Change and continuity

Human understanding of light has wavered over the centuries. Some famous philosopher/scientists, including Rene Descartes, insisted that light consists of waves; others, including Isaac Newton were convinced that light consists of particles. In the twentieth and twenty-first centuries, most scientists who deal with the physics of light acknowledge that light is both wave and particle. The particles, called photons, also have wave-like qualities. Moreover, electrons also possess the same paradoxical wave-particle duality. Even protons and neutrons, consisting of quarks, appear to have wave-particle duality. Therefore, everything in the material world rests upon the paradox that the component parts of every item are, at the same time, tiny particles of matter and also waves of energy.

One result of this paradox is that knowledge is limited about each particle. For example, no one can know the precise position of a particle and also how it is moving. This principle was first enunciated by a scientist named Heisenberg and is called the “Heisenberg uncertainty principle.” One famous scientific joke involves a police officer pulling over a car driven by Dr. Heisenberg. When the officer asks the doctor the standard question, “Sir, do you know how fast you were going?” Dr. Heisenberg replies, “Please don’t tell me, because if you do, I’ll never figure out where I am.”

By the way, there is also a Salvageable uncertainty principle. Ask me what that principle says, and I will answer, “I’m not sure.”

Larger material items, made out of enormous quantities of protons and neutrons and electrons, generally follow rules of geometry and physics that make sense to the average human mind. A police officer’s radar gun accurately measures the speed of a moving car. That car might be shown, by the radar gun, to be traveling seventy miles an hour. That measurement does not prove that an hour ago the car was seventy miles away. Until a few minutes ago, the car might have been sitting in a parking lot only a few miles away. But, for large material objects, we can account for both the speed and the location of that object and can accurately report both statistics at any given moment.

Philosophically, though, the motion of a material object and its location remain a puzzle. Greek philosophers more than twenty-four centuries ago were already asking how any object could move through an infinite number of points in a finite time. Dividing time into an infinite number of punctiliar moments does not solve the philosophical quandary. We can observe an object at rest and can measure its size and describe its location. We can observe an object in motion and determine its speed and direction. Trying to gather all that information at the same time seems as though it should be easy, but problems remain. As we begin measuring size and location and speed in appropriate units, we are forced to make statements that are philosophically untenable. The car that is moving seventy miles an hour does not disappear from the highway this instant and reappear seventy miles away an hour later. Assuming that its speed and direction do not change, it will be present on every bit of paved highway between here and its destination at some point during the next hour. Chopping the highway into miles, feet, inches, or any other unit—while also chopping time into hours, minutes, and seconds, or any other unit—leaves the location of the car between those identified units a mystery. If, for example, we film the car at a rate of twenty-four frames per second, each frame will show the car at a different location on the highway without any explanation of how the car traveled from one point to the next point, since an infinite number of points exists between those two points.

Aside from that problem, the car in each frame of the film is not the same car. The car constantly changes. From instant to instant, it burns a tiny bit of gasoline. Its tires rotate, and tiny bits of rubber from the tires (perhaps mere molecules) separate from the tires. From time to time, dirt and insects are added to the windshield and other parts of the front surface of the car. Take the same car at any two points along its journey and compare its description; one will see that it is not the same car. Tiny changes have occurred to make the car slightly different as it travels down the highway and also travels through time from past into present and on into the future.

We are all like that car. We change continually. None of us is the same person who woke up this morning. We have breathed air in and out of our lungs, and some of that air has been taken into our body to be used by our cells; other air that was in our bodies has left our bodies. We eat, we drink, and we use the bathroom. We wash, removing dead skin cells from the surface of our bodies. Sometimes we cut our hair or trim our nails. Even our minds change as we experience and remember new events every instant of our waking lives (and also while we sleep). You are not the same person you were when you were a child. You are not the same person you were ten years ago. You are not the same person you will be ten years from now.

On an atomic and molecular level, we change constantly. On a cellular level, we change constantly. In other ways, we continually change while we travel the timeline of our lives. Yet, as we view that timeline from outside of time, we also perceive continuity. Because that timeline is unbroken, we are able to describe ourselves as the same person through the years and over the course of a lifetime. In the same way, a car remains the same car in spite of the many changes that happen to it—a new tank of gas, an oil change, new tires, replacement of damaged body parts, replacement of damaged engine parts. Over twenty years, every piece of a car could be replaced, but legally and philosophically it remains the same car. The philosophic implications of continuity as we change are enormous. J.

