I've got your number

An inevitable side-effect of writing six times a week here at Skeptophilia is that I get some weird gifts sometimes.

This explains why I am the proud owner of:

• a cardboard-cutout Bigfoot that you can dress up with various stickers (he's currently wearing a kilt and a jaunty-looking tam-o'shanter)
• a certificate insuring my dog in case of alien abduction
• a very creepy-looking ritual mask from the Ivory Coast
• a book entitled UFOs: How to See Them
• a deck of steampunk Tarot cards
• a drawing of a scowling alien with a speech bubble saying "Nonbelievers Will Be Vaporized"
• a car air freshener shaped like a Sasquatch (fortunately, it doesn't smell like one)
• the poster made famous from Fox Mulder's office, with a UFO and the caption "I Want To Believe"

The latest addition to my collection comes to me from a loyal reader of Skeptophilia.  I got a surprise package from him in the mail, and when I opened it up, it turned out to be a book called...

... Mysteries and Secrets of Numerology.

This book, by Lionel and Patricia Fanthorpe, is a complete analysis of the practice of numerology across the world, as viewed through the critical lens of believing every bit of it without question.  I checked out how it has fared on Amazon, and found that it has thus far received two reviews:

1: This book is full of wonderful information regarding numerology.  I got a copy from the library, but I will be buying my own to keep as a reference for numerology and sacred geometry.  Well Done!... and:

2: Fine.  This purchase was for some research I was doing and I came away amazed that anyone can take this entire subject matter area seriously.  The book drones on forever and that makes it great bedtime reading...  Yes, I did work the examples on my own set of numbers as well as those other family members and it didn't help me understand them any better than I did before.  They're still boring.  I put this book in the same category as those purporting to provide proof of alien abductions happening every day, all over planet earth.  If you really must find something in which to believe to give your life purpose, or help you amaze your friends, this book is for you.

So it's gotten a fairly mixed reception so far.

Undeterred by the second review, I read through it.  I will admit that I skimmed past the parts of it where the authors calculate numerological values for everyone from Hippocrates to Alexander Graham Bell.  I did note that the authors concluded that the "dark side of his numerological 1" for the famous British murderer Hawley Crippen "may have been what drove him to the rash and impetuous murder" of his second wife, Cora.  Which seems like a stretch, as from pure statistics one out of every nine people on Earth are "numerological 1s," and as far as I can tell, very few of them murder their second wives.

[Image is in the Public Domain]

The practice of numerology goes back a long way.  The whole thing seems to have begun with the mystical practice called gematria, which basically assigned numbers to damn near everything -- and woe be unto you if your number turned out to be bad.  The whole 666 being the Number of the Beast thing comes from gematria; and there's a lot of equating one thing for another because they "have the same number."  Here's an example from the Third Book of Baruch, one of the biblical apocrypha, as explained in the above-linked Wikipedia article:

A snake is stated to consume a cubit of ocean every day, but is unable to ever finish consuming it, because the oceans are also refilled by 360 rivers.  The number 360 is given because the numerical value of the Greek word for snake, δράκων, when transliterated to Hebrew (דרקון) is 360.

Makes perfect sense to me.

In any case, back to the Fanthorpes' book.  The last section, while no less ridiculous, was at least kind of interesting.  We're told therein that because all sorts of factors can contribute to a person acting a particular way, or an action having a particular outcome, there's no reason not to believe that "numbers can exert invisible and unsuspected influences just as powerful."  We're then instructed that we should all pay more attention to the numbers in our lives, and especially look for the good influences of the numbers 1 (which, I note, didn't help Crippen much), 3, 6, 7, and 9.  Only in the second-to-last paragraph do the Fanthorpes bring up the central problem with the whole thing: "These attempts to use numbers as influences to attract good things and to protect against negative things are very interesting, but are open to the question of whether -- when they seem to work -- they are actually self-fulfilling prophecies."

Well, yeah.  The whole book is basically Confirmation Bias "R" Us.

So I'm sure you're all dying to know what my number is.  The book gives detailed instructions on how to calculate your number, although it does say there are different ways of doing so.  "Therefore," the authors write, "two equally well-qualified and experienced numerologists working with slightly different systems could reach very different conclusions."  (Which to me, is just a fancy way of saying, "we admit this is bullshit.")

I used what they say the "simplest way" is -- writing out the English alphabet underneath the numbers 1-9, starting with A=1, B=2, and so on; after you reach I=9, you start over with J=1.  Following this protocol, my whole name adds up to 76.  You're then supposed to add the digits (giving 13) and then add those (giving a final answer of 4).

