A Meditation on Zorn’s Lemma by a Newly Hatched Grampa

Brooding on the lovely picture of the grandchildren it is presumptive to say they are “mine” although they were sired in truth by my son. Seriously this is recursive, for it seems just yesterday when I held their father upside down like a nutbar and now he is holding kids of his own, staring cheeky like at the camera with that delinquent gaze more like his uncle than me.

An obscure mathematical result in graph theory, Zorn’s Lemma, is that “in a graph of infinite length there is at least one chain of infinite length” or “if the human race never dies out, there is a man or woman alive today whose descendants will never die out.”

When I first read of Zorn’s Lemma (in Donald Knuth’s book The Art of Computer Programming) I got all excited and told my wife, these children’s Granny, she said, “of course, that’s obviously true and profoundly stupid, Edward”. Words to that effect.

But Donald Knuth and I were impressed with the idea which was expressed, if memory serves, incorrectly, as “if the human race never dies out, there is a man alive today whose descendants will never die out.”

That sounds cooler if you’re some sort of savage, but isn’t it is mathematically incorrect?: There need be only one person with infinite descendants, right?

The problem is subtle. IF the ONLY way of having descendants is heterosexual reproduction, THEN Knuth’s phrasing (if I am correct that that is what it was) is correct: there IS a man alive today, and his Better Half, and THEIR descendants are the Immortals.

BUT there is a probability that only a WOMAN live today will be The Mother of the Immotrals having artificially inseminated herself…right? BUT, she would have to use black arts since artificial insemination means using…sperm, and there is a Father after all. Frankly I do not know how to make a baby using only a woman and no spermaceti. If memory serves, my active nay enthusiastic participation was a sine qua non.

What’s interesting is that I was in my self-depreciating Mama’s boy way preemptively here writing myself out of the picture, dammit. But wait. Fathers are important. It’s just that they have been, ever since WWII, rat upon and shat upon and made into palookas.

I need to followup soon with an essay on the disappearance of the father, how modern technology and capitalism erases him only for him to return, at the bottom of the wood pile. Sir Kenneth Branagh’s work a meditation on this, consider his tender Henry V:

I will weep for thee, since this revolt of thine
Is like unto another fall of man

says the King so fondly to the traitors Scroop, Grey and Mortimer.

Brian Blessed in As you Like It, tenderly inviting the starving Orlando to feed: Hamlet Senior with his look of such infinite love and sorrow in Gertrude’s bedroom and Sarastro in Branagh’s Magic Flute trying to end the war between him and the Queen of the Night. We find the father so inconvenient yet he insists upon his reality in Branagh.

Mitt Romney speaks darkly in his god damned darkening, dialectic of enlightenment and demon-haunted world of how homos concoct children with dark arts. But in fact, now that I have thought about Zorn’s Lemma, and beat six kinds of merry hell out of it whilst brooding over my lovely grand-daughters as the aging eagle broods over eagle eggs, I can conclude that if the human race never dies out, there is a man alive today whose descendant will never die out.

And a sub lemma happens to be that even if the Human Race does die out as it does in HG Wells The Time Machine, with the last man, reduced to a Troglodyte, expiring on Power Station Beach on Lamma Island, that man’s ancestors constitute a chain that goes back to the Rift Valley of Africa and the real Adam and Eve. And why do the paleologists say that Lucy was the mother of all? Where is Adam in the scientific account? Did Lucy screw a subhuman? But that would violate the rule as I understand it that different species cannot mate.

I do not know, and my head hurts along with my butt. I do conclude that we have gone from absurd sexism to erasing the father and treating him like shit without every once stopping in the middle.


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