Picturing our lives as a timeline, a threat or string running through time from beginning to end, makes a lifetime seem something like old-fashioned film, the way movies were created and shown before the digital age. One could hold a reel of film in one’s hands and have the entire experience in one place, but the film on the reel said nothing. The film had to be threaded into a projector and shown on a screen to have meaning. As a motor moved the film through the projector, a flashing light shone through each frame—twenty-four frames per second. Trial and error showed that aspect to be ideal for viewing. Seeing twenty-four images each second, a viewer saw action and motion that seemed normal—they could be filmed by a camera that took twenty-four photographs per second, or they could be a series of drawings or still photographs that were carefully arranged to imitate normal action and motion.

An average human life—we will say seventy-six years—would require many reels of film. One would need enough reels to contain over one million feet of film. Nearly 57 billion frames would need to be shown at twenty-four frames per second to cover those seventy-six years. We can take this metaphor to think about time and about living our lives in time. However, this metaphor has a simple yet important shortcoming. In spite of the successful illusion captured by film shown twenty-four frames per second, time does not move in tiny bursts the way film operates.

If time clicked along at twenty-four units per second, a photon or neutrino (or anything else moving at the speed of light) would jump 7,750 miles between each frame. Science shows no evidence of particles jumping from point to point in space. Particles appear to move at a consistent rate, existing in every inch or centimeter between any two locations. Time, then, must also operate consistently, not jumping from instant to instant with a tiny gap between instants, but flowing effortlessly through every conceivable instant.

Early philosophers questioned the geometry of points and lines and planes and three-dimensional space. If a moving object must pass through an infinite number of points to reach its goal, how can it ever arrive? It must first reach the half-way point, but before getting there it must reach a point half-way there, and on and on cutting the distance in half again and again but still having more intervening points to achieve. Now, it seems, time must do the same. We approach an instant… we reach that instant… we pass that instant… and somehow, that instant has traveled from the future into the past although it was scarcely present at all.

Experience tells us that objects indeed travel through space and through time. The problem of traveling through an infinite number of points in space and an infinite number of instants in time does not bother moving objects in the least. Change, it seems, is a constant reality in our world. But, in a world where everything continually changes, how can we hold to the belief that anything stays the same? If each of us is constantly changing, how can any of us remain the same person throughout a lifetime, or even in the course of one year? J.

Looking at time

Greek mythology described three goddesses called the Moirae, or the Fates. They were responsible for the lifespan of each person. One of the fates spun the thread of life, the second measured the thread, and the third cut it. They decided how long a life would be and how it would end. People who feel helpless about their lives, who feel that everything is decided for them by outside forces, are still called “fatalistic.”

To spin and measure a life and determine its end, the Fates had to work outside the stream of time. They could see every life from beginning to end, being able to measure that life and cut it at the end. More recent writers have also imagined beings that could see human lives outside of time. Kurt Vonnegut, for example, describing beings from another planet who saw time the way we see space. When they looked at one of us, they saw our entire lifespan, from beginning to end. Vonnegut called himself a Free-thinker; he was not a Christian. He found comfort in the thought that every person lasts forever in the universe as a glowing thread that runs through time. That permanent life might exist entirely in the past, but Vonnegut proposed that the past life still exists from some points of view, making that person immortal in one sense of the word.

Vonnegut was not fatalistic, though, about that lifespan. The value of a permanent life, preserved as a thread through time, was found in the choices made by each individual during the duration of that thread of time. If we imagine someone—God, or the Fates, or beings from another planet—seeing our lives from outside of time, knowing what we will do before we do it because they can see it already done, that knowledge does not rob us of our freedom. We make choices, steering our lives through time. We are free, because knowledge of what we will choose is not power that forces us to choose what is already known by someone who exists outside of time.

