The Heavens declare the glory of God and the skies showeth his handiwork (Psalm 19:1)
When we step outside the walls of a school, when we walk about in a park, when we look up at the sky, as we are about to, we observe. We take in and experience the world.
And we all know that there is something different about this experience than the one we have inside the classroom. In the classroom, you learn your Latin, such as audere est facere; or in umbra, igitur, pugnabimus.
In the walls of a school, you learn the history of things that happened many hundreds of years ago. And In these walls you learn your algebra, your trigonometry, your maths as the British say.
It is partly about math that I am gong to speak. Because surprisingly enough math, like many of the other things you study has a way of making its way outside these walls. This is because math began outside of them.
It does so because you have a soul and that soul by which you learn and is the same soul which experiences the world of nature. Wherever you go, there inside you exists the whole universe of your knowledge and experience–a cosmos.
And so it happens from time to time that something you have experienced at home or in the world suddenly makes sense because of something you learn here…and of course vice versa, what you have experienced outside these walls gives meaning to your daily lessons. This all happens so naturally that you are usually not even aware of it, and are even bored of this fact.
I would like to show one remarkable way that the class room and the world coincide. Or more precisely, the manner in which the mind and its ways of thinking come to think about or know the World better because it has learned something abstract in the classroom, that, we have all learned how to count.
Counting
If I were to tell you that we were going to a hike a very lovely trail in the Adirondacks, that is upstate New York where I am from, you would probably not pack your math textbook. Nor would you need to. You might keep in mind the number three however before you rolled around in any Ivy we might encounter. That is the ordinary way that number helps us. “That plant has three leaves, be careful.” We identify it partly by number and geometry.
But there is a more special way that number helps us, in that it can actually show us what is in itself not visible or knowable otherwise.
Thousands of years ago, as early as early as the Babylonians, people made very precise observations of the skies. They noticed that the year took approximately 365 days…remarkably close to the Babylonian 360 degrees we designate the circle by!
They also saw that it was not precisely 365 days, but that the seasons and the annual position of the sun shifted a bit over the course of years. One could only notice this if one is counting, counting both the days which have passed and comparing the passage of days to the position of the sun & stars on the horizon to its position one year ago.
To simplify the story, people noticed that the seasons were not divided up evenly, say into 4 sets of 91 days. Instead, winter had about 89 days and summer had 93.
Imagine the many years it took to get an accurate picture of all this and the careful observation that was necessary! Never believe those who tell you that the ancients, the Babylonians, the Greeks, etc. merely made up theories and forced the universe to fit into them.
This oddity of the length of the seasons is called the solar anomaly. It was very disturbing especially to the Greeks. If one watches the motion of the stars over a period of seasons, one has the distinct impression that things are moving in circles. One is right to have this impression!
But if the heavens are moving in circles, why would it appear that the sun slows down or speeds up?
Hipparchus, one of the great mathematicians and astronomers, a founding father of Trigonometry, proposed that while the heavens moved in circular orbits or spheres. The earth was not the center. Or rather, the earth was the off-center center of the universe.
By placing the dot, the middle of the circle a bit out of center, it meant that the sun continued to move in a perfectly circular orbit, while we on earth experienced it speeding up or slowing down depending on whether it was closer or further from us in its orbit.
Let me draw your attention to a simple fact–this idea that the sun was speeding up or slowing down, the fact that there was a regular annual motion but also one which had this weird speed irregularity–none of this can be seen with your eyes, no matter how hard or long you look.
It is math, the most basic of math, counting, which revealed these weird changes amid the regular cycle of the sun. There is more complicated math and instruments needed to measure the position of the sun. But to grasp that it seems to slow down or speed up is simply a matter of counting once the data is gathered.
Without counting, we would never have known this about the orbit of the sun, nor would we ever have learned what we did a thousand years later when Copernicus, Galileo, Kepler, and others came on the scene.
What did we learn?
Kepler followed after Copernicus and Galileo and accepted a heliocentric universe in which the earth, not the sun moved. But this did not do away with the solar anomaly, the problem of the seasons. That the earth was apparently slowing down or speeding up was no better than that the sun did so.
A new model was proposed, a rather radical one, based in part on what Kepler referred to as a kind of magnetism, but which via Newton we now refer to as the force of gravity. Kepler proposed that orbit is not circular but elliptical, and that depending whether the earth is near or far from the sun its speed changes.
It is perhaps this story which discredits Ancient Greek science most of all. Those foolish Greeks had insisted on circular orbits. If they had not, if they had stuck to observations these mistakes would not have been made, we are told.
But this is precisely the point of this lecture. Nobody has ever observed elliptical orbits. There is not some illuminated galactic highway through which the earth makes its annual journey, and certainly no one has ever stood out in space observing this motion for a year.
We have since proved the elliptical orbit by technical-instrumental observation whose details I will not bore you with.
