Copernicus & Elegant Simplicity

The Aesthetics of Science

Questions

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 Information Dynamics founded in elegant simplicity? What are the similarities between the theories of Copernicus & BD? Is is possible for the theoretical model to lead the data, rather than describe it? What aspect of the current paradigm frustrated both Copernicus and BD? Article Summary

Aesthetics inspires Copernican Discoveries

Copernican Revolution

In the year of his death Copernicus (1473-1543) published On the Revolutions of the Heavenly Spheres his paradigm-shifting book, in which he proposed his heliocentric system, where the planets circled around the sun. This eventually caused such turbulence, astronomically and socially, that it is referred to as the Copernican Revolution.

Arrow from Religion to Science – Copernicus’ insight

In the case of Copernicus’ revolutionary insight the Arrow distinctly pointed from Religion to Science. Copernicus’ religious beliefs motivated him to challenge the Ptolemaic status quo, not his scientific observations. Indeed it took a few generations of scientists to establish his insights as scientific truth via the essential correspondence between formula and data that was lacking from the Copernican model. This occurred due to the increasing precision of data collection combined with theory revision – the essential duty of normal science.

Copernican heliocentric more beautiful, less precise than Ptolemaic geocentric

Note that Copernicus was a theorist, not an experimenter. His main objection with the Ptolemaic system was its lack of elegance – with its complicated epicycles, equants and deferents – not its lack of precision. In fact his theory that the planets, including the earth, proceed in perfect circular orbits about the sun was less precise than the Ptolemaic system – even though it felt better to those who believed in the inherent elegant simplicity of the divine order – strangely enough a view shared by most scientists, including yours truly.

Copernicus Syllogism – Complicated Ptolemaic System false because not Elegant

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.

Perfect Circle is Heavenly Plan

His reasoning continued in a similar fashion. Since the Circle is the ultimate in elegant simplicity God as Nature must have employed this for his planetary motion. But then came the big step – the logical leap which has transformed the world – not on data collection – just on a sense of the way the natural world should be. He reasoned further that if planets move in circles and that they don’t move in circles around the Earth that they must move in circles around something else – namely the Sun.

Note that he 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 suggested and validated. However he was making the radical suggestion that the Sun was the center for the planetary orbits, not the Earth.

Aesthetics trump Precision in Science

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 far surpassed by the messy calculations of the Ptolemaic model. This eventually led to the formation of Science as we know it. As such the Aesthetics of a Scientific Model trumps the Precision.

What about Correspondence between Data & Formula?

This is a strange and counter- intuitive notion – as most of us believe that accuracy is number one in Science – the correspondence between Data and Formula that is at the heart of the Scientific Syllogism – which 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: Simple Formula trumps the Complex

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 to validate 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 – certainly a powerful element in the determination of relative truth and frequently a greater motivation than accuracy (the correlation between formula and data)? This is not just a matter of aesthetics but for practical reasons as well.

An Orderly God rules Predictable Planets

By Copernicus’ time period the predictability of planetary positions was well established globally. As God ruled the heavens this meant that He must be orderly as well. Further if He was orderly, his Order must embody perfection as He was the embodiment of perfection. Although these insights derived from Science they were religious in nature.

God’s Perfect Order must be Simple

Further if the Order was Perfect it must be simple – for Order is never complex - as the more complex a system becomes it becomes the greater the potential for disorder more elements to go wrong. “Keep it simple, stupid,” is a modern expression that reflects the sentiment.

Simple Order is Stable and Durable

If Order is simple it is also more stable as well. And stability is linked with durability as well – fewer things to go wrong. So as the world has been around a long time it must have stable, durable, simple systems. This had already been reflected in the political world in the succession of leaders. In the early days of the Rome the strongest general became the leader. This led to constant civil wars, which led to devastation and internal weakness due to competing claims to the crown. Due to its relative simplicity dynastic succession was chosen as a partial solution to the problem of succession in both China and Europe. To ensure social stability and hence survival the powerful generals would frequently support a child or even a baby who had the proper blood line as the successor to the Crown or Throne. The dynastic system was simplified even further to primogeniture – where the oldest becomes king – deflecting the problem of competing siblings. These social solutions just reflected the notion that simple is more stable and hence more durable. If society, why not God and his Natural Order.

Simple Systems Energy Efficient leading to Conservation

Another feature of simple systems is that they are energy efficient as well – fewer moving parts to cause wear and tear, so to speak. The complicated invention frequently breaks down and is hard to replicate, while the simple invention is easier to fix and is easier to replicate. As an example: the electric car was thwarted due to its simplicity and hence efficiency - not enough things to go wrong – potentially putting the lucrative car parts business and repair shops out of business. It’s easy to see that 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 conservation.

Simple Systems more usable, comprehensible, and memorable

Those are inherent reasons that Nature would be Simple, hence Orderly – leading to efficiency and stability – which in turn lead to conservation of energy and durability – all features of long term of permanent systems. Utility is another reason Scientists prefer simple systems. A simple formula is more usable, comprehensible, and memorable. Even the simplest of us can memorize Einstein’s famous equation – without even knowing what it means. Beginning Engineering students mindlessly plug numbers into equations coming up with correct results without even understanding the underlying process.

