Numerology

It was hardly news when a headline in April 2018 trumpeted another end of the world prediction, since we get those all the time. What stood out about this one was the person who made the prediction: "BIBLICAL PROPHECY CLAIMS THE RAPTURE IS COMING APRIL 23, NUMEROLOGIST SAYS". It was the first time numerology had made national headlines in a long while, so far as I could recall; but the fact that it did should be of some concern to those of a rational bent. Rational as we are, we will give it a fair shake and take a look at numerology today, and see if this prediction truly did warrant that much consideration.

Numerology is a type of divination — a way to see what would otherwise be unseeable, something that people have strived to achieve since time immemorial. It uses numbers associated with the person about whom you wish to learn — often the date of their birth, or the number values of the letters in their name. One popular method is to add up all the digits to get some total, then add up the digits in that total, and repeat until you end up with a single digit, 1 through 9. This, according to some, reveals which of 9 possible personality types best describes you, or life paths which lie in store.

The key point to note is that there are (and have always been) many different versions of numerology. Therefore just about anything you can say about it is only generally true for some versions, and not for others — for instance, the example I gave is unrelated to some numerology methods. Thus, you can't test "numerology" per se, because that's not specific enough. And when you do turn to a specific system, often you find that the results are uselessly vague and generalized, much in the same way that all horoscopes basically describe everyone.

Numerology is, in essence, one of many ways that people have sought to explain and understand the world. The main questions it raises are why do some modern, intelligent people find numerology compelling; and second and more important, is it actually reliable enough to be useful? Let's talk about that first question: why do some smart people believe in an ancient method of divination that seems so contrived and arbitrary?

The basic answer, as many regular Skeptoid listeners can probably guess, is confirmation bias. Once one receives a numerology-derived horoscope or fortune — or lucky number or lucky color or whatever was produced — one tends to see it everywhere. We all respond to many phrases in most horoscopes, because they tend to be things that we all want to be true about ourselves, and in most cases they are true about most people. To anyone who has not studied the ways that these divinations work with human psychology, they do indeed seem compelling; compelling enough that you don't have to be stupid to be persuaded that there's something there.

At its core, numerology as divination is predicated upon determinism. If my personality was already carved in stone by my given name and birthdate, it means that my life path is already determined for me; and by extension, it implies that my parents were influenced by some power to name me the way they did, and even the day of my birth was determined in advance. Determinism is a difficult concept for many to accept, but in this case it can be justified by numbers, and numbers don't lie.

They also have a lot of really neat properties — properties that can easily seem to be mystically significant. Remember most people don't study numbers, and when presented with a neat little number trick, they can be pretty easily surprised. One factoid that I found more than once while reading explanations of numerology is that every series of odd numbers starting at 1 adds up to a perfect square. 1 + 3 + 5 is 9, the square of 3; 1 + 3 + 5 + 7 + 9 is 25, the square of 5; and so on. You could add odd numbers until doomsday and the sum would be a perfect square. Now, with a bit of study, it's trivial to see why this is the case, and while it's elegant, it's not surprising or unexpected. It's a simple consequence of number series. Yet to someone who hasn't done that study, it can produce a surprisingly big "wow" moment. Numbers don't lie, and thus these surprising patterns can seem to imply a deterministic pattern to the universe.

Nearly every text on numerology also discusses Benford's Law, and usually in the context of proving that numbers do have properties that are both mystical and unexplainable. Benford's Law states that, for many number sets found in the real world — such as stock prices or Amazon.com sales figures — the most common first digit of a multi-digit number is 1, followed by 2, followed by 3, and so on, all the way to 9 which is the least common first digit. Numbers in such sets have 1 as the leading digit 30.1% of the time, and have 9 as the leading digit only 4.6% of the time. Intuitively, we expect large sets of numbers — which we assume to be random — to have an even distribution of digits. But in many cases they don't, and it's provable. This, to some proponents of numerology, is evidence in favor of the wisdom of numbers.

However, mathematics explains Benford's Law neatly. Such number sets have a logarithmic distribution. If we take the Amazon.com sales figures as an example, lots of people place orders with small totals, and there are fewer and fewer orders at the highest totals. When we get to the next order of magnitude, we see the same pattern repeated in miniature. Each order of magnitude that the data set covers illustrates it again. The distribution of first digits forms a nice logarithmic curve, and this distribution is simply a natural consequence of a logarithmic curve. No black magic, and nothing unintuitive once the concept is understood. Elegant? Yes. Mystical? No.

