Dr. Adrian Bejanof Duke, author of Design in Nature, has been kind enough to help clarify our understanding of how the constructal law will drive the design of future K-12 learning systems. The constructal law requires that systems that carry some flow tend towards a tree-shape design (see earlier posts for clarification). I queried him thusly: with massive interconnectivity amongst teachers, students, and nodes of knowledge management around the globe, will this not lead to a structure of the knowledge web that can be more accurately mapped as a net or web, not a tree-shaped structure? I did not understand why schools or colleges must be the largest flow points of knowledge in the future.
Dr. Bejan:
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.
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.
My mistake was in seeing the future of learning as defined by our concept of school, when in fact this has never been the critical nature of learning. The critical nature of learning is the creation and management of knowledge, the exact words I have used to define the system I call the cognitosphere. Knowledge has always been created and flowed through this system, and up to now most of that flow has been through nodes we call schools. That is changing, and the rate of change is increasing. From our point of observation access to knowledge is becoming increasingly democratic, tending toward anarchy, which made me see the design resulting in an amorphous web or net. This is not actually the case: the number of connected points in the system are increasing, but the structure of the system will still evolve in a tree-like design based on the unchangeable critical nature of learning: the flow of ideas.
If you believe schools have a role to play in the future of the learning experience, you care about this. Empirical observation aligns with the demands of the constructal law: learning will have more depth, power, and importance where the flow of ideas is greatest, whether or not that flow is at all related to schools. If you want your school, or schools in general to maintain importance, they have to be at or near the core of the tree-shaped design of the cognitosphere. If they are on the fringes, they will be largely irrelevant. You can’t control the design of the universal system of knowledge; you very much can control where your school, teachers, and students are within that system.
Grant,
I’ve been following this idea flow between you and Dr. Bejan very closely and carefully. I am thinking about the tree vs. network quite a bit. Of course, I don’t have it figured out, but I want to think with you on this exploration.
You write, “Knowledge has always been created and flowed through this system, and up to now most of that flow has been through nodes we call schools.” I do not mean to parse your posts, as I don’t think that’s very fruitful for understanding the whole. However, this sentence really puzzles me. School as we have known it represents about 13-17 years, give or take a few years. I’m taking some liberties, but I get those numbers from K-12 + 4 years undergrad. I know that this does NOT represent all people’s formal education experience – not by far. But 13-17 years is at least one definition of time in “school.”
However, if we take the average U.S. lifespan to be roughly 80 years old (more taking liberties on my part – to exclude other countries, average male and female, etc.), then “school” represents less than 25% of our existence. I don’t think that most of the flow of knowledge has been through schools. Don’t get me wrong – I agree that “school” has been the primary island or repository of formalized knowledge, but I disagree, especially today, that most of the flow of knowledge goes through schools.
Have you read Manuel Lima’s work on networks? I think he even writes of “Networks, not trees.” What about the terminus of the trees? Versus the ability to limit any significant terminus of networks.
Can you help me understand? Maybe we need to Skype! When I re-read this post, sometimes I think I read it one way. Then, other times, I read it another.
You are not misreading; I think you are sharing my struggle with the constructal law. I will clarify one point: I was not referring to the flow of all human ideas, but just to those that flow through the population of school age children and their teachers. I can see Dr. Bejan’s point that even network-like structures will gain and lose strength, but my gut tells me Lima’s neural network more accurately describes where education is heading. Thus, that dinner is very much needed, or some virtual 4-way conversation that could be recorded. It may sound just like fun, but isn’t this the ground that Unboundary wants to get right? There is a huge difference between a K-12 environment that maps into a tree-like design as opposed to a neural network design.
Manuel Lima: http://www.youtube.com/watch?v=nJmGrNdJ5Gw
Also, see @MaryAnnReilly http://maryannreilly.blogspot.com/#uds-search-results (search for “rhizome”)
And, of course, I have NOT yet read Dr. Bejan’s book. So I probably should have done that first. I will do so ASAP.
Perhaps Deleuze & Guattari said it best:
“We’re tired of trees. We should stop believing in trees, roots, and radicles. They’ve made us suffer too much. All of arborescent culture is founded on them, from biology to linguistics. Nothing is beautiful or loving or political aside from underground stems and aerial root, adventitious growths and rhizomes.”
from A Thousand Plateaus: capitalism and schizophrenia p.15
What if flow doesn’t lead to arbor-like structures? How does that open possibilities?
