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Assumptions in Science
by Jeffrey Sax
November 3, 2003
have been proved to be useful in ordering things easily acquire such an
authority over us that we forget their human origin and accept them as
– Albert Einstein
Assumptions form an integral part of the scientific method. Every scientific
theory is based on a collection of assumptions. These assumptions demarcate the
domain where the theory is valid. The theory can’t be applied reliably to a
situation if one or more of its assumptions are violated.
The fact that a theory 'works' says nothing about the universal validity of
its assumptions. It says nothing about what will happen if one of the
assumptions does not apply. All too often, however, as the theories that
rely on them become more universally established, the assumptions themselves
become self-evident truths that are validated by the success of those theories.
Every assumption sets a boundary on the kind of pursuits that are considered
valuable within a field. When an assumption becomes a truth, this boundary
turns into a solid wall. This has the beneficial effect that the implications
of the theory and its assumptions are very thoroughly investigated. Even within
the walls, there are vast regions of unexplored terrain. Limiting our
explorations to the region inside the wall allows us to give these unexplored
regions the attention they deserve.
The downside is that highly original ideas aren’t really given a chance.
Anything that lies beyond the wall of truth is considered a waste of resources.
Ideas are dismissed before their implications can be studied in any detail.
Progress is inherently limited to what lies inside the wall. For all intents
and purposes, there is nothing outside the walls.
When the subject of the theory is the nature of reality, the implication is more
far-reaching. In this case, the reality we live in is bounded by those same
walls. Nothing can exist beyond them. Any evidence that something beyond those
walls might exist is discarded. Anyone who believes there is something beyond
those walls is delusional and is unworthy of attention.
Yet history has shown time and again that the most significant breakthroughs
come when someone dares to look over the established walls. These scientists
have had the courage and insight to investigate how different or less stringent
assumptions may cover a wider area and still match the terrain. Eventually the
impenetrable walls are torn down and replaced with fences that simply mark the
area where the assumption is valid.
The scientific method
According to Karl Popper’s concept of falsifiability, a theory can only be
called scientific if there is a possibility to prove it is false. This means
the theory must be based on assumptions that can be verified. If a theory
cannot be falsified, then it is of little value to science.
We will now look at two examples of assumptions made in the physical sciences
that proved to be false. Each of these examples will teach us an important
lesson about the role of assumptions in the development of science.
In the 4th century B.C., the Greek mathematician Euclid of Alexandria
wrote one of the pivotal works in the history of science. His Elements,
which spanned 13 volumes, not only set out the foundations of geometry for the
next two millennia. It also presented very clearly the axiomatic and deductive
structure that to this day characterizes mathematics and the exact sciences in
general. Euclid started out with a set of postulates or axioms. The axioms
contained some common notions, such as a point and a straight line, which were
considered self-evident. The axioms themselves were also believed to be
obvious, and were given without proof. From these, he deduced dozens of
theorems and relationships between geometrical objects.
The most famous of these postulates is the fifth postulate, also known as
the parallel postulate:
if a straight line falling on two straight lines makes the interior angles on
the same side less than two right angles, the straight lines, if produced
indefinitely, will meet on that side on which the angles are less than two
In its more familiar form, the postulate states that, given a straight line and
any point not on it, there exists one and only one straight line that passes
through this point and never intersects the first line, no matter how far they
Many mathematicians felt uneasy about this postulate. It felt less intuitive and
obvious than the first four of Euclid’s postulates. However, it was necessary
to prove important theorems such as Pythagoras’ theorem. For centuries, many
mathematicians believed this postulate could be derived from the first four
postulates. Countless attempts were made, and many proofs were published, but
all of them were flawed. Nevertheless, the truth of the postulate was never
Until the year 1823. In that year, Janos Bolyai and Nicolai Lobachevsky both
independently realized that, if they relinquished the parallel postulate and
replaced it with a different postulate, they could create a consistent and
entirely new kind of geometry. Where the fifth postulate produced what would
later be called Euclidian geometry, the alternative postulates produced
In non-Euclidian geometry, there are either zero or infinitely many straight
lines through a point that don’t intersect another line. The sum of the angles
of a triangle can be larger or smaller than 180 degrees. Pythagoras’ theorem is
no longer valid, which means that distances between points are measured
Less than a century after Bolyai and Lobachevsky’s discovery, non-Euclidian
geometry turned out to be one of the mathematical corner stones of one of the
major breakthroughs in 20th century physics: Einstein’s special
theory of relativity. Einstein proposed that space-time is non-Euclidian. As a
result, if it was forced to fit into a Euclidian world, it would appear to be
Euclid’s parallel postulate was unchallenged for over twenty centuries. To
question its validity was considered a worthless pursuit. Many disciplines
developed and flourished based on Euclidian geometry: mechanics,
electro-magnetism, much of chemistry. In the end, however, the postulate turned
out to be only an assumption.
