The Scientific Method and the Flat Earth

The Scientific Method as Often Taught

In primary and secondary education, the scientific method usually is defined using the following steps. First, a question is posed. Second, one does preliminary research to see if this question has already been answered. If not, then the third step is to develop a hypothesis, or educated guess, to answer the question. Fourth, one develops an experiment to test this hypothesis. If the hypothesis is true, then the experiment ought to produce a certain outcome. This amounts to a prediction of the hypothesis. This usually is where the independent and dependent variables come in. As part of the experiment used to test the hypothesis, the experimenter can manipulate a variable that will change some other variable. The variable that the experimenter manipulates is the independent variable. The second variable is the dependent variable because its value depends upon the independent variable. Fifth, the scientist conducts the experiment to determine the outcome. Sixth, the scientist reaches a conclusion. If the experimental results match the prediction of the hypothesis, then we say that the hypothesis is confirmed. However, if the results of the experiments are different from the prediction, then we say that the hypothesis is disproved.

If the hypothesis is disproved, then the scientist goes back to the second step, either to alter the hypothesis or to scrap it entirely and develop a new hypothesis. The subsequent steps in the process are repeated until a hypothesis is developed that is confirmed. But the process doesn’t end there. Science must be repeatable, so even a hypothesis that is confirmed must undergo further scrutiny. The scientist may develop other tests for the hypothesis.

The scientist will then share his results and conclusions with other scientists so that they also can test the hypothesis. With each successful test, we gain more confidence that the hypothesis may be correct. Sometimes people say that the hypothesis is proved through positive test results, but technically this is not correct. There may be another hypothesis that we haven’t considered that equally explains the experimental results thus far. How do we know which hypothesis is correct? When an alternate hypothesis is considered that explains the experimental evidence thus far, it is important to develop new experiments that can distinguish between the two hypotheses.

Many people mistakenly think that a theory is an unproven idea (there is that word “proof” again), as opposed to fact.

We can never be completely sure that a scientific idea is correct. However, with each successful test, we gain confidence that a hypothesis is true. Eventually, we may say that a principle that is well established by the scientific method is a law. For instance, in biology, we have the law of biogenesis, that life only comes from life. On the other hand, if we have a set of principles that have been extensively tested and confirmed, then we say that it is a theory. For example, in physics, we have four equations that together form a theory of electricity and magnetism. Many people don’t understand what a theory is. Many people mistakenly think that a theory is an unproven idea (there is that word “proof” again), as opposed to fact. However, the notion of a theory being an unproven idea is more applicable to a hypothesis that hasn’t been confirmed yet. Furthermore, this is a false dichotomy between theory and fact. Theories and facts are not opposites. Rather, we use facts to confirm a theory or disprove it.

This definition of the scientific method is simple and easy to understand. It also is very applicable in a high school biology class, the highest level of science education that most people achieve. However, it is woefully incomplete. Therefore, anyone who takes this as the final, absolute word on science is ignorant of how science truly works.

The Scientific Method in Reality

The scientific method is based upon inferences, which use a form of reasoning that we call inductive reasoning. This contrasts with deductive reasoning. What is the difference? Deductive reasoning works from general cases to reach specific conclusions. On the other hand, inductive reasoning works from specific cases to reach general conclusions. Classic deductive reasoning consists of a syllogism with a major premise, a minor premise, and a conclusion. For instance, consider the following syllogism:

All cows are brown.
Bossy is a cow.
Therefore, Bossy is brown.

If one properly reasons from true premises, then we can be certain that all conclusions reached are true.

The first statement, “all cows are brown,” is the major premise. Notice that it makes a general statement about a characteristic of all cows. The second statement, “Bossy is a cow,” is the minor premise. It’s called the minor premise, because it makes a statement about a specific case, not about a general case. The third statement, “therefore, Bossy is brown,” is the conclusion. Notice that if both the major and minor premises are true, then the conclusion is true. If one properly reasons from true premises, then we can be certain that all conclusions reached are true. Any errors that arise in deductive reasoning result either from false premises or from faulty reasoning. There are many formal and informal errors of deductive reasoning. Here is an example of one:

All cows are brown.
Bossy is brown.
Therefore, Bossy is a cow.

