First, I want to thank Elliot Benjamin for responding to our recent article, Apophenia and the Intentionality Fallacy. This is a fun dialogue and I, personally, have been enjoying thinking through Elliot’s reasoning on why he believes license plates synchronicities necessitate deeper explanations than merely chance and coincidence. In addition, I want Elliot to know that I never meant to show him any discourtesy or disrespect by my occasional use of flavorful, if at times razor pointed, language. I have always enjoyed a heated discussion on controversial issues (as anyone who has seen my volleys on various forums from Eckankar to Radhasoami Studies will know), and in this regard I am grateful that Elliot has continued the discussion even if he fundamentally disagrees with the import of my criticism.

Now before I tackle two of his main points in his recent essay (mathematical probability and his invocation of quantum entanglement), I decided to take up Elliot’s own experiment and do it myself. We are currently on school holiday so I have a bit more free time than usual. So, I said to myself, “Elliot finds this number 496 to be significant. Other mathematicians do as well (My wife, included, as she is a math whiz and once was asked to teach statistics at UCSD). Why not see if I too can discover similar number patterns just as he reported, with the most recent sighting being in the Caribbean.” As Elliot himself explains further,

“But I believe that when we are studying the deepest realms of human experience, subjectivity becomes essential to truly gain understanding of what these experiences are all about. This was one of Ken Wilber's key points in his description of experiential knowledge in his book Eye to Eye, and it is also a foundation of what is referred to as “extended science”.”

In other words, I reflected to myself, “Do the experiment and see what happens.” With this intention in mind, I focused on the number 496 and said, “Be aware. Be open.” Instead of using license plates, I simply selected any random piece of paper that had number sequences on them. And to my amazement, the very first thing I picked up was a receipt from Don Diego’s Mexican Restaurant in Indian Wells (they have a wickedly good potato taco) that had the numbers 496 in bold. A direct hit and in my first try? What are the odds for that? I mused. Before I could continue in this exercise, I had to retrieve my checkbook from the car in order to write a check for the pool man. As I pulled out a check, I couldn’t help smiling to myself, the check number was 496. This, I thought was too much. I was in the zone, which reminded me of how a gambler gets on a lucky streak. Right then I glanced down at my driver’s license and laughed to myself out loud and realized I was seeing 496 in almost anything. I was born on 04, 29, 1956. Take the last digit of each sequence and you get (yep, you guess it): 496. I felt as if Rod Serling was going to knock at my door any minute and say in his eerie smoke laden voice that I had just crossed over to the “Twilight Zone” (and I think the pun here was unintended).

But right after I did this, I realized that Elliot had focused primarily on license plates so I wasn’t precisely following his protocols but something parallel to that. This got me to thinking that maybe I should just go to the computer and see precisely what numbers the DMV gives out. Perhaps there are certain common number clusters they give out which can account for recurring sequential patterns. So I typed in the letters DMV into the Google search engine and randomly selected a few websites. When I opened this one up I was awestruck yet again:

N C License Plate Agency
Call: (919) 496-4655

Now as I mentioned in the earlier article we wrote on this subject, I have had a number of very odd synchronicities in my life. And they were significantly more impressive (at least to me) than what just transpired with my little experiment.

It seems fairly obvious to me that what we witnessing here is how human patternicity (looking for a pattern or a meaning in apparently random events) intertwines with probability. As I suggested in Apophenia, anyone, anywhere and at anytime can play this parlor game and more often than not unearth some remarkable results.

However, Elliot Benjamin seems convinced that the probability of his seeing the number 496 is far too unlikely to be reduced to chance and intentionality. Here is the crux of his argument:

“So I am back in the Caribbean and I am walking past a few cars and the first license plate I notice says “4696.” I do some quick mathematical calculations and come up with something like a probability of perhaps 1 in 2000, utilizing the same kind of probability assumptions as I did in my Synchronicity and Mathematics article and taking into account that the “496” is not in succession. But then in a few minutes I see the “496” in succession at the top of the pile of license plates in a novelty store, and I'll assign the probability of something like 1 in 10,000, taking into account there are 6 slots of possibilities. Finally, since these two events are mathematically independent to the best of my knowledge, I multiply the probabilities together to arrive at (1/2000) X 1/10,000) = (1/20,000,000) = 1/20 million. As I described in my previous Synchronicity and Mathematics article, this is the kind of problem I have with explaining highly unusual events completely by chance and coincidence, and why I continue to be open to alternative explanations, in whatever terms one is comfortable in using—science, spiritual, etc.”

