Essay donated by Dr. Zvi Shkedi

"2. Torah and Science: Science or Fiction?
Classification of scientific knowledge, Science
theories, Logical fallacies, speculative
mathematics, and the great flood

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The Classification of Scientific Knowledge:

Scientific research is a human process. It is a process by which people try, and occasionally succeed, to find answers to questions about the universe. All the knowledge which people tend to describe as "science" or as the "fruit of science" can be classified into four categories:

Let's examine each of these categories in detail:

Not all information which is claimed to be "scientific" will fit precisely into one of these four categories. It is possible to have borderline information which may fit into two adjacent categories. It is also possible for different people to have different opinions on where to classify the knowledge. The two categories which are most prone to such overlap are "speculative theories" and "imagination".

To illustrate how all these categories can apply to one specific observation, let's look at the example of "dinosaurs". When a researcher finds a collection of large bones, which are much larger than those of any known animal, the existence of the bones is a fact. When the researcher tries to fit the bones together like a puzzle, he may come up with a skeleton of a large and unknown animal. If the researcher believes in his puzzle and draws a picture of the animal to which these bones used to belong, such an animal could be either a scientific theory or a speculative theory. If all the bones "click" together in only one possible order, and it is impossible to fit the bones together in any other order, the general shape of this animal would be a scientific theory. If, however, it is possible to fit the bones together in more than one order (as is often the case), resulting in different animal shapes, then any shape depicted for this animal would be a speculative theory. When book authors illustrate their books with life-like pictures of dinosaurs, showing details which cannot be derived from bones (e.g. skin color, hair, facial expressions, eyes, ears) such illustrations fall into the category of imagination.

Getting students to blindly accept information made up by others, is not education but indoctrination. The fact that most students today believe that they know exactly what dinosaurs used to look like, is a disgrace to current science education. Authors and teachers alike have yet to learn how to teach students the skill of differentiating between facts, theories, and imagination.

Theories in Modern Science:

Scientific research is usually divided into two categories, experimental and theoretical. Experimental scientists who publish their research results, devote most of their publications to the experimental procedures and findings. Following the experimental section, it is common to suggest a theory to explain the experimental findings, or to connect the experimental findings with one or more theories suggested by other scientists. Both the authors and the scientists who read the publications know that the theoretical suggestion at the end of an experimental publication is a speculative theory. They know that it is only one of several possible theories which "could make sense". Non-scientists who read such a publication usually don't understand that the theoretical suggestion is a speculative theory. They often misunderstand the theoretical suggestion and believe that the entire purpose of the publication is to "prove" a new scientific theory.

Theoretical scientists write their publications differently. They usually open with a review of available experimental findings, continue with the results of their theoretical research, and conclude with suggestions for further experiments to be performed to validate or to resolve uncertainties in their theory.

Experimental scientists rely on theoreticians to guide and to suggest new experiments. Theoretical scientists rely on experimentalists to provide them with experimental data on which they can base their theoretical research. This interaction and cooperation is the core of modern scientific research.

Every experimental result needs to be uniformly reproduced and validated by other experimental scientists in order to be accepted as a scientific fact. Similarly, every suggested theory must be tested and validated by experiments in order to be accepted as a scientific theory. Every suggested theory also carries an additional burden before it can be accepted as a scientific theory:  a) it has to be consistent with all known experimental findings, b) no contradictions are permitted, c) all attempts to prove the theory wrong must fail, d) all experiments performed to test the theory must yield favorable results, and, e) the theory must be capable of making predictions which can be tested by future experiments.

The requirement of a theory to be capable of making testable predictions is one of the distinctions between modern science and old-style science. In old-style science, everyone could suggest theories. If they sounded right and were free from contradictions, they were recognized as scientific theories. Experienced scientists know that most of the theories so developed, are wrong. An experimental basis and lack of contradictions are no longer recognized as sufficient. To limit the proliferation of wrong theories, the requirement of making testable predictions is now uniform among scientists. Theories which cannot produce testable predictions are no longer considered scientific. Untestable theories are the fruit of human imagination. Any subject which appears superficially to be scientific or whose proponents claim is scientific, but, contravenes the testability requirement, is classified as pseudo-science.