To be “outside of time” is difficult, if not impossible, for us to imagine. We still think of beings outside of time of having their own timespan while observing our timespan. But, outside of time, before and after do not exist. All events are seen in one gaze or glance. Time, like space, exists insofar as it is measured. We measure a distance between two objects and define that space, whether it is as tiny as the space between an electron and a nucleus in an atom or as large as the observable universe from one end to the other. We measure emptiness or void in space, but we cannot measure the nothing that exists outside of space. Likewise, we measure time between two events, but we cannot measure time outside of events. No time existed before the “Big Bang,” or before God said, “Let there be light.” To ask what existed before the Big Bang or what God was doing before he began to create is nonsense; there is not empty or void time before time begins—there is only nothing.

But, if our lives are viewed from outside of time, the viewer can also see imaginary time. The viewer can see where we would have gone in our lives if we had made different choices. We see the road we traveled in the past; looking right and left, we glimpse other possibilities that we have not visited. The viewer outside of time sees the entire landscape, all the things that could have been in the past and present and future, things that were not and are not and never will be.

Fatalistic people deny that freedom. To them, only the road exists. They might blame God or the Fates for their journey; they might blame their inheritance (coded in their DNA) and the limitations of their situation in life, or the traumas that they endured in childhood. Fatalistic philosophers claim that we have no freedom. Clearly, we exist under many limitations. We must breathe to survive; we must eat and drink; we must rest and exercise. We can be only one place at any given time. We cannot levitate (although we can make machines that lift us into the air and that even fly us from place to place). The Fates, or God, or the laws of the universe place parameters around our existences; but they do not deny us all freedom. If we had no freedom, God would not make commandments telling us what to do and what not to do. If we had no freedom, governments would not make laws and punish people for breaking those laws.

Sometimes people claim to be helpless, unable to stop themselves from sinning or from breaking the government’s laws. They blame their DNA, their childhood, their environment. Their defenders say that people should not be punished for crime; they should be rehabilitated. Jail is for correction, not for revenge. The legal system recognizes a certain level of helplessness called insanity. The insane (according to legal judgment) are not in control and cannot be punished for their crimes. Still, for the protection of society and for their own protection, they must be restrained and kept from breaking more laws.

Debate continues about freedom and predestination. Some believers insist that, because God is Almighty, whatever happens is what God wanted to happen. People who refuse to believe in God are unbelievers because God made them that way. Others say that faith is a choice. God forces no one to believe; his Judgment is based upon the way individual people used their freedom, whether they used it to trust God and follow his plan, or used it to deny God and reject his plan. Yet other believers hold to a paradox called “election.” While people are free, they are unable to come to God under their own power. Without God’s help, they are dead in sin, enemies of God, incapable of coming to him. By his power, God brings the dead to life. He grants saving faith and gives individuals the power to obey his commands, starting with the commandment to believe his promises. Those who are made alive are free; they can remain alive, or they can choose death. But on Judgment Day, all the saved will credit God with their salvation, acknowledging that they could not be God’s people without his help. On Judgment Day, all the lost will accept the blame for their rejection of God. They chose their rebellion; they preferred death to life.

In other matters, though, people are free. The clothes we choose to wear are not predestined by God or by nature and nurture. The acts of kindness we perform or fail to perform—and the acts of cruelty and neglect we perform or choose not to perform—are all free choices we make as we travel our timestream. Sometimes we face big decisions; many other times, paths we might prefer are closed to us. Sometimes the little choices we make change more than we expected. We cannot see the future. We cannot even see the present with all its possibilities. We live in time and we move through time; the flow of time is one dimension of our lives. J.

Philosophy and time

In our every-day world, we experience space as three dimensions—high and low, right and left, thick and thin. Time acts like a fourth dimension. We can go any direction in space—in theory, we can travel an infinite distance in any direction. Time is different—we move only one direction, and we all travel at the same speed as we journey out of the past, through that instant that is the present, and on into the future.

Things are never as simple as they seem. We live on the surface of a sphere, and up and down are defined for us by our relationship to the sphere. If we tunnel down, we might eventually reach the center of the sphere. Traveling further, we would be going up again until we reached the surface of the sphere on the far side. On the other hand, traveling up would send us away from the sphere, but if each of us traveled up away from the sphere, we would all be going different directions away from the sphere, getting farther and farther from one another.

