Copernicus & Elegant Simplicity
The Aesthetics of Science
Synopsis
Copernicus’ insight into the nature of planetary orbits, which ultimately inspired the Scientific Revolution, was based on his personal belief as to God’s nature. He didn’t believe that God would create a messy, complicated planetary system such as was precisely described by Ptolemy. He believed that the complicated Ptolemaic geocentric system was false because of its lack of elegance. He proposed a heliocentric system due to aesthetic considerations, not because it was a better fit with the data. Copernicus believed that elegant simplicity was one of the features of God and by extension the Universe he created. In short he believed that natural law should have this aesthetic feature. As an extension of this principle, scientists have adopted Occam’s Razor as a criterion for evaluating theories: a simple Formula always trumps the Complex.
The scientific community’s obsession with discovering natural laws that are both elegant and simple has yielded fruit so many times that aesthetics is an unquestioned underpinning of scientific formulations. There are many logical reasons for this quest for simplicity. Employing the mechanical model as an example, Nature would favor the simple over the complex, as it would tend to be more stable, durable, and energy efficient. In support of this theory, elegant simplicity is a feature of many foundational Scientific Formulas from a variety of diverse disciplines. In fact, the theory of elegant simplicity is as unquestioned as the theory of gravity by the scientific community. The Living Algorithm of Behavioral Dynamics (BD) fits into this mold, as it epitomizes elegant simplicity.
There are many parallels between the theories of Copernicus and BD. Frustration with the current paradigm inspired the development of both theories. Both theories represent radical paradigm shifts that consolidate existing evidence and provide future promise. Just as Copernicus required Kepler to champion his novel perspective, BD also needs a champion if the scientific community is to embrace his choice-based paradigm regarding living behavior.
What part did aesthetics play in the development of Copernicus’ theories about planetary orbits? Why is a heliocentric Universe more beautiful than a geocentric one? When is Aesthetics more important to scientists than Data? Why is elegant simplicity at the heart of Science? What is it about simple systems that appeal to both scientists and God? Is Behavioral Dynamics (BD) founded in elegant simplicity? What are the similarities between the theories of Copernicus & BD? Is it possible for the theoretical model to lead the data, rather than describe it? What aspect of the current paradigm frustrated both Copernicus and BD?
Aesthetics inspires Copernicus’ Heliocentric Theory
In the year of his death, Copernicus (1473–1543) published On the Revolutions of the Heavenly Spheres. In this paradigm-shifting book, heproposed a heliocentric system, where the planets circled around the sun, rather than the earth. This notion eventually caused such turbulence, astronomically and socially, that it is generally referred to as the Copernican Revolution.
What factors led Copernicus to challenge the status quo? Although there were ongoing data discrepancies, aesthetics provided the primary inspiration for Copernicus’ revolutionary insight. Copernicus’ innate sense that the divine order is elegant and simple motivated him to challenge the Ptolemaic status quo, not scientific considerations.
Copernicus was a theorist, not an experimenter. His main objection to the Ptolemaic system was its lack of elegance — not its lack of precision. Based in complicated epicycles, equants and deferents, Ptolemy’s mathematics did a great job of predicting planetary location in the sky — a feature that astrologers relied upon. In contrast, Copernicus’ theory that the planets, including the earth, proceed in perfect circular orbits about the sun was initially less precise than the Ptolemaic system.
“Until Kepler, the Copernican theory scarcely improved upon the predictions of planetary position made by Ptolemy.”1
However, the heliocentric model had an aesthetic appeal that was lacking from Ptolemy’s complicated geocentric system. One of Copernicus’ contemporaries stated that nature would never create such an inaccurate and cumbersome system. Copernicus’ radical paradigm shift was very appealing to those who believed in the elegant simplicity of the divine order. Strangely enough, most contemporary scientists share this perspective, including yours truly.
Copernicus reasoned that Nature, as a subset of the Divine World, must be perfect like God. As such, it should be orderly, simple, elegant, and beautiful. Because the Ptolemaic system didn’t fit this model, it must be false.
Copernicus Syllogism
God as Nature = Perfect, Orderly, Simple, Beautiful
Ptolemaic System = Complicated
Therefore: Ptolemaic System = False
For millennia from the ancient Greeks through the Arab Empire on through to medieval Europe, scholars and mystics alike considered the Circle to be the ultimate in elegant simplicity. As such, God must have employed this form for planetary motion. Although complicated, Ptolemy’s geocentric system followed this paradigm. To fit the observational data, planetary orbits consisted of circles within circles within circles, at least according to this model.
