Complex Systems, Boundary Events, and Hierarchies

By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/COMP Theory/Model; 14 Mar. 2014

“Mathematics must make great advances in order to understand complexity.” —Stanislaw Ulam

Have frequently mentioned and discussed the Tree of Life of the immense taxonomies of the living millions of species and viruses, the Plate Tectonics Model in geology, and Hertzsprung-Russell Diagram, the biochemical receptor sites concepts, before, and how mathematics does not describe very much of verbal statements, no poems, nor much else which is complex systems. This will create a better understanding of why this occurs and the place the Comparison Process takes in these events and ideas. Have also discussed these events in “Depths within Depths” as well as the “Continua and the Dualities” articles It’s now time to show how more of it fits together.
Sort of a biological field trip format again, beginning with something odd in north Phoenix which puzzled me at the time, and from this simple cameo can come a basic new model of how the universe is organized as is our brain cortex and how that works to understand complexity of all sorts.

On north 51st Ave. in Phoenix there is an odd event there. The road jogs to the west, without much warning. Just why that should be was interesting enough, but the deeper meaning of it becomes clear once we begin to think about boundaries of the macroscopic world, geometries and related subjects. Our generation is the first to have enough information to try to figure out how things work on a deeper level that has come before. The science have become so specialized that it’s hard for many in those fields to begin to understand each other. Or as has been so comically said, “We are now learning more and more about less and less until we will soon know almost everything about almost nothing.”

The hugely expensive search for the Higgs boson, supposedly found for about $15 Billions in new equipment and running costs, cannot be confirmed by a different team because it’s so outrageously expensive using current technologies to do so. These are the Exponential Barriers discussed before. This is crisis in physics, too. We cannot afford to do science this way, either. These are boundary events, just like has been found and so well discussed in Kuhn’s “The Structure of Scientific Revolutions.” These show the structure/function limits and capabilities of current methods, systems and understanding.

See sections 6, 10, 11, the Exponential barrier.

This is how those unexpected findings create a world change in our views of most which is around us, in short, a massive epistemological change which is ongoing currently. It’s what Kuhn so brilliantly wrote about and about which we are still mining and learning more to this day, some 50 years later.

Thinking about 2 dimensional flat planes versus the surfaces of spheres gets us to an understanding. The surveying methods used to make maps and lay out our grid patterns of roads are based upon plane geometry, that is flat, 2 dimensional lines and the surfaces connecting those. So if we try to impose a flat plane on a round one, tho of great size, so that the roundness is at once visible, what do we get? We get a mismatch, a problem.
Try taking a flat piece of paper and wrapping it around an orange. We can’t do it. It makes folds in the paper. The two surfaces are NOT commensurable. This is the problem we get when trying to impose a flat surface grid pattern on a round surface. And that’s why 51st Ave. had to jog, to make up for this imposition and it does it all along Bell Road for miles. The longitudinal lines approach each other slowly, and if the system is not carefully adjusted every few miles to that fact, the road will need to be adjusted over to make up for it. This is a mismatch. The systems do NOT compare.

If we think about that carefully, then we realize that it could have been proven easily centuries ago that the world was not flat. Because if the world was flat, then there would have been no mismatch. Because it’s round, as every surveyor of large areas knows, the baseline MUST be adjusted. For centuries that’s been done without realizing it was going on. They just ignored it, and adjusted it. Because map making of considerable accuracy has been going on since 2800 BC, esp. in Egypt, they no doubt saw this in their very long northwards going baselines and also corrected for it. It meant the world was round, just like the sun and moon, but it took Western Europe until the time of Cristoforo Colon to figure it out again. Careful, accurate surveying using long line of sights in clear air could have established this fact in flatter regions 1000’s of years ago. It’s as much a cultural and human mental state observation as it is a scientific fact.

In the same way, just these mismatches between the Ptolemaic model of the solar system, which put the planets in perfectly circular orbits, had to be corrected by adding epicycles, as Kuhn so well points out. Because ALL planetary orbits HAD to be perfect circles, therefore they could accept little circles to correct the measurements. As Kuhn pointed out, the epicycles approximated the ellipse, too.

Moving onward to Kepler, he saw much the same mismatch. and using Tycho Brahe’s extremely accurate measurements of the orbit of Mars, found a significant discrepancy from circularity of 8 arc minutes. That discrepancy justified and created the Keplerian elliptical orbits model and a much better and easier way of calculating planetary orbits. His creativity was a Least Energy solution.

