A Yard of String

Galaxy magazine had a monthly science column written by Willy Ley.

Ley was born in Germany in 1906 but fled that county in the mid-1930s and settled in the US.

When Isaac Asimov was the toastmaster at a science fiction convention and Willy Ley was in the audience, he spent some time making Willy Ley jokes:

Willy Ley, at the time, and for years afterward, wrote a monthly science column for Galaxy, as I did for F & SF.

I said, for instance, “I happened to refer yesterday to Willy as the second-best science writer in science fiction, and I was told that that was a terribly rude comment to make under the circumstances and that I ought to apologize. Well, Willy, I don’t understand what the circumstances are that made it rude, but I’ll be glad to apologize right now and in public. Willy, I’m sorry you’re the second-best science writer in science fiction.”

I also told a couple of stories that I borrowed from Randall Garrett and that may quite possibly have been true.

In one, Randall said, “Tell me, Willy, do you prefer to be called Willy or Veelee?”

And Willy, in his thick Teutonic accent (which some people said he practiced before the mirror so that he would never lose it), answered, “Veelee oder Veelee, id mages no diwerenz.”

In the other, Randall came up to Willy, who was sitting relaxed, with a cigar in his mouth. Randall looked sadly at Willy’s majestic corporation (for he was no longer the slim youth he had been when I had met him—and neither was I), tapped it lightly, and said, “Willy, Willy, you ought to diet.”

And Willy looked down upon his abdomen indulgently and said, “All righd. Vot color?”

But he was an excellent popular science writer. Here’s an excerpt from his column from June 1952 for Galaxy.

Ball of string.

Let’s talk about a yard of string now, to give a wonderful example of how “reasoning” can lead you astray. The circumference of the Earth along the equator is 24,902 miles or, since there are 1760 yards in a mile, 43,827,520 yards. Now we’ll level all the mountains that happen to be along the equator and put a string around, at sea level, tight. And now we lengthen this string by precisely one yard. How high, provided that it is supported all around the equator at the same distance, would that string be above sea level?

“Reasoning” will say, without a moment’s hesitation, that it will be insignificant. Possibly a bacillus, if it really wanted to, could squeeze across the equator under that string. The truth is that a cat could do it, for the string would be about six inches above the ground.

Impossible? Let’s see what the radius of the larger circle would be—we are all agreed that it must be larger; being one yard longer, the question is merely whether it would be visible. The original sea level circle was given by 2r x π, the new circle is obviously 2 r π +1 (if “r” has been expressed in yards) and the new radius R must be r + x.

And x turns out to be 1 divided by 2 π. If we take π as 3.1415, this gives 0.1592 of a yard, or 5.8 inches.

The point is here that the increase of the radius is independent of the original radius. The increase of the radius must always be equal to the increase in the circumference divided by 2 π.

Go ahead and try it with anything circular you have access to. You’ll always find that an increase of the original circumference by one yard will increase the radius by slightly less than six inches.

In case neither the formula nor the experiments fully convince you, you may imagine another example which might help. Here we have a board three yards long—but we imagine it to be so thin that its thickness is negligible and we tie a string around length-wise. Obviously the string will be six yards long.

Now we lengthen the string once more by one yard. The result will be two loops at both ends, each loop sticking out by one quarter of a yard or 9 inches. Here it is apparent that it would not matter whether the board is originally three yards long, or 100 yards, or 77 miles. If you add a yard to the length of the tight string, you’ll always get two loops at both ends, sticking out a full nine inches.

Common sense, as you can see, is not always common, which has been noted by others in the past—but neither does it always make sense!

—WILLY LEY

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