Dogs, Snowflakes and the Constructal Law

Why Every Dog and Snowflake Is Not Unique

One of the biggest bromides in dog training is that every dog is unique. On one level it’s directed at those who lock into a method and refuse to adapt to the dog. Of course there’s merit in criticizing a closed mind, we all should be willing to learn. However it extends to the idea that a good trainer borrows a little from this trainer, and that trainer, adding various techniques to their “tool kit” so that they always have the right tool for the job. And again there’s merit to borrowing from others.

However what we really should be building is a model rather than a tool kit. A method that evolves from a coherent model isn’t limited in its capacity to accommodate changing circumstances, or borrow from others as an improvement of the method. In my view every new wrinkle in behavior should be seen as a variation on a theme, not as a random wild card. A coherent model should be able to explain how new energy gets into the system and the capacity of the animal mind to generate novel approaches to problems and be able to do so in a manner that’s consistent with an overarching theory.

On the other hand the every-dog-is-an-individual mantra resists the development of a model and subsequently produces many self-contradictions that all the tools in the tool kit aren’t going to be able to fix. Many dogs are overly fixated on their owners and yet trainers teach owners to train their dogs to sustain eye contact (through a technique I invented for competitive dog trainers). They see it as just another tool. However without the benefit of a model they don’t realize that they are feeding the dog’s addiction to its owner, which pushes the dog deeper into the state of fixation and subsequent overloads. A coherent model points out the error. Also, learning theorists say reinforcement theory is a comprehensive explanation for learning, but then simultaneously hold that dogs might randomly disobey a “cue.” Apparently there can be exigencies coming out of nowhere that can’t possibly be taken into account. Another example of an incongruity is the belief that intermittent rewards are more powerful than regular rewards, and yet dogs in drive never tire of predictable rewards. What gives? Some say dogs play for the fun of it, but then believe every aspect of canine social behavior is about dominance and submission.

But the main problem with the Every-Dog-Is-Unique theory is that it violates the fundamental tenets of nature, most especially, the Constructal Law. In this video, Adrian Bejan who discovered and articulated this new principle of thermodynamics (“Design In Nature”) explains the universal fundamental that determines the common structure to every snowflake.

Likewise due to the way the animal mind is configured as a flow system, as the individual develops a sense of a Self, it is simultaneously integrating its body/mind with the flow configuration within which it is immeshed. This means that it’s uniqueness is a function of its participation in the flow configuration. An animal does not develop a sense of a Self as an agency independent and in some way unique. Individual uniqueness is not a thing in and of itself, it can’t be isolated from the whole. It can’t be arrived at through a principle of random variability.

I use points on a page to illustrate this point.


In the above illustration we see a random scattering of points. Because they are randomly scattered they have no uniqueness to them. Every point is exactly the same as every other point. Whereas in the illustration below, because the points are configured as a circle, each one has a unique value, a longitude and latitude in terms of the field they collectively create.



The points have no value, no unique singularity, until they achieve a network of affiliations. This network or order, will always arise due to a current. The illustration below shows the incredible complexity that evolves when there is a fundamental denominator, i.e. the center of the circle through which the current passes. The center and the current is what every point has in common. The configuration is what confers individuality.



Uniqueness is a function of flow and flow radiates and persists according to the Constructal Law.



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Published January 9, 2014 by Kevin Behan
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21 responses to “Dogs, Snowflakes and the Constructal Law”

  1. Chris Fowler says:

    This is, for me, one of the most resonant posts. The inconsistencies in the dog training theories have always bugged me, confused me.
    The idea of an overarching principle is efficient, and easier for simple minds , like mine, to grasp.
    However, I have a question. NDT encourages the owner/handler to ‘be the moose’, be the point of attraction. But you just pointed out that a dog
    can overly fixate on the owner to the point of a debilitating addiction. That seems inconsistent to me. Could you sort that out for me?