Experienced scientists who read scientific publications know how to identify theories which their authors admit to be speculative. Such speculative theories are often presented using vague phrases like: "we can infer that ..."; "it is consistent with ..."; "it is possible that ..."; "undoubtedly ..."; "we must conclude that ..."; "it may have occurred at ..."; "there is no doubt that ..."; "it appears to be ...";  etc.

An easy way to find out if an author considers his theory speculative, is the "court testimony test". If the author's statement were to be presented as testimony in a criminal trial, would it be accepted as clear-cut evidence?  If the answer is "no" - it shows that the author knows his theory is speculative, therefore he qualifies it with vague or cautionary language.

Logical Fallacies:

Unfortunately, too many imaginative and speculative theories are promoted by those who are more interested in publicity or politics than in intellectual honesty. Such theories are often presented as if they are scientific theories or facts, even though they lack the necessary ingredients to be considered scientific.

The understanding of logical fallacies is rarely included in the education of science students. Those who have not been trained to detect logical fallacies can easily be led to believe that they witness a new scientific discovery. Let's start with a simple example - proving the effectiveness of "elephant repellent powder". Can you find the fallacy?

Many years ago, when I visited Brooklyn, I saw a person walking up and down the streets, puffing white powder into the air.
- "What are you doing?" I asked him.
- "I spread elephant repellent powder" he answered, "it keeps the elephants away".
- "But, there are no elephants in Brooklyn", I said.
- "You see, it works!" he replied.
I immediately started spreading this powder in my own town and it really worked. We were never visited by elephants.

The next example includes a series of fallacies. Can you find all of them?

Chicken lay eggs with calcium shells even when they are fed a diet with no calcium. From here we learn that chicken have the ability to convert other elements into calcium. Now that we have established that one element can be converted into another, there is no reason why people cannot convert other elements into gold. Indeed, various successful recipes for making gold have been published.

The inversion of cause and effect is another common fallacy. The following example shows how an effect can easily be turned into a cause.

A journalist interviewed ladies wearing expensive jewelry. He discovered that all the ladies, or their husbands, earn a high income. The journalist concluded that wearing expensive jewelry causes people to earn a high income.

Pseudo-scientists are particularly fond of using logical fallacies as evidence for their speculative theories.

Another type of fallacy incorporates deceptive mathematics. Appendix A shows two example of deceptive mathematical proofs. The first one proves that 0=2, while the second one proves that 2=1. Combining these two equalities will yield the additional conclusion that 1=0. From here it easy to show that not only 1=0, but also 2=0, 3=0, 4=0, and so on. This proof, that all numbers are equal to zero, mathematically verifies the famous saying: "Vanity of vanities, said Kohelet; vanity of vanities, all is vanity." (Kohelet, ch.1, v.2)

It is difficult to imagine how many articles have been published in scientific journals, using similar methodologies to prove the validity of various speculative theories.

Speculative Mathematics:

The process of scientific discovery and analysis employs various mathematical tools. Two of these tools, which are of particular interest to our discussion are "interpolation" and "extrapolation".

 If we know the location of a car at one point in time, and we also know the location of the same car at a later point in time, we can calculate, with some certainty, the location of this car at any point in time in between. This process is called interpolation. Obviously, the process of interpolation depends heavily on the ASSUMPTION that the car continued to move at a constant speed without interruptions.  If we try to calculate the location of this car 1 minute earlier than the first point, we still have some chance of being correct. Since 1 minute earlier than the first point is OUTSIDE the known range between the first and second known points, the process is called extrapolation. We can also use extrapolation to calculate, with some degree of certainty, the location of the car 1 minute later than the second point.

Now try to use extrapolation to calculate the location of the car 50 years earlier then the first point. If you ask a computer, the computer will calculate an answer with great accuracy. Is the answer correct? Absolutely not. No one in his right mind will support a theory that this car started it's journey 50 years ago and continued moving for 50 years, in the same direction, at a constant speed, without interruption. Most likely, the car did not even exist 50 years ago. Yet, the computer will calculate its theoretical/ imaginary location with great accuracy.  The purpose of this example is to demonstrate the danger of using extrapolation in scientific research.