Elegant Simplicity a feature of many foundational Scientific Formulas

The above advantages of Elegant Simplicity are based in reason and utility. But these are not determining factors. As much as we hope for simplicity, some things are confused, disorderly and complex whether we like it or not. Sometimes this has to do with lack of understanding. Other times this is just the way it is. However the great miracle of Science is that Scientists have discovered elegantly simple equations – with an incredible aesthetic component – that accurately describe Nature’s processes – further confirming 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 a joke passed among engineers is that 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).

BD's Fractal Regeneration Equation epitomizes Elegant Simplicity

Note that the final entry in the list was Behavior, as in the Information Dynamics of Life. The Fractal Regeneration Equation – the Cell for the system – is simplicity itself – only 3 components and no processes more complex than addition, multiplication and division. However as the other equations are intended to describe the behavior of matter they are static in nature. In contrast the Fractal Regeneration Equation is context based and self-reflective just like Life.

Parallels between the Copernican System & Information Dynamics

Overall System of Information Dynamics Beautiful

There are many parallels between the Copernican System and Information Dynamics. stands in similar relation to the current study of behavior, as did the Copernican scheme to the Ptolemaic system. Although the prior systems in both cases have a relatively high level of accuracy, both are incredibly complicated – very little integration – which means they are lacking in the feature of elegant simplicity – Beauty. In contrast while lacking in experimental verification the two revolutionary systems are the epitome of elegant simplicity.

General Public can understand Solar System and Insights of BD

While the general public can easily understand planets revolving around the sun, they had an impossible time grasping the Ptolemaic system of epicycles and such. Similarly while the general public can and has easily grasped the concepts underlying Information Dynamics – even offering insightful corollary insights based upon the concepts – few except the professionals understand or care about the subtleties and refinements of the current theories of behavior. We are grateful to Dr. John Medina for providing a glimpse into the discoveries of modern Science into behavior with his book brain rules. However the insights only apply to fundamental, yet mundane, levels of existence – those relating to business and education. Nothing to do with Art, Love or Inspiration.

As exhibited the systems of Copernicus and BD are both based in elegant simplicity As such they are easy to understand and apply by the general public. There are other parallels as well. If interested read on.

The Formula comes before the Data?

Sometimes, as in the case of Galileo, Newton, and Kepler, the Data leads to the Mathematical Formula. Other times, as in the case of Copernicus and Information Dynamics the formula comes first. This has to do with the function of ‘normal science’, which is the refinement and verification of the paradigm relevant to the field. A new or shifted paradigm is introduced – because it feels right, both aesthetically and logically, converts to the construct, perhaps of a new field, attempt to validate the insights through experimentation – which yields data and theory refinement – which leads to new formulas to fit the new improved Data.

Introductory paradigm experience based?

In contrast the introductory paradigm, which introduces a new Science or shifts the attention of an old Science, might not be based upon data at all or may even be less precise than the old paradigm (the correlation between data and formula might be even less for the new than for the old). What is the advantage of the new paradigm if it doesn’t provide for greater accuracy? It provides a mathematical handle for making predictions. Without the formula the data is worthless and vice versa.

With Mathematical Handle Experience leads to Quantifiable Data

However there are two types of Data – numerical and experiential. The first is the ultimate goal, but the second is frequently the root of the first. For instance everyone has had the experience of falling objects – but until Galileo’s data-yielding experiments inspired Newton’s formulas no one had a mathematical handle with which to grasp the data. Similarly the Experiences of Interruption, the Zone, Creativity, Inspiration, and Mob Behavior are ubiquitous, and yet unexplained. It’s not that these experiences were uninteresting to scientists; only that there were no mathematical handles with which to deal with the Data or generate new testable Data that were features of these experiences. Information Dynamics provides these handles – but no experiments.

Looking for Real Scientists to test the Formulas

As such the intent of these many pages on the scientific basis of BD is to acquire converts from the set of real scientists who would test the validity of the many hypotheses through experimentation and the consolidation of interdisciplinary research. As an untrained laborer this humble waiter has none of the tools requisite for this requirement. As such he is not a real scientist. His primary calling was to take the path of Outsider in order to see outside the Box.

Paradigm of time period frustrates Copernicus & Outsider

Like Copernicus he was frustrated with the scientific paradigm of his day for 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, Learning, Attention and so forth – in short the Realm of Academia and Business. It had very little to nothing to do with the Realm of the Artist – the refined cultural experiences of Art, Music, Literature, or History.

A dropout from academia’s normal science due to Rat Studies

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 in humankind.

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 – nowhere else anyone would want to be.

Summary of Parallels between Copernicus and BD

Both the Copernican system and that of BD are based in elegant simplicity, whose results and insights are easy to understand. Further a conceptual model initiated both disciplines rather than anomalies in data. Finally both founders were frustrated with the state of affairs in their respective eras – unwilling to accept the popular and professional paradigms – because they just didn’t seem right.

If you are interested in how Copernicus’ converts created Science to validate his elegant, yet imprecise, system, read on.

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