  2. Kevin Behan says:

    The all important distinction revolves around flow. If an owner is fixated on getting their dog to perform stuff, to display personality, to attend to them, then this is static and will create overloads in the dog as it instinctively will need to get things moving since their relationship isn’t predicated on the E–.>UE–>RE nature of emotional reality. The dog will fixate on owner’s attention and then that which shifts their gaze, will be perceived as unsettling, threatening, a disturbance of the eye-to-eye connection between the dog and its owner, which has become its metric of survival.The dog then gets imprinted that the inevitable overloads is its definition of flow, and that is on the crudest level true since at least things are now moving. (In fact in the wild this proves adaptive.) Meanwhile such an owner believes that the purpose of sociability is companionship. But the evolutionary purpose of sociability is to improve flow, companionship being a wonderful but subsidiary effect of working together to improve the configuration. We can easily see the truth of this were we to substitute human into this, for example, raising a child to be a companion would not end well. So when owner and dog work together to overcome obstacles of resistance, which is what the core exercises are about, then they are aligned and in sync around a common current (E–>UE–>RE) that is moving according to the principle of emotional conductivity, i.e. resistance to flow of emotion is inevitable, but by improving the configuration together, stress becomes resolved. In this group dynamic the dog and owner become one emotional being, so you get the joy of companionship without the anxieties of dependency.

  3. Here’s what I got (translated?) from Bejan’s video. (I translated the video for a friend who doesn’t have access to YouTube videos.)

    I hope this is helpful to others as well.

    First, heat flows through the snowflake. Then, since flow systems configure themselves to provide easier access to the currents that flow through them, the snowflake begins to take whatever shape is necessary to provide that access. Here’s how that happens:

    When moisture at a certain temperature in the atmosphere meets a dust particle, it forms a bead, which is warmer than the surrounding air. Since heat flows in all directions, the cold water molecule at the center of the bead begins to flow outward in all directions: heat > flows outward from the center. This creates a six-sided (hexagonal) structure, peculiar to water molecules, creating a specific physical form having a center node with six needles reaching out in all directions. This is a structure that most easily moves heat from the center of the budding snowflake to the colder surrounding air. Then, as these needles move outward, new nodes are created at their tips, causing further embellishment of the nascent architectural form. But since each needle is still connected to the center, and since the structure is maintained through the laws of thermodynamics—i.e., heat flows > outward in all directions—the new nodes only branch out in three directions. One of the needles can’t very well branch backwards, and the other new needles can’t easily branch backwards either because the air in that section of the structure is no longer cold.

    Every variation from then on is a function of new needles continuing to branch out, away from the center, until they no longer find cold air.

  4. Chris Fowler says:

    “So when owner and dog work together to overcome obstacles of resistance, which is what the core exercises are about, then they are aligned and in sync around a common current (E–>UE–>RE) that is moving according to the principle of emotional conductivity, i.e. resistance to flow of emotion is inevitable, but by improving the configuration together, stress becomes resolved. In this group dynamic the dog and owner become one emotional being, so you get the joy of companionship without the anxieties of dependency.”

    What would be an example of such a scenario?

  5. Kevin Behan says:

    It’s basically a way of being, at least in the overall between dog and owner. In specific instances, it would be exhibited by a dog looking for a way to align and synchronize (corresponds respectively to laminar and turbulent exchanges of energy) in order to find the flow resolution for its strong force of attraction toward its owner. When we see dogs meet and greet and then synchronize their leg lifting and circling to investigate each other, then get connected and then go off on a common course and then overcomes some degree of resistance, maybe chase a deer together, that is E->UE->RE principle of emotional conductivity (RE if they bring the deer down that is).

  6. Chris Fowler says:

    It is easy to visualize facilitating flow with ones dog when you are both ‘working’, herding sheep, looking for bad guys, etc. But the average dog owner is not involved
    in these activities. I know you have described previously, riding along in the car, or just taking a walk through the woods as similar in nature, all beings aligned in the
    same direction moving forward. But my question is, when does the everyday activity of walking, throwing balls, asking for a sit or stay, cross the line into an unhealthy attraction?
    An example of my confusion, all of my dogs watch my every move, we all live together in a small house which sits on many fenced acres. I board a few dogs for other people. My dogs all run along with me, while I get all of the dogs moving thru the woods together several times daily. I would say all 4 of my own dogs are fixated on every move I make, they know what a certain pair of shoes vs a certain pair of boots means. They all jump up and come to attention when my laptop closes etc., etc. It doesn’t take long for the boarders to act the same way. I am the pied piper.
    I am wondering if I have created much stress for them all, as I have allowed them to weave their focus so close to my own. I do push/pull with all of them, they all
    respond differently. The most anxiety ridden dog I have seems to be the most inspired by push/pull!
    If flow is the overarching principle, what is the overarching key to achieving flow? Working together to overcome resistance, I know, but beyond the core exercises, what does that mean? What is the ‘way of being’ supposed to look like between the everyday dog and owner?