With better measurements, it was discovered that the orbits were ALSO in 3 dimensions and the same mismatches between planar ellipses were found with the modern figures. In fact, Mercury circles the sun in a complicated rosetting orbit. So “elements of orbit” are now used which are better matches, but in fact, in the long run, the measurements of the orbits of the planets are such that they cannot be predicted more than about 50K years into the future without having real loss of accuracy. Prediction fails due to variations of the orbit.

In fact, the solar system is a complex system, not a series of easily computed orbits. If Jupiter were suddenly taken out, the inner planets steadily would spiral into the sun. The problem is that of the N-body problem, which mathematics no computers can solve, because it’s simply too complex to do so. Gleick points this out in his book, “Chaos”.

This greater overview is the problem of the sciences today. They cannot understand complex systems using linear mathematics, algebras and logics. There is a huge mismatch between predictions and outcomes. For an N-body problem of N= or >3, there is no clear solution possible. For interactions of 8 major planets in our solar system, plus the asteroids, the solution becomes of astronomical complexity, (pun intended) and unsolvable.

Now consider the problems of the some 25K genes’ interactions in the human body. It’s impossible to solve, and adding the many thousands of other compounds such as foods and gene products, it becomes even more impossible to solve.

Consider the complexities of the single eukaryotic cell. It contains many thousands of compounds in it, all interacting, many organelles such as nucleus, ribosomes, cell membranes, mitochondria (plus chloroplasts in plants), etc., that the N zooms up to the number of molecules interacting which is a very huge number, also. Essentially, modern mathematics cannot practically, or intrinsically DEAL with those complexities. Effectively the way is closed. The doors to understanding are shut. What are we to do?

The traveling salesman problem was a deep problem for mathematics for years. As the number of places to visit increases, the complexity of the problem gets harder and harder. No computer can solve it, either, even by the brute force approach. It was very expensive for any kind of large delivery system to just guess as to which routes to use for their multiple deliveries. Theoretically they could not approach within about 20% of what they figured was the most efficient route, nor could they compute it.

But how was this solved? “Observe the wisdom of the ant.”

Ants and bees had solved that problem 100 Million years ago, or before. And they did it with a very simple algorithm and process. The bees went to the nearest flower, took nectar, then went to the next nearest flower, took nectar, and after doing that several times their memories, in the neural networks we call their minute brains, collections of a million neurons, achieved a 75% solution of the problem, consistently. Ants did it by laying down a pheromone trace which they could follow, and sequentially the most efficient (least energy principle) route was created by following the pheromone trace that was the most traveled on, because it was also the fastest. Then the line got straighter and straighter to the nest, as well.
Using computer simulation of these two strategies, even better solutions to the problem were eventually found. The UPS and FedEX deliveries are now about 80% of the theoretical maximum, using these methods first found by the ants, bees and termites, perhaps as much as 100-200 of millions of years ago!!

And just how was this done? Complex systems solved it, those found in the bee and ant brains, and trial and error. Complex systems of millions of interacting neurons out computed and out performed any computer we’ve ever had. This was humbling to say the least, but it shows the immense power of complex systems to do what humans cannot do, given time and understanding. This insect solution has in the meantime saved the national and international delivery systems many 1000’s of extra miles/day and 1000’s of hours of less travel time per city, too. It’s a least energy principle in action. Again, the COMP. Comparing the outcomes of the traveled routes for the best one, the least energy solution.

And how did the observing scientists find this out? The same way Von Frisch figured out how the bees told the other workers to find the flowers yielding nectar. HE COMPARED what they were waggling, pointing and buzzing, etc., to where the bees were going and decoded the system they were using. The comparison process, in fact. It was the same way the ant method was decoded, and comparing where the bees went to find the fastest route. Same method was used to understand the ant pheromone system, the comparison process. The same method Champollion and Young used to decode the Rosetta stone. The same method used to translate and decode ANYTHING written, or any event. The Comparison process.

