Numerology, Quantum-Generated Numbers, and Coincidences

by John Allen Paulos

Numerology can easily result from free association and, given its assertions, it certainly seems like it has been. In any case, I thought I’d try my hand at it.

In particular, the date 9-11 and the destruction of the WTC twin towers have together given rise to all sorts of numerological claims. Here are a few more.

The twin towers were destroyed, so to the numerologist this might suggest the number 11, since 11 has twin digits and looks like the twin towers. The Pentagon was also damaged, suggesting the number 111.

Combining the omens implicit in the date of the attack and the three buildings involved yields 9111, which can be viewed as suggesting the product 91 x 11.

But the number 91 x 11 itself has a twinning property. What do I mean? Well, take any 3 digit number and multiply it by 91 x 11 and note that 643 x 91 x 11 = 643,643 and 819 x 91 x 11 = 819,819, and 547 x 91 x 11 = 547,547, and so on.

Moreover, 91 = 7 x 13, and 13 is widely considered to be a most unlucky number, easily outweighing the good luck that 7 often indicates.

Conclusion: 9111, the exact date of the destruction of the twin towers and the damaging of the Pentagon were numerologically foretold. After all, what is the probability that a 4-digit number would become so relevant to these tragic circumstances? It would seem the chances are a minuscule 1 in 10,000.

I could go further. The 3 damaged structures, 111, divided by 3 x 1, equals 37, and .37 is approximately equal to 1/e, where e is the base of the natural log. Likewise, 444 divided by 3 x 4, equals 37. So does 888, divided by 3 x 8, equals 37, and 999 divided by 3 x 9 equals 37, and so on. Symbolically, any number xxx divided by (x+x+x) always equals 37. This brings that most distinguished number, e, into the picture, a number whose ubiquity provides more fodder for the numerological aspects of the 9-11 attacks or, indeed, for almost anything else.

I will restrain myself and only further note that there are numerological dialects that play off of 18 in Judaism, 19 in Islam, 3 in Christianity, and many other variants. Also relevant is the numerological significance of the number 1, the symbol of unity and primordial power, not to mention 666.

Whatever the variant, however, such arithmetical acrobatics are perhaps more easily performed by mathematicians, usually for a playful lark as above, but sometimes (happily, very rarely) for more troubling reasons. John Nash, a brilliant mathematician who suffered from schizophrenia for years, is an instance of the latter. He is depicted in a scene in A Beautiful Mind, the movie and book about him, scouring newspapers searching for numbers and factoids that once linked together would tell a coherent story about what was really, really going on behind the conventional accounts in the news.

Of course, concocting such nonsensical fables is not that hard to do even for the mathematically untalented. If some of the numbers and factoids don’t quite fit the narrative, one can usually force them to fit by taking near misses to be further evidence of whatever fantastic story is being cobbled together.

More generally, everyday people not only numerologists, enjoy noticing coincidences, but too often cloak them in the mantle of fancy math and science. Apophenia is everywhere you look. We are indeed pattern-seeking animals, frequently possessing little in the way of critical checks. Astrology, creationism, horoscopes, and numerology are all old instances of this tendency.

This fascination with coincidences has been tapped into by a new app called Randonautica that I wrote about in my recent book, Who’s Counting? The app uses “quantum-generated numbers” to formalize play with coincidences. As with numerology, it’s harmless fun as long as you don’t assume that these coincidences have a deep significance, an assumption some people undoubtedly and unfortunately do make.

The app interviews the “Randonauts” and asks them to think of something they’d like to discover more about. It then produces, using their personal information, quantum-generated random numbers which are converted to the GPS coordinates of a nearby location. Next the participants are encouraged to go to the spot so specified and see what turns up there that is connected to their interest, whether it be a dead relative, a song lyric that keeps coming to mind, a question about a problematic relationship, or whatever.

There are many cases of seemingly (and I emphasize “seemingly”) uncanny discoveries. The appeal of Randonautica is what appears to be the resonance between the Randonauts’ expressed interests and the locations to which the quantum-generated numbers direct them. There is also the allure of the counterintuitive and mysterious properties of quantum mechanics. It’s flattering, and for some seductive, to imagine that one’s interests and questions have an effect on the numbers generated and that one is somehow communing with the universe.

But there is no evidence that humans can affect random number generators. People have tried to find some, but no dice (or, rather, all dice). What there is evidence for are the countless ways that any location can be linked to any interest. Near misses count as hits. There are so many numbers, names, acronyms, events, and individuals that people know and that can be used to weave a plausible connection into the quantum-generated location.

As I’ve often written, the most amazing coincidence of all would be the complete absence of all coincidences. We simply can’t avoid coincidences.

In any case, returning to 9-11, I remember walking around lower Manhattan on September 11, 2002, the first anniversary of the WTC attacks on 9-11. Presumably, my quantum-generated numbers would have brought me there. I had just read that Johnny Unitas, the former star quarterback for the then Baltimore Colts, had died that day. A boyhood idol of mine and arguably the number 1 quarterback in all of football, Unitas wore jersey number 19. Putting 1 and 19 together yields 911 backwards.

Alas, “backwards” is the appropriate word here just as it is with Lewis Carroll’s Queen insisting “sentence first, verdict afterwards.” I must admit, however, that sometimes it’s fun to walk backwards.


John Allen Paulos is a Professor of Mathematics at Temple University and the author of Innumeracy, A Mathematician Reads the Newspaper, and a new book, which was recently released.