  7. Kevin Behan says:

    We need to remember that living in close quarters with a number of dogs, and not embarking from time to time on death-defying/life affirming missions, is not natural. Sociability evolved in such a norm. So there is all this energy and no where to go. So we have to be humble. We’re not going to be able to make a perfect flow system so that emotion that becomes unresolved is then perfectly resolved. We have to learn to take dogs for granted (this reduces the pressure), get our Will back (don’t worry about the dog’s happiness) and not project our needs onto them.

  8. “We have to learn to take dogs for granted (this reduces the pressure), get our Will back (don’t worry about the dog’s happiness) and not project our needs onto them.”

    I can definitely see how these three things make for a smoother-running relationship with one’s dog.

    I’d like to get a bit more input on the problem with “the eyes” exercise, though.

    I’ve found that in most cases it helps ground a dog’s energy quite dramatically. In fact I’ve always seen it as a foundational exercise for learning to stay. But I’ve also used it to instantly defuse aggressive situations.

    About eight years ago I was working with a big briard/chow mix who had a specific form of leash aggression. If he saw a dog his size or bigger on the street he’d go into stalking mode, shoulders lowered, staring at the dog. If he was allowed to get close enough he seemed fine, but he was actually waiting for any little movement from the dog to “permit” him to go in for the “kill.”

    After a couple of weeks of doing just the eyes exercise — where when he went into stalking mode I got him to look up at me instead — the aggression went away. (No matter how many times I tried to get his owner to do the pushing exercise, teach him to speak on command, or to play tug and fetch with him I got nowhere.)

    With another dog — a miniature schnauzer who was “leash aggressive” toward other dogs and some people, and would also try to bite skateboarders, joggers, and cyclists, and who also had a hair-trigger bitiness and barkiness around elevator doors –, the eyes exercise had a dramatic calming effect on him.

    Mind you I was also pushing with him, teaching him to speak on command, teaching him to play tug and fetch, teaching him the down-while-running, and a lot of other things as well. But the eyes exercise was enormously helpful in getting him to stop vibrating out of control.

    So I never saw it as creating a problem of fixating on me or the owners. I saw it as a first step to toward grounding the dog’s energy and creating true calmness.

  9. I have one other question. The snowflake example clearly relies on the laws of thermodynamics, but canine behavior and learning aren’t about the movement of heat through a system. So what is the corollary?


    Does emotion follow the laws of thermodynamics or is there another underlying principle of physics at work? Certainly emotions exert a specific kind of pressure on the dog’s psychology, but I’m not sure I see the connection between snowflakes — how their shapes are the result of heat transference — and canine behavior.

  10. Chris Fowler says:

    Wow, unless I can figure out some death defying activities, I guess I am going to have to reset my attitude.
    But, that is what I was looking for, a more simple idea of the overarching model that can be practiced daily.
    As always, thank you for your time, you have been more than gracious with my questions.

  11. Kevin Behan says:

    What I’m running into is the exact opposite. I’m seeing dogs that have been trained in the eyes exercise by Positive trainers, yet they let the dog sleep on the bed, attend to its owners’ every move about the house, throw the ball relentlessly and take lots of long walks, but of course the dog has become ballistically aggressive. Then after I get some push/bark/bite going on and the dog is loosening and ready to engage playfully with another dog, when their head-to-head reaches a certain level of intensity, the dog breaks away and rivets his gaze on his owner’s eyes and that’s the end of his attempt to engage sociably with the other dog. We have to try again later. What I’m striving for is for a dog to be able to “make-a-trait-on-demand” without the influence of the owner, and to shift from vision (predatory sense) to smell (social sense). At any rate that’s been my experience.