If we travel north or south on the surface of the sphere, we eventually reach a pole. We could go no further north; we could only go south from the North Pole—and the same would be true of the South Pole. East and west, though, are infinite journeys. No matter how far east we travel, more east lies beyond us; no matter how far west we travel, more west lies beyond us. We could circle the Earth many times and still never come to the end of east or of west.

Albert Einstein’s theories of relativity acknowledge the three familiar dimensions of space and the single dimension of time, but Relativity also reveals that all four dimensions change when we deal with the very large, the very small, and the very fast. A traveler moving near the speed of light would experience less time than a similar traveler on the Earth—even if they were born on the same day, after journeying at the speed of light, the first traveler would be younger than the second. Curvature of the fabric of space and time, according to Relativity, account for gravity, which is why during a solar eclipse astronomers can view stars that lie behind the sun. Other strange things happen in space and time according to the theories of relativity—and every test devised to determine whether Relativity is accurate have affirmed Einstein’s theories. For our daily lives, though, the geometry of Euclid and the physical laws of Isaac Newton suffice. Variations from those systems only happen in extreme cases such as galactic events and subatomic physics.

Often we represent time as a line. We mark events on that line, showing which are earlier and which are later. We locate births and deaths on that line to show how long each person has lived. Changes in the universe happen in only one direction and are not easily reversed. If one pours a class of colored water into a tank of clear water, the colored water gradually mixes with the rest of the water until it all has the same hue. This change requires considerable effort to reverse, to remove the color from the water. This tendency of thing to even out over time is called “entropy,” and entropy indicates a direction in time, the direction we all are traveling.

When I was younger, people frequently rode in the back of pick-up trucks. We had no seat belts; our safety depended upon the skill of the driver and upon chance. We accepted the risk, trusting the driver and assuming that nothing would occur that he or she could not handle. Imagine yourself sitting in the back of a truck, looking at the road you have just traveled. You see what is behind you; you cannot see what lies ahead. Some parts of the past journey are clearer than others, just as we remember some past events better than we remember others.

Or do we? Some people claim to remember different time lines—a world where Nelson Mandela died in the 1980s and not 2013, a world in which the children’s authors spelled their name “Berenstein” and not “Berenstain,” a world in which New Zealand is to the west of the Australia and not to the east. Most of us assume that human memory is fallible—that we might misremember facts like those, or lines from a movie or a song, or the appearance of a cartoon character. That does not prevent our minds from pondering what might happen if we could journey off our timelines and explore imaginary time. Sometimes imaginary time is useful. If the dog slipped outdoors when we weren’t looking, it might have run any direction. We consider how much time has passed since the dog escaped and estimate how far it might have gone; that helps us to think of places to search for the missing dog.

Time feels relative. Some minutes drag on at excruciating length while others pass by far too quickly. Some past events feel far more recent than they truly are, while other past events seem far more distant than they really are. The week before Christmas can be far too short with people who need to prepare and far too long for people eagerly anticipating the holiday. We are traveling the same timeline, but we do not experience it in the same way.

But what if we could view our lines in time from an entirely different perspective? 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.

Let’s get small, part two

If you tear a sheet of paper into tiny pieces of paper, you will not be able to determine if you have discovered the smallest possible piece of paper. Therefore, you cannot prove in this way that whether paper is made of nothing but paper. Remember: there are three possibilities: every piece of paper might be divisible into smaller pieces of paper, continuing endlessly to smaller and smaller pieces; or there might be a smallest piece of paper that cannot be divided; or paper might be made out of small pieces of something else, small pieces which together have the properties of paper. We will test the third possibility. Weigh the piece of paper; then set it on fire. When it has burned, weigh the ashes that remain. In this way, you prove that paper consists of at least two ingredients. One ingredient is the ash that is left; the other ingredient somehow disappeared in the fire.

In the ancient world, many philosopher/scientists concluded that the material world and everything in it consists of four elements: earth, water, air, and fire. From this experiment, they would say that paper must consist of earth (the ashes left when the paper was burned) and fire (the missing weight that disappeared when the paper was burned). For centuries, philosopher/scientists called alchemists proposed theories and conducted experiments to learn more about the material world and the substances in this world. Often alchemists are portrayed as magicians trying to turn lead into gold. They did, in fact, attempt to make that change. However, they also performed many other investigations which led to the modern discovery of the science called chemistry.

