Constructal Theory: The Science
by Tim McGee, Helena, MT, USA on 01.11.07
Scientific thought is too often dominated by the reductionist point of view - I suppose it is the nature of the beast. In order to become established, modern scientists must spend a good portion of their lives studying some increasingly small sub-section of the natural world. Indeed, picking apart every little detail can lead to important, world changing, discoveries. But, increasingly we need to start putting the pieces back together. There have been tentative steps towards understanding these connections, and often the little steps have had tremendous impact. From Einstein's theories of general relativity and electromagnetism that enabled us to tap the energy of the atom, to Darwin's theory of evolution, the cornerstone of modern biology, we have reaped the rewards from putting pieces together. These scientists did not focus their studies on increasingly myopic topics, but instead expanded their ideas and fields in order to see the patterns in nature. Instead of being reductionists, they accepted a more holistic view while maintaining their scientific integrity, and may very well be called 'constructionists'. The theories they espoused challenged our world view, and changed our lives. Constructal Theory or CT (rather aptly named) is one theory of the same ilk.
We have looked at CT in contrast to biomimicry, and drawn connections with sustainability. But what of the science? Where are the facts? Like gravity, CT is a theory. And like gravity, we can observe that the theory appears to be correct. When we have enough observations that support a theory, we can begin to say with confidence that this is indeed a scientific fact (until there is enough conflicting evidence- then we search for a new theory).
For the past ten years scientists around the world have used their expertise to observe the predictions of CT, and found ever increasing mountains of supporting evidence that it is a law of nature. Books and journal articles are emerging that cover the CT of specific fields and topics. The website dedicated to sharing this mountain of information is constructal.org. The website contains links to major publications and discussions on the issue of CT. Please feel free to delve deep into the science, a good primer would be this article (PDF) that details much of the research done recently. But for our purposes today, the following are some of the exciting ways constructal theory is expanding throughout science.
1. Climate Systems and Empirical Models
One of the hallmarks of CT's power is looking to see where it can displace an 'empirical model'. An empirical model is based only on data and is used to describe, not predict a system. An empirical model consists of a mathematical function (or equation) that captures the trend of the data. One of the problems with an empirical model is that they are notoriously poor at predicting events that have never happened before. Often the whole model must be thrown out if one element in the system has dramatically changed. Constructal threory's power on the other hand is that it explains why a system looks the way it does. This allows anyone with that understanding to predict with better accuracy, and predict the results of unprecedented events.
To get around to the point here- our climate is notoriously hard to predict. We currently use very complex empirical models consisting of multiple inputs to help us create weather and climate predictions- and as anyone who depends on the weather can tell you- we are not very good at it.
A study that looked at how CT might apply to climate systems was completed by creating a constructal model with 4 inputs-the temperature of the sun, the solar constant, cloud cover and the Earth's greenhouse factor. Out of these simple inputs the CT climate model achieved a first in all of climate science- it predicted the latitudinal boundaries of the Earth's three circulation zones - the Hadley, Ferrel and Polar cells - which comprise the main global circulation on Earth.
But that's not all...the simple model went on to achieve a good approximate speed of atmospheric and oceanic flow and the average temperature on Earth. The ability of constructal theory to displace empirical models gives us a key to understanding the results when we make unprecedented changes- something we are doing a lot of these days.
2. Biological Locomotion and Allometric laws
Another area of interest is when CT can identify or align with allometric laws. Allometric laws reflect proportionality between two elements of a biological system. For example, Kleiber's law, named after Max Kleiber, is the observation that for the vast majority of animals their metabolic rate scales to 3/4 power of the animal's mass. For example a cat, having a mass 100 times that of a mouse, will have a metabolism roughly 31 times greater than that of a mouse.
Constructal theory points out why this is the case, arguing that it is a law of all nature that there will be an inherent geometry that best distributes the imperfection, and is optimized for the many trade offs considered within the system. This inherent natural geometry applies to any organism wishing to be optimal. Most biological organism are fairly optimal most of the time, especially when you are dealing with something as serious as food, or locomotion. It is no surprise then to find CT predicts the allometric laws of biological locomotion we have observed for years in all modes of transportation (running, swimming, flying).
3. Social Dynamics and the Broad Range of Sciences
One of the newer fields constructal theory is assisting is the study of social dynamics. Adrian summarizes the seed of the idea behind this nicely.
No flow system is an island. No river exists without its wet plain. No city thrives without its farmland and open spaces. Everything that flowed and lived to this day to “survive” is in an optimal balance with the flows that surround it and sustain it. This balancing act—the optimal distribution of imperfection—generates the very design of the process, power plant, city, geography, and economics.
