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Question Time

Ask Dr. Silverman 8 — Infinity: Behind Every Real Infinite is a Silver Lining Infinite

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 infinity in a finite way (you’re welcome).

Scott Douglas Jacobsen: What types of infinity exist in the real world if any? What types of infinity exist in the abstract world? Why do some of those abstract infinities exist in the real world? Why do some of those abstract infinities not exist in the real world?

Professor Herb Silverman: Early puzzles about the infinite might have begun with the ancient Greek philosopher Zeno. One version of his paradox of the infinite is this: “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 lived long 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.

As a youngster 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 later learned that infinity is a theoretical construct created by humans, and that the number “infinity” does not exist in reality (as a real number). Infinity, like gods, is not sensible (known through the senses). Mathematically there are many types of infinities, just as people believe in many gods. 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 concept of infinity in mathematics is sometimes called potential infinite, as opposed to an actual infinite. The question arises as to whether an actual infinite exists. The answer is in dispute. Some argue that the continuity of space and time entails the existence of an actually inﬁnite number of points and instants. So the continuity of spacetime provides evidence of an actual infinite in our universe. Others argue that it has never been proved that space and time are composed of real points and instants.

Einstein’s theory of general relativity suggests that an expanding universe (as we observe ours to be) started at a time in the finite past when its density was infinite. Einstein’s theory also predicts that the center of a black hole has infinite density. These infinities, if they do exist, would be actual infinities.

Another question is whether our universe is spatially finite or infinite. The idea of a finite universe raises the question of what is beyond. As far as we know, the universe is everything there is. Also, based on the Big Bang, our universe has been around a finite amount of time (approximately 13.8 billion years), but there might have been infinitely many big bangs and big crunches before that.

Why do people other than mathematicians and scientists care whether there is an actual infinity or just a potential infinity? Because there are many religious people who equate God with the only actual infinity. If an actual infinite can’t exist, and God is infinite, then God can’t exist.

Probably the most popular argument for the existence of God is a form of the Kalam Cosmological Argument, popularized by well-known Christian apologist William Lane Craig. It can be stated as the following brief syllogism.

1. Whatever begins to exist has a cause;

2. The universe began to exist;

Therefore:

3. The universe has a cause.

Craig concludes that the cause of the universe had to be an uncaused, personal creator of the universe who apart from universe is beginningless, changeless, immaterial, timeless, spaceless, enormously powerful, and known as God.

Note that this argument says that God doesn’t need a cause because God has always existed. Since time began with the Big Bang, it would be difficult to say that God has been living infinitely long. Further, I would argue that the first premise is wrong. Not everything that begins to exist need have a cause. That appears to be the case in the quantum world of subatomic bits of matter. Since the Big Bang was a quantum event, there is no reason to say that our universe needed a cause.

Moreover, I find it interesting that those who try to argue rationally for the existence of a creator always seem to accept that creator through faith. Even if the Kalam argument worked, which it doesn’t, why conclude that there was a single personal creator of the universe? Who knows — there could have been trillions of agents involved in the creation of our universe (or even infinitely many).

It’s hard for us to wait for science to come up with definitive answers about the universe, so we speculate about some of them. I say, stay tuned.

Jacobsen: Thank you for the opportunity and your time, Professor Silverman.

Photo by Tim Gouw on Unsplash

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Scott Douglas Jacobsen is the Founder of In-Sight Publishing. Jacobsen supports science and human rights. Website: www.in-sightpublishing.com