So my number is 4, which unfortunately is not one of the "auspicious numbers" mentioned above.  Four, apparently, means "a foundation, the implementation of order, a struggle against limits, and steady growth."

I suppose it could be worse.

In any case, I'm not going to lose any sleep over the fact that I didn't get "9" (the number of "immense creativity").  Nor am I going to do what the authors say some folks have done, which is change their name to one that has a better number.

It might be worth getting a second opinion, however. Maybe I should see what the "steampunk Tarot cards" have to say on the matter.  That should be illuminating.

****************************************

Canine mathematics

I remember a while back reading an interesting paper that concluded that dogs have a concept of fairness and morality.

There have been a number of studies confirming this, most strikingly an investigation involving border collies.  Pairs of dogs were trained to do a task, then rewarded with doggie biscuits.  The thing was, Dog #1 was rewarded for correctly doing the task with one biscuit, and Dog #2 with two biscuits for doing the same task.

Within a few rounds, Dog #1 refused to cooperate.  "I'm not working for one biscuit when he gets two," seemed to be the logic.  So -- amazing as it seems -- at least some dogs understand fair play, and will forego getting a treat at all if another dog is getting more.

It also implies an understanding of quantity.  Now, "two is more than one" isn't exactly differential calculus, but it does suggest that dogs have at least a rudimentary numeracy.  The evolutionary advantage of a sense of quantity is obvious; if you can do a quick estimate of the number of predators chasing you, or the size of the herd of antelope you're chasing, you have a better sense of your own safety (and such decisions as when to flee, when to attack, when to hide, and so on).

Guinness, either pondering Fermat's Last Theorem or else trying to figure out how to open the kitchen door so he can swipe the cheese on the counter

But how complex dogs' numerical ability is has proven to be rather difficult to study.  Which is why I found a paper I stumbled across in Biology Letters so fascinating.

Entitled, "Canine Sense of Quantity: Evidence for Numerical Ratio-Dependent Activation in Parietotemporal Cortex," by Lauren S. Aulet, Veronica C. Chiu, Ashley Prichard, Mark Spivak, Stella F. Lourenco, and Gregory S. Berns, of Emory University, this study showed that when dogs are confronted with stimuli differing only in quantity, they process that information in the same place in their brains that we use when doing numerical approximation.

The authors write:

The approximate number system (ANS), which supports the rapid estimation of quantity, emerges early in human development and is widespread across species.  Neural evidence from both human and non-human primates suggests the parietal cortex as a primary locus of numerical estimation, but it is unclear whether the numerical competencies observed across non-primate species are subserved by similar neural mechanisms.  Moreover, because studies with non-human animals typically involve extensive training, little is known about the spontaneous numerical capacities of non-human animals.  To address these questions, we examined the neural underpinnings of number perception using awake canine functional magnetic resonance imaging.  Dogs passively viewed dot arrays that varied in ratio and, critically, received no task-relevant training or exposure prior to testing.  We found evidence of ratio-dependent activation, which is a key feature of the ANS, in canine parietotemporal cortex in the majority of dogs tested.  This finding is suggestive of a neural mechanism for quantity perception that has been conserved across mammalian evolution.

The coolest thing about this study is that they controlled for stimulus area, which was the first thing I thought of when I read about the experimental protocol.  What I mean by this is that if you keep the size of the objects the same, a greater number of them has a greater overall area, so it might be that the dogs were estimating the area taken up by the dots and not the number.  But the researchers cleverly designed the arrays so that although the number of dots varied from screen to screen, the total area they covered was the same.

And, amazing as it sounds, dogs not only had the ability to estimate the quantity of dots quickly and pick the screen with the greatest number, they were apparently doing this with the same part of their brains we use for analogous tasks.

"We went right to the source, observing the dogs' brains, to get a direct understanding of what their neurons were doing when the dogs viewed varying quantities of dots," said study lead author Lauren Aulet, in a press release in Science Daily.  "That allowed us to bypass the weaknesses of previous behavioral studies of dogs and some other species...  Part of the reason that we are able to do calculus and algebra is because we have this fundamental ability for numerosity that we share with other animals.  I'm interested in learning how we evolved that higher math ability and how these skills develop over time in individuals, starting with basic numerosity in infancy."

I wonder, though, how this would work with our dogs. As I've mentioned before, Cleo (our Shiba Inu) has the IQ of a lima bean, and even has a hard time mastering concepts like the fact that regardless how many times she lunges at her own tail, it's going to remain firmly attached to her butt.  Guinness is smarter (not that the bar was set that high), but I don't know how aware of quantity he is.  He's more of an opportunist who will take advantage of any situation that presents itself, be it a single CheezDoodle someone dropped on the floor or (as happened a while back) a half-pound of expensive French brie that was left unguarded for five minutes on the coffee table.