Notice that if the two premises in the original syllogism above are true, then it is impossible for Bossy not to be brown. The major premise of the second syllogism is the same as in the first syllogism, but the minor premise in the second syllogism is worded differently. There are many ways that Bossy could be brown and yet not be a cow. For instance, it may be true that all horses are brown, so Bossy could be a horse. The faulty conclusion that Bossy is a cow commits the fallacy of affirming the consequent. We call it this because the major premise establishes that being brown is a consequence of being a cow. However, in this faulty example, the minor premise merely affirms the consequent of the major premise, but it does not address the condition of the major premise. The affirming the consequent fallacy is important to the discussion here, as it shall arise shortly.

How does one arrive at general propositions, such as “all cows are brown?” This is where inductive reasoning comes in. Suppose that a person has never seen a cow, but one day someone points out a cow to this person. The person may examine the cow and infer that there may be some general properties that cows have. For instance, he may consider the size and shape that cows have (this is how most of us recognize cows when we see them). Or this person might note that the cow has horns. Or he might notice that the cow is brown. Later, this person might be shown a second cow. Perhaps unlike the first cow, this one doesn’t have horns. But this cow might also be brown. Then this person sees a few more cows, and they all are brown. Eventually, this person may begin to develop the idea (hypothesis) that all cows are brown. The obvious way to test this hypothesis is to seek out and examine more cows. As the person examines more and more cows and finds that they all are brown, he becomes more confident that his hypothesis is correct: that all cows are brown. But how many cows must one examine to be sure? Ten? Twenty? Fifty? A hundred? Only by examining every cow can one be certain that all cows are brown. But that isn’t practical. For example, even if one thinks he had examined every cow, could he ever know for certain that he indeed had found every cow? Could there be a few cows hiding somewhere? On the other hand, all it takes is one non-brown cow to disprove the hypothesis. Therefore, one can never be sure that one’s hypothesis is true, though one could be certain that a hypothesis is not true.

This is how inductive reasoning works, going from specific cases, individual cows in this example, to reach a general conclusion about something, all cows in this example. This also is how the scientific method works. With the simple methodology of the scientific method one is likely to encounter in high school as described above, one does experiments to either support or disprove a hypothesis. When flat-earthers use their high school definition of the scientific method, they assume that this is the only definition of science. It never occurs to them that their high school curriculum may have idealized and simplified the true situation of how science works.

But that methodology was developed for experimental science. The cow example was observational science. There was no experiment done. No one manipulated the cows in any way. There was no independent variable that was manipulated to change a dependent variable. All one did was seek out and observe the colors of cows.

By its very nature, astronomy is an observational rather than experimental science.

Except for meteorites or samples returned from the moon, astronomers can’t take their subjects into the lab to do controlled experiments. Rather, we must patiently and passively wait for our subjects to reveal themselves and record what we observe. But as we do this, we can draw inferences about the causes of what we observe.

Inductive Reasoning Used in Astronomy

The history of astronomy is filled with inductive reasoning, though it isn’t always as formal as in my example of concluding that all cows are brown. For instance, each day, the sun rises, moves across the sky, and then sets. It doesn’t take much inductive reasoning to conclude that each night the sun passes under the earth to rise the next day. At night the moon and most stars also rise and set. Therefore, inductive reasoning leads to the likely conclusion that the moon and stars pass beneath the earth each day too. However, stars in the northern part of the sky don’t rise or set. Instead, those stars move in circles around a point in the sky that we call the north celestial pole. We call these stars circumpolar, meaning “around the pole.” The sky has the appearance of a dome or hemisphere above us. Since objects in the sky move across the sky and under the earth daily, it isn’t a great leap to infer that instead of just a hemisphere above us, there is a sphere around us. Furthermore, one may infer that celestial objects are attached to this celestial sphere, and it is the spinning of the celestial sphere that explains the daily motion of astronomical bodies. This theory of a spinning celestial sphere centered on the earth was the scientific consensus in the West for two millennia. This theory was abandoned only four centuries ago, though we continue to use this model in some applications today.