Modern science would determine that most of the ash produced by burning the paper is an element called carbon. Carbon is one of the elements found in paper. Modern science also reports that water is not an element. Each molecule of water contains three atoms—two atoms of hydrogen and one atom of oxygen. Water molecules can be broken. Connect wires to the terminals of a battery and put the wires into a glass of water. Bubbles will form at each wire—hydrogen molecules at the cathode (attached to the negative pole of the battery) and oxygen molecules at the anode (attached to the positive pole).

If you could see a molecule of water, it would look like a Mickey Mouse head—two little atoms of hydrogen set sixty degrees apart on a larger atom of oxygen. Remember that these molecules are very tiny. A large number of them are required for the water to have any properties that our senses can detect. But another interesting fact about a glass of water is that –in addition to chemicals contained in the water—even a full glass of water contains much empty space.

To prove this, try the following experiment. Take a measuring cup and carefully add half a cup (four ounces) of water. Now carefully add a tablespoon of water and notice that the water level is above the half-cup (or four ounce) mark. Add a second tablespoon of water, and you now have five ounces. Add two more tablespoons of water, and you have six ounces, or three-quarters of a cup of water.

Now add a tablespoon of sugar and gently stir until all the sugar is dissolved. Notice that the water level has not increased above the six-ounce mark. Do so again, and you still have only three-quarters of a cup of water. A third time will not have the same results, because all the sugar cannot dissolve. But, even with three tablespoons of sugar in six ounces of water, you will still be far closer to the six ounce line than you are to the full cup of water. The dissolved sugar has found empty spaces between the molecules of water in your cup.

Matter contains atoms, but it also contains much empty space. Empty space exists between electrons and nuclei in each atom (and none of the sugar was able to fit into that empty space in the water). Empty space exists between molecules in even the most seemingly solid substances. Empty space exists beyond the atmosphere of the earth. Except for the brief times when the Moon, Mercury, Venus, or some asteroid crosses between the Earth and the Sun, that distance is more than ninety million miles of empty space. Even with one of those objects in the way, the bulk of that ninety million miles is empty space. More empty space separates the Sun from other stars, and yet more empty space lies between the galaxies. Most of the universe is empty space.

Empty space is not nothing. People who confuse emptiness, or the void, with nothing make the same mistake that the Cyclops named Polyphemus made in Homer’s Odyssey. Clever Odysseus introduced himself to the Cyclops as “No one.” Later, when Odysseus poked a sharpened stick into Polyphemus’ eye, the Cyclops roared out, “No one is attacking me! No one has blinded me!” None of his friends came to help him; they thought that, if no one was attacking him, everything was fine. Likewise, in Lewis Carroll’s Through the Looking Glass, the king asks his messenger who he passed on the road and the messenger answers, “nobody.” The king remarks that nobody is slower than his messenger. Indignant, the messenger says that he believes nobody is faster than he is. “He can’t do that,” the king said, “or he’d have been here first.”

In the same way, even experienced philosophers sometimes confuse themselves, mistaking emptiness or the void with nothing. Earlier philosophers felt that empty space was impossible. For anything to move, they figured, it must displace something else. When you walk into a room, you displace some air. When you lower yourself into a bathtub, you displace some water. (When Archimedes realized the significance of that displacement, he was so invited that he invented streaking.) Those early philosophers were certain that, from the very smallest pieces of the world to the very largest, everything must displace something else as it moved. They were the ones who coined the expression, “Nature abhors a vacuum,” which has nothing to do with housecleaning.

But Nature cannot abhor a vacuum; nature is almost entirely vacuum. From the empty space inside each atom to the empty space between galaxies, most of the universe is empty space. But emptiness, or void, can be measured. The tiny space between electrons of an atom and its nucleus can be measured (and that empty space is much bigger than the nucleus of the atom, let alone the electrons). The empty space between planets and the sun, or between stars, or between galaxies, can be measured. Because it can be measured, it is not nothing.

