits the behavior we call awareness, called an anesthetic.

    So, let’s first titrate increasing amounts of complexity into a system of atoms and try to decide at what point I would begin to use the words “aware” and “self aware” to describe the behavior of the system. I would not use the word aware to describe the properties of atoms, or molecules like amino acids, or polymers of amino acids like proteins, and I doubt that you would either. Instead, we need to move up the scale of complexity to a bacterial cell, an organized structure of thousands of different functional polymers contained in a membranous compartment. We can agree that a bacterium is alive because it has the potential to use energy and nutrients to grow, reproduce and evolve. But what if we add a little chloroform to the solution bathing the cell? The bacterial cell is not dead, but it cannot move and is completely unresponsive to stimuli. It is anesthetized, perhaps we could even describe it as unaware. But if we remove the chloroform, the cell “wakes up” and we might now use the word aware to describe its behavior. That is, it responds in appropriate ways to environmental stimuli, swimming away from a noxious solute, and toward a nutrient source for example. And if it meets another bacterium of its own kind, it might even engage in a microbial version of sex, as Steve noted above.

    Now let’s titrate in more complexity, all the way up to a multicellular organism with a nervous system. Most would agree that mammals are aware (unless they are anesthetized!) but if we go in the other direction toward ever simpler organisms, common usage would draw the line between jelly fish and sponges. The latter lack an organized nervous system, and just by looking at a sponge you could not tell whether or not it was anesthetized. 

    Getting back to mammals, we agree that they exhibit the property we call awareness, and if they are anesthetized, they are unaware. What could be clearer? Now let’s titrate in just a bit more complexity, this time in the organization of the brain and its response to sensory stimuli. A few mammals -- elephants, dolphins, primates -- recognize their mirror images as “themselves” and respond to something unusual in their mirror image. I reserve the phrase self-aware for that specific behavior. 

    Finally we get to human consciousness. Although we don’t usually think of it this way, I think that this is also a titratable property of the nervous system, because we can again titrate in an anesthetic. As the anesthetic increasingly affects different nervous functions in the brain, one by one the functions shut down, and perhaps the last thing to go is what I would call awareness.

    By the way, my mathematician friend in Cambridge took an interest in this discussion. If you don’t want to read the original paper, here is his logic in a nutshell:

    “Basically what I did was to consider a function going from N separate systems to a single system with N components. Integrating this, and getting an average, generates the formula. The '2' in the formula is, to be precise, log 10 to the base e, or about 2.3. 

    "Concerning the final list, remember this is a log-scale, as with earthquakes. Thus between 70 and 67, the human is 1,000 times more complex than the next on the list, which seems reasonable enough given our ability to write such papers and handle integral calculus. But one assumes that, in emotional intelligence, the gap is not so wide.”

    Gerhard Adam
    Thanks for your breakdown of the word usage.  I agree with your statements and can see that we are really haggling over a bit of terminology more than concepts.

    Without beating a dead horse, my point in using self-awareness to describe even the bacteria is that the "awareness" being experienced had to include a sense of itself in order to make sense of its ability to interact with others of its kind.  Therefore I was considering that this wasn't simply a state of environmental awareness, but an actual primitive awareness of itself as distinct and belonging to a specific group.

    The conscious self-awareness was the state of where an animal is aware that it is aware.  In that case, it is capable of recognizing itself specifically as an entity which it can evaluate or consider in a more abstract sense.

    I'm not clear on how or why you made a jump to human consciousness as being distinct.  There's no question that human intellect and abstraction far outpaces the other animals, but why would you think that this represents any degrees of consciousness?  This becomes an even larger question when one considers how many things in our existence we aren't conscious of, so it becomes a bit easier to see how such a thing can occur (i.e. being self-aware without being consciously self-aware).

    Specifically I think we tend to overrate human consciousness since the vast majority of daily activities barely consider it except as a background assumption.  In other words, we recognize that things are happening to us or because of us, but it rarely involves a real act of concentration.  In truth, the majority of people cannot maintain a state of conscious awareness for very long. 

    Part of what drives my definition is that we have indications that even when the human is considered to be unconscious, the brain is still processing all the information to which it is exposed through the senses.  Admittedly there is nothing for it to act on if we are immobilized, but nevertheless it is aware of external events.  If we consider something like sleep as a state of unconsciousness, then we can also see how the brain can alert the conscious centers of the brain to wake up and pay attention, so in effect, we can see something like the boundary operations between consciousness and unconsciousness.

    In any case, I very much appreciate your comments and suspect that we aren't really saying much that is substantively different.

    BTW, I'm assuming that the mathematical paper you're referring to is the one you identified in the reference previously?
    Mundus vult decipi
    Actually they should be testing wolves and not dogs. Although a wolf is a dog, we considerably rate dog intellect by their ability to function as a dog, disregarding the fact they are wolves in actuality. And as a wolf, a dog is severely mentally retarded. Wolves have a huge intellectual advantage. A wolf can calculate algebraic systematics in how to hunt prey. The only dogs capable of this are huskies, because they are virtually just domesticated wolves.

    As for cats, it is impossible to rate their intelligence because they are enormously stubborn. But they will surprise you. You kind of have to give them the right opportunity, a sense of trust, and a show of compassion and attention for their needs. They behave very similar to a human. Humans are remarkably stubborn, lazy, and obnoxious. We only demonstrate our true potential of intellect during times where are given the right opportunity and demonstration of truth and attention.

    Without trust, a human can easily become irritable and if prolonged, violent.

    As for dolphins, it is hard to actually test their true potential, because they are aquatic and most sensory mechanisms aren't really useful given their lack of form (no arms, unlike the chimpanzee and gorilla) and the fact they live in the water.

