01/29/2014 06:10 pm ET Updated Mar 31, 2014

War, Mathematics and God

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I've been actively engaged in two wars in my life, but I don't receive or deserve veterans' benefits. My most recent service occurred during the manufactured war by Fox News, the "War on Christmas." Yes, I plead guilty to wishing people "Happy Holidays" around winter solstice time, and I have even been known to provide a pagan history lesson to those who insist on telling me that Jesus is the reason for the season.

My earlier war arrived as a card game I learned at five, a game called "War." Two players are dealt 26 cards face down. Each then simultaneously shows the top card, and the player with the higher card takes both exposed cards and places them at the bottom of the player's stack. If both cards are of equal value, there is a "war." Each combatant places the next three cards face down, and the fourth face up. The card of higher value captures all the cards played and puts them at the bottom of his or her stack. The war ends when one person has all 52 cards.

I was very good at "War," or so I thought. I hadn't yet heard about "confirmation bias," which can cause us to remember more victories than defeats.

When I finally realized that the game was skill-free, I lost interest. Knowing that the outcome is completely determined once the deck is shuffled and dealt, I began to invent variations. For instance, I'd put all four aces (the highest value) in one stack and the remaining 48 cards in the other stack. After playing five times, the stack with four aces won all, but once. I concluded that it was better to start with the four-ace stack.

I hadn't realized that I was applying a naïve version of a Monte Carlo method, where a large number of repeated trials produce reasonably accurate probabilities for the outcome of an event. In fact, the simplistic childhood card game of "War" has much in common with my subsequent career as a research mathematician. Mathematics is also a completely determined game that starts with a set of assumptions called axioms (the axioms for "War" are shuffle and deal) and follows rules from which the truth of mathematical statements (conjectures) can be discovered. What makes mathematics more interesting than "War" is the ingenuity required to prove or disprove conjectures based on the axioms.

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. Most ancient religions are also loosely based on an axiom or a set of axioms. The most common axiom is "God exists," which is not as self-evident as it appeared to be in a pre-scientific world.

I ask you: Which abstraction is more practical for better understanding and solving real world problems: mathematics and its scientific implications, or God? Even religious believers no longer attribute an eclipse to God's wrath. We know that the next total lunar eclipse will be on April 15. And most believers accept that earthquakes have more to do with plate tectonics than with God's anger over specific human behaviors. A "God axiom" might give comfort to some, but it lacks predictive value.

The assumptions (axioms) in monotheistic religions usually include these attributes for their God: omniscient, omnipotent, omnibenevolent, and infinite. However, religious apologists who want to avoid contradictory axioms have difficulty trying to justify an all-powerful, all-knowing, and all-loving God who allows so much needless suffering.

As a youngster with an Orthodox Jewish background and an interest in mathematics, an infinite God with infinite power who lived an infinite amount of time fascinated me. I felt that studying "infinity" would help me understand God. Later, I learned that infinity is a theoretical construct created by humans, and that the number "infinity" does not exist in reality. So if finite man created infinity, I reasoned, perhaps finite man created God and gave him infinite attributes. Infinity is a useful concept to help solve math problems, so maybe an infinite God could merely be a useful concept to help solve human problems.

Mathematicians, unlike most theologians, recognize that their axioms are just made up, but believers assume their god is real and infinite because a finite god would be limited and could be replaced by a more powerful god. However, we now know 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.

Since the standard God axioms are contradictory, I wonder if there is a way to believe in a God with all those attributes when there is no objective evidence that such a God could exist. Yes, but it requires an infinite amount of faith.