“Ok, settle down, class,” yelled Mrs. Sullivan over the noise. The class quickly settled down, waiting for her next comments. “Ok, it is Science Friday again. Where did we leave off last Friday?”
Gail raised her hand. “Gail?”
“We were all repeatedly dropping a book, which fell to the floor each time. We were pretending we were doing this before Newton published his book on motion and gravity. We were dropping the book to figure out what caused things to fall to the ground. Jenny said we could figure this out using Operational Science, where we do repeated experiments and directly observe the results,” said Gail, proud of having given a good summary.
“Excellent, Gail. And did our repeated experiments show us the cause of why things fall?” asked Mrs. Sullivan.
“No, it did not. We realized that we were witnessing a phenomenon, but we were not actually observing the cause of it. We realized that we need to form a hypothesis that explains the cause. But that is about as far as we got. I don’t think we had enough clues.”
“Clues?”
“Yes, dropping the book gave us a few clues, such as the book fell every time we dropped it, it seemed to take about the same amount of time to hit the floor, and it hit the floor with a loud bang. I don’t think this was enough to form a hypothesis. I can tell you had the same idea, since you gave us all the assignments to do further research. We probably need more clues.”
“We need something, that’s for sure,” said Mrs. Sullivan. “How did people explain things falling before Newton? Grace and Marlene, you were off to research the earliest hypothesis you could find in history for why things fall. What did you find?”
Aristotle’s Ancient Explanation
Marlene and Grace looked at each other. Marlene said, “You go.”
Grace stood up and said, “I don’t think we know what the earliest reason people had for explaining things falling, but the first well-documented explanation came from Aristotle, the Greek philosopher who lived around 350 BC.”
She continued, “Aristotle thought that things fall to the ground because they are trying to reach their ‘natural place.’ He believed that everything is made of four elements—earth, water, air, and fire—and each one has its place in the universe. For example, heavy objects, like rocks, are mostly made of ‘earth,’ so they naturally move downward toward the center of the Earth. Why the center of the Earth? Because people thought the center of the Earth was the center of the universe.
“Lighter things, like fire or smoke, rise because they are trying to reach their natural place up in the sky. Aristotle also thought heavier objects fall faster than lighter ones because they have more of the ‘earth’ element. He didn’t test these ideas with experiments—he just came up with them based on what seemed to make sense at the time.”
Grace sat down.
“Well, I guess we have our hypothesis, then. Any questions?” asked Mrs. Sullivan.
Bob said, “I don’t know. It seems like something just made up that sounds good. Also, Aristotle was wrong. Heavier objects do not fall faster than lighter ones, and I can show that in my presentation. Grace, how long did people believe that explanation?”
“It looks like it was the academic explanation up until Newton published his work on gravity and motion, so about 1700 years.”
Bob said, “Didn’t the Greeks invent a lot of things?”
“The ancient Greeks gave us geometry, formal logic, mathematics, philosophy, ethics, legal systems, astronomy, geography, sculpture, architecture, a working model of the solar system, and with Aristotle, a tremendous number of observations in biology,” said Mrs. Sullivan.
Bob looked puzzled. “But by the looks of it, they did not give us a good explanation for why things fall. They did not provide us with gravity. But wait, didn’t Galileo study gravity by dropping stuff from the Tower of Pisa long before Newton?”
Galileo’s Breakthrough
This time, Marlene spoke up. “Well, yes and no. It’s not well-documented that Galileo dropped anything off the Tower of Pisa, but he did conduct an experiment that was very important in the context of falling objects. Wait here, I have a demonstration for you.”
Marlene and Grace went out into the hallway and came back carrying a long piece of wood and a cloth bag. Marlene set one end of the wood on the edge of the teacher’s desk and the other end on the floor, forming a ramp.
She explained, “Ok, this is a 12-foot piece of cove molding that you might use around doors and windows. It is made of oak hardwood and is very straight. Notice it does not sag in the middle. I am going to use it to duplicate Galileo’s experiment.”
She pulled out a steel ball from the sack and explained further, “Now if you look closely, the molding has a shallow depression in it that forms a kind of Hot Wheels track for this steel ball to roll down. Also, note that I have placed several pieces of bare wire across the molding. When I set the ball at the top of the track, it rolls down. When it rolls over each wire, you can hear a clicking sound. Now here goes.”
She let the ball go. It rolled over the equally spaced wires, making click sounds. As it went faster and faster, the click sounds got closer and closer together.
“What Galileo was looking for was the answer to the question: how do objects move when they are falling? He figured he could repeatedly roll the ball and move the wires down the ramp until the clicks came at a precise tempo. Galileo was a music teacher, among other things. He sang a song to keep the cadence. I already experimented and put pencil marks in the right spot for each wire.”
