Beyond reason in creation and in redemption

I am thankful for fellow blogger Clyde Herrin for two reasons. First, he has been kind enough to repost several of my recent posts on his blog, thus expanding my potential audience. Second, he has given me food for thought in his comment on my recent “Summer Solstice” post. You may recall that I suggested that an Obsessive-Compulsive Creator would have given us thirty-day months and a 360-day year, allowing day and month and year to match mathematically. Clyde suggested that, in the beginning, the solar system operated in sync according to simple math, but that sin and the consequences of sin threw the system into a more chaotic set of relationships. He pointed me to a post of his ten years ago (which I had already read and liked some time in the past) in which he suggests that the turmoil of the Flood threw the earth’s day off from its previous length by about twenty-one minutes, resulting in the mismatch of days to years that complicates our calendars today.

I replied to Clyde that, in my opinion, God delights in complexity within creation and does not limit himself to simple relations. I mentioned complexity in biology and in subatomic physics, and I then offered the thought that God purposely put the sun, moon, and planets (including our earth) into a complex dance that does not simplify to easy mathematics. Continuing to ponder the possibilities after posting that comment, I have arrived at even more evidence that the patterns in our solar system are intended to be complex.

The evidence has been known for a very long time. Two thousand years ago, Greek mathematicians used geometry to study the world and even to comprehend complex ideas in number theory. Reality frustrated these mathematical geniuses. They wanted every number in the universe to be a fraction, a ratio, a balance of two other numbers. But these students of nature discovered that the relationship of the diameter of a circle to its circumference is not a rational number. It cannot be expressed as a fraction of two other numbers. That relationship of the trip around a circle to a trip across a circle is called “pi,” a number about (but not exactly) one-seventh more than three. Likewise, the relationship of the diagonal of a square to the side of a square is another irrational number, which happens to be the square root of two. Every square in the world, no matter how big or how small, has the same relationship of diagonal to side, and the number that describes that relationship is never a fraction or ratio of two other numbers.

It is no coincidence that we call those numbers irrational. Not only are “pi” and “the square root of two” not expressed by fractions, or ratios of two numbers; they also do not make sense to people who want mathematical simplicity in their world. It seems that God delights in complexity and does not settle for simple relationships in his creation. For people like Clyde and me, who believe in an Almighty God who created heaven and earth and all that exists, that raises interesting questions. Is the Almighty God limited by rules of geometry, so that circles and squares could not exist apart from the irrational numbers that describe them? Or could God have created a world with different mathematical rules and different geometric proportions, a world that was fully rational even to ancient Greeks who studied the world and the things it contains?

Such questions go beyond science and mathematics and geometry. Identical questions can be raised about ethics. Is the Almighty God answerable to rules about good and evil, or does he get to write all the rules? Those who call Him Almighty define “good” as “whatever God likes” and “evil” as “whatever God does not like.” Our debates about good and evil, then, come down to God’s statements to us about what he likes and what he hates, the behavior of which he approves and the behavior of which he disapproves. Yet some people feel qualified to judge God, to apply their own rules to the Creator and decide whether he meets with their approval. To such people, God speaks as he spoke to Job: “Where were you when I created the world?”

Imagining a world with different rules for mathematics and geometry goes beyond our comprehension. Imagining a world with different rules for right and wrong goes beyond our imagination. God, at his essence, is love; for love flows among the Persons of the Father and the Son and the Holy Spirit. We are created in God’s image. The most important commandments God gave us are that we love him and that we love one another. God’s other commandments teach us how to love. Sometimes, what seems loving to us attacks others and harms others rather than truly loving them. God’s love sometimes is “tough love,” discouraging us from harmful behavior we might characterize as love and guiding us into true love for God and for one another.

But, because God is love, he also rescues us from the consequences of disobeying his rules. We cannot disobey some rules: we cannot defy gravity, and we cannot cause the relationship of the diagonal of a square to its side to become a rational number. In cases where we have broken God’s commandments telling us how to love, God rescues us from the consequences of our failure. Jesus, on the cross, bore the burden for our sins to reconcile us to God. Jesus defeated our enemies—even our own sins—and shares his victory with us. In a sense, God breaks the rules of justice, of power and authority, to establish grace and mercy and peace in our lives.