But more important are these facts: First, only the intersection of an aspect of human rationality, that is math, and that of observation brought about an awareness of this problem in the first place.
Second, by all intents and purposes, the observable experience of the motion of the sun suggests that it moves in a circle. We experience the returning seasons, years, and if we are watchers of the skies, we experience their movements as circular. Nobody feels or sees or notice something elliptical in the skies.
Finally, Kepler’s circular revolution, having done away with perfect circular orbits, having corrected those Greeks, having shown the slingshot speeding up and slowing down of earth, has yet left us with something that has enormous continuity with the original story.
In fact, if we were to draw the ellipse which represents the earths orbit, you might be surprised. The ellipse is often pictured in the outline of an egg shape to make clear that it is not a circle, but an ellipse has a range between perfect circularity and a straight line. The eccentricity of the earths orbit varies from 0.0034 to almost 0.058. What does that mean? It means that if I were to draw such an orbit for you, you would probably not be able to recognize with your eyes that it was not a perfect circle.
We are left with the remarkable experience of having ended where we begun. And this remarkable journey was possible only because of this weird thing we do called counting.
The not out-there stuff we do, the mental thing, made it possible to learn about out-there things such as the ongoing cycle of heavenly motion and even its irregularities. But having followed this journey thus far, we end up somewhere closer to our ancient predecessors than many realize or care to admit. We end up staring into the skies and seeing something like the precision of circles drawn with the compass, and yet we also know there is more to the story. But remember, it is more not less, it is a deepening or development of the story, not some wholly other cosmos we inhabit.
On the New Geometry
I would like to conclude with some thoughts on today’s remarkable event, a total solar eclipse.
We stand ready to view today’s eclipse because we stand within several millennia of scientific tradition. If we do not quake, as we hear our ancestors supposedly once did, it is because of this fact. But perhaps, when we do step outside to see this eclipse something in us may quake…and perhaps it should.
For what does it portend?
An eclipse from the human point of view cannot simply be considered part of the ordinary course of the heavens. We experience it as a disturbance. It is not unusual for for someone to experience such an event but one in a life time. It is in truth an interruption, this blotting out of the sun which has illuminated every single one of the days of our life without fail.
The very regularity of life, of seasons, and of time, all which we have come to unconsciously depend upon is here brought to our consciousness and marked as something which is not quite so dependable as it seems. We are made conscious that the order we rest in can be disturbed, perhaps even brought to an end.
The days and seasons mark something of the eternity of an everlasting circle, an image of our security, and that all will be upheld. It is an order which means life to us, one which gives us place and peace.
But in coming to depend upon this order in such an unthinking, unconscious way, are we not perhaps a bit like the Ancient Greeks whom we are told placed to much confidence in the perfection of circles?
Do we not tremble, even a little bit today in this upsetting of the regular. Despite the predictive power of science, when experience such an event for ourselves, existentially, bodily, we suddenly feel the heavens are a bit stranger than we realized, perhaps, a bit more dangerous. The heavens and its patterns are not eternal, we suddenly realize!
Today does indeed mark a break with order, even if this break signifies a yet greater order, a yet more terrible course or circle which the cosmos runs and signifies.
An eclipse, as ancient and modern science teaches, is part of the regular cycle of heavenly motion, and so it marks a kind of return, though on the individual human scale it does this in no easy manner. But what kind of return does the darkening of the day, the overshadowing of the sun mark? What does it signify. At first glance, it signifies an end, even doom and disorder. But let us take a larger view. Or let us look at it from the point of view of the person and what the person is both universally and historically.
The soul, each individual, is on a journey, a pilgrimage. And this pilgrimage seems to end in death. Therefore, for the majority of human history, the life of man can be symbolically described by the geometry of a finite line.
It was not always so. There was once the mysterious form of existence we enjoyed in Eden which had something of the shape of the infinite. But since that time, all life has been marked by two points, a beginning and an end, birth and death.
Despite this fact, not all people have accepted this geometry as definitive of our condition. Not everyone has understood human life to be characterized ultimately by death. This is true of many religions of the past, and especially true of our own. T.S. Eliot in his Four Quartets wrote:
We shall not cease from exploration, and the end of all our exploring will be to arrive where we started and know the place for the first time.
He did not think the soul’s journey ended in death, but in homecoming, as an odyssey.
That the journey of the year is a circle, itself suggests unending motion, the perfection of eternity. A circle has no beginning and no end, perfectly whole and present at each moment. But an eclipse is an interruption, a seeming break in this perfection. An eclipse is a brief overshadowing or threat to the eternity of cosmic motion.
What if I were to compare our life in heaven to a perfect circle, a life in which we shall eternally share in God’s glory? What would death be? Death would only be that momentary eclipse, that brief overshadowing of the sacred order, but one ultimately dwarfed by eternity. The grave is then but a passing reality–a finite point on an infinite line–a point which has no part, as Euclid explains.