The simplicity of the divine order also extended to velocity. Not only did planets move in perfect circles, they also moved at a uniform velocity. Originating with the Pythagoreans and validated by Ptolemy’s astronomy, these twin beliefs permeated the Mediterranean sphere. For two millennia, there was a nearly universal consensus regarding the truth of this paradigm. Virtually no astronomer questioned this geometric perspective.
But then came the big step — the logical leap that has transformed human culture. Rather than experimentation, Copernicus’ reasoning was founded upon an innate sense that the laws of natural world should be simpler than those suggested by the Ptolemaic model. Ptolemy’s mathematics implied that planets move in complicated circles within circles around the Earth. Turning this model inside out, Copernicus became committed to the notion that planets actually revolve in simpler circles around the Sun. He spent his life developing this hypothesis.
Copernicus wasn’t saying that the Earth circled around the Sun — just the planets. At this point in history, the Earth wasn’t perceived to be a planet. It took another few centuries for this viewpoint to be first hypothesized and then validated. Further, his model was still based upon the Pythagorean paradigm that planets move in perfect circles at a constant velocity. He was, however, making the radical suggestion that the Sun was the center of planetary orbits, not the Earth.
Many of the leading proto-scientists of the day became converts to the Copernican theory due to the aesthetics, not the accuracy of the model — which was about the same as the messy calculations of the Ptolemaic model. This aesthetically driven perspective eventually led to the formation of Science as we know it. For Copernicus’ paradigm-shifting theory, the Aesthetics of the Scientific Model trumps the Precision.
This is a strange and counter-intuitive notion. Most of us believe that accuracy is number one in Science. Indeed the correspondence between Data and Formula, the heart of the Scientific Syllogism, points to truth. So why were the scientists of the day willing to take up the crusade for Copernicus, when Ptolemy’s system was far more accurate? We must examine another scientific criterion to discover the answer.
Occam’s Razor is a scientific criterion for determining the better of two theories. In essence it says Simple is best. A simple theoretical formulation will always be chosen as the operative theory over a complex theory that employs multiple formulas and pages of text to support its premises. Because of this intuitive sense, scientists justified spending their entire careers validating the simpler and more elegant Copernican system.
Why is Elegant Simplicity the Heart of Science?
Why do Scientists have this intuitive sense that elegant simplicity is a feature of natural law? This belief is certainly a powerful element in the determination of relative truth and frequently a greater motivation than accuracy (the correlation between formula and data). This belief is not just a matter of aesthetics but has practical reasons as well.
By Copernicus’ time period, the predictability of planetary positions was a well-established fact of life. As God ruled the heavens, He must be orderly as well. Further if He was orderly, his Order must embody perfection, as He was the embodiment of perfection.
Although the insights regarding planetary order derived from Science, the extension to God and nature was based in religious beliefs. Rather than antagonistic, Science and Religion had a healthy interactive feedback relationship. The Copernican theories exhibited this positive affiliation. This same mutually beneficial rapport between scientific discovery and religious beliefs occurs frequently, for instance in the lives of Johannes Kepler and Benjamin Franklin. Indeed, this is one of themes of my Scientific Manifesto: Rather than enemies, Science and Religion can be friends.
If the Divine Order is Perfect, then it must be simple — for Order is never complex. Why? The more complex a system becomes, the greater the potential for disorder, as more elements can malfunction. “Keep it simple, stupid,” is a modern expression that reflects this sentiment.
If the Order is simple, it is also more stable, as stability is linked with durability — fewer things to go wrong. As the world has been around a long time, it must have stable, durable, simple systems.
Simple systems tend to be more energy efficient — fewer moving parts to cause wear and tear. The complicated invention frequently breaks down and is hard to replicate, while the simple invention is easier to fix and is easier to replicate. Efficiency leads to conservation of energy as well. An efficient army or community doesn’t waste materials, thereby conserving resources. An efficient human makes every movement count, thereby conserving energy. It was easy to surmise that to survive for eternity the Natural Order ruled by God would also be based in energy efficiency.