And he supports that message about his love and his grace by leaving in his creation other mysteries that defy reason and logic and the way we would do things—including quantum mechanics, including irrational numbers, and including the complex dance of the sun, the moon, and the planets. J.

Let’s get small, part three

Some of the earliest philosopher/scientists taught that material objects—whether solid, liquid, or gas—are made of atoms. By “atoms,” they meant tiny pieces that could not be divided into smaller pieces Over time, philosopher/scientists convinced themselves that four kinds of atoms exist: water, earth, fire, and air.  For centuries, they conducted chemical experiments based on the assumption that all materials in the world are built from those four kinds of atoms.

Today we teach that water is not an element. Water consists of two elements—hydrogen and oxygen. The hydrogen atom is the simplest of all atoms, containing one proton as its nucleus and one electron somehow related to the nucleus. Oxygen is more complicated. Oxygen has eight protons in its nucleus, as well as eight neutrons (in the most common form of oxygen—other forms, called isotopes, also exist). Oxygen also has eight electrons. When a molecule of water forms, each of the atoms of hydrogen “shares” its electron with the oxygen atom, linking the three atoms into one molecule. And these molecules are so tiny that a huge number of them must be in the same place for them to behave with the properties our senses detect as water.

If the tiny world of molecules and atoms were that simple, scientists and philosophers would be delighted. Further experiments in modern times, though, have shown that the atoms are not unbreakable—they consist of even smaller parts. (One physicist commented on continuing discoveries of subatomic particles by saying that it seems as if God is making up new complications as quickly as researchers unravel the previous complications.) Electrons, for example, are so tiny that they cannot be measured—estimates of the size of an electron vary wildly. This difficulty comes from the apparent fact that electrons are not tiny particles, specks of something solid, but instead are packets of energy. An electrician designs devices that rely on electricity, treating the moving electrons as “currents” as if they flowed like water in a stream. But individual electrons jump around like nothing we experience in our regular lives as larger creatures.

In that difference, electrons resemble photons. Photons are also packets of energy that act like tiny particles in some ways, but they also travel as waves of energy—sometimes as visible light, sometimes as radio waves, X-rays, or other frequencies. Electrons of photons do not follow the rules of physics that were used from the time of Isaac Newton to the time of Albert Einstein. Nor do they seem to exist in the kind of geometric space that has been used since the time of Euclid. Euclid’s geometry and Newton’s physics are not wrong. They merely are unable to describe realities for very tiny things (and also for very big things). Because of our experiences with objects that are neither very tiny nor very big, we tend to think in terms of Euclid’s geometry and Newton’s physics. We imagine the entire universe existing an infinite distance in every dimension—up and down, back and forth, right and left. We imagine time also existing an infinite distance into the past and into the future. Both time and space are more flexible than we generally imagine—which is why Einstein’s theories of relativity are difficult for our minds to grasp. But for the Christian, who describes time and space as created by a God who transcends both time and space, the flexibility of those creations should not be a great surprise.

In a molecule of water, then, we have ten protons and ten electrons and eight neutrons. Beyond that, each proton and each neutron are made of three quarks. Each electron has a negative charge equal to one, and each proton has a positive charge equal to one, but quarks have fractional charges which provide the sum charge of a proton as positive one and the sum charge of a neutron as zero. Although six kinds of quarks exist, only two are commonly found in atoms—two up quarks and a down quark in each proton, and two down quarks and an up quark in each neutron. So a molecule of water consists of sixty-four very tiny mysterious pieces, each of which is as much energy as it is matter—plus some particles called gluons that hold the quarks together in their protons and neutrons.

Immanuel Kant would be pleased to know that today’s scientists describe reality at the tiny level as completely unlike what we experience in our everyday world. Kant insisted that the phenomena we observe are very different than the noumena that really exist and that cause us to observe things. Time and space are nothing like what we generally consider them to be. This comment allows us to transition to consideration of the nature of time—what time really is, and how it relates to the lives that we live. J.