The Aleph —

By Dr. John C. (“Jack”) Adler, as told to Bill DeSmedt 

Last time, we looked at the anatomy of a black hole, what little there is of it (just mass, spin, and charge, remember?).

More particularly, we looked at its core singularity, and at how an event horizon keeps that part quarantined from the rest of the universe. And we closed with a hint that maybe that wasn’t always and everywhere the case.

What we’re talking about is called a “naked singularity” — one that isn’t decently veiled by an event horizon. And the question here is: is such a thing even possible?

A lot of physicists are really hoping it’s not. Back in the day, Stephen Hawking had declared naked singularities to be anathema. Roger Penrose went one him better: Sir Roger’s “Cosmic Censorship Conjecture” claimed that Mother Nature herself forbids a singularity from exposing itself in public.

But calling something a conjecture is really just a fancy way of saying it’s a guess (my own Vurdalak Conjecture being no exception). And Sir Roger’s guess hasn’t been doing all that well lately: Back in the early nineties, Stephen Hawking bet Kip Thorne 100 pounds and a T-shirt that nature would never allow a naked singularity to form.

By 1996 he’d paid up.

Because that was the year Matthew Choptuik, doing some supercomputer simulations at my alma mater U. Texas, Austin, found the first stellar-collapse configuration leading to full-frontal singularity. Ever since then seems like somebody comes up with a new way to do that every other year or so. It’s looking like the cosmic censors are whistling in the dark.

Still, I know where they’re coming from. As a group, physicists have got a lot riding on the proposition that the cosmos is a nice, dull, predictable place. And a naked singularity would sure stick a burr under that saddle.

Fair warning: this’ll be kind of a detour. Still, it doesn’t seem fair to keep on rattling on about how weird singularities are, and never get around to describing the weirdness itself. So, if you’ll bear with me a minute here, we’ll try to lift the hem of Mother Nature’s garment and take a peek.

To begin with, let’s imagine we’ve somehow stripped the event horizon off of our singularity, and it’s standing there in what my granddaddy’d call its bare nekkids. Well, what’s it look like?

If only I had a nickel for every time somebody’s asked me that one!

 But try thinking about it like this: The singularity’s just a point source. You wouldn’t be able to see the thing itself at all — it’d be too infinitesimally tiny. What you might see would be instantaneous cross-sections of all the world lines caught up in its vortex.

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Worldlines take some explaining in their own right. Think of the path of an object through time and space, as if you could see it from outside — a God’s-eye view maybe. From hyperspace, all the moments of your life blur together into a continuous four-dimensional “tube”: It splits off from your mother the moment you’re born, and comes to an end (or maybe not) at the hour of your death. Slice through the tube anywhere along its length and you’ll get a three-dimensional cross-section — a cross-section that is you yourself at that particular moment in time.

Or think of it like a motion picture: if every instant of your life, every “now,” were a single frame in a movie, then your worldline would be the whole reel taken together, considered as a single continuous entity.

Now think of everything and everyone tracing out a worldline path through space and time like that. And imagine all those worldlines — at least the ones local to earth — getting tangled up in a black hole. Then, assuming you could gaze into that hole’s singularity, it’d be like seeing all of recent history, only with everything all jumbled together and happening at once.

Last time I taught Astrophysics for Poets 101, a lit major came up to me after class and told me how that all reminded her of a story called “The Aleph.” Turns out Jorge Luis Borges, the Argentinean fantasist, wrote this short story about a funny-looking sphere someone finds in the basement of a Buenos Aires apartment.

Now, strictly speaking, aleph is the name of the first letter of the Hebrew alphabet (which later gets itself transmuted into the Greek alpha). It’s also the designation that Georg Cantor, the creator of set theory, gave to the class of sets of transfinite numbers, starting with Aleph-Null, the (infinite) number of all integers and going on up from there.

All of which may or may not have a bearing on Borges’ Aleph, which is only about an inch across, but somehow manages to encompass everything in existence — lions and tigers and bears, and such.

Stare into this Aleph and you’d see … well, here, Jorge tells it far better than I ever could:

    I saw tigers, pistons, bisons, tides, and armies; I saw all the ants on the planet; I saw a Persian astrolabe; I saw in the drawer of a writing table (and the handwriting made me tremble) unbelievable, obscene, detailed letters…

    In that single gigantic instant I saw millions of acts both delightful and awful; not one of them amazed me more than the fact that all of them occupied the same point in space, without overlapping or transparency. What my eyes beheld was simultaneous…

    …and I felt dizzy and wept, for my eyes had seen that secret and conjectured object whose name is common to all men but which no man has looked upon — the unimaginable universe.

That’s about as good a guess as to what a naked singularity might look like as any, I’d say.


Jorge Luis Borges, “The Aleph,” in Jorge Luis Borges, Collected Fictions, translated by Andrew Hurley, Penguin, 1998.