I was honored to receive the following comment from Dr. Adrian Bejan at Duke about my post on his book yesterday. Since many of you may not follow the comments, I will re-post here. I am also asking Dr. Bejan to perhaps weigh in one more time with a clarification that can help us understand or predict some evolution in these massive knowledge connections as they pertain to the development of global K-12 learning.
Dr. Bejan wrote:
Thank you for this very interesting essay and discussion. The current grass-roots contributions to K-12 education are in accord with the constructal law, not against it.
They are the early design of a new flow system, like the new rain falling on the smooth plain, and like the Internet in its early stages. In time, the better ideas contributed to this global K-12 flow tissue will attract more users, and will become bigger nodes, trunks and big branches…and on this way to the “few large and many small” design of all flow systems that are old enough to have perfected their flowing (like the textbook publishers, river basins, and most popular web sites).
The natural emergence of hierarchy (i.e., tree shaped flow structures) is already happening in this new way of distributing knowledge on the globe. It has been this way with every new technique of spreading ideas. More examples are in the articles and videos posted at http://www.constructal.org.
My follow-on question:
I understand the evolution and geometry of the system, and in particular the example of a stream system (I am a geologist from back in the day). And I understand how good ideas with more impact will tend to create larger channels of flow which will drive the design of an interconnected knowledge system, what I am calling the cognitosphere. At the same time those channels are growing larger, is there not a counter-mechanism that is increasing the distribution of nodes and connections as more students, teachers, schools, and other knowledge centers connect in an increasing way? Is the geography of these possible connections the same as the geography of a plain on which rain falls? The plain has a limited number of surface gradients down which water can flow before those flows coalesce. It seems that the number of connection pathways available to the global terrain of K-12 students is much larger: billions of students and teachers, and millions of other sources of idea creation and sharing. As these increasingly connect point-to-point, bypassing larger channels in the hierarchy, how will that impact the design being driven by the constructal law? Is it just a matter of scale? Whereas a stream or vascular system may have N number of component sizes, should be predict a much higher number for N in the system of global knowledge connectivity? Flow on the Internet has been channeled through some very large for-profit mechanisms that are certainly present in the sphere of K-12 learning, but K-12 learning has a degree of freedom that we can imagine is not slave to those same profit forces.
I don’t think this is just an interesting coffee table discussion for K-12 schools. We are in the process of re-imagining what learning looks like, and working with first principles and laws of physics makes a heck of a lot more sense than working against them!
Thanks again to Dr. Bejan for helping us understand the nature of the constructal law as we apply it to the radical pace of K-12 education innovation.
Incidentally, from an Asynsis geometry perspective only, K-12 as you describe it looks like a Feigenbaum diagram close to one of the chaotic bands, with numerous nodes or bifurcations. They will be directly correlated to the energy input into the system, (as the periodicity increases equate to greater energy inputs – or volume of information the system is carrying) and also are analogous to the local creativity of that system at that point in time and phase space.
Nevertheless, those bands can suddenly morph back into larger, fewer flows spontaneously – and this is a scale-invariant, recursive property.
These are also, incidentally Asynsis principle geometries as demonstrated by this 2006 paper, a geometric signature that I first predicted as published in AD magazine back in 1995.
http://asynsis.wordpress.com/2012/05/06/entropy-begets-design-qed/
http://asynsis.wordpress.com
The Feigenbaum diagram (or Logistic map as it is also called), is directly correlated with analogous zones in the Mandelbrot set, also with Asynsis geometries. They are both only models of the real world but offer powerful support to the Constructal law in that they demonstrate the thermodynamics-led “tree -shaped flows” Dr Bejan vividly describes have related geometric signatures at an almost archetypal level. These behaviours have a fractal, analogical temporal structure and are optimal.
So K-12 propagation, of information flows evolving to course more easily, optimally and analogically (often with more power and consequent complexity), over time will as he says, sometimes be either big and fast or small and slow, which is power law behaviour.
K-12 evolution will have a fractal dimension over time, which may itself evolve.
Depending also on the resistance of the medium they are flowing through and the forces behind those flows. So K-12 will either persist with its current dynamical multi-nodal tributary form or evolve into something more like a major river. It will also have both, depending where you look at the system or at what scale, which will be inherently self-similar to certain limits.
That river itself may also change its course, as real ones regularly have, sometimes radically.
Ta Panta Rei – You never Step in the same River Twice – All is Flux. Heraclitus.
I submitted a response 24 hours ago. Did you receive it?
No, sir, I did not receive a second comment if you sent it. I would like to see it; thanks.
Too bad. I did not keep a copy of what I typed here and sent last night.
Here I try to respond again to your “follow-up question”, and I hope it works :
The channels and the wet (seepage) banks flow together, during strong or weak rainfall. The flow is from area to point, from the plain to the river mouth. It is tree shaped.
In education of all kinds, including sports training, the area is the inhabited land, and the point is the university, or the K-12 school.
The pathways are tree shaped, because they connect the area (an infinite number of points, approximated by the large student population) to one point, or to two or three points—the school, the art school after hours, the basketball team practice after hours.
No, the number of connection pathways available to K-12 students is not much larger than the pathways of water in the river basin. That number is smaller, because the plain (soil, silt, sand, pebbles) is freer to morph than the human society of a certain era. Habits, which are good, do constrain the design.
The channels that have come to dominate the Internet happened naturally because they serve the largest numbers of Internet users. No one is “slave” to anything. Users click voluntarily on what works better and faster for them, and from this common urge to move faster and more efficiently (with less effort) on the web sphere emerges the rived-basin of channels that the Internet has become.
Your penultimate paragraph hits the nail on the head. It is good for all of us to know the laws of nature, i.e. the laws of physics, the universal laws, the first principles. The laws empower us to improve and to fast forward the design of the future into which we will walk with confidence.
Adrian Bejan
Duke University
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