Marlene moved the wires to the right spots and rolled the ball again. This time, the clicks kept the beat like a metronome as Marlene sang Mary Had a Little Lamb.
“See? As the ball rolls faster, the distance each wire must be greater than the one before it to keep the beat to the song. At this point, he had his answer. If you measure the increasing distance between each wire and plot it against time, you end up with a relationship between time and distance during the fall. The relationship is that the distance travelled by a falling object is proportional to time squared, or d ∝ t². Galileo discovered the First Law of Falling. From this, you can get the Second Law of Falling, which is that the rate at which a falling object speeds up is constant.”
The class started clapping their hands in appreciation. But Marlene interrupted them and said, “But wait, that’s not all.”
She reached into her bag and pulled out a billiard ball. She placed it at the top of the track and let it roll while she sang the song again. Once again, the clicks kept time with the song.
Marlene looked up at the kids watching and said, “And with this, Galileo discovered a Third Law of Falling, which is that objects fall at the same rate regardless of how much they weigh. Aristotle was wrong.”
As the class applauded, she took a bow.
“Brilliant!” exclaimed Mrs. Sullivan. “But what did Galileo decide was the cause of objects falling?”
“He didn’t have an explanation.”
“Really?” asked Bob. “Didn’t he get in trouble with the church for publishing books about the orbits of planets? He must have figured out how gravity affects their motion.”
“Nope. It never occurred to anyone until Newton, about 100 years later, that the same thing that causes things to fall has anything to do with the planets, moons, and stars. The same applies to Kepler and Copernicus. No explanation for why things fall.”
More Clues, Still No Cause
“No wonder we are having trouble figuring it out,” said Mrs. Sullivan. “It appears that Galileo conducted some excellent Operational Science by conducting repeated experiments in the lab. He discovered three laws of falling in the process, but still no hypothesis for why things fall. Now, Bob, you said you had an idea for some other experiments. Can you report on that for us?”
“Sure!” said Bob. He pulled a laptop out of his backpack, went to the front of the class, and connected it to the big monitor. He brought up a video of him and some friends dropping a bowling ball off a cliff.
“Ok, so my friends and I set up a cell phone on a tripod and recorded repeated droppings of a bowling ball off a cliff. Then, I used my video editing software to watch them frame by frame like this. Notice that for each frame, we can measure the distance it fell, and that each frame has a timestamp. We got the same results each time for the bowling ball and a baseball. Galileo was correct. Objects fall to the Earth with a constant acceleration, with distance fallen equal to 32.2 feet times each second squared, regardless of how much they weigh.”
More applause from the class. Bob took a courtly bow.
Mrs. Sullivan said, “Brilliant! So with these careful experiments, did you come up with a cause for why things fall? A hypothesis?”
“No,” said Bob. “We still don’t have enough clues, I think. We have the same clues but with more accuracy.”
Mrs. Sullivan turned to Jennifer and asked, “Jennifer, are we doing Operational Science right? If so, why don’t we know the cause of things falling?”
Jennifer paused, looking thoughtful. “Yes, it looks like we are doing it right, but I agree with Bob that we still don’t have enough clues.”
“Clues? Didn’t you say that it was Historical Science that had to use clues to guess the cause of something? This is not history we are doing here. We are dropping things right in front of our eyes.”
“Yeah, I don’t know. It seems that Operational Science helps us gather more clues and better ones, but it doesn’t necessarily reveal the cause of things. I think there’s something wrong with the distinction between Operational Science and Historical Science. It seems like there are more reasons why we can’t see a cause than it being something that happened in the past.”
Newton’s Mysterious Hypothesis
The class sat quietly for a moment, absorbing Jennifer’s insight.
“Ok, I don’t think we can wait any longer,” said Mrs. Sullivan. “Newton provided a hypothesis for the cause of things falling, which ultimately became part of a theory that laid the foundation for modern science. We’d better hear what Newton had to say about falling. Jennifer?”
“Ok, I have my posters from my Newton presentation last year. Newton formulated this hypothesis so well that it remains a cornerstone of science and engineering to this day. There are two properties Newton assigned to gravity. Here is the first one: Any two objects in the universe attract each other with a force between them. The force is proportional to the product of their masses. Double the mass of either of them and you get double the force.”
The class looked puzzled. Bob spoke up, “Really? So, any two objects attract each other. Like my pencil and your book are attracted to each other?”
“Yes, that’s right.”
“So, how do we show that? I don’t see it moving, and I don’t feel any force on my pencil except from the Earth. What experiments did Newton do to see that?”
“None. Newton did no experiments on that. Nor did anyone else at that time that we know of.”