These are some reasons for sensing that the laws of Nature would be simple, rather than complex. Yet as much as we hope for simplicity, some phenomena are confused, disorderly and complex. Sometimes we don’t understand the simplicity that underlies the complexity due to a lack of understanding. Other times, a simple explanation does not appear to exist for a phenomenon, e.g. living behavior.
However, one of the great miracles of Science is that researchers have discovered a multitude of elegantly simple equations that accurately describe Nature’s processes. The interlocking nature of these many formulas evokes a sense of awe and wonder. We are amazed both that Nature is so orderly and that humans have been able to uncover these laws. The uncountable number of equations with this incredible aesthetic component provides further validation for the notion that Nature’s laws are ultimately simple.
In Copernicus’ day none of the great equations were known — as algebra and equations were still unknown — at least in Europe. However since that time, researchers have discovered an abundance of these formulas. In fact, there is a joke passed among engineers that is relevant. Only one equation need be known for each type of discipline. Some of these are listed in the table below. For instance, “All you need to be a mechanical engineer is ‘F = ma’.” — (one of Newton’s laws of motion).
The final entry in the list links the Living Algorithm (LA) with Living Behavior. The LA is the foundational equation for my Theory of Attention, a.k.a. Behavioral Dynamics (BD). The theory addresses Living Behavior through the mathematical Rhythms of Attention. These rhythms permeate our existence.
Living Algorithm -> Theory of Attention -> Living Behavior
The LA epitomizes elegant simplicity. The formula contains only 3 components and only employs basic arithmetic processes, i.e. addition, subtraction, multiplication and division. Further, the Living Algorithm is self-reflective just like Life. [Note the other equations in the table don’t have this self-reflective component. Matter doesn’t require this feature.]
Further, my personal research was certainly inspired by the aesthetics of the unfolding model. Economy combined with beauty provided validation for my ongoing Theory of Attention. It is simple to comprehend, provides mathematical support for our common sense, and has some beautiful graphs that mimic the forms of Nature.
Parallels between the Copernican System & Behavioral Dynamics
There are many parallels between the Copernican System and the author’s Theory of Attention (AT). For instance, AT stands in similar relation to the current study of living behavior, as did the Copernican scheme to the Ptolemaic system. The prior systems in both cases have a relatively high level of accuracy. Yet both systems are incredibly complicated. The absence of integration indicates that the two systems are lacking in elegant simplicity — Beauty. While lacking substantial experimental verification, the two revolutionary systems are the epitome of elegant simplicity. [Behavior Science = the Current Science of Living Behavior.]
Another similarity: Both the Copernican theory and the author’s Theory of Attention represent radical paradigm shifts. Generally speaking a paradigm shift provides a new handle with which to address the myriad problems of an old and fragmenting paradigm. This was true in the case of Copernicus.
The Ptolemaic geocentric model provided predictions regarding planetary position that were good enough for the astrologers. However, over the centuries, astronomers had been forced to make many adjustments. These tiny corrections had been necessary to get the observed planetary positions (the empirical facts) to line up with the mathematical predictions (the model).
Many theoreticians had provided temporary fixes to these ongoing problems. Copernicus was not impressed with these partial solutions. In his book, he complained about the current state of affairs.
“With [their astronomical investigations], it is as though the artist were to gather the hands, feet, head and other members for his images from diverse models, each part drawn excellently, but not related to a single body, and since they in no way match each other, the result would be monster rather than man.”2
The celestial system envisioned by his contemporaries lacked integration. A fresh perspective was required to tie the loose ends together. As happens frequently, recurring data discrepancies results in the need for a paradigm shift.
“Copernicus’ more elaborate proposal was neither simpler nor more accurate than Ptolemy’s system. Available observational tests provided no basis for a choice between them. Under those circumstances, one of the factors that led astronomers to Copernicus was the recognized crisis that had been responsible for innovation in the first place. Ptolemaic astronomy had failed to solve its problems; the time had come to give a competitor a chance.”3
Copernicus’ notion of a solar system gave astronomers a new handle with which to address the problems associated with the collection of planetary positions over long periods of under Ptolemy’s earth-based system. This fresh perspective enabled different types of solutions that weren’t possible under the Ptolemaic system. Yet it took the better part of a century before Kepler was finally able to fully exploit these potentials.
