Is it possible that the scientific revolution of Copernicus, Galileo, Kepler and Newton has evolved into a condition where abstract cause and effect reasoning now prevents human beings from relating morally to the climate crisis? In a cosmos of immense spaces where the Earth is just another object is it possible that contemporary has sown the seeds of inertia in humans regarding climate issues? Does the sheer enormity of abstracted information around humans today divorce them from the intimate contact with nature that would enable them to include the earth in a more intimate way in their daily lives? Does this estrangement from the rhythms of nature absolve humans from the moral decisions needed to solve the climate crisis?

Obviously this list could go on but are the climate crisis, political crisis, environmental crisis, and social crisis that are presently deepening in an alarming way simply mistakes or is there something deeper behind them for humans to consider? A final question could be posited. Are these tendencies unique to our age or is there some historic precedent?

Even into the most ancient times when science, art and religion were much closer in their intent there were two fundamental poles in the way that human beings interacted with the great mystery of the earth. In the ancient world astronomy, architecture and the forming of calendars were the marks of how the people lived on the earth as a culture beyond just hunting and gathering. The Egyptians were pragmatic in their problem solving using geometry to build their buildings and employing phenomenological astronomy to produce calendars. But the Egyptians had only rudimentary arithmetic. The Babylonians developed place value arithmetic to a high order that resulted in accurate astronomical tables for predicting eclipses and complex calendars and counting systems but their knowledge of geometry was undeveloped.

The differences between these two civilizations reveal the possible fundamental polarities in the contemporary process of mathematical scientific inquiry, those being geometry and arithmetic. In some ancient societies geometry was more symbolic and metaphysical while arithmetic was practical and effective. This polarity reflected the world view of the culture in which it was found. This polarity can even be seen within one culture. For instance, in Greek times the earlier Platonic world view of archetypes and a geometrizing universe gave way to the more pragmatic and logical Aristotelian view of numerical categories and abstract reasoning.

Antikythera mechanism

Sometimes the two streams came together and a kind of hybrid vigor was the result. Such a vigorous coming together is pictured in figure 1. This device is known to scholars as the Antikythera mechanism. It was discovered in the remains of a Roman ship and has been dated at 100BC. It contained 37 separate gears that allowed the seaman to reckon the date, including leap years, and the position of the moon and planets against the Zodiac. It could also predict eclipses and the Saros period for families of eclipses. The Saros cycle predicts that a similarly positioned eclipse will take place after a cycle of 223 lunar months. The device also carries out subtractions, multiplications and divisions.

In one elegant mechanism the star groups of the Zodiac and the planets moving against them in geometrical, proportional relationships are linked to the abstract demands of computation. Here the polarities of the more Platonic view that the planets are the homes of the gods are linked to the more empirical Aristotelian view that planets are calculable entities. These poles are brought together in a celestial computer, all before the time of Christ. The geometry of the ratios and proportions of the mechanism duplicated the phenomena that could be seen with the naked eye, the motions of the planets in front of the fixed stars. The computational capabilities of the device supported the more abstract calendrical and arithmetical functions.

The incredible wedding of practicality, knowledge and technical ability found in the Antikythera device became the total focus of the next wave of culture when Roman engineers, and architects made it possible for the Roman War machine to flourish. Geometry and along with it the symbolic sacredness of metaphysics was essentially lost to the Romans in favor of computation.

The Arabs of the post Roman era brought Hindu and Greek scholars to Arabia where great centers of science, literature, religion and philosophy were established. Especially in the realm of science, the most characteristic energies of the period can be seen. A tremendous outpouring of science that formalized algebra, algorithms, negative numbers, arithmetic progressions and geometries that prefigured Fibonacci and the use of geometric progressions arose in a relatively short period.

But in this flowering a definite separation of the mathematics of the ancient world and the mathematics of the new world was begun, especially in the realm of astronomy. The computational inheritance that inspired the Arabian schools favored abstraction and arithmetical computation as the primary method of science. Geometry was only seen useful in the realm of geometers. The early and late Medieval times in Europe continued the split between the more metaphysical and geometrical Platonists and the rational, categorizing Aristotelians right up into the time of the Renaissance and beyond.