That is the key point. And it can be easily proven to be the case, again and again. Let’s take plate tectonics. This is a complex system, which cannot be solved by mathematics. Nor can it be created by same. The description of it is almost all verbal and visual. Cartooning has been used to show how it works and what the land world looked like 100’s of millions of years ago. Wec an look backwards in time to recreate this because of the remnant geological observations which allow it to be pieced back together in many cases, although it’s large;y approximate. All of the some 15 plates (16 if the East African plate is considered one, as it’s splitting off from the African plate) are all interacting with the others. This creates an impossible to solve 3-D, roughly spherical, N-body problem.

Essentially, the parts of the tectonic theory are the upwelling, sea floor spreading zones, the same on land from the Dead Sea to the south down the center of the Red Sea, inland at the Afar triangle and southwards to the Rift Valley zone of East Africa, too. East Africa is splitting apart. Africa split off from west Asia about 20 M years ago. There are a great number of plates. They are upwellings, subductions, faultings in complex patterns and so forth. The subduction zones often create volcanoes where the plate edge goes into the magma layers, is melted and the lighter rock rises up again, to create volcanoes. There is no center of the plate movements. There is no privileged space. Everything is pushing against everything else. It’s impossible to predict with any certainty how things will look in millions of years, because the computations can’t deal with all of these complexities. The plate tectonics model is a complex system.

The same is true of the weather. Of the stock markets. Of the economy, of social systems. The same is true of trying to understand the human brain and the complexities of each of the millions of known species, let alone all of the extinct ones. As Stanislaw Ulam stated, “Calling the universe non-linear is like calling biology the study of all non-elephants.” The problem is everywhere. 99.9+% of the universe’ events are alinear, complex systems.
So how could we have even developed plate tectonic model?

By studying, looking, thinking creatively, describing/measuring to find the patterns of sea floor spreading, of subduction, melting, etc., leading to volcanoes’ creations and eruptions, of the fault line movements, and so forth. How can we predict when a volcano will erupt? Or a fault line will rupture causing a great quake? We can’t. It’s a complex system.

And this is the key, clearly we have developed a coherent description about earth surface movements. It was done largely by using the comparison process which can handle alinearity. The same comparison process in the bird brains and other brains, which can handle complicated movement problems of flight and highly skilled activities and movements of human beings, viz. alinear systems, totally without mathematics.

Even more complex systems are found in the human body. We have a high incentive to understand these complex systems. Those are the very serious issues and problems of living and survival and reducing suffering, and increasing function. And we have it, the huge corpus of medical conditions and information built up over the last centuries of observation and study. It’s called anatomy, physiology, medical pathologies and the study of those, the differential diagnosis and the treatments. It’s almost all verbal. It describes almost entirely verbally what is going on, with some assistance from math and measurements. It uses observations, history, physical examinations, and then careful reasoning to figure out what’s going on and then bases the treatment on the outcomes of scientific studies, (the Method of Comparison) to find the best possible, current treatment methods as well as to continue to explore and find better ones. And it works. It’s verbal, visually descriptive and the examination, history, and differential diagnoses CANNOT be mathematized at all. Perhaps in the future, but perhaps not at all for most apps. Mathematics is an assistant, but NOT even a major player in the ways in which we diagnose and treat the most serious medical conditions. This fact has been overlooked for some time and it’s time to set the record straight. Mathematics alone is incapable of making the diagnoses and treatment protocols. Almost all of it is Verbal description We use verbal descriptions from comparison process methods throughout.
This is the key to understanding. Comparison processes CAN handle and deal with complex systems. Logic, math, and linear methods cannot do that task very well. How can this be? And the way to understanding it is again by using the comparison process to see what is going on.

Hierarchies have been discussed here a number of times. The massive taxonomies of all known living species, living and extinct. There is the physical reductionist method, starts with particles, then goes to atoms, then to molecules/compounds, then to chains of carbon atoms, organic and biochemistries. The simple to the complex method. Then there is a discontinuity, and we go from single cells, to multicellular living species and the larger multicellular systems with organs in them. Finally we get to neural networks, then larger collections of same in the birds, mammals, then to primates, and then to higher apes, of which we are a closely, the latter with 100,000’s of cortical cell columns, previously addressed and described, which underlie how our brains work.

Boundary events are those events which occur unexpectedly. These are the surprises we find when we carefully investigate, examine, observe, (that is, COMPARE) events around us. Flight is just such an event. We see this massively in our biological world, but not elsewhere. We see spiders using their silk to create flight in the winds. We see the maple and other seeds which spin and take off in the wind. We observe seeds surrounded by a great deal of fluff in huge numbers of species of plants, from dandelion, to cottonwood seed, to Kapok, and even the fluff surrounded seeds of the Chorisia tree, with its incredible flowers. Those can fly in the wind. This is a boundary event.