A modern physicist says that the universe is expanding. Ask, “into what is it expanding?” and the physicist answers, “Nothing.” They physicist does not mean empty space or a void; the nothing that surrounds the known universe is not measurable empty space or void. Christians say that God created the universe out of nothing. They do not mean that He created out of void or empty space. Before God created, according to Christian teachings, nothing but God existed—not even empty space, not even a void. The difference is very important to Christian teachers and to modern physicists. J.

Let’s get small, part one

You have before you a piece of paper. Being a philosopher and a scientist (for the present, we will take those words to be synonyms), you use your senses to analyze this piece of paper. You see that it is white. You see that it is flat. Seeing a measuring device, you use it to determine that the paper is eight and one half inches long and eleven inches wide—or, if you prefer, 261 mm (millimeters) x 279 mm. Measuring the thickness of the paper is not so easy, but you are a clever philosopher and scientist. You stack one hundred sheets of paper and find that the stack is one-half inch tall, or 1.2 mm. Therefore, you know that one sheet of paper is one-two-hundredth of an inch thick, or 0.012 mm—about the smallest size your eyes can see or your fingers can feel.

Scent and taste do not reveal useful information about the paper, but your hands tell you that the paper is smooth, but the edges and corners feel sharp. Left alone, the paper makes no noise. With your hands, though, you can cause it to make noises when you flap it in the air, when you crumple it, or when you tear it.

Tearing the piece of paper gives you a new thought. You now have two pieces of paper, both remaining white and flat, with the same thickness and width, but neither as long as the original. How long can this process continue? Can you continue to tear the paper into smaller and smaller pieces? And will each piece remain a piece of paper? Modern science teaches us about molecules and atoms while we are young, but for centuries philosophers and scientists were lacking that information. For centuries they wondered how small a piece of paper could remain paper, and what it might be if it was no longer paper.

With a microscope, you can see that paper consists of fibers. Perhaps with tiny, delicate tools, you could isolate one fiber from the paper and chop it into shorter and shorter lengths. Even this experiment will not answer the age-old question about what tiny parts might make up a piece of paper. Logically, three possibilities exist. Perhaps the process can continue forever—however small a piece of paper you have, you can divide it into two smaller pieces. Perhaps the process reaches a limit—a small particle of paper exists that cannot be divided into smaller pieces. Or perhaps at some point we will find tiny pieces that are no longer paper, but are something else, ingredients, elements of which paper is made. By tearing and shredding the paper, we will never determine which of these results is real.

We set the paper aside for a little while, and instead we consider a drop of water. How big is a drop? For convenience, we will define one drop as one twentieth of a milliliter (0.2 mL) or one one-hundredth of a teaspoon. Modern science tells us that one drop of water contains 1.5 sextillion molecules of water. Sextillion is a real number, unlike jillion or zillion. It is written as a one followed by twenty-one zeroes. When dealing with huge numbers or tiny numbers, scientists prefer to use “scientific notation”—in the case of one sextillion, writing the number as 1 x 10²¹. Another shortcut is to use special measurements, such as nanometers or Angstroms. To try to put this number into perspective, though, let’s take that drop of water and divide it in half. Then divide the half-drop in half again, and do so a third time, a fourth time, a fifth time, and on to a tenth time. Now we have a speck of water that is about as high and wide and thick as the thickness of one piece of paper—and it still contains 1.5 quintillion molecules of water.

With special instruments, we continue dividing that one speck of water—slightly less than one thousandth the original drop—in half, and divide that half in half, until we have done that process another ten times. The invisible bit of water we have now is one millionth the size of the original drop, and it contains 1.5 quadrillion molecules of water. Repeat the process another ten times, and what we have is one billionth the size of the original drop and contains 1.5 trillion molecules of water. Now we are getting to numbers we recognize—at least if we pay attention to the national budget. Billions and trillions are somewhat familiar. Along the way, we may begin to appreciate just how tiny one molecule of water happens to be.

But another thing has happened. By the eleventh or twelfth division of that drop of water, what we had left was not really water. It still contained water molecules—an unimaginarily huge number of molecules—but that water was no longer wet. Drop it on your skin, and you would not feel it. Drop it into a glass of water, and you would not hear it land or see the ripples. It takes an enormous number of molecules of water to be sensed as water, just as it takes an enormous number of molecules of chlorophyl before we can see any green in a leaf.