Here is another example of extrapolation. A car is moving at a constant speed from east to west. On day 10 of the month, the car is in New York city. On day 13 of the month the car is in Los Angeles. Where was the car on day 7 of the month? Every child can calculate its theoretical location on day 7 without even using a computer. The mathematical formula is extremely simple and accurate. No one will dispute the correctness of the formula. Yet, how correct is the result? Did the car really start its journey in the middle of the Atlantic ocean?

The above examples demonstrate the danger of assuming that things always change at a constant rate. Such an assumption ignores the fact the everything in nature is constrained by boundaries.  A boundary is a point in time or a location in space beyond which a certain rule or pattern no longer applies. A boundary is an abrupt change in conditions. The pattern of motion or behavior on one side of the boundary is very different from what it is on the other side. In the first example above, the point in time when the car started moving, is a boundary. Before this point in time the car did not move; after this point in time the car did move. Another boundary condition in this example is the point in time when the car was manufactured. Before this point in time the car did not exist; after this point in time the car did exist.

The scientific process of extrapolation is valid only within a certain smooth range which does not cross a boundary. Extrapolation may never be extended beyond or across a boundary. If a scientist (or a computer) ignores the existence of a boundary, we end up with calculated results which look accurate, yet, are completely meaningless.

What is the boundary in the second example above? The car started moving in New York from east to west. East of New York is the Atlantic ocean, and cars don't usually run on the ocean. The boundary between the ocean and the land is an abrupt change in conditions. Any attempt to calculate the location of the car beyond this boundary (which means, at any day earlier than day 10 of the month) is scientifically meaningless. We can calculate an artificial number which looks exact, but this number has no scientific meaning. Now, in this example, what happens if we don't know the location of the boundary? How do we know if a calculated result is valid or not? The answer is simple - we don't know. Any attempt to claim that we know, is not science but speculation.

Another mathematical tool employed in the process of scientific discovery and analysis is a little more complicated - functions and equations. Every change and every motion in the physical universe can be described by a mathematical function or can be obtained through a solution to its applicable set of equations. We don't always know what the equations are. And, even if we know what they are, we don't always know how to solve them. But, we know that the equations and their solutions exist.

In precise mathematical terminology, calculating the location of the car moving from New York to Los Angeles involves a solution to a very simple equation which describes the car's movement. The car's movement can also be described as a function of time and as a function of the car's location. When we state the speed of motion of an object, we are in effect writing the equation which governs the motion of the object. The speed of motion is the distance the object moves within a given period of time. This is the simplest possible equation. When we know the equations and at least one boundary condition (for example, the speed of the car and the starting point or the end point of its motion), we have an opportunity to solve the equations and get results. But, we have to be very careful to avoid a common pitfall in this analytical process. To understand the pitfall, let's try to solve the following scientific question:

A person walks from Phoenix Arizona, in a straight line north, towards Salt Lake City in Utah. The distance from Phoenix to Salt Lake City is 500 miles. The person can walk 10 miles in one day. How many days will it take the person to get to Salt Lake City?

This question was presented to many people. School children, teachers, school principals, rabbis, and doctors. They all said 50 days.  Is this your answer too?  Remember, this is not an exercise in fourth grade math. This is a scientific question. If you think the answer is 50 days, try again without peeking at the next paragraph.

Hint:   This is not a trick question. The distance from Phoenix to Salt Lake City is indeed 500 miles;  Salt Lake City is indeed north of Phoenix; and the person is indeed capable of walking 10 miles a day. If you still think the answer should be 50 days, open a map of the area.

Are you still perplexed? You are in good company. If you run your finger on the map, following the route that this person has to walk, you will discover that he has to cross the Grand Canyon...  Ooooops.