So, while there are some interesting things to learn about the underpinnings of numerology, that by itself says nothing about the validity of these systems. While numerologists themselves simply assert that their methods work, they have nothing other than anecdotes to support the claim. Many customers of numerologists and other believers support it with anecdotes of their own. But in science, we need more than merely the personal belief of advocates; if we relied on that alone, we'd be forced to accept unicorns, Mothman, Ouija boards, and leprechauns, all without tangible evidence. I'm sure that most numerologists would agree that those things shouldn't be accepted without evidence either, so we're now going to turn to empirical tests of numerology.

As stated before, such tests are necessarily limited in scope to a single specific numerology system, so it's a true and fair comment that science-based results of a single system say nothing about some other system that some other numerologist might promote. With that in mind, we're going to take a look at two empirical tests that were done.

One was performed in a partnership between research analyst Gilad Diamant and numerologist Matti Hilary Sternberg in 2012. Their method, which they jointly developed and agreed to, was to take data from people, some of whom had been conventionally diagnosed with a cognitive impairment such as autism or a learning disability, then perform a separate diagnosis using numerology, then compare the results. Working with cognitive psychologist Ido Gandel, they filtered out records to control for things like people not yet being of the right age for a conventional diagnosis, and so on.

This left them with a matrix of four possibilities for each subject:

1. Those who were diagnosed both conventionally and numerologically
2. Those who were diagnosed conventionally but not numerologically
3. Those who were diagnosed numerologically but not conventionally
4. Those who were diagnosed neither conventionally nor numerologically

If there was anything to numerology, the researchers expected to see a statistically significant departure from a 50/50 hit/miss ratio, which is what would be predicted by pure random guessing. Of the 81 subjects studied, 39 had an existing diagnosis, and 42 did not. Let's see what the numerologist did with this.

First of all, her methods were established beforehand. We will skip these details, as lead author Diamant wrote:

Even before we began to collect the data, ...she defined exactly what formulas she calculates the probability of getting [a diagnosis], based on the name and date of birth. The formulas are highly complex, in the sense that there is no way that a person who is not an expert in numerology can begin to guess at all [that] is being done. [There] are several stages of calculation that are based on each other, until the final numerological prediction is reached...

Overall, the numerological diagnosis tended to find a few more positives than the conventional version: 45 were diagnosed, and 36 were not. How did the results compare? Of those subjects who did have a conventionally diagnosed impairment, numerology diagnosed 24 correctly and gave 15 false negatives; of those who did not have a conventionally diagnosed impairment, numerology was split right down the middle, giving 21 false positives and 21 negatives. In other words, the accuracy of numerology was determined not to be significantly different statistically from random guessing.

Another test was performed in 1993 by Maurice Townsend with the UK's Association for the Scientific Study of Anomalous Phenomena, a group consisting mostly of believers in the paranormal. This test was to evaluate a single claim of numerology: that people whose names add up to the single digit 7 are most likely to be psychic or "psychically aware" — that's one of those nine personality types or life paths. They sent out questionnaires to members of their association, and also collected as many as they could from people who were not members, reasoning that members were more likely than the general public to consider themselves psychic. Besides collecting their name, birth date, address, and birth place, the form asked these four questions:

1. Are you an ASSAP (or similar organization) member?
2. Have you ever had any apparently paranormal experiences?
3. Do you regard yourself as psychic or sensitive?
4. How interested are you in the paranormal, on a scale of 0 to 5?

Date and address formats were normalized in order to make them comparable, and a computer was used to perform the numerology calculations error-free. Townsend graphed all the results for each question, with each graph consisting of nine vertical columns, each column representing the number of respondents who numerologied out to the corresponding personality type. If the claim were true, then Townsend expected to see a higher distribution of 7s among people who indicated psychic ability and interest in the paranormal.

A statistical analysis was not performed, but it was easy to tell at a glance that the claim was not supported by this particular test. Not even close. In fact, of the nine possible personality types, 7 ranked only 7th. People who numerologied out to 1, 2, 3, 5, 6, and 8 were all better represented in the groups who reported psychic ability and paranormal interest, and only 4 and 9 were less common than 7. Considering that this particular divination experiment was performed in good faith by people who generally do tend to believe in the paranormal, it was not exactly a ringing endorsement for numerology.

If even these most common of all numerology techniques can fail so spectacularly in tests so simple that anyone could perform them, it suggests that numerologists, and those who follow them, may not be subjecting their belief to an everyday level of responsible skepticism. Of course we should always remain open to new evidence, but for now, I wouldn't count on numerology.

By Brian Dunning
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