Kepler

The contrast between the geometrical / metaphysical pole found in the work of Kepler and the emergence of the computational mathematical brilliance of Isaac Newton illustrates this ongoing split perfectly. Kepler was a highly skilled mathematician who could calculate orbital periods in degrees, minutes and arc seconds in his head. However the bulk of his output is in a dense and intricate geometrical reasoning style. His work was deeply geometrical and driven by a search for harmony of the spheres as a kind of religious fervor. The Kepler boyhood home in the town square of a small village outside of Stuttgart stands literally in the shadow of the church that dominates the square. The intricate geometric reasoning coupled with sacredness of mystical experience of the harmony of the spheres that Kepler brought from the ancient world, had to be met the precise phenomenal observations of Tycho Brahe. Without these pragmatic observations Kepler would not have been able to make his breakthrough. The qualities of religious feeling and profound geometrical capacities that would have endeared Kepler to the ancient world are the exact qualities that have caused some contemporary scholars to diminish his contribution to contemporary science. It has been said that Kepler found the three laws of the orbits of planets in spite of himself.

Newton

It would be tempting to think that Newton was the epitome of the other pole, the rational, calculating hard nosed pragmatic genius. While it is true that Newton’s work marked a threshold from Medieval geometric, symbolic reasoning into the mechanistic and technological present he himself was not so convinced that this was the best fit for his insights. “I likewise call attractions and impulses, in [a certain] sense, accelerative, and motive; and use the words attraction, impulse, or propensity of any sort towards a centre, promiscuously, and indifferently, one for another; considering those forces not physically, but mathematically: wherefore the reader is not to imagine that by those words I anywhere take upon me to define the kind, or the manner of any action, the CAUSES or the PHYSICAL REASON thereof, or that I attribute forces, in a true and physical sense, to certain centres (which are only mathematical points); when at any time I happen to speak of centres as attracting, or as endued with attractive powers.” (Principia, Definition VIII)

Here, in his own words, the champion of the cause and effect physicality that drives physics research in the realm of technology denies that the mathematical reasoning he is discovering has a relation to the physics that it spawned. The renowned Newton scholar, Professor E.A.Burtt described this dilemma being faced by the giants of the scientific revolution by saying that. “To get ahead confidently with their revolutionary achievements, they had to attribute absolute reality and independence to those entities in terms of which they were attempting to reduce the world. This once done, all the other features of their cosmology followed as naturally as you please. It has, no doubt, been worth the metaphysical barbarism (author’s italics) of a few centuries to possess modern science. Why did none of them see the tremendous difficulties involved? Here, too, in the light of our study, can there be any doubt of the central reason? These founders of the philosophy of science were absorbed in the mathematical study of nature.”

Why would this in itself be the source of “metaphysical barbarism”? Wasn’t the study of nature from a mathematical point of view present since the very beginning of history? But we need to be particularly careful here. Since the transformation of Hindu and Greek mathematics and astronomy into Arabia a new impulse had entered the use of mathematics. That impulse was the tendency to link earthly phenomena, like the path and velocity of a falling body to the path and velocity of a celestial body, through an extrapolation based on mathematical calculation. Of course this is what we just heard Newton deny that he was doing. But it is just what posterity has taken up from his work as his signature contribution. What this says is that everywhere the prime mover is just the forces and masses of mathematically arranged elements.

This categorizes our earth as a numerical rock permeated by forces completely beyond the control of, and sometimes at direct odds with, the causal activity of human beings. This is in a whole other universe from the experience that the earth is our mother that is linked to us through the common consciousness of shared forces. It opens the door to the experience that the cosmos is an ever expanding alien dimension of terrible forces ruled by intractable mathematical laws.

It also instigates a human will to power to solve the mysteries of those terrible forces and control and subdue the forces of the earth before they control us. In this shift of consciousness the mother has somehow become the enemy.