In similar fashion, Data Stream Dynamics, the mathematical foundation of the author’s Theory of Attention, provides a mathematical handle for mental energy. The model is a powerful explanatory tool that integrates many disparate phenomena. Many ubiquitous experiences are as yet unexplained, e.g. Sleep, Attention span, the harm of Interruptions, the Flow Experience, Inspiration, and Mob Behavior.
It’s not that these experiences are uninteresting to scientists. Indeed, scientists from many disciplines have generated many hypotheses regarding the reasons behind these commonplace occurrences. Yet, an academic consensus has not emerged from this proliferation of theories. In similar fashion to Ptolemaic astronomy, an overriding vision regarding the sources of human behavior is lacking.
Although Copernicus’ sun-centered theory generated some interest among astronomers of the day, it hadn’t really caught on and was actually fading in the decades after his death. Despite its problems, Ptolemy’s mathematics was both easier to compute and did a far better job of predicting planetary position than did the mathematics of the Copernican system. There was really no impelling reason to fix the existing system. But then came Kepler’s mathematics to provide the handle.
As with Medieval astronomy, the current understanding of mental energy and Attention lacks a mathematical handle with which to consolidate the accumulating experimental results from a variety of academic disciplines. In similar fashion to Kepler’s mathematics, Data Stream Dynamics provides this handle. As an example, this unique mathematical perspective integrates experimental findings and models regarding Attention, biology and evolution in a neat little package.
Both data discrepancies and aesthetic considerations inspired Copernicus to introduce his revolutionary paradigm. Yet he required a champion, i.e. Kepler to continue and further his ideas. Religious beliefs provided the primary inspiration for Kepler to take up the flag, not because the heliocentric theory had proven more effective. Thomas Kuhn suggests that this duo of innovator and champion(s) is almost essential for the acceptance of a new paradigm. He further indicates that the hero is generally inspired by aesthetic rather than scientific considerations.
In light of this notion, one intent of these many pages on the scientific basis of Attention Theory is to acquire converts from the set of professional scientists. Perhaps the resonance between AT and common sense will attract a new generation of researchers. Hopefully, a young champion, akin to Kepler, will arise who will establish the validity of the theory’s many hypotheses through experimentation and consolidate the findings via interdisciplinary research. As an untrained laborer, this humble waiter possesses neither the prestige, nor the academic tools requisite for this requirement.
Our Author is not a professional, but instead an amateur scientist. Love, not money, motivated his pursuits. He deliberately took the path of Outsider in order to see outside the Box.
Like Copernicus, he was frustrated with the scientific paradigm of his day regarding human behavior. He didn’t believe that rat studies would reveal anything about the Experiential Data that really interested and motivated him. What did it say about Art or Music? What did it say about Inspiration or Creativity? At the time, the main focus of Psychology was on Personality, Memory, and Learning — in short the Realm of Academia — phenomena that could be readily quantified — to him trivial aspects of human existence. Current research has very little, if anything, to do with the Realm of the Artist — e.g. techniques for maximizing the creative experience.
From his humble beginnings, our Outsider was inordinately curious and dedicated to understanding the Mathematical patterns that seem to underlie existence. But if the world he was born into could only give him Behavior Modification, he was gone — rather fill his days on independent studies — didn’t know where he was going — didn’t even know if he was going anywhere — thought he wasn’t — almost gave up — Universe sent him an academic bone to keep him moving — but knew he wasn’t going to spend the glory of existence studying rat behavior to understand the higher states of human consciousness.
Dropped out of academia’s normal science to pursue the Open Road — the path not frequently traveled — by himself and alone — without encouragement — but a deep faith in Divine Providence — that somehow someway that he was following the correct path because he was in the Arms of the Beloved — the place everyone hopes to be.
In summary, Copernicus’ heliocentric system and the author’s Theory of Attention share certain similarities. Both founders were frustrated with the state of affairs in their respective eras. They were unwilling to accept the popular and professional paradigms because they just didn’t seem right. Both were forced to entertain and then initiate a paradigm shift to address their objections. Finally, elegant simplicity is at the heart of both the Copernican system and Lehman’s Theory of Attention.
Footnotes
1 Thomas Kuhn, The Structure of Scientific Revolutions, The University of Chicago Press, 1962, p. 156
2 Kuhn, p. 83
3 Kuhn, p.76