It’s seen with sugar gliders and flying squirrels. And in its most developed form with millions of insect species, 1000’s of birds and 100’s of bats, not to exclude the ancient birds and flying reptiles, the Pteranodons and the incredible colored, downy species. But how do these species actually fly? The dynamics of gliding were well worked out by the Wright Brothers and many since, but true, flexible wing gliding and powered wing flapping is a boundary event which creates the most successful and widely varied life on the earth, the insects. No one knows how this works, except that it does. Again, a complex system. How can any computer simulate a changing wing dynamic? It’s beyond math. Using complicated 3 dimensional photography it can be studied and perhaps some understanding can be created by those observations and study. But so far, little else has helped. There are many theories, of course, but none of these works on most species which fly. It’s simply too complex to figure.

Boundary events are events which mark the transition from one hierarchy to another. They may be small, or major and hardly trivial. In the tree of life, the Taxonomies, they are those which mark the creation of legs which allow animals to live on land. This transition is also marked by lungs, and skin changes which can conserve water. another boundary event would be the creation of sex, that is male/female in a single species, in all the myriad ways in which this can be done.

Binocular vision, hands, and a complicated cortex are what marked the change from primate to higher apes. A boundary event which created humans were upright posture, which freed the hands, and better enabled long distance sight. Another would be opposable thumbs. Another would be complex speech and vocal cords. The last of course, is the creation of human consciousness, similar to that of the great apes, but vastly amplified by the greatly enlarged human cortex, those 100,000’s of cortical cell columns which give us the capacity to process large amounts of information. Color vision would also be included. Each of these were unexpected and found.

In cultures, esp. in the sciences, boundary events are the discovery of radioactivity, as an aspect of elements’ isotopes. This created an enormous change in physics and everything that has touched including nuclear power, nuclear medicine, dating methods and so forth. If we review “Depths in Depths” cited above, we again see those boundary events which marked major changes in the sciences and our understanding of the unlimited complexity of the universe of events within biological systems and outside of them.
Events change, the rules change at the boundaries of the hierarchies. When the first hydrogen atoms were formed early in the universe’ history, it was the creation of the compounds and molecules from these new kinds of elements and atoms. When the first supernovae exploded, they created 1000’s of new isotopes among the elements higher than carbon atoms, too, and these were flung out into space. From those eventually came living systems. Again, boundary events.

When the massive carbon chains were created using hydrogen and hydroxyl groups, etc., this again marked a boundary event, we call organic chemistry, which then became biochemistry and living cells. From there it became multicellularity with complicated, specialized cells, and so forth. The creation of the worms, with their many, repeated, segmented bodies, each of which could create legs, and were capable of massive specialization, eventually resulting in the notochord and then the backbone, still segmented, resulting eventually in fish, amphibians, marking the transition from marine to land life, to reptiles, birds, and then mammals. Humans are still segmented animals. We need only look at our backbones, those repeated segments derived from adding on again and again, simple parts. Even the dermatomes of the skins and nerves show these segmentations throughout.

In cultures, boundary events are marked by new religions, new belief and political systems, and the sciences. Each of these subtypes, unexpected from the previous forms, just as feathers were used at first for warmth and then made flight possible in the birds. These are transitions from one form to another, and the characteristics which mark those transitions, which can be very complex.

Plate tectonics is just such a boundary event, created when enough lighter rock, viz. granite and quartz differentiated out from the more common, more dense basaltic rock. Again just piling up a great deal of isotopes of the lighter and heavier elements would not have given necessarily any idea that such a thing as continental drift was possible. And yet it exists and is real.

Taking the hierarchy of the change from Atoms to molecules shows this very clearly. Bonding of atoms is real and is due to the electron level characteristics. Simply knowing the structure of atoms does NOT give the necessary knowledge that atoms can bond with each other and create vast, almost unlimited numbers of chemical compounds. Nor does it show, without actually testing and trying it out, that carbon atoms can create very long, relatively stable chains of atoms, which is the basis of organic chemistry, biochemistry and the complex polypeptide/protein chains so necessary for life. The rules change at the boundaries, and these rule changes are the boundary events which mark those edges.