I doubt he worried about quantity in either case, frankly.

But the Aulet et al. study is fascinating, and clues us in that the origins of numeracy in our brains goes back a long, long way.  The most recent common ancestor between humans and dogs is on the order of eighty million years ago -- predating the extinction of the dinosaurs by fourteen million years -- so that numerical brain area must be at least that old, and is probably shared by most mammalian species.  It's a little humbling to think that a lot of the abilities we humans pride ourselves on are shared, at least on a basic level, with our near relatives.

But now y'all'll have to excuse me, because Cleo is barking like hell at something.  Maybe it's the evil UPS guy, whom she and Guinness both hate.  Maybe a squirrel farted somewhere in this time zone.  Maybe she's frustrated by the fact that she still can't quite catch her own tail.  

Or maybe she's stuck on one of her linear algebra homework problems.  You can see how that's a possibility.

****************************************

Patterns and meaning

I remember a couple of years ago noticing something odd.  While eating breakfast on work days, I'd finish, and always give a quick glance up at the digital clock that sits on the counter.  Three times in a row, the clock said 6:19.

I know there's a perfectly rational explanation; I'm a total creature of habit, and I did the same series of actions in the same order every single work morning, so the fact that I finished breakfast three days in a row at exactly the same time only points up the fact that I need to relax a little.  But once I noticed the (seeming) pattern, I kept checking each morning.  And there were other days when I finished at exactly 6:19.  After a few weeks of this, it was becoming a bit of an obsession.

[Image licensed under the Creative Commons Mk2010, LED digital wall clock (Seiko), CC BY-SA 3.0]

So being a rationalist, as well as needing a hobby, I started to keep track.  And very quickly a few things became obvious:

• I almost always finished breakfast (and checked the clock) between 6:16 and 6:22.
• 6:19 is the exact middle of that range, so it would be understandable if that time occurred more often.
• Even considering #2, 6:19 turned out to be no more likely than other times.  The distribution was, within that six minute range, fairly random.

So I had fallen for dart-thrower's bias, the perfectly natural human tendency to notice the unusual, and to give it more weight in our attention and memory.  The point is, once you start noticing this stuff, you're more likely to notice it again, and to overestimate the number of times such coincidences occur.

The whole thing comes up because of a link sent to me by a loyal reader of Skeptophilia called, "Angel Numbers Guide: Why You Keep Seeing Angel Number Sequences."  I'm not going to recommend your going to the site, because it's pretty obviously clickbait, but I thought the content was interesting from the standpoint of our determination that the patterns we notice mean something.

The site is an attempt to convince us that when we see certain numbers over and over, it's an angel attempting to give us a message.  If you notice the number 1212, for example, this is an angel encouraging us to "release our fears and apprehensions, and get on with pursuing our passions and purpose... [asking you to] stay on a positive path and to use your natural skills, talents, and abilities to their utmost for the benefit of yourself and others."

Which is good advice without all of the woo-woo trappings.

Some numbers apparently appeal not only to our desire for meaningful patterns, but for being special.  If you see 999 everywhere, "you are amongst an elite few... 999 is sometimes confrontative, and literally means, 'Get to work on your priorities.  Now.  No more procrastinating, no more excuses or worries.  Get to work now."

Since a lot of the "angel numbers" involve repeated digits, I had to check to see what 666 means.  I was hoping it would say something like, "If you see 666, you are about to be dragged screaming into the maw of hell."

But no. 666 apparently is "a sign from the angels that it's time to wake up to your higher spiritual truth."  Which is not only boring, but sounds like it could come from a talk by Deepak Chopra.

So the whole thing turns out to be interesting mostly from the standpoint of our desperation to impose some sense on the chaos of life.  Because face it; a lot of what does happen is simply random noise, a conclusion that is a bit of a downer.  I suspect that many religions give solace precisely because they ascribe meaning to everything; the Bible, after all, says that even a sparrow doesn't fall from the sky without the hand of God being involved.

Me, I think it's more likely that a lot of stuff (including birds dying) happens for no particularly identifiable or relevant reason.  Science can explain at least some of the proximal causes, but as far as ultimate causes?  I think we're thrown back on the not very satisfying non-explanation of the universe simply being a chaotic place.  I understand the appeal of it all having meaning and purpose, but it seems to me that most of what occurs is no more interesting than my finishing breakfast at 6:19.