We will return to the water again and will look at its molecules and consider even smaller parts of the molecule. But, first, we will experiment again with the paper. J.

Reality starts getting weird

Our senses tell us of the world around us, the world in which we live. But how can we be sure that the information delivered by our senses is complete? What if other information lies outside our perception, realities we cannot comprehend because nature or its Creator have not equipped us to detect those realities?

My example of the singing refrigerator hints at such a possibility. My sister and I could hear the sounds the refrigerator made. Other family members could not hear them and refused to believe that such sounds existed. Human ears vary slightly regarding the pitches they can detect and report to the brain. Such a difference in hearing appears to be only the tip of the iceberg.

In the 1860s, at the height of the Victorian Era, scientists began to detect some sort of radiation associated with electricity and magnetism. Twenty years later, further research had provided a better understanding of that radiation. What we humans know as visible light—red, green, blue, and white—is only part of the spectrum of light waves in the world. Other wavelengths are longer or shorter than the wavelengths our eyes witness. Radio waves and microwaves had been found in the latter part of the nineteenth centuries; X-rays would not be discovered until 1895. Not only did science unveil the existence of these waves that have always been there; inventors swiftly found ways to harness this knowledge for the benefit of humankind.

Imagine telling a scientist from the year 1850 that in our time invisible waves are used to allow people to communicate across thousands of miles, to speak to one another and hear immediate replies. Imagine describing the way the same invisible waves convey not only sounds but also images—even moving pictures—all around the earth. Imagine adding to that fantastic tale the detail that bones and internal organs of a person can be observed without removing that person’s skin. These innovations would surely be as marvelous and unexpected as motorcars, airplanes, and other modern tools that we take for granted today.

A few people claim to believe that the Earth is flat, insisting that evidence of a spherical world is misinformation distributed to fool the general public. Perhaps somewhere a few people also insist that all light is visible light. They might claim that reports of radio waves and microwaves and X-rays are a trick and that such things do not exist. Cell phones, garage door openers, TV remotes, and medical and dental X-rays are all part of the trickery, clever illusions to persuade us to believe in unseen waves that constantly surround us and pass through us.

Because science stumbled upon these unseen versions of light, we must accept the possibility that other real things exist in the world, unobserved because we have not yet found a way to look for them. Meanwhile, further studies of the observable world bring us new and amazing bits of news. For everything we consider solid and reliable—the red apple in the refrigerator, and the square table in the middle of the room, and my foot, and my shoe, and the ant crawling on the floor next to my shoe—all these things are formed from an unimaginably large number of unimaginably tiny pieces. And those pieces follow rules that are far different from the rules of geometry and physics we have learned about the world our senses observe. Even the light that enables us to see those things follows a different set of rules. This is where things start becoming truly weird. J.

Our senses and our world, part three

If we agree that a tomato in the dark refrigerator is only potentially red—not truly red when no light is shining on it—then must we agree that the properties of objects do not exist when they are not perceived? Is sugar not sweet when it is not being tasted? And is salt not salty when it is not being tasted? Are they only potentially sweet and potentially salty? If that is the case, then we have abandoned dualism and are functioning in the realm of idealism. In that realm, minds and thoughts and ideas (and spirits) are real, but the material world is only in illusion formed by our minds and thoughts and ideas (and spirits).

Imagine a small pile, half a teaspoon, of white crystals on the kitchen counter. They might be sugar or salt, but you don’t know which. Clearly, by tasting a few of the crystals, you will know if the pile is sugar or salt. Does that mean that the crystals are neither sugar nor salt until they have been sampled?

Taste is the quickest way to discern sugar from salt, but a chemist could provide other tests that would identify the crystals apart from their taste. Sugar consists of hydrocarbon molecules, but table salt is a lattice of sodium and chlorine ions. These chemical facts remain true even if the crystals are not tasted. Therefore, we do not have to taste them for them to be either sweet or salty.

By the same token, the brown table in the center of the room is not brown in the dark, but it is still a table, hard and unyielding. If I walk into that table in the dark, it will bruise my shin and cause me to lose my balance. Even in the dark, when it is no longer brown, that table retains all its other physical properties as a material object.