  12. Kevin Behan says:

    Thanks btw for the great summation of Bejan’s video. (Earlier you voiced some skepticism about the Constructal law and I would be interested for you to elaborate.) I believe that emotion is the embodiment of all these laws of nature, most especially the laws of motion (leads to electromagnetic-like emotional affects) and thermodynamics. Heat for example would correlate to friction between individuals that is captured as stress and then is transferred through the system so as to build a configuration along the way that is constantly importing objects-of-resistance into it as an improvement. The transference of stress also leads to a branching architecture which we otherwise recognize as personality, (based on the accumulation of Direct–Indirect–Active–Reactive matrix of values from the individual meeting with resistance and filtering this through its particular position within the configuration) but have to date misunderstood it by not seeing the phenomenon as a derivative of thermodynamics. In the current evolutionary way of looking at things, there is not yet a coherent explanation for the evolution of personality or even sexuality for that matter.

  13. Thanks for explaining your reasons for “abandoning” the eyes exercise. I can certainly see how the relational values that positive trainers strive for would backfire the way you’ve described. I find that it’s nearly impossible to deter most dog owners from engaging in the kind of relational values with their dogs that create behavioral problems. But for some reason most of the clients I get don’t have ballistically aggressive dogs. They’re usually more anxious than anything else.

    I haven’t read Bejan’s book, and I can certainly see the value in his illuminating how both natural and man made systems gravitate toward a branching form to facilitate flow. Whether it’s the flow of energy or the flow of information, I can clearly see the value in that. For instance, Japanese scientists did an experiment where they arranged oat flakes in the pattern of the cities around Tokyo, then gave slime molds access to the grain. The path the slime mold took almost exactly resembled the layout of the Japanese rail system connecting those cities. So I have no trouble seeing the connection between how “lower” life forms create access to flow and how city planners, etc., do. Flow is flow.

    And as I’m sure know I also have no trouble with the ideas that dogs exhibit feelings of emotional attraction and resistance or that they experience feelings of tension and release. These things seem quite palpable to me. I just have trouble seeing how emotional friction = heat. That seems too metaphorical.

  14. Kevin Behan says:

    If I understand Bejan’s theory correctly, we really have to flip the question around for whenever we see order, then there has to be an underlying current. Therefore it’s incumbent to any theorist to answer that question, what is the current? It’s not possible to have a theory if that question isn’t resolved since absolutely all manifestations of order, natural or man-made, follow the Constructal template. It seems to me that emotion is the only thing that qualifies as a current since it satisfies all the laws of physics, a) force of attraction, b) conservation of energy as in emotion/stress inverse relationship, laws of motion, embodied cognition, there’s a quantum dimension, it’s the most primal part of human nature and ingratiates us into the environment, and so on. So if a motorist is emotionally attracted to the airport to catch a flight to the tropics and he hits traffic, he experiences a very real pressure in his body as he watches his departure time grow closer while staring at a river of brake lights. Whatever that mix of physiological changes and neurochemical activity that are transpiring in his body would be heat, literally because its effects are measurable and people speak intuitively in such terms when describing what they’re experiencing. It’s funny, science wants to know what animals are experiencing and were animals able to talk, they would gladly listen. When linguists deconstruct the evolution of languages they listen carefully to how the people of the world speak. But when all of humanity reports on the energetic principles of emotion that doesn’t get entered into the scientific domain. Also when we see that the sequence of tension and release patterns of behavior end up with individuals constructing a branching architecture, we could apply the Constructal lens to make sense of what’s going on and get rid of the idea of competition for limited resources.