The Grand Canyon is a discontinuity in the path from Phoenix to Salt Lake City. The Grand Canyon actually presents three types of discontinuities. The first is the walk down; the second is the need to somehow cross the Colorado river; and the third is the climb back up.  When doing scientific analysis, crossing an unknown discontinuity leads to very large errors and meaningless results. The less we know about the discontinuity, the larger the errors.

Even if we know exactly how to write and how to solve the equations that describe a process, once we have to cross an unknown discontinuity the equations are no longer valid and are not solvable. Any attempt to guess an answer beyond an unknown discontinuity is not science - it is speculation or imagination. It is not even a speculative theory.

Now let's get back to extrapolation. We already know that extrapolation does not work beyond boundaries. How valid is an answer if we have to extrapolate beyond an unknown discontinuity?

Extrapolation is a very unreliable tool when dealing with scientific analysis. Real scientists never rely on extrapolation in their research. Solving equations within a known range is a much more reliable tool, as long as we don't try to cross a boundary or an unknown discontinuity. Now, what happens if we try to combine two evils - extrapolation AND crossing an unknown discontinuity? The errors will be so bad that the results will not even qualify as "imagination" in the classification above.

The Great Flood:

The story of a Great Flood is a widespread theme among most of the world's cultures. It is best known by the Biblical story of Noah. It is also known in other cultures, such as stories of Matsya in the Hindu Puranas (India); Deucalion in Greek mythology; and Utnapishtim in the Epic of Gilgamesh (Babylonia - Iraq).

The date of the Great Flood has been the subject of many research projects. According to the Bible, the great flood occurred in year 1656 following the creation of the world  (2104 BCE). Various archaeological findings date the flood to within the range of 2000-2700 BCE.

The Great Flood was caused by a massive climatic change in the atmosphere and a similarly massive geological change in the earth's crust. Almost all of the humidity in the atmosphere condensed, came down as an avalanche of rain, and flooded the earth. Volcanic activity shifted or broke up tectonic plates, and parts of the earth's crust were pushed up to form mountains. (Fossils of sea creatures and seashells were found high up on mount Everest.) The volcanic heat caused the water to boil, so, all the archaeological findings from before the flood reach our hands after having been immersed in salty hot water. These changes resulted in a massive unknown discontinuity in the parameters used today by scientists who try to date various archaeological findings.

Bible critics try to refute the account of the first appearance of the rainbow following the flood. Did the laws of physics change to enable the appearance of a rainbow? they cynically ask. No, the laws of physics did not change. What changed is the atmospheric conditions. Before the flood the humidity in the atmosphere was near 100%. Under such conditions it was impossible to have simultaneous rain and sunshine, so, it was also impossible to ever see a rainbow. After the flood, the atmospheric humidity dropped to what it is today, and the appearance of the rainbow was enabled. The appearance of a rainbow is evidence of low atmospheric humidity, and, therefore, can be presented as a guarantee that such a flood will never occur again. This massive atmospheric change is another discontinuity in the parameters used for dating early history.

Dating studies using carbon-14 and other similar methods work only if all the relevant parameters remain constant over the entire range of time being studied. Every decent chemist knows what happens to natural materials immersed in salty hot water for a long period of time. Scientists involved in such studies know that the parameters were NOT constant, and that the Great Flood was a massive discontinuity. However, those who admit to such knowledge risk losing their jobs or their research grants. So, to protect their livelihood, they have no choice but to conveniently ASSUME that the relevant parameters did not change over time, and to conveniently IGNORE the discontinuity caused by the Great Flood.

Any attempt to calculate a date based on today's known parameters is risky "extrapolation". Any attempt to calculate a date earlier then the Great Flood carries with it the added vice of trying to cross an unknown discontinuity. Together, the extrapolation of today's parameters across the unknown discontinuity of the Great Flood results in errors so big that only "science fiction" could qualify as the category of the results.

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Copyright© 2007-SEP by Zvi Shkedi. The author permits not-for-profit republication of this article with proper credit and without changes.
Originally posted: 2008-MAR-30
Latest update: 2008-MAR-30
Author: Zvi Shkedi