The center will hold

Things fall apart; the center cannot hold;
The best lack all conviction, while the worst
Are full of passionate intensity.

So wrote William Butler Yeats in 1919, in reaction to World War I and the 1918–1919 flu pandemic — a far worse time than this.

Yeats was wrong: the Center of human civilization held then, is holding now, and always will hold.

What is the Center of human civilization?  Mathematics, and all that follows from mathematics.  Mathematics is certain!

Let me dismiss a quibble: Kurt Gödel is said to have undermined mathematics with his Incompleteness Theorems.  What nonsense!  The Gödel theorems are only valid mathematical theorems, not revelations from God.  Gödel correctly showed that a particular method of proving the mathematical consistency of arithmetic would not work, not that proving consistency is impossible.  Gödel himself outlined a consistency proof based on the Theory of Types, and Gerhard Gentzen gave another valid proof based on transfinite induction.  The interested reader can consult Wikipedia for details, but the bottom line is this: mathematics is as certain as it has always been thought to be.

What follows from the certainty of mathematics? 

The Existence of God

In 1948, the great British mathematical physicist Sir Edmund Whittaker (FRS, Copley Medal) proved in his book Space and Spirit that St. Thomas Aquinas's five proofs for the existence of God — Aquinas' Five Ways — are valid when translated into modern physics (Aquinas based his formulation on Aristotelian physics).

Let me give only one of the modern proofs, the updated Second Way, or the Argument to the First Cause.  (Aquinas got this proof from Moses Maimonides: see Guide for the Perplexed.)

The modern version needs only two assumptions: (1) time exists (Aquinas tacitly assumed this), and (2) the Second Law of Thermodynamics, which says the entropy of the universe always increases.

These two assumptions, both firmly established by physics, imply that the universe is not complete in itself.  Time, physics tells us, is like a line.  If this line were curved into a circle, then the universe would be complete in itself.  But time cannot be cyclic, because entropy must always increase.  If time were cyclic, the entropy at some time point in the future would have to return to the same value it had in the past, contradicting the fact that it always increases.

So if we look at any sequences of causes into the past, either there is a finite sequence of causes beginning with a First Cause that has no prior cause, or else the sequence is infinite.  In this case, the set of the infinite sequence of causes defines a First Cause (the technical mathematical expression is "the set defines the completion of the sequence"). 

In either case, a First Cause exists, and, in Aquinas's words, the First Cause "all persons call God."

Inevitability, Whittaker's proof will be rediscovered — mathematics always wins.  So future society will acknowledge the existence of God, just as it acknowledges the fact the Earth is a planet, established by Aristarchus, forgotten during the Dark Ages, but rediscovered by Copernicus.  Under God, morality will return.

Yeats should have remembered an earlier poet, Henry Wadsworth Longfellow:

God is not dead, nor doth He sleep.
The wrong shall fail,
The right prevail

Frank J. Tipler is Professor of Mathematical Physics at Tulane University.  He is the author of numerous technical papers, mainly in cosmology and general relativity, and the books The Anthropic Cosmological Principle (co-author), The Physics of Immortality, and The Physics of Christianity.

Image: Botticelli.

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