Bo Adams sent me a message the other day: what a great conversation we would have at a dinner with Mary Ann Reilly, Adrian Bejan, and Manuel Lima on the structure of things, both in nature and man-made!
Our societies and the education systems that are nested within them are complex systems that evolve over time. They follow Constructal law behaviours and Asynsis principle geometries. They are Evolution exemplified. Lamarck and Darwin, Design and Natural Selection combined.
There’s been a major breakthrough recently in the field that might shed light on how education can be both a tree and a net. It’s called Modularity.
“By simulating 25,000 generations of evolution within computers, Cornell University engineering and robotics researchers have discovered why biological networks tend to be organized as modules – a finding that will lead to a deeper understanding of the evolution of complexity.”
“The team discovered that evolution produces modules not because they produce more adaptable designs, but because modular designs have fewer and shorter network connections, which are costly to build and maintain. As it turned out, it was enough to include a “cost of wiring” to make evolution favor modular architectures.”
This is the principle of least action in excelsis, the archetypal geometry of the Asynsis principle-Constructal law of nature & culture.
“To test the theory, the researchers simulated the evolution of networks with and without a cost for network connections. “Once you add a cost for network connections, modules immediately appear. Without a cost, modules never form. The effect is quite dramatic,” says Clune.
The results may help explain the near-universal presence of modularity in biological networks as diverse as neural networks – such as animal brains – and vascular networks, gene regulatory networks, protein-protein interaction networks, metabolic networks and even human-constructed networks such as the Internet. “Being able to evolve modularity will let us create more complex, sophisticated computational brains,” says Clune. Says Lipson: “We’ve had various attempts to try to crack the modularity question in lots of different ways. This one by far is the simplest and most elegant.”
More information: “The Evolutionary Origins of Modularity,” Proceedings of the Royal Society B, Jan. 30, 2013.
Read more at: http://phys.org/news/2013-01-biological-mystery-boost-artificial-intelligence.html#jCp
http://www.facebook.com/pages/Asynsis/134142719983026
https://twitter.com/ASYNSIS
http://asynsis.wordpress.com
http://constructal.org
Am I correct in understanding that in this model, the modules in the social system of learning are school or school-like entities? I understand how the development of those modules would follow the model as, in the past, network connections between schools have been faster and more efficient than between individuals. Rapidly procreating direct access amongst individuals or small groups seem to be bypassing network connections between larger modules like schools. At what point does a small group of net of individuals cease to be called a system of modules? At what point might the module model break down? If network connections become close-to-infinitely cheap, does that friction not disappear from the system?
Hi Grant,
“If network connections become close-to-infinitely cheap, does that friction not disappear from the system?”
That’s a a very interesting take on the modularity-nesting behaviour of these new evolutionary computer simulation models that trade performance against connection cost for optimal results.
I suspect It will depend on how the models themselves specifically define performance and connection costs.
There will always be a connection cost in terms of the thermodynamics of the process, as only a static system will have no cost. All dynamical systems will have an energy cost. What the Constructal law behaviours and Asynsis principle geometries appear to be revealing to us is that even with a minimal (flowing most easily-least action), energy cost/entropy production scenario – you will see modularity evolve in time, with often (subject to selection pressures and deterministic/chaotic contingencies), greater force, hierarchy and consequent complexity.
These modules (such as in the bands of order versus bands of chaos in the analogous Feigenbaum diagram), will also break down and reform, according to certain parameters and constants; including the one associated with the Asynsis principle, the golden ratio – which emerges as an asymptotic convergence associated with each bifurcation node.
Information evolves to flow analogically and optimally from entropy.
In so doing, it self-designs its own flow, so even if there are just a small group of nodes, the actual information and ideas they are exchanging will themselves be flowing in a fractal, tree-shaped manner, from areas to points, or vice versa.
For what those particular bands of system collapse and reformation would be for online distributed education, well that would be an interesting question for Jeff Clune and his team to model and for Dr Bejan to comment on too.
In a certain sense, because we are dealing with an online, dynamical, evolving, networked and modular computer nodal system, the internet is its own model.