  15. Annie says:

    I love this discussion! I remember seeing both of the dogs that LCK was referring to, and observing that he was able to connect to them through a gaze. It has more to do with his calm expectation. I think that the intention of the gaze is read perfectly by a dog. If the owner is the type who needs to establish his/her authority, this instantly adds to the tension already being experienced by the dog. “Somebody” around our house makes Luke very intense and fixated, simply by the way he stares at Luke and speaks to him. It’s unnerving to observe the dynamic….Luke staring, frozen in posture. If I’m walking Luke and he becomes distracted by another dog, I have kibble in my pack that I always carry, to break his attention. Once Luke turns his head, I pass him the food and break into a little run, to release the moment. Also, I’ve found that if I drape his leash across his chest and provide a light restraint,doubling up the lead in my hand, it has a calming effect. Lastly, (but not related), is to pass on the title of a fantastic book, “The Alphabet Versus the Goddess” by Leonard Shlain…he theorizes that the acquisition of written language heightened the linear, hunter-masculine-competitive aspects of humans, actually increasing the size of the left hemisphere and changing our DNA…

  16. “I remember seeing both of the dogs that LCK was referring to, and observing that he was able to connect to them through a gaze. It has more to do with his calm expectation…”

    Yeah. Something like that. To me it was more like, “You need an outlet for your emotions? Good! Plug them into me!”

    With the schnauzer there was more to it, in that I got him to love playing tug and fetch, and just playing in general. With the big briard/chow mix, I think he felt safe with me and liked that I was “in charge.” And really all I was doing — at least in my mind — was giving him an alternative outlet for his feelings.

  17. Sundog Fitz says:

    I am about half way through Bejan and the “dots” are ever so slowly starting to connect to create some flow for me but I have to admit at this point there are still a bunch of random resistance points that I cannot quite draw into NDT. What has my attention now is the concept of scale and complexity as they relates to the dog mind and emotional drive.

    Regarding scale, if I am getting this right, Bejan discusses efficiency for moving mass (animals, humans, rivers, swimming, flying, running etc) and that the Constructal law predicts optimal horizontal and vertical resistance ratios. Regarding complexity, Bejan states that “The tendency in nature is not towards greater complexity but better flow access globally. This direction often gets lost because many natural flow systems become larger in time and their finite complexity increases”. His illustration shows that the bigger athletes are stronger and faster, flow better.

    In the snowflake world of dog breeds of various sizes and specializations I can see (sort of) how the moving of mass of the animal has evolved towards greater efficiency and I can vaguely see how each breed’s special function moves towards better flow; each breed has a specialty that provides a more direct culmination in successful hunting for them as individuals or even in their group.

    But where I am just not able to put these two concepts together is the idea that a smaller dog experiences, creates, has access to smaller emotional flow capacity than a larger dog.

  18. Kevin Behan says:

    Great point, but actually it turns out that this is generally the case. The smaller dogs are experiencing a faster frequency (lower thresholds), the bigger dogs a slower one (higher thresholds.) The Yorkie is a hair-trigger yipper, the Newfy sleeps all day. This makes constructal sense in that the smaller dogs evolved to go after small prey, the bigger dogs big prey, so they’re adapted to a particular subsystem within a larger flow system. Keep the Constructal questions coming.

  19. b... says:

    Thanks for clarifying the size issue.
    I resisted making this assumption based on Kevin’s writings that the size of the dog relative to its surroundings makes no difference in how the dog feels (I may be oversimplifying). But based on what is said here, it seems that a smaller dog operating at a higher frequency would indeed be more reactive to stimuli and thus be more easily stressed in a busy noisy urban environment.

    Physically the higher frequency idea seems concordant with higher metabolism/heart rate in smaller animals.

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Books about Natural Dog Training by Kevin Behan

In Your Dog Is Your Mirror, dog trainer Kevin Behan proposes a radical new model for understanding canine behavior: a dog’s behavior and emotion, indeed its very cognition, are driven by our emotion. The dog doesn’t respond to what the owner thinks, says, or does; it responds to what the owner feels. And in this way, dogs can actually put people back in touch with their own emotions. Behan demonstrates that dogs and humans are connected more profoundly than has ever been imagined — by heart — and that this approach to dog cognition can help us understand many of dogs’ most inscrutable behaviors. This groundbreaking, provocative book opens the door to a whole new understanding between species, and perhaps a whole new understanding of ourselves.
  Natural Dog Training is about how dogs see the world and what this means in regards to training. The first part of this book presents a new theory for the social behavior of canines, featuring the drive to hunt, not the pack instincts, as seminal to canine behavior. The second part reinterprets how dogs actually learn. The third section presents exercises and handling techniques to put this theory into practice with a puppy. The final section sets forth a training program with a special emphasis on coming when called.
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