A new book is due out on the subject this spring. Given the broad range of scientific application it isn't surprising that there are articles from fields as diverse social science to materials science, from biology to physics- constructal theory impacts all areas of nature and all of our lives- we just didn't know it until now.
Constructal Theory: Introduction to the Inverse of Biomimicry
Constructal Theory: Sustainability
Constructal Theory: The Science
Constructal Theory: The Applications
Images used with permission from author::Constructal Theory Web Portal::Shape and Structure, From Engineering to Nature
Constructal theory is all well and good: a nice counter to reductionist specialization that that has effectively stultified inter-disciplinary cross-pollination. However it is unlikely that anything of any consequence, outside of perpetuation of academic careers, will ever emerge from current theorizing about Kleiber's Law. As handled by West et al., the club of the Santa Fe Institute, the equation has been perverted to support what is ludicrously known as the metabolic theory of ecology, and to justify intellectually dishonest papers (like that of Van Savage in the PNAS this year) that seek to understand how the increased mass of an organism effects the basal metabolic rate of its cells.
West and his clowns make hyperbolic statements about how Kleiber's Law might hold the secret to the aging process, while simultaneously averring that metabolic rate scales strictly according to mass. They insist that the equation describes the superior efficiency of capillary delivery of nutrients, and is pertinent to life over 27 orders of magnitude, even to that which has no capillaries. It's risible that they claim the equation describes the capillary-dependent superiority of metabolic efficiency when the term for metabolic efficiency is not in the equation, nor is there any term for fluid dynamics.
Interestingly Lloyd Demetrius of Harvard, in his 2004 paper analyzing the effects of caloric restriction on the longevity of mice, defines the exponent of mass, what West et al. insist is 3/4, as instead (4ME - 1)/ 4ME, where ME is metabolic efficiency. The exponent 3/4 is attained when ME is 100%. In other words, West et al. assume the efficiency they say the equation models, and by doing so, since such efficiencies are found nowhere in nature, remove Kleiber's Law from any biological consideration, whether ecological or gerontological. You can be sure of one thing, however, their positions in the academic hierarchy will be un-threatened by any tests of deductive inferences from their scheme since it has no tangency with reality, biological or otherwise.
Demetrius defines ME as the ratio of redox efficiency between energy sources and the reduction reactions of the organism necessary for its survival and maintenance. Consider then the graph of Kleiber's Law pushed by West and his coterie of sycophantic pedants in which the X axis is mass, and the Y axis is metabolic rate, and the graph of Kleiber's Law favored by Demetrius in which there is a different curve for each mass, the X axis is ME, and the Y axis is metabolic rate. There is a world of difference in the pictures, with the Demetrius version clearly modeling how most of life can be found between 15 and 45 % ME. This version agrees with the new data based upon imaging of oxygen consumption by cells, data that is a far cry from anything that might be found on the standard straight line graph favored by West and his posers.
Furthermore, the graph of Kleiber's Law that embodies ME rather than allegedly modeling it, results in a series of curves that distinctly portrays how aging is a result of the antagonism between basal and organism metabolic rates, given any mass and ME. In order to appreciate this one need only equate, as West et al. do, that metabolic rate is directly related to MPLS or maximum potential life span. West et al. hold this, and so are entirely unable to account for the immortality of certain strains of cancer cells which, if their preferred graph is correct, should live less than one second. But, hey, consistency is not as important as tenure and celebrity.
And so we see that constructal theory is not at all aided by, and is in fact obscured by the treatment of Kleiber's Law favored by its most widely-known proponents. For example, in his 2007 PNAS paper Van Savage et al. (which includes West et al.) laughably make the claim that the metabolic rate of the organism is the product of the average metabolic rate of its cells and the number of cells in the organism. Remember, these jerks believe that metabolic rate is strictly scaled to mass alone, and has nothing to do with ME which would reflect how these cells or organized, as if this too were important in the metabolic rate of the organism made up of these cells.
As a result of this pathetic handling of allometric, metabolic scaling Savage, West, and the other careerist academics expose mathematical biology to the contempt of traditional biologists who correctly point out that basal cell metabolism cannot account for motor activity, and that more massive rats live shorter lives, not longer. But the greatest disservice these assholes perpetrate is the prevention of the realization that by harnessing electrochemistry to alter slightly the ME of the human, the life span of that human can be increased by up to 100% easily, and the synthesis of muscle mass can be triggered independently of muscle use. This latter finding (yes, it is a finding and not just an hypothesis) would be exceedingly welcome in the field of rehabilitation to overcome muscle wasting following stroke or concussive nervous system damage, or immobilization due to orthopedic casting.
So the next time you read about these self-congratulatory imbeciles and how their ideas are so so wide-ranging but, so far, completely lacking in any consequence, just
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