The Nine Billion Names of God: Anyone done the math?

Cafe Society
1

Every science fiction fan knows of “The Nine Billion Names of God”, a short story by Arthur C. Clarke. The premise is that there’s a Tibetan monastery that has decided that the purpose of man is to enumerate all of the Names of God. They’ve (through methods not described in the story) determined that all of the Names can be written in a nine-character alphabet that they’ve devised, and that there are some rules that all true Names must follow, and decide to simply exhaustively list all of the words in this alphabet that follow those constraints, secure in the knowledge that all of the Names will be contained in that list. For this purpose, they rent a computer and hire a couple of engineers from an American company to print them out.

But great though the story is, it occurs to me that the math doesn’t really work out. First of all, there’s the matter of time. We’ll assume, for the sake of argument, that either their rules have a fairly low false positive rate (that is, that most of the words that meet the constraints are true Names), or that the “nine billion” figure is actually a count of all of the words that meet the constraints, and that the true Names are a subset of that number of unknown size. But either way, the computer must still be printing out nine billion words. This is said to take about a hundred days, and we know that the monks aren’t very far along in the project yet when they rent the computer: They’ve been at it for 300 years, and expected it to take 15,000 years. But 9,000,000,000 words in 100 days is 90,000,000 words a day, or 3,750,000 an hour, or over a thousand per second. While it’s reasonable for a computer (even one that Clarke was envisioning) to calculate that many words, how on Earth could it print them that fast?

And then there’s the matter of the quantity of paper. The short story collection I’m reading this in has 672 (fairly thin) pages, with 41 lines per page, and I count 53 characters in a typical line, for a total capacity of 1.4 million characters in the book. We don’t know exactly how long the Names are, but with nine billion Names constructed out of a mere 9 characters, most of them must be at least 11 characters long, plus another for a space between Names*. So this volume I’m holding could hold about 120,000 Names. At that rate, it would take 74,000 books this size to hold all of the Names. This book is 0.032 m by 0.108 m by 0.177 m, so that means it’d take 45 cubic meters (or about that many tons) of paper to hold all of the Names.

Clarke was surely capable of doing the math. What happened here, that he didn’t? It’s not like such a respected science fiction author to just throw out random numbers without giving them a sanity check.
*Never mind that the story also says

By very straightforward math, they apparently did bother to go on to words of ten characters.

2

They might be printing to microfiche, or else in VERY tiny print.

3

It’s not microfiche: There’s a reference to pasting the pages into books as they come off of the printer. I suppose that very small print is possible, though.

4

I don’t know if printing the words were relevant to the end of the story. Before they got the computer the monks were keeping track of the names by writing them down. Going by the end, God apparently thought that storing the names in the computer’s memory was good enough.

5

The story has a plural amount of printers running and a plural amount of monks pasting the pages into books. Without specifying exact numbers, it can be scaled up fairly easily to meet whatever number of pages/day is required I would think.

6

Hypothetically, they could have a customized printer(s) that does the work in parallel. Or if you don’t want to resort to a customized printer you could have thousands of printers. The computer sends word 1 to printer 1, word 2 to printer 2, and so on. With enough printers by the time word N is sent to printer N, then printer 1 will be done and ready to print word N+1.

(or what Folly said, I only read the OP before replying)

7

I’d cheat and say that spaces aren’t needed. And then, for example, “AABB” would cover “A”, “B”, “AA”, “BB”, “AB”, “AAB”, “ABB”, and “AABB”. You should be able to get all the names in under 4000 pages, then.

Eta: even less if the length of a name is unconstrained.

8

Allow me to introduce the line printer.

I’ve seen them back in the day (I don’t remember which model) - and they print so fast that the paper (fan fold) flies out of the top without hitting the guides. They were fairly loud, too.

At 11 characters and space per name, 80 characters per line, and at 2500 LPM, it would take 540,000 minutes or 375 days to print all the names. Add paper swap, changing ribbons, and general maintenance, call it 1.5 years. Divide it up between 6 printers, and you’re looking at 3 months.

It would still take a shit-ton of paper.

9

We wrote a program that printed several lines of all periods.

…
…
…
etc.

The printer rapped them out with a noise like gunshots. Startled the beehoosis out of the poor night-shift operator.

10

Now I’m wondering if Clarke was using the old British English definition of “billion”—which would have been 9,000,000,000,000 names! :eek:

11

One of the most fun programs I worked on when I was a student was a Fortran program that printed characters on the CDC line printer in such a way that it played music. Granted, a fair amount of imagination was involved. :smiley:

Still, the William Tell Overture a/k/a Lone Ranger theme was a big hit.

12

There are people still doing this with dot matrix printers. Like the Imperial March from Star Wars.

13

I worked on this project for a while: HP Web Presses. The high end of those things can print print more than 1000 feet of 26-inch wide paper every minute, whole books in seconds. They take whole banks of computers just to render the images fast enough.

(For comparison, they print as fast or faster than conventional plate printing presses, except that on the digital presses, every page can be different.)

I’m not sure whether the story was meant to be set in the (at the time of writing) future or not, but today it wouldn’t take long at all.

14

In the story, the initial commission takes place in Manhattan.

It is mentioned that the names are at most nine characters long, but we are not told how many characters there are in the alphabet.

There are about nine billion valid names, so they have to print out, collate, and bind at least that many (we are never told the exact number) in three months: a prodigious job any way you look at it. That is why the monks paid top dollar for the mainframe rental and the custom line printers, and clearly a lot of manpower was involved as well.

15

I just wanted to note that the paper used to write the prayers in Tibetan prayer wheels is extremely thin and fine, so that they can fit a lot of prayers in there. I’ve seen things on the internet about people now wrapping up microfilm and microfiche in there. So I can easily see them printing out the names on the thinnest paper technology would allow in a printer back then.

I agree that the numbers seem absurd, but I take the story in the spirit it’s meant - Clarke was drawing a parallel between the extravagantly huge numbers of Tibetan religion* and the impossibility of fulfilling them on human time scales with the incredibly fast operation of computers (even in those early days of Moore’s Law) and asking what happened when the two collided. That it resulted in the fulfillment of religious prophecy much earlier than intended is the result of technological advance.
*I suspect – but don’t know enough about Tibetan philosophy to be sure – that the very large numbers were meant to be a poetic way to say “eternity” or “this’ll never happen”, but some literal-minded religious official took it seriously.

16

Huh, when I read it and double-checked for that possibility before, it seemed quite clearly unambiguous the other way, but now that I see someone else saying that, it looks like your interpretation is correct.

And we can’t scale up the number of printers indefinitely: The whole setup is powered by a fifty-kilowatt generator (which is also powering the computer itself, electric lights, and unspecified other amenities), and everything has to be brought in on a DC-3. I don’t know exactly how much power a high-speed printer consumes, but I suppose it’s at least in the right order of magnitude for 50 kw total… but while we’re not told how many DC-3 flights there are per day, we are told that the specific computer used was chosen because it was small enough to transport that way.

17

I never tried to work out the math on the names, but the last line bothers me.

“Overhead, without any fuss, the stars were going out.” If a star disappeared, it would take years for observers on Earth to notice. So God apparently extinguished the light in transit. If He extinguished all light, the protagonists wouldn’t be able to see anything at all on Earth.

Regards,
Shodan

18

Or God anticipated when the humans would be done with their Great Task, and preemptively extinguished each star at the right time, so that its last light would be arriving at Earth just at the End.

19

Right after He planted the fossils to mess with our heads, put a belly button on Adam, and created a burrito that was too big for Him to lift.

Regards,
Shodan

20

Can God make a Chick so hot He can’t pick her up?