“But death is different!” We might object. People do not get up and resume their orbit, so to speak, after death. The sun shines again, but we stay dead.
From the standpoint of faith, it is easy to dismiss this plaintive argument. If not for God, we must remember, the circle would indeed remain broken, our orbit shattered, the eclipse of the grave, eternal…life, a finite line.
But Love who ordered the heavens, who planned eclipses, who himself was eclipsed would not have it so.
Let me digress. This is where Love and science (reason/logos) meet.
Science, which we have been speaking of today is based upon our recognition of order, it is based upon our faith that this universe is not truly ruled by death, chance, or even despair. In the idea of science, although many modern scientists are unaware, is faith that there are laws, rules, patterns everywhere. Science is secretly conducted in the hope of reason, and reason is secretly the pattern and wisdom of love. Every true scientist therefore seeks to encounter the mystery of eternal love, though he or she may not know it.
Our universe is an embodiment of love–that ordered bond which holds all things together. Science implicitly believes in this Love which sets all things in motion. I borrow here from Dante.
At any good liberal arts school, we seek to remind ourselves of this fact, that all truth is a sign and promise. The fact that the universe exists as a rational pattern, as an ordered-reality under law, is a sign not only that we are created by Love but ordered unto that Love.
So in science, when we seek to uncover laws, rules, processes and patterns, what we are really doing is saying, “show me yet another sign of your Love, O God, another imprint of your hand… Show me how you uphold the whole order of things, things infinity small and unimaginably big, how each being, great and small exhibits the order in which it you fashioned and uphold it.”
It is not always easy to see this about the world or about ourselves, that we are each and all together God’s, ordered and upheld by him. But one day, we shall look not out into the world but into the very face of its Creator, and we will know not by faith, but by sight how every moment of our lives and those of our fellows was ordered around an unfailing love, the very love which sets the heavens in motion.
Just as the heavens and its motions are hidden from us at first glance, but only discovered after years, no, centuries of study, so too shall the history of man, each one of us and our whole species, be revealed in that time.
Yet it already has been revealed, if only by faith. What do I mean? Let me finish saying this:
It has been revealed in Christ. Christ’s whole being orbited around the father, and yet, when he became man he limited his existence to the finite line we spoke of. Even more than the movement of the heavens, the geometry of Christ’s life reveals God’s unique handiwork.
When the circle of communion had been broken, that is when death had separated man from Eternity, Christ established a new geometry by entering into our story, by taking on in himself a beginning and an end.
This new geometry was first initiated by the Infinite One circumscribing himself to the finite line which ends in death. But in doing so, he printed upon finitude something wholly new.
The new geometry took the figure of the line, the line which led to death and to hell, and added a second line of intersection, a horizontal axis. The geometry of the cross was thus initiated, and somehow, enigmatically, the cross represents the restoration of a circle, for it brought closure to that which had been broken. What had been a period or conclusion in the eclipse of death is now but a beginning, a point upon a circle made perfect through faith. One can indeed describe a sphere by two intersecting lines folding upon themselves chiastically, which is exactly what Plato does in his Timaeus.
The geometry of the cross restored the old geometry of the first creation, and what is more, brought something of the eternal geometry of God himself into this world.
In the institution of this new order, the geometry of the cross, the old order was not rejected but exalted, even as it did homage to the new.
The heavens themselves were humbled and did homage when the lesser sun, that is the sun which passes us overhead each day, was itself overshadowed. When Christ hung there and breathed out his last, the heavenly sun showed itself not, signifying the terrible nature of the new order which was being instituted. The sun in the sky which provides light each day could not help but admit that the true Light of the world, which the world knew not was undergoing death.
The sun in the visible heavens was darkened when the Sun of God allowed his own life to be eclipsed upon the cross. But in this eclipse, in this doom, a new motion, a new energy and direction, an unhoped for hope and possibility entered into the creation.
Darkness itself was transmuted and made part of the circle, caught up in the mysterious work and pattern of love.
Darkness and death, two of the mysteries of our existence became now mysteries of the resurrection and of salvation. The very meaning of finitude, of beginning and end, was transformed on the cross in the flesh of Christ.
And so what we see today is a reminder, not only of the strange order of the nature world, the regularity, and yes, the rationality of creation, but also a reminder that there is no aspect of this creation which is untethered from that more wonderful and terrible knowledge—that knowledge of the divine pattern of salvation and resurrection–a plan which can never be eclipsed (for it accomplishes its work in the shade/umbra).
Love who sets the heavens in motion yet moved himself for us in ways unthinkable that he might establish this new geometry.
Human science and the created order pale before this science or knowledge of God, a God who in all his wisdom and mercy foreordained that the creation would be a witness not only to his power, but his humility. He foreordained that the circular motion of the heavens would itself pay homage to the new geometry of the cross, in which death, disorder, and doom are transmuted into the promise of life.
Same & Other 