In ancient times there were trade routes across the Mediterranean Sea. As people traveled northward, they noticed that the north celestial pole moved higher in the sky, admitting more of the celestial sphere into the circumpolar region. But this caused stars low in the southern sky to fall below the horizon, rendering them never visible. Conversely, this trend reversed when traveling southward. A reasonable inference is that the earth is a sphere. Could it be that it was the earth that was spinning each day rather than the celestial sphere? Yes, though it would be a very long time before anyone could devise a test that would distinguish between those two possibilities. In many respects, it doesn’t matter because either possibility can explain most of the observations. The theory of the celestial sphere around a spherical earth was a very robust one. It can explain many phenomena. It also can be used to predict many things successfully. It does a very good job of explaining and predicting aspects of the sky, such as the locations of astronomical bodies, including when and where they will rise and set. Many detailed observations were carried out effectively to test this theory.

The Ecliptic

Among these observations were measurements of the positions of the sun and moon. Not only does the sun appear to move around the earth daily, but the sun also moves through the stars annually. Many ancient cultures managed to map the sun’s annual motion among the stars. We call the path that the sun follows through the stars, the ecliptic. Why does the sun annually move along the ecliptic? Today we would say that this is apparent motion caused by the earth’s orbit of the sun. Some ancient astronomers agreed with this conclusion, though the majority opinion probably was that it was the sun that was moving. Why did the sun move so? There was no satisfactory answer to that question in the ancient world.

The ancients discovered three things about the ecliptic. First, the axis of the ecliptic is tilted by about 23 ½ degrees to the north celestial pole. We call this tilt the obliquity of the ecliptic. You should recognize that this is the cause of the seasons. Second, many ancient cultures discovered that the sun doesn’t move along the ecliptic at a uniform rate. Rather, the sun moves most quickly in early January and most slowly in early July. Today we would explain this by noting that the earth’s orbit is elliptical, not circular. In early January, we are closest to the sun (perihelion), and we are farthest from the sun in early July (aphelion). There are several ways of looking at this, but the easiest way is to conclude that when at perihelion, the force of gravity is strongest, so the earth must move most quickly then. Since this explanation comes from Newton’s law of gravity, which did not exist until 3½ centuries ago, there was no explanation for the sun’s changing speed along the ecliptic in the ancient world. Third, the ecliptic slowly slides along the celestial equator, a circle 90 degrees from the north celestial pole. This precession of the equinoxes takes nearly 26,000 years to complete one cycle. Again, an explanation of the precession of the equinoxes had to await Newtonian gravity to be explained.

Like the sun, the moon moves through the stars. However, rather than taking a year to pass once through the stars, the moon takes only a month (our English word “month” comes from our word “moon”). Today we agree with the inference in the ancient world that the moon orbits the earth each month. The moon’s orbit is very close to the ecliptic, being tilted about five degrees to the ecliptic. As the moon goes through the synodic month, the orbital period of the moon with respect to the sun, the moon goes through phases. One can easily infer that the moon’s phases are caused by sunlight reflecting off the moon, with how much of the lit portion of the moon visible being the phases that we see. This leads to the inescapable conclusion that the moon is spherical.

Phasing Out Old Ideas

Aristotle reasoned that since the moon (and sun) is a sphere, it follows that the earth must be a sphere too.

Here flat-earthers generally disagree with ancient cosmologies. Flat-earthers insist that the moon is not a sphere, and that it does not shine by reflecting sunlight. That leaves flat-earthers with no explanation for lunar phases. Nor do they exhibit any interest as to the cause of lunar phases. Why do flat-earthers reject this very good inference? I suspect that it has to do with an argument for the earth being a globe that Aristotle propounded in his book, On the Heavens, written about 350 BC. Aristotle reasoned that since the moon (and sun) is a sphere, it follows that the earth must be a sphere too. This is an argument by analogy. This presupposes that the earth must be like the moon, but there is no a priori reason for believing this. This argument is not rigorous, as flat-earthers correctly point out. However, I suspect that part of the reason flat-earthers reject the moon being a sphere is that they sense the implication of the argument by analogy. If flat-earthers truly were convinced that Aristotle’s argument by analogy is flawed, they would have nothing to fear by admitting that the moon is a sphere. The fact that they strenuously object to the moon being a sphere, signals that they doubt that Aristotle’s argument truly is wrong. In a way, they use an argument by analogy: since the earth is flat, the moon must be flat too.

