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
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:
||B) Scientific theory
||C) Speculative theory
Let's examine each of these categories in detail:
||A) A fact is something which is well proven and established by
experiments. All experiments yield the same consistent results. All
attempts to disprove the fact have failed, and will most likely always
||B) A scientific theory is an attempt to explain an observation in a
logical way. Most scientific theories are expressed in the form of
mathematical equations or formulas. A scientific theory must be stated
in such a way that enables experimental scientists to perform
experiments to test the validity of the theory. A claim or opinion which
does not avail itself to experimental testing is not a theory - it is
just a private opinion or imagination. A scientific theory must be based
on facts which support the theory, and, there cannot be any fact or
observation which contradicts the theory. However, since the factual
basis on which the theory is based is not sufficiently broad or
complete, we still call it a theory rather than a fact. When a theory is
a) completely free from contradictions; and, b) all experiments trying
to prove the theory are consistently successful; and, c) all experiments
trying to disprove the theory are consistently unsuccessful; then, the
theory might be upgraded by scientists to the status of "well
established theory" and sometimes even to the status of "fact". If, on
the other hand, scientists find even a single fact or observation which
contradicts the theory, the theory gets downgraded to the status of
Example: According to Kabbalah, the world consists of four elements:
soil, water, air, and fire. In today's scientific terminology, these are
called: solid, liquid, gas, and energy. The Greek philosopher,
Aristotle, added a fifth element - the "aether" - the substance from
which the universe is made, filling up all space in which the first four
elements are absent. Scientists invested a huge effort and conducted
endless experiments trying to prove or disprove the existence of the
aether. When it was finally proven that the "aether" substance does not
exist, and what is left behind in the absence of matter is "vacuum", the
"aether" theory was downgraded to "failed theory". Only experienced
scientists know that the majority of theories found in science libraries
are failed theories.
||C) A speculative theory is an attempt to explain an observation without
a sufficient foundation of scientific facts. Such a theory may sound
right, may be pleasing to our senses, and may even offer a possible
explanation of an observation. However, the observation may also have
other possible explanations which can be very different. What makes a
theory "speculative" is the possibility of other theories and the lack
of sufficient evidence to prove which one of these theories is the right
one. A speculative theory must also be subjected to experimental
validation. For example: When a person does not come home from work at
the time his wife expects him to be home, the wife will usually develop
a speculative theory as to the reason her husband is not home. There can
be many possible theories, but the wife does not know which is the right
one. If she chooses to believe in one specific theory, it would be a
Speculative theories cause a lot of controversy in society. When
scientists debate speculative theories their objective is usually to
find the truth. However, when non-scientists debate speculative
theories, their objective is rarely the truth. Many debates over famous
speculative theories are more about promoting a social, emotional,
religious, or anti-religious agenda.
||D) Imagination is just that. Some people use their imagination to
explain certain observations without support from scientific facts.
Every observation which we do not understand triggers our imagination
and we try to develop some explanation in our mind. Almost all human
beings develop at least one imaginative explanation during their
lifetime. The milky way is there because someone spilled milk in the
sky. The moon is made of a green cheese and a cow eats from it during
the second half of each lunar month. During the day we hear more noise
than at night because the movement of the sun in the sky makes noise.
Sea water at night is warmer than by day because the sun warms it up
from underneath the earth at night. People come from monkeys - they turn
into people when nobody is watching. Do dogs evolve into cats or do cats
evolve into dogs? There is no limit to human imagination. All so-called
"theories" which do not avail themselves to experimental validation are
included in this category of imagination.
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
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
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.
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
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
- "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,
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.
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
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
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
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.
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