If a tree falls in the forest and no one is there to hear it, does it make a sound? As it begins to tumble, it crashes into other trees, and the crackling of the branches sends vibrations through the air. When it finally hits the ground, it creates a thump that shakes the ground. That thump will be discernable for some distance in the ground, and it also will cause vibrations in the air. Now perhaps no person is in the forest to hear the crackling and the thump. If a scientist has left a listening/recording device in the forest—trying to gather evidence of a surviving ivory-billed woodpecker or of Bigfoot—that device will register the sound of the falling tree. Squirrels and sparrows will hear the crackle and the thump. But what if there are no squirrels, no sparrows, and no scientific listening device? Will the tree still make a sound? A Christian (or Muslim or Jew) is likely to say that God is still in the forest. God will hear the sound of the falling tree. If God is not present, then there is no tree and no forest, and (of course) no sound. On the one hand, this proposal lends itself to Berkeley’s brand of idealism—things we call material are ideas in the mind of God, and as a result they are real to all created beings that have senses and minds.

But a tree is big enough to make a sound. One leaf, falling from the tree, might not make a sound that is heard by any human being, squirrel, sparrow, or scientific device. Does God still hear the leaf when it lands on the floor of the forest? Perhaps. Philosophy alone cannot answer that question.

But substances in the material world must have a certain quantity to possess the qualities we apply to those substances. The half-teaspoon of sugar or salt was sweet or salty. One molecule of sugar, or one sodium ion linked to one chlorine ion, would have no flavor. Half a teaspoon of water is wet. One molecule of water is not wet. A steel knife is sharp. One iron molecule from that knife is not sharp.

I will address the atomic theory of material substances more completely a bit later in this writing. But we must concede right now that the smallest particles of matter lack the qualities that they attain when they gather in large numbers. A single molecule of chlorophyl is not green. It is too small to reflect any light. But millions of molecules of chlorophyl, gathered in the same leaf, are green. This fact forces us to reconsider our opinion about the reality of the material world, that world which is revealed to us by our senses. J.

Our senses and our world, part two

Because of light, we see things around us—and even things, such as stars, that are far from us. Because of sound, we hear things. Sound travels as waves through air and water and even through solid substances. When those waves reach our ears, our eardrums and the tiny bones behind them move, and nerves carry messages about those movements to our brains. Loud sounds and soft sounds, high sounds and low sounds, brief sounds and continuing sounds—all these are faithfully reported to our brains. Sometimes we enjoy the sounds we hear. Sometimes they warn us of dangers to which we must react. Sometimes we ignore what we hear. Even while we sleep, even while in a coma, we continue to hear, because our ears (unlike our eyes) have no muscles. Therefore, we should never assume that a person in the room with us cannot hear the things we say.

Our hearing is not identical, even as our seeing is not identical. Some people hear higher pitches than other people; some people hear lower sounds than other people. My sister and her household once had a singing refrigerator—all day and all night, it alternated through three high-pitched tones, not shrill and piercing tones, but sounds that were present to those who could hear them. Her husband and their daughter could not hear the refrigerator sing. They thought my sister was inventing a story when she mentioned its song. When my children and I commented on the song, my brother-in-law and niece thought we were joining my sister in her joke. They could not hear those three sounds. As a result, they assumed that no such sounds existed.

We smell various scents when small particles of matter in the air reach our noses. Flowery perfumes, smoke, food cooking on the stove, freshly-cut grass, the plastic in a new car—all have distinctive odors that we notice when those particles enter our noses. Taste works like smell, except that we taste only the things that we put into our mouths. Sugar is sweet, acidic foods are sour, alkali foods are bitter, and salt is, well, salty. Chocolate is both sweet and bitter; lemonade is both sweet and sour. Whenever we taste something, our tongues report to our brains what we are eating, and our brains decide how much we like what we are eating. Most flavors combine both scent from the nose and sensations from the tongue, which is why food tastes different when our noses are obstructed due to colds or allergies.

The skin on our bodies includes nerve endings that tell us about the things we touch. These distinguish hot and cold, sharp and dull, soft and firm, and various other distinctions. They also report the intensity of contact, presenting pain when the touch is dangerous. The nerve endings in our skin are constantly reporting to our brains everything that touches them. The brain then decides how to react to the information it is receiving from our skin.