The moon’s orbit crosses the ecliptic in two points. We call these points of intersection the nodes. Many ancient cultures discovered this fact. Those same cultures also noted that eclipses, both lunar and solar, can happen only when the moon is close to the ecliptic. The word ecliptic derives from this fact. What is the implication of this discovery? It helped ancient cultures infer the cause of eclipses. A solar eclipse happens only when there is a new moon, when the moon passes between the earth and sun. But a solar eclipse doesn’t happen every new moon, because the new moon usually passes above or below the ecliptic so that its shadow misses the earth. Only when the new moon is close to a node does a solar eclipse occur. A similar thing is true for lunar eclipses. Lunar eclipses happen only at full moon, but only if the moon also is near one of its nodes. Otherwise, the earth’s shadow is too high or too low, thus missing the moon. And this leads to the conclusion that it is the earth’s shadow falling on the moon that causes a lunar eclipse. The earth’s shadow during a lunar eclipse always is a circle. A flat, round earth could cast a circular shadow, but only for certain orientations. The only shape that consistently casts a circular shadow regardless of orientation is a sphere. Aristotle made this argument in his book, On the Heavens.

Again, flat-earthers must reject these reasonable inferences with all their might.

Again, flat-earthers must reject these reasonable inferences with all their might. There are two reasons for this. First, this inference about lunar eclipses is evidence that the earth is a globe rather than being flat. Second, in the zetetic model that most flat-earthers hold to today, the sun and moon never rise or set, but instead are contained within the dome over the flat disk of the earth, continually moving in circles above the earth. Since in the zetetic model the earth never can come between the sun and moon, the earth’s shadow cannot fall on the moon. Therefore, acceptance of the conventional explanation of lunar eclipses would destroy the zetetic model.

There are other inferences about these astronomical matters that many ancient cultures made. For instance, societies around the world independently discovered the saros cycle, an 18-year, 11⅓-day period over which eclipses repeat. The saros cycle can be used to anticipate when eclipses might occur, but not with much precision. But this doesn’t stop flat-earthers from claiming otherwise. Though flat-earthers usually don’t mention the saros cycle by name, they often mention a periodicity that ancient cultures knew about that supposedly allowed those societies to predict eclipses accurately. Flat-earthers often falsely claim that this is the method that modern astronomers use to predict eclipses. But this overlooks how ancient cultures discovered the saros cycle. For an eclipse to occur, two things must be true, the moon must be near a node, and the moon must be at the proper phase (new moon for solar eclipses and full moon for lunar eclipses). The first condition will repeat each draconic month, the orbital period of the moon with respect to its nodes. The draconic month is 27.212220 days. The second condition will repeat with the synodic month, which is 29.530588 days. Many ancient societies knew the lengths of the draconic and synodic months, though not this precisely. They did know that 223 synodic months and 242 draconic months are almost exactly equal, 6,585⅓ days (the saros cycle). Therefore, they understood that similar eclipses would repeat with the saros cycle. There are many saros families of eclipses going on simultaneously.

Notice the inconsistency here. Flat-earthers often insist that astronomy isn’t a science because it doesn’t follow their understanding of the scientific method. But flat-earthers readily accept the notion that ancient societies came to understand the saros cycle via observations of many eclipses over a long time period and noting periodicities in the eclipses. This isn’t true, but flat-earthers seem to have elevated their false understanding of the history of the saros cycle into some sort of science.

Conclusion

I could say much more about the history of astronomy and the role of inductive reasoning has played and continues to play in astronomy. But it ought to be clear that in astronomy we rarely do experimental science. Rather, we astronomers do observational science. Again, I emphasize that astronomy, being an observational science, rather than an experimental science, is still science. People must understand that the scientific method that they learned growing up was highly idealized, and it was presented in a manner that is tailor-made for experimental science, such as biology. But this description of the scientific method is much too restrictive.

Affirming the consequent is a fallacy of deductive reasoning.

In closing, some critics of science, including flat-earthers, claim that science commits the fallacy of affirming the consequent. Affirming the consequent is a fallacy of deductive reasoning. If science used primarily deductive logic, then that would be a valid objection. But science employs primarily inductive reasoning. Affirming the consequent is not a fallacy in inductive reasoning.