However, this fact does not invalidate Euclidian geometry itself or the sciences
that have it as one of their corner stones. Euclidian geometry was and still is
an enormously successful tool for describing every-day physical phenomena. To a
very high degree of accuracy, our world is Euclidian. And so to a very high
degree of accuracy, the assumption of the parallel postulate holds true.
No one in their right mind would consider throwing away the achievements of
Newton’s mechanics or Maxwell’s electro-magnetic theory because Euclid’s
parallel postulate is not true in our physical universe.
The theory of heat
Another example of an assumption that eventually proved false concerns the
nature of heat. According to this theory, all mechanical interactions involve
some conversion of mechanical energy into heat. Therefore, any self-contained
mechanical system must eventually come to rest, as eventually all the available
mechanical energy has been converted into heat. The assumption under scrutiny
here was worded by James Clerk Maxwell as follows:
“Admitting heat to be a form of energy, the second law asserts that it
is impossible, by the unaided action of natural processes, to transform any
part of the heat of a body into mechanical work, except by allowing heat to
pass from that body into another at a lower temperature.”
The assumption is that heat is a form of energy that is essentially different
from mechanical energy.
This classical theory of heat was immensely successful. It has been used to
accurately describe heat exchange, efficiency of engines. It is, quite
literally, the foundation of rocket science!
Later in the 19th century, Maxwell, Boltzmann and others developed
the modern kinetic theory of heat. According to this new theory, heat is
nothing more than kinetic mechanical energy of the molecules that make up the
solid objects, liquids, and gases of the classical theory. The molecules move,
too. They bounce around and tumble chaotically, colliding with each other like
little billiard balls. The temperature of a body is a measure for how much its
molecules are moving.
The conversion from mechanical energy to heat is then nothing more than the
redistribution of that mechanical energy from the body as a whole to its
constituent atoms and molecules.
For example, when a ball is rolling on the floor, its molecules are all moving
in an orderly, coherent fashion. During this process, the molecules of the ball
collide with molecules in the air and on the floor. Mechanical energy is
exchanged between the molecules in the ball and the molecules in its
surroundings. This results in a gradual loss of coherence, until finally all
the coherent mechanical energy is converted into chaotic movement of molecules
of the ball as well as the floor and the air. When the ball has come to a halt,
the temperature of the ball, the floor, and the air will have risen slightly.
Won’t the molecules themselves come to rest after a while, just like the balls
on a pool table? The answer is no. No energy is lost in the collisions between
molecules. The energy has nowhere to go! The molecules will just keep bouncing
around happily ever after. This constant motion of molecules is actually
visible in a phenomenon called Brownian motion. Named after Robert Brown, a
botanist, who first observed the constant motion of particles suspended in
water or air. The molecules themselves are too small to see, but they do carry
enough energy to show the effect of their collisions with particles that are
visible under a microscope.
The kinetic theory of heat went on to become even more successful than its
predecessor. It was able to explain everything the previous theory could
explain. It was able to explain Brownian motion. It was even able to quantify
the heat capacity of substances, which is a measure for the amount of energy
needed to raise the temperature by a certain amount.
However, for most applications, including sending astronauts to the Moon, the
original theory, based on the assumption that heat was an essentially different
form of energy, was good enough. The reason it was good enough is because this
assumption has no or very little bearing on the further development of the
theory of heat. The kinetic theory of heat provided an alternative foundation
for thermodynamics, but the same quantities used in the classical theory can be
easily derived in the kinetic theory. The structure of the theory on top of the
new foundation remained the same.
Today, very few people still hold on to the original concept of heat as an
essentially different form of energy. One of the reasons it was given up so
easily is that it was clearly shown that it was not necessary. It was
demonstrated that the new kinetic theory of heat led to the same results. More
importantly, the new theory stayed well within the bounds of the established
The two examples in this section illustrate two important points:
Genuine progress is only possible by thinking outside the walls of established
assumptions. Unfortunately, this activity is discouraged for the most
well-established and basic assumptions of science.
Even if an assumption lies at the base of a theory, it may be possible to
replace this assumption while keeping the theory built on top of it intact.
Heath, Sir Thomas Little (1861-1940) The thirteen books of
Euclid's Elements translated from the text of Heiberg with introduction and
commentary. Three volumes. University Press, Cambridge, 1908. Second
edition: University Press, Cambridge, 1925. Reprint: Dover Publ., New York,
 James Clerk Maxwell, Theory of