    Chimpanzees aren't really that smart. The Bonobo possesses unremarkable intelligence, but that is mostly due to their comparable intellect with humans, since they are so closely related to us. They may in fact be homina, rather than just a homini when it comes to tribe and sub-tribe affiliation with human beings. As for a Chimpanzee, they demonstrate a lot of frustration and anxiety. It is very hard to get them to do much of anything without them going bananas. Bonobos on the other hand have demonstrated ability to settle disputes similar to a human, through peaceful resolutions. That is remarkable.

    Elephants are almost scary with how intelligent they can be or become.

    One important variable not included in the formula for complexity is a measure of heterogeneity. Although the heterogeneity of the units of the system is not stated, we might assume that the description of separate units defines each as unique. It is also possible that each unit is identical, and defined by its unique interactions within the system, but I will assume the former, that each unit is unique. In either case, we can measure complexity by the information required to describe two similar systems with equal degrees of precision. In this case, a system of 100 unique units, each of which interacts in exactly the same way with all 99 other units in the system is less complex than a system composed of 100 unique units in which each connection or interaction is unique.

    How about pigs?

    Fred Phillips
    Intriguing result, especially given the well-known difficulties in defining complexity (see e.g., Melanie Mitchell, Complexity.)

    I hope future elaborations will use the intensity of connections (not just the number of connections), for example, how frequently and efficiently nerve signals are transmitted along a link. Top see the importance of this, imagine a brain made from lego blocks. It would be complex - huge number of nodes and huger number of links - but not in a manner pertinent to this discussion, because no signals would be transmitted.

    Another elaboration would state the matter in terms of developmental stages - not just a blanket "intelligence." Here I'm thinking about my dogs. The dogs differ mentally from human two-year-olds in two ways and only two ways: They cannot speak, and they will never reach the mental stage of human 3-year-olds.

    I'd be interested to see the addition to the list of whales, cows and pigs.

    We were discussing the program "whale wars" and the enthusiasm people show for protecting whales and dolphins, in part, due to their level of intelligence.

    thank you,


    What about Lions, Tigers, Leopards, Jaguars, Cheetahs, and other species of wild cats? How does their intelligence compare to domestic cats using your formulas? Is their intelligence higher because their brains are bigger, or does the EQ control for that? It seems to me that Lions, with their social prides, and cooperative hunting, and the other big cats who hunt cooperatively with mothers and cubs for often the first two years of the cubs lives, should be more intelligent than other species who have not developed social systems as complex.
    What about the wild wolf pack? Are they smarter than domestic dogs, or being about the same size, considered the same intelligence? Or could some domestic breeds of dogs that have been selectively bred for intelligence be smarter than their wild counterparts?

    How would you apply the formula to a computer (serial architecture, how much serial is equivalent to parallel) and where would your computer land in the list after say adjusting for connection speed somehow? Are you arguing that even the fastest serial machine can never be self-aware?
    ive been looking through a huge number of lists that show the top ten smartest animals and why dont most of them include pigs. they are sooooo smart have you seen what they can do if you measured their intelligence youll find it amazing how high their score miight be might even be higher then some of the animals on the toop ten list above that you have its just a thought let me know what you think

    How close are nations and corporations to becoming living mega-organisms in their own right? I would love to see this kind of complexity formula applied to this question. I agree with Fred and Aaron above, that more factors should probably go into the formula. Aaron mentioned heterogeneity (I would say diversity or differentiation or specialization) and Fred suggested distinguishing and quantifying the kinds of connections between subunits, since connections are not all equally significant. I would agree.

    Very nice article, Dave. Thanks for that presentation.
    Citizen Philosopher / Science Tutor
    What does it mean?
    I think it means that if one starts out with a pre-determined result, one can always find a combination of adjustable parameters that will reproduce that result.

    Of course, this is just a blog post and it is unfair to referee it the way one would a scientific paper, but if it was a serious analysis and if one were intending to use that analysis to advance a serious scientific hypothesis, then one would have to compare the ranked list produced by the model against that generated by a "null model" and also determine the statistical probability of coming up with the former ranking by pure chance. To assign any interpretation, one would also have to use a measure of "intelligence" that is not trivially correlated with the descriptors used in the model. I suspect that most people's assessments of animal intelligence are derived at least in part from reports about brain mass and volume of brain tissue (most readers have probably not had an opportunity to scientifically assess the intelligence of gorillas and dolphins in the field).
    What is interests me about all of this is the fact that even after all the science in the world was done, it was still almost exactly the same as a group of highly intelligent organisms perceptions requiring no tests. Philosophy in action.

    this really helped me on my project. still i need some help.

    isn't that interesting that human is consistently ranked #1 in ALL categories? -:)
    just a reminder, in colonial european time, white europeans consistently ranked people of african descent as the lowest in IQ and white european the highest in IQ. until today, many "sociologists' of the "bell curve" fame still maintains white people are superior in IQ and blacks are lower in IQ.
    to me, all these are junk, rubbish.

    isn't that interesting that human is consistently ranked #1 in ALL categories? -:)
    When animals create and give these tests, you will have a point.
    This isn't science. This is massaging data to fit your own personal beliefs.

    I believe that we as humans are predisposed to think that our fellow primates are have relatively higher intelligence than other species. Partly due to the fact that their ability to mimic our bipedal locomotion and have a prehensile grip with which to fascilitate communication with us.

    Recent revelations of self awareness of dolphins and elephants lead me to believe once we are able to better communicate with those two particular species they will be realized to surpass all other primates in cognitive ability.

    Particularly with aquatic mammals, the lack of much research on other species or even good understanding of their life habits, they may as a group turn out to be the most evolved of all non-human species in intellect.

    We just dont know how to let them show us thier abilities as thier natural environment is so forbidding to us.