FMBR Editorial: May, 2001
Measurement & Reality
William C. Gough & Dean Brown
Have you ever heard the expression: "If you can't measure it, it ain't real." Every day scientists and engineers work with equations and formulas that contain irrational and imaginary numbers (for definitions see page 3). The scientific precision with which we model and alter Nature using electromagnetic theory, relativity theory, and quantum theory would not be possible without the use of irrational and imaginary numbers. They are an absolutely essential element of modern science. Their is nothing "imaginary" about what the equations and formulas describe in our physical world, whether it be electric currents or atomic processes. Yet most scientists and engineers consider the "imaginary component" and the "hyper-dimensional spaces" that also result from their calculations to be "fictional", i.e., not a part of our "real" world. Why do they believe this?
The underlying issue is that all our scientific instruments that we use to "measure" our world have limitations. They can only measure real numbers that are rational. Real numbers that are irrational can only be approximated and imaginary numbers are not measurable at all. The rational numbers are an infinitesimal part of the total real numbers, and say nothing about the "imaginary spaces." In physics this is known as the "measurement problem."
What is the deeper implication of this limitation to our "scientific understanding" of the reality of Nature? The answer is -- all measurements are tentative. Between any two measured points an infinite number of possibilities may occur. Explore the points between the points and one discovers mysteries. At the U.S. Atomic Energy facilities in Idaho a test nuclear reactor was calculated to be stable, however, the reactor after 80 normal operations went unstable with the loss of a life. The scientists found that the cause was an unstable resonance located between the originally calculated points. Not only are we limited by the need to use rational numbers in our computer calculations, but measuring instruments are intrinsically uncertain due to Heisenberg Uncertainty, entropy, faulty models, etc. Science can never overcome these intrinsic handicaps. In fact, the frontiers of science always reach for further refinements in the data -- science is insatiable. Einstein's theories would never have been validated if the instrumentation of 1910 had not been greatly improved.
The "certainty" of science is even more elusive! Every theory, every model, every ontology, is always superseded by a more refined one. The more we know, the less we know -- science unfolds by progressive revelations. The goal of every scientist is to overturn or refine the prevailing theory. Science rests on a shaky foundation -- so don't look to science for certainty. There is the reality of one's direct experience, and there is the reality of mathematical proof. And then there is the consensual reality as expressed in the media -- which drifts on shifting sand. Yet each individual through direct experience can explore undiscovered realities of the Absolute. These realities are beyond our space and time but often have been described by mathematics -- they are realities that the limited physical instruments of science can never measure.
Real numbers can be rational or irrational. Examples of real rational numbers are: 2, 5, 2/3, 7/4, etc. Examples of real irrational numbers are: e, pi, the square root of 2 or of 3, etc.
Imaginary numbers result when one takes the square root of a negative number. Examples would be the square root of -1, or of -5
Bill Gough & Dean Brown, May 2001