“What? That is a rather outrageous leap of imagination without any experiments to support it. Why didn’t he do any experiments about that?”
“Because the force is too weak. The only thing you could use for that experiment would be the Earth and another object. The force between any other two objects that Newton could use is too weak to measure or even see in any way. And he couldn’t get far enough away from the Earth to remove its attractive influence.”
Bob was still shaking his head. “How does that explain why falling objects accelerate at the same rate regardless of their weight? So far, this seems more fantastic than Aristotle’s idea. You said there were two properties. What is the second one?”
“Right,” said Jennifer, switching to the next poster. “The force between any two objects diminishes with the square of the distance between them. Move them twice as far away, and the force is four times weaker. Four times farther away, and the force is sixteen times weaker.”
“I am afraid to ask this question again, but what experiments did Newton do to come up with that?” asked Bob, looking more puzzled by the minute.
“Again, none. The distance Newton is talking about is the distance from the centers of mass of the two objects. For the Earth, that is the center of the Earth. We are already 4000 miles or so from the center of the Earth. Newton could not move far enough from the center of the Earth to see any decrease in attraction. Even if he climbed the highest mountain, it would not be enough for the instruments available to Newton at the time, and he would still have the mass of the mountain to contend with.”
“So Newton had no clues at all? No Operational Science?”
“No, I didn’t say that. Newton had clues. He had Galileo’s laws of falling, which we have all duplicated here. He had Galileo’s clues.”
“Right, but those clues don’t just tell you what Newton was proposing. He must have had other clues?”
“Yes, planets and moons.”
“What?”
“He had the motion of planets and moons. You know, historical observations of how the planets and the Moon move in the night sky.”
“Really? Which planet did he bring into his lab?”
Jennifer laughed and said, “No planets in the lab. He did no experiments on planets and moons. They are too big and too far away.”
Bob laughed, “I am getting more and more confused by the minute. I thought we would get closer to figuring out how Operational Science is used to explain causes, but Newton seems like he came from another planet. I know the story about Newton watching the apple falling from the tree, but I am not so sure that it is more than a myth. How did Newton make a connection between apples falling and planets moving through the night sky?”
“Flying cannon balls,” said Jennifer.
“Ok, now I give up,” said Bob, throwing his hands in the air.
The class erupted in nervous laughter at Bob’s exasperation. Even Jennifer looked a bit sheepish about her cryptic answer.
The Real Distinction
Mrs. Sullivan started laughing, and for a few seconds, it looked like she was not able to stop. When she finally composed herself, she said, “Bob, your frustration is not unusual. Remember that no one provided a testable hypothesis for why things fall for as long as people have been watching them fall. Not even serious people looking for explanations for things around them, like Copernicus, Kepler, or Galileo. It was only a few hundred years ago that we began to understand things like this. It was not due to a lack of trying.”
She walked to the front of the class, her expression growing more serious. “What changed, besides Newton being a genius, was not what he imagined, but the methods he developed to validate his flights of fancy. We can say that the spark was lit with Galileo, but it was Newton who laid the foundation for modern science. And more than what he discovered about the universe, his most significant innovation was not just how we take flights of fancy in forming explanations, but also how we create them so that they can be rigorously tested.”
The class sat quietly, sensing that something important was coming.
“What we discovered over the last two Fridays was that what Jennifer has been calling Operational Science is not what provides us with hypotheses that explain causes, but instead what gives us accurate clues that we can use to form those explanations. What we observe through Operational Science is what we call ‘laws’ in science, not theories. Laws are us observing phenomena and recording them. Theories are explanations for causes that we cannot observe directly.
“What Jennifer was calling Historical Science, where we use clues to try to speculate on causes, is not just for things that happen in the past, but for all causes that we cannot directly observe for whatever reason, with historical events being only one reason for why the cause is hidden.”
She paused, letting this sink in.
“As we can see, forming a functional and testable hypothesis about what causes things to fall is no different than creating a useful and testable hypothesis for how life diversifies over millions of years. We start with clues we carefully coax from what we can observe, and we work like forensic detectives, forming various hypotheses and testing them.
“While scientists have used the term ‘Historical Science’ to describe the science of evolution, it is not to distinguish it from something called Operational Science. It is worth noting that, unlike other theories, the reason the cause is hidden from us is that it operates over millions of years, rather than causes operating over millions of miles that affect the motion of planets and moons. Science does not make the distinction that Jennifer’s pastor gave her. Science distinguishes between laws and theories instead.
“Next Friday, we are going to find out how Newton formed his hypothesis and how he taught us to go further than Aristotle to the point where we could rigorously evaluate our hypotheses.”
On that, the bell rang, and Mrs. Sullivan said, “Class dismissed.”