Essays in Idleness

The term “infinity” was an invention of the Devil. This, gentle reader will understand, is my humble opinion. Or if the Devil didn’t invent it, he “evolved” it, from the more innocent usages that conveyed “unlimited,” or “countless,” or “unknowably” large or small. What is finite has an ending, can be finished, finis. What is infinite cannot be; it is open-ended. There is, where we look for an end, nothing there.

Nothing is quite the opposite of something. Perhaps this is a fact no longer taught in our schools: that “nothing” can do nothing for you. Whereas, “something” might. For in its modern usage, “infinity” has become a thing. It has become “virtually” an agent, a kind of god, demanding to be worshipped. The very Christian idea of Alpha and Omega — from the first to the last letter of the (Greek) alphabet, from beginning to end — is subtly replaced in our minds with the progressive idea, “from one to infinity.”

Which is where the human mind checks out. “So what is infinity plus one?” one asks. There can be no answer. Today we are hanging on a cross of “infinity.”

The mathematician Georg Cantor (1845–1918), in his lucid moments (when out of insane asylums), invented set theory. It may be found, lodged in the heart of post-modern reasoning. My hero Wittgenstein, among others, explained how pernicious it was. Scholastic theologians had already spotted the fly in the “infinite” ointment. It is pantheist, and in Cantor’s “final” posit of an infinity of infinities, it is a direct challenge to the unity or uniqueness of the revealed God. Cantor himself was under the impression that God existed, in the sense that God had communicated set theory to Cantor of all people. I, at least, am sceptical of those who claim direct communication with God, especially those who spend a lot of time in bat houses, and wonder with whom they were really chatting. (I don’t doubt that the mad can be brilliant, however.)

To Cantor, there is the infinity of zero. There is an infinity of points in a line, and of lines between any two points. And more infinities are coming, until we have an infinity of them. The non-algebraic constants (such as pi or Euler’s e) — very real in nature — become officious “transcendentals” that we must salute when we meet in the street. With Leibniz we can still breathe; with Cantor we are drowning.

While I’m in a position to deny being a mathematician or a physicist, I distantly descry the tragedy of string theories, “many-worlds,” and even the assumptions behind the standard model of particle physics. My intuition is that they involve the breakdown of logic and reason; that they create maths that “work” on their own premisses, but do not apply to anything. At some point, the “reality” of math takes leave of the reality of reality, and we find ourselves spending billions of dollars to equip the hunt for a “theory of everything” that can only be an artefact of a phantom.

And that is what our “infinity” has become: a thing, when it is not a thing. By those uncomfortable with the holy simplicity of God, a substitute has always been sought. In the days before Cantor it was sought in the belief, the “settled science,” that the material universe had no beginning and will have no end. Once that error collapsed in the empirical cosmology of the 20th century, the Cantor hypothesis kicked in. Except, it is not an hypothesis. It is the brilliant imposition of a “number theory” that reconceives math as an empirical science; that can intrude upon what is really only a tool or technique of science with the appearance of an absolute. Or in short: go get lost in Ludwig Wittgenstein, Elizabeth Anscombe, and the others who have seen the contradiction in all worldly, absolute claims.

“Infinity,” when it takes on divine qualities, becomes an idol. The same might be said for the term “evolution,” which has conquered the realm of biology, and subverted all the social sciences and humanities by reckless analogy. It is the “infinity” of biotech. Anything for which the cause can’t be known, is assumed to have been caused by “evolution”; whereas, evolution isn’t a cause, and never can be. It can only be a trend.

Instead of the naïve, nursery notion of a great bearded father in the sky, we get “the theory of evolution.” Instead of the loosh habit of attributing anything we can’t understand to God, we get the mentally ill habit of attributing it to bushy-faced Darwin. Instead of the something of God, we get nothing, to explain everything.