"He didn't have any personal armor!"
I sat up. I couldn't help it. "What?"
"None at all! Naked as a baby. So that proves he isn't human, doesn't it? I mean, if he can't take the simplest care of himself, he's only a kind of animal, right?"
I thought. "Well, I suppose so," I said. Really, the concept was hard to swallow.
"Good," she said, "because he's, well, in the freezer. I didn't want to waste him, Howard. And it isn't as if he was human."
I thought for a second. Well, why not? You get tired of rabbits and mice, and since there hasn't been any open sky for pasturing for nearly fifty years, that's about all there is. Now that I thought back on it, he was kind of plump and appetizing at that.
And, in any case, that was a problem for later on. I reached out idly and touched the button that controlled the last light in the room, the electric fireplace itself. "Oh," I said, pausing. "Where did he come from?"
"Sorry," her muffled voice came. "I forgot to ask."
I reached out thoughtfully and found my glass. There was a little bit left; I drained it off. Funny that the creature should bother to come down. In the old days, yes; back when Earth was open to the sky, you might expect aliens to come skyrocketing down from the stars and all that. But he'd come all the way from-well, from wherever-and for what? Just to make a little soup for the pot, to donate a little metal and power. It was funny, in a way. I couldn't help thinking that the feds would have liked to have met him. Not only because he agreed with them about the pumps and so on, but because they're interested in things like that. They're very earnest types, that's why they're always issuing warnings and so on. Of course, nobody pays any attention.
Still. . .
Well, there was no sense bothering my small brain about that sort of stuff, was there? If the heatpumps were dangerous, nobody would have bothered to invent them, would they?
I set down my glass and switched off the fireplace. Tandy was still and warm beside me; motionless but, believe me, by no means asleep.
How to Count on Your Fingers
EVERYONE knows that the decimal system of counting, which is based on the ten digits 0 through 9, has driven out all other systems and has become universal, by virtue of being simplest and best. Like a good many things that "everyone knows," there is one thing wrong with that statement. It isn't so.
True, it is not that any of the predecessors of the decimal system is likely to make a comeback. There is, for instance, vanishingly little chance that we will return to the Babylonian sexagesimal (to the base 60) system-though that is a tough old bird and will not be finally dead as long as we count 60 minutes to the hour, and 360 degrees to the circle. There are traces of systems to other bases surviving in such terms as "score" and the French word for 80, "quatre-vingt," suggesting an extinct system to the base 20; and in terms like "dozen," "gross," and so on, which appear to derive from a system to the base 12.
In science fiction most of the speculation on numbering systems of the future has dwelt on this base 12 ("duodecimal") system, but it is hard to understand why. It is argued that a 12-digit system simplifies writing "decimal" equivalents of such fractions as *1/4 and 1/6, but that seems a small reward for the enormous task of conversion. Setting aside the merits or demerits of the duodecimal system itself, think of the cost of such a change. For a starter, our decimal system of coinage either goes down the drain, to be replaced by a new one, or lingers on as a clumsy anachronism like the British £/s/d. And that cost is only the bare beginning. Science is measurement and interpretation; without measurement, interpretation is foggy soul-searching; and measurement is number. Change our system of writing numbers, and you must translate nearly the entire recorded body of human knowledge-lab reports and tax returns, cost estimates and time studies, knowledge about the behavior of nu mesons, and knowledge about transactions on the New York Stock Exchange.
The project of converting the world's essential records from one system of numbering to another staggers the mind. Its cost is measurable not merely in millions of dollars, but in perhaps millions of man-years.
That being so, why is this enormous project now in process?
The answer is, simply, that machines aren't any smarter than Russian peasants.
This is not meant to run down the Russians, but only to observe that UNIVAC and Ivan have a lot of things in common-and one of these things is a lack of skill in performing decimal multiplication and division.
Let's take a simple sum-say, 87 x 93-and see how it would be done by us, by Ivan, and by UNIVAC. You and I, having completed at least a couple of years of grade school, write down a compact little operation like this:
87
x93
----
261
783
====
8091
That wasn't hard to do. If we had to, we probably could have done it in our heads.
However, Ivan would find that pretty hard, because he didn't happen to go to grade school. (And neither did UNIVAC.) What Ivan would do in a similar case is a process called "Russian multiplication" - or sometimes "mediation and duplication." (Which is to say, "halving and doubling.") It consists merely of writing down two columns of figures, side by side. The first column starts with one of your original figures, which is successively halved until there is nothing left to halve. Ivan didn't understand fractions very well, so he simply threw them away-he would write half of 25, for instance, as 12.
The second column starts with the other number, which is successively doubled as many times as the first number was halved. As follows:
87 93
43 186
21 372
10 744
5 1488
2 2976
1 5952
Having gotten this far, Ivan examines the left-hand, or halved, column for even numbers. He finds two of them-the fourth number, 10, and the sixth, 2. He strikes out the numbers next to them in the right-hand (or doubled) column-that is, 744 and 2976. He then adds up the remaining numbers in the right-hand column:
93
186
372
1488
5952
====
8091
Having gone all around Robin Hood's barn to do it, as it appears, he was wound up with the same answer we got.
That may not seem like much of an accomplishment, at first glimpse, until you stop to think of Ivan's innocence of the multiplication table, and then it becomes pretty ingenious indeed. Ivan turns out to be a clever fellow.
Yet he was not so clever, all the same, but what he would have laughed in your face if you had accused him of seeking help from the binary system of numbering.
But that is what he did, and that, of course, is what UNIVAC and its electronic brothers do today.
To see how UNIVAC does this, let's take some numbers apart and see what is inside them.
Our own decimal numbers-87, for example-are simply a shorthand, "positional" way of saying (in this case) 8 X 10^1 plus 7 X 10^0. The larger the number the shorter the shorthand becomes. 1956, for instance, is shorthand for one-times-ten-cubed, plus nine-times-ten-squared, plus five-times-ten, plus six-times-one. Or:
1 X 10^3 = 1000
9 X 10^2 = 900
5 X 10^1 = 50
6 x 10^0 = 6
====
1956
(In case it has been a long time since you went to high school, 10^1 just means 10; 10^0 means ten divided by ten, or 1. No matter how long it has been since you went to high school, you ought to remember that 10^2 means ten times ten, or a hundred, and so on.)
It has been said in many science-fiction stories (and not very often anywhere else) that this is homo sapiens' "natural" system of counting, because, look, don't we have ten fingers on our hands? As a theory, let's not worry ourselves about this too much; if true, it will have plenty of chance to prove itself when our exploring rockets turn up some 12-digited and duo decimal extraterrestrials. (Or, alternatively; when our archaeologists discover that the Babylonians had six times as many fingers as the rest of us.) Still, if we assume the fable is true, we can conveniently "explain" UNIVAC by saying that the computer, not having ten fingers to count on, has to use a simpler system. The name of this simpler system is the "binary" or "dyadic" system, and it is this system that most of the world's numbers are being translated into now, in order to be taped and fed into computers.