For instance, polypeptide chains can be used as biochemical signaling devices. This is not clearly known from the study of molecules alone. It takes a very large, very advanced cell organization to see this. A simple poplypeptide chain can produce very important hormonal and regulating effects, such as insulin and gastrin, for example. They are 100’s of such examples such as pituitary hormones, GIP, VIP, gastrin, endorphins and so forth.

In addition, certain organizations of complex proteins chains of amino acids can catalyze chemical reactions at lower temperatures than would be expected. Humans create nitrogen fertilizer, essentially ammonia and ammonium by the Haber-Bosch process which requires 100’s degrees of heat and 100’s of atmosphere of pressure. Then we look at Rhizobacteria, one of my favorite bacteria, which live in the roots of legumes, the bean and pea family. They can fix atmospheric nitrogen at soil temperature. And why? because they use protein chain chemistry called enzymes. These are the boundary events from complex biochemistry to living systems. Those new, immanent, unexpected surprises which await us when atoms are connected into larger and larger groups. No one could possibly have imagined that enzymes could have created complex chemical transformations by looking at bonding.

Indeed, the problem is this. We cannot build up biochemistry of enzymes from physics. That’s a boundary event. Physics can’t build up a system of understanding of living systems, simply because of those boundary events, such as complex interactions of the amino acid chains which can create hormonal effects and the enzymes which literally create all metabolism. The Quantum mechanic equations do NOT include those boundary events, which marks the next hierarchy from biochemistry to living cells, let alone complex division and reproduction which gave rise to each cell. Quantum mechanics is incomplete. ALL scientific models are incomplete.

This is why mathematics cannot follow. It’s simply too simple to do it. We cannot model nor describe anything past basic biochemistry because the rules have changed at each boundary event of the hierarchies. It’s why complex system are beyond the ken of even the most advanced mathematics. That’s why they cannot deal with plate tectonics, or solve the N-body problem. Nor can mathematics use its symbology to translate much of anything spoken or written into entirely mathematical symbols which are meaningful. It’s too limited. And those are the facts.

So we have the elementary stable particles, which are then assembled into the next hierarchy, the atoms and elements and isotopes, and then the next hierarchy created by chemical bonding. Then comes organic chemistry of the carbon bond, and then the biochemistry built upon that. And then the complex protein/polypeptide chemistries at a next hierarchical level. And finally comes the cell, the multicellular hierarchies we call multicellular organisms, which contain the next hierarchies of the organ systems.

And finally, comes the neurons, the neural nets, the ganglia and finally the brain. And at the top of this, some FIVE levels above the biochemistry/protein boundary the human mind based upon the complicated neuronal networks of some 50K-60K interacting cortical cell columns, yet another hierarchy, from which arising at the brain interface of the interactive CCC’s, comes the mind itself, of which no math can possible understand, nor describe in very much detail.

At the top is the comparison process, which creates signal detection, recognition, pattern recognition, language, visual imagery, sensory integrations, thinking, analysis, long term memory, the emotions and much else.
If mathematics cannot even tell us how and why enzymes work, and how to understand those processes at the biochemical level, allowing us to design new enzymes and so forth, from the immanency, the boundary events of chemical transformations, then how can it possibly, 4 more levels up describe and understand the mind? Let alone plate tectonics, a complete and accurate solution of the complex orbits in the solar system, nor understand the living cell? That is the boundary problem of the hierarchies. From the simple biochemistry which at first is more understandable and stops there dead cold at the protein chains, and the even more complex organelle and unlimited N-body problems posed by the complex cell. These are the limits of mathematics. We need a much more advanced kind of mathematics which can describe and give us measurable numericity to understand those systems, first. Such methods do not exist.


But time and again, from the immense taxonomies of the millions of species, to the millions of chemical compounds, to musics, to language, and speech, to creativity and beyond, the brain/mind interface can understand, comprehend and build and grow. This progression then leads us inevitably to the comparison process, and the next installment in these articles.

What is the COMP? How does it work outside of normal logic? How does it give rise to logics? How does it avoid the pitfalls of Godel’s proof and normal logic? Is it exempt from the limits of verbal and mathematical logic? Very likely. And that’s why it works where verbal logic and mathematical logic, the very basis of our linear maths, cannot follow. The following article will discuss the major Uber characteristics, the boundary event characteristics of the comparison process and why and how it works and creates the mind.