There are several problems with Elliot’s probabilistic premises, not the least of which is that assigning probabilities necessitates strict parameters and controls. If Elliot wishes to have us seriously regard his self-reported stories as suggestive of something that can withstand scientific scrutiny, he has to set up strict and clear protocols on precisely what he is trying to measure. He provides us with neither. For instance, saying that one found the number 4696 and then assigning a probability factor to it (such as when he says, “1 in 2000”) doesn’t make any sense, since any number he saw could be given (with this type of methodology) the same odds. No, what should be done before assigning any probability to a number seen on a license plate is a clear rationale about what exactly is being tested.

So, for example, Elliot should write down on a piece of paper exactly what he is looking for on his initial drive in the Caribbean. Is he looking for 496 before he goes out for a drive? Getting a “series of three or four numbers or letters within a full license plate depiction of 6 or 7 possible slots” (such as 496) isn’t as difficult as he assumes. But one must be absolutely clear beforehand about what exact sequence one is looking for. You cannot scatter shot look at license plates and then ad hoc choose differing combinations (such as ACT or 496) on the basis of personal needs or whim. One should be exceedingly precise beforehand about what three number sequence would constitute a “hit.”

Ironically, by allowing for 6 or 7 placeholders for a three number sequence we actually dramatically increase (not decrease) the probability of finding such a combination. In the case of the number 496, the odds of finding that sequence on a license plate with 6 or 7 placeholders isn’t improbable at all. It is to be expected, especially if we allow more cars in our survey. Now to see the number 496 on a license plate with 6 or 7 placeholders and then to see a different license plate with the number 496 on a license plate with 6 or 7 placeholders would constitute a nice coincidence. Ironically, in mathematics, this is much more common than one might suspect, particularly if the sample size is increased.

The best example of this three number match that I know of is called the Birthday Paradox. In my upper division Science and Religion course at CSULB and my Critical Thinking class at MSAC, I usually introduce this wonderful mind teaser to my students during the sixth or seventh week just as they are getting irritated with midterms coming up.

With some humor, I look around the class and ask, “What do you think the odds are that two students in here have the same birthday, keeping in mind that a typical year has 365 days in it?” Given that there are usually only 30 or so students in my course, most of them respond that the odds are not very high.

I then dramatically exclaim (doing a fairly awful Uri Geller imitation) that two students in the course should have the same birthday and that if I am wrong I will buy pizza and drinks for the entire class next week.

At this point, the students are excited since they feel very confident that I am going to lose the bet. Once a more boisterous student shouted out, “Come on, Lane, you are going down. 365 days, 30 students, do the math.”

I then go around the room systematically and ask each student his or her birthday. I have done this game tens of times and to the deep consternation of my students I have only lost the bet once (even though I always buy pizza the next week anyways).

When the class hears that two students have exactly the same birthday (once it so happened that the first two students I called upon had the same birthday), they seem quite perplexed. How can that be and why was Lane so confident that he would be right?

Simple answer: math. The Birthday Paradox is explained quite nicely on the website How Stuff Works.

“This phenomenon actually has a name -- it is called the birthday paradox, and it turns out it is useful in several different areas (for example, cryptography and hashing algorithms). You can try it yourself -- the next time you are at a gathering of 20 or 30 people, ask everyone for their birth date. It is likely that two people in the group will have the same birthday. It always surprises people!

The reason this is so surprising is because we are used to comparing our particular birthdays with others. For example, if you meet someone randomly and ask him what his birthday is, the chance of the two of you having the same birthday is only 1/365 (0.27%). In other words, the probability of any two individuals having the same birthday is extremely low. Even if you ask 20 people, the probability is still low -- less than 5%. So we feel like it is very rare to meet anyone with the same birthday as our own.

When you put 20 people in a room, however, the thing that changes is the fact that each of the 20 people is now asking each of the other 19 people about their birthdays. Each individual person only has a small (less than 5%) chance of success, but each person is trying it 19 times. That increases the probability dramatically.

