Herb Silverman is the Founder of the Secular Coalition of America, the Founder of the Secular Humanists of the Lowcountry, and the Founder of the Atheist/Humanist Alliance student group at the College of Charleston. Here we talk about mathematical training, comprehension of the universe, and the effects on secular activism and personal worldview.
Scott Douglas Jacobsen: In terms of the mathematical training for you, and as you have a high level of mathematical training and expertise connected to a lifetime of activism, how does the comprehension of the relations of numbers to one another and of numbers to physics and cosmology, and of physics and cosmology to the universe as an apparently neutral operator, influence secular activism and personal worldview?
Herb Silverman: As a youngster from an Orthodox Jewish background and an interest in mathematics, I was fascinated and puzzled by an infinite God with infinite power who lived in infinite space for an infinite amount of time. I felt that studying “infinity” would help me understand God. I became intrigued by Zeno’s Paradox of the infinite, and here’s one version of that: An arrow goes halfway to its target. It then goes another halfway, and repeats the process an infinite number of times. Therefore, it can never reach its target. But, of course, the arrow does reach its target.
Zeno was a philosopher, not a mathematician, living in an era before the concept of a limit (the basis of calculus) was discovered independently by Newton and Leibniz. They showed that infinite sums can converge to a finite limit. In Zeno’s case, we can begin with one half, then add half of that (one fourth) and keep adding halves. This infinite series has the limit 1, which is the Zeno target.
I later learned that infinity is a theoretical construct created by humans, and that the number “infinity” does not exist in reality. Since the concept of infinity can help solve math problems, it seemed to me that an infinite God was created by humans to help solve human problems. Infinity, like gods, is not sensible (known through the senses). Mathematically there are many types of infinities, just as people believe in many gods. My mathematics students have sometimes falsely treated infinity as if it actually existed as a real number, and such misuse often got them into trouble. And so it is with many god believers who treat a so-called infinite deity as a real person.
Religious believers assume their god is real and infinite because a finite god would be limited. However, we can show mathematically that there can’t be a largest infinity. In fact, there are infinitely many infinities. So, any infinite god could theoretically be replaced by a more powerful infinite god.
The nineteenth century mathematician Leopold Kronecker once said, “God created the integers, all else is the work of man.” I interpret this statement to be more about the axiomatic approach than about numbers or theology. To build a system you have to start somewhere (Kronecker started with integers). Mathematicians usually begin with axioms that seem “self-evident” because they are more likely to guide us to real-world truths, including scientific discoveries and accurate predictions of physical phenomena, though there may be doubt as to whether the axioms themselves are true. Most ancient religions are also loosely based on axioms. Their most common axiom is “God exists,” which is not as self-evident as it appeared to be in a pre-scientific world. A “God axiom” might give comfort to some, but it lacks predictive value.
Mathematician are interested in conclusions that may be deduced from axioms, regardless of whether the axioms are actually true. Mathematicians, unlike most theologians, recognize that their axioms are just made up. So, a perfectly valid and logical proof may have nothing to do with reality. Part of the beauty of mathematics is seeing the strange and mysterious places that apparently simple and innocuous assumptions may lead.
Case in point: The Euclidean geometry taught in high school contains five reasonable axioms, like “all right angles are equal” and “there is exactly one straight line between two points.” Euclid’s fifth axiom, known as the “parallel axiom,” says that for a point not on a straight line you can draw exactly one line parallel to the original line that passes through the point. By eliminating Euclid’s fifth axiom, mathematicians developed systems known appropriately as non-Euclidean geometries.
Is this axiom changing merely a useless game? Even if it is, mathematicians can justify it on aesthetic grounds if the subsequent reasoning is deep, innovative, and creative. This particular story has a happy ending even for the most practical individual. Einstein developed his general theory of relativity by making use of the theoretical mathematics of non-Euclidean geometry, and applying it to what we now understand to be a non-Euclidean, four-dimensional universe consisting of three-dimensional space and one-dimensional time. Euclidean geometry, however, still works just fine here on planet Earth. (“Superstring theory” might eventually reconcile quantum mechanics with general relativity, though the theoretical mathematics behind it requires at least a ten-dimensional universe. Sounds impossible, but so did a four-dimensional universe in the days of Euclid.)
Some mathematical discoveries seemed so unusual at the time that they were assigned strange names like “irrational” number, a number that can’t be expressed as the quotient of two integers. The square root of two is one of infinitely many irrational numbers. My mathematics research field, complex variables, might sound supernatural because it deals with what are called “imaginary” numbers. There may be no perfect God, but there are “perfect numbers,” defined as numbers equal to the sum of their divisors. The first is 6 (1+2+3). The next perfect number is 28.
Whether intentionally or otherwise, many scientists may be viewed as secular activists because they have made obsolete many “God of the Gaps” arguments. We can accurately predict future eclipses, which are no longer attributed to God’s wrath. With every natural scientific discovery, there’s less reason to believe in the supernatural. The eighteenth-century French mathematician and astronomer, Laplace, did groundbreaking work on the stability of our solar system. When Emperor Napoleon asked him why he didn’t mention a creator, Laplace said: “I had no need of that hypothesis.” Perhaps a future Laplace will explain to a future Napoleon why our universe had no need of a God hypothesis.
Regardless of current disputes about infinity, I’m happy that we can freely discuss our views without meeting the same fate as Giordano Bruno in 1600. He taught that the universe was infinite with an infinite number of worlds like ours. At that time, it was considered heretical for finite man to discover the nature of the infinite, which was deemed clearly allied with the nature of God. This brilliant mathematician and cosmologist was burned at the stake, one of the last victims of the Inquisition.
Jacobsen: Thank you for the opportunity and your time, Herb.
Scott Douglas Jacobsen is the Founder of In-Sight: Independent Interview-Based Journal and In-Sight Publishing. He authored/co-authored some e-books, free or low-cost. If you want to contact Scott: Scott.D.Jacobsen@Gmail.com.
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