Did you know that there are illegal numbers?
I didn't, at least not until yesterday. It turns out, of course, that the issue isn't the number itself, but the information it contains (or makes reference to). Numbers by themselves, as simple mathematical symbols, are pretty devoid of meaning -- although to the suspicious-minded, it sometimes doesn't look that way. While physicist Richard Feynman was doing highly classified work at Los Alamos, he repeatedly got in trouble, and was accused of sending encoded information to his wife. He recounts the following experience in his autobiography, Surely You're Joking, Mr. Feynman!:
Anyway, one day I'm piddling around with the computing machine, and I notice something very peculiar. If you take 1 divided by 243 you get .004115226337... It's quite cute. It goes a little cockeyed after 559 when you're carrying but it soon straightens itself out and repeats itself nicely. I thought it was kind of amusing.
Well, I put that in the mail, and it comes back to me. It doesn't go through, and there's a little note: "Look at Paragraph 17B." I look at Paragraph 17B. It says, "Letters are to be written only in English, Russian, Spanish, Portuguese, Latin, German, and so forth. Permission to use any other language must be obtained in writing." And then it said, "No codes."
So I wrote back to the censor a little note included in my letter which said that I feel that of course this cannot be a code, because if you actually do divide 1 by 243, you do, in fact, get all that, and therefore there's no more information in the number .004115226337... than there is in the number 243, which is hardly any information at all. And so forth. I therefore had to ask permission to use Arabic numerals in my letters.
The thing is, Feynman is being a little disingenuous, here. Numbers can mean more than just a bare symbolic representation of a mathematical quantity. After all, using a number in two different ways -- both to represent a quantity, and to encode a meaningful mathematical statement -- is the trick behind the proof of the brilliant Gödel Incompleteness Theorem, something I'm certain Feynman knew.
It's not always that deep, of course. Sometimes what they mean is banal. A good example is the current idiotic "6-7" thing that apparently is rampant amongst teenagers, and which makes me glad I retired from teaching high school when I did.
In any case, it's evident that implicit meaning is just as important to people as the explicit one. To take one infamous example, consider 666, supposedly the "Number of the Beast" in the Book of Revelation. Some people take that one extremely seriously. Ronald and Nancy Reagan lived in a house in Los Angeles, on 666 St. Cloud Road, until they petitioned the city (successfully) to change it to 668. There was a highway named U. S. Route 666 in New Mexico, until in 2003 it was changed to U. S. Route 491 -- prompting a spokesperson to say, "The devil's outta here, and we say goodbye and good riddance." (I bet the priest in The Exorcist wishes he'd known it was that easy.) In 2013, a maintenance worker in a metal manufacturing plant in Clarksville, Tennessee quit his job when he was assigned an ID badge ending in 666, and the company refused to change it. "I cannot accept that number," he told ABC News. "If you accept that number, you sell your soul to the devil."
What's wryly amusing about all this is that some scholars believe the identification of the Number of the Beast as 666 is a scribal or translation error, and the actual Number of the Beast is 616, because if you transliterate "Nero Caesar" into Hebrew and then use the rules of gematria to turn it into a number, you get 616.
Somehow, though, I doubt that's gonna catch on. The biblical literalists seem pretty set on 666.
So forbidden numbers have a long history. These days, they seem mostly to center around one of three things; trade secrets, classified information, and code for suppressed (or oppressive) ideologies. Because you can encode information in a string of digits, that string then becomes more than just the bare mathematical representation. It even goes beyond that, though, because afterward, any pattern can be made to stand for numbers, if only you know the correspondence. There was a legal case centering around a pattern of colors on a flag:
Sometimes, numbers can be labeled as illegal in certain contexts, usually when there's some external meaning that's been attached to them. In 2012, there was a report that internet search engines in China were blocking any searches containing the numbers 4, 6, and 89 -- because the Tiananmen Square Massacre happened on June 4, 1989. The numbers 14 and 88 are associated with white supremacy -- a well-known slogan by white supremacist David Lane has fourteen words, and 88 is code for "Heil Hitler" (H is the eighth letter of the alphabet). 88 regularly shows up in neo-Nazi tattoos -- and far-right Slovak politician Marian Kotleba was criminally charged for donating €1,488 to various charities. He was found guilty of "supporting and propagating a movement whose aim is the repression of human rights and freedoms," and sentenced to six months in prison, although on appeal the sentence was suspended.
They take these things seriously in Slovakia. Not like in another nation I can think of, where being a white supremacist with sketchy tattoos gets you appointed as Secretary of Defense.
So sometimes, numbers can mean a lot more than the seem to at first, and making them illegal -- or at least, illegal in some contexts -- makes better sense than it might appear at first.
I do have to agree with Feynman, though, that pointing out an interesting pattern in the decimal expansion of a fraction is pretty unlikely to be a way of giving away the nation's nuclear codes. Doubt that'd work even if you made a flag out of it.
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