If you want to calculate the exact probability, one way to look at it is like this. Let's say you have a big wall calendar with all 365 days on it. You walk in and put a big X on your birthday. The next person who walks in has only a 364 possible open days available, so the probability of the two dates not colliding is 364/365. The next person has only 363 open days, so the probability of not colliding is 363/365. If you multiply the probabilities for all 20 people not colliding, then you get:

364/365 * 363/365 * … 365-20+1/365 = Chances of no collisions

That's the probability of no collisions, so the probability of collisions is 1 minus that number.”

I fully realize that Elliot Benjamin could argue that his alleged synchronicity has different odds than the Birthday Paradox. I agree. However, his assignation of probabilities is post hoc and not a priori and since he doesn’t set up strict (and objective) guidelines about what precisely constitutes a hit beforehand with proper protocols in place (so someone from the outside would readily agree with his methodology), we are left with intentionality and patternicity as the key linchpins in his license plate experiments. As I pointed out in Apophenia, Elliot Benjamin’s license plate synchronicities reveal more about him than about the strangeness of the world.

For instance, just today my wife Andrea and I were having lunch at Native Foods, our favorite Vegan restaurant, in Palm Desert, and as she was going through her email on her iPhone, I thought I would go outside and look at license plate numbers and see what interesting patterns I could find. However, before I ventured outside I said to myself, “How likely is it that I can find two cars with the same exact three number sequence?” Elliot claims that he found two license plates that had similar numbers in the Caribbean: the first was 4696 and the second one was 496 at a novelty shop. This very much impressed Elliot and he gives the odds as 1 in 20 million of this happening by chance.

How and why he arrives at these specific odds is itself odd and doesn’t hold up under closer scrutiny for a host of reasons, some of which I previously listed. I am tempted to call Elliot Benjamin’s method “Voodoo statistics” but before I crib and slightly alter George Bush’s famous criticism of Ronald Reagan’s economic strategy, I think it is best that I bite my tongue first. I respect Elliot Benjamin and, as my wife Andrea pointed out, he has a wonderful way with words, even if I may disagree at times with what they portend.

So I walk out to the parking lot ruminating on what the odds would be to find two license plates that have the same three numbers in sequence. And lo and behold as if Mr. Littlewood himself was guiding the proceedings (or was it Carl Jung calling down from the Collective Unconscious?) I find two completely different cars parked right next to each other with the exact same three numbers in sequential order: 895 and 895.

This is unbelievable, I thought. What a strange coincidence. Nobody is going to believe me. So, I pulled out my own iPhone and not only took pictures verifying what I found, but even video taped it. Thankfully I did so quickly, because just when I stopped shooting, one of the cars drove away.

Do I think what just happened (to cite Elliot’s words referring to his own coincidences) is “not necessarily beyond scientific explanation if one enters the realm of quantum physics, where if my limited understanding of quantum physics is correct, thoughts can indeed affect physical realities and “spooky action at a distance” is the norm.”?

No. I think it was a fun coincidence and nothing more. I don’t for a second believe that we need to invoke quantum entanglement to explain what can already be fully understood by simple math and statistics. There is nothing spooky going on if what is happening can be explained by number theory intersecting with human intentionality and meaning seeking.

I think we can all find synchronicities in our lives, especially if we consciously intend to seek them out. I want to extend my thanks to Elliot Benjamin for giving me the impetus to do some of my own amateur sleuthing in license plate correlations. I genuinely wish I could side with Elliot Benjamin here, because then I could take this new found paranormal skill to Las Vegas and see if I could have the roulette wheel ball match my chosen number and thereby exponentially increase my wager. But alas such psychic skills have yet to pay out at gambling facilities.

In conclusion, I think readers should be forewarned before venturing out and trying their hands (which should remain, lest we forget, on the steering wheel) at finding synchronous license plate numbers. Once a number gets in your head (and following Dawkins’ and Blackmore’s memetic infection theory) it can be difficult to let it go. I feel like the main character in Jorge Borge’s classic short story, The Zahir, where he gets completely obsessed with a 20 centavo coin and can think of nothing else until he reaches the conclusion that he will either go completely mad or find God as a result.

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