*************************************

I've always had a fascination with how our brains work, part of which comes from the fact that we've only begun to understand it.  My dear friend and mentor, Dr. Rita Calvo, professor emeritus of human genetics at Cornell University, put it this way.  "If I were going into biology now, I'd study neuroscience.  We're at the point in neuroscience now that we were in genetics in 1900 -- we know it works, we can see some of how it works, but we know very little in detail and almost nothing about the underlying mechanisms involved.  The twentieth century was the century of the gene; the twenty-first will be the century of the brain."

We've made some progress in recent years toward comprehending the inner workings of the organ that allows us to comprehend anything at all.  And if, like me, you are captivated by the idea, you have to read this week's Skeptophilia book recommendation: neuroscientist Lisa Feldman Barrett's brilliant Seven and a Half Lessons About the Brain.

In laypersons' terms, Barrett explains what we currently know about how we think, feel, remember, learn, and experience the world.  It's a wonderful, surprising, and sometimes funny exploration of our own inner workings, and is sure to interest anyone who would like to know more about the mysterious, wonderful blob between our ears.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

I've got your number

An inevitable side-effect of writing six times a week here at Skeptophilia is that I get some weird gifts sometimes.

This explains why I am the proud owner of:

• a cardboard-cutout Bigfoot that you can dress up with various stickers (he's currently wearing a kilt and a jaunty-looking tam-o'shanter)
• a very creepy-looking ritual mask from the Ivory Coast
• a book entitled UFOs: How to See Them
• a deck of steampunk Tarot cards
• a drawing of a scowling alien with a speech bubble saying "Nonbelievers Will Be Vaporized"
• a car air freshener shaped like a Sasquatch (fortunately, it doesn't smell like one)
• the poster made famous from Fox Mulder's office, with a UFO and the caption "I Want To Believe"

The latest addition to my collection comes to me from someone who is not only a loyal reader of Skeptophilia but is one of my best buds -- writer and blogger Andrew Butters (who writes over at Potato Chip Math, an awesome blog you should all check out on a regular basis).  Recently I got a package from Andrew, and when I opened it up, it turned out to be a book called...

... Mysteries and Secrets of Numerology.

This book, by Lionel and Patricia Fanthorpe, is a complete analysis of the practice of numerology across the world, as viewed through the critical lens of believing every bit of it without question.  I checked out how it has fared on Amazon, and found that it has thus far received two reviews:

1: This book is full of wonderful information regarding numerology.  I got a copy from the library, but I will be buying my own to keep as a reference for numerology and sacred geometry.  Well Done!

... and:

2: Fine. This purchase was for some research I was doing and I came away amazed that anyone can take this entire subject matter area seriously.  The book drones on forever and that makes it great bedtime reading. 

Yes, I did work the examples on my own set of numbers as well as those other family members and it didn't help me understand them any better than I did before.  They're still boring.  I put this book in the same category as those purporting to provide proof of alien abductions happening every day, all over planet earth.  If you really must find something in which to believe to give your life purpose, or help you amaze your friends, this book is for you.

So it's gotten a fairly mixed reception so far.  

Undeterred by the second review, I read through it.  I will admit that I skimmed past the parts of it where the authors calculate numerological values for everyone from Hippocrates to Alexander Graham Bell.  (I did note that the authors concluded that the "dark side of his numerological 1" for the famous British murderer Hawley Crippen "may have been what drove him to the rash and impetuous murder" of his second wife, Cora.  Which seems like a stretch, as from pure statistics one out of every nine people on Earth are "numerological 1s," and as far as I can tell, very few of them murder their second wives.)

[image courtesy of the Wikimedia Commons]

The last section was the most interesting, however.  We're told therein that because all sorts of factors can contribute to a person acting a particular way, or an action having a particular outcome, there's no reason not to believe that "numbers can exert invisible and unsuspected influences just as powerful."  We're then instructed that we should all pay more attention to the numbers in our lives, and especially look for the good influences of the numbers 1 (which, I note, didn't help Crippen much), 3, 6, 7, and 9.  Only in the second-to-last paragraph do the Fanthorpes bring up the central problem with the whole thing: "These attempts to use numbers as influences to attract good things and to protect against negative things are very interesting, but are open to the question of whether -- when they seem to work -- they are actually self-fulfilling prophecies."

Well, yeah.  The whole book is basically Confirmation Bias "R" Us.

So I'm sure you're all dying to know what my number is.  The book gives detailed instructions on how to calculate your number, although it does say there are different ways of doing so.  "Therefore," the authors write, "two equally well-qualified and experienced numerologists working with slightly different systems could reach very different conclusions."  (Which to me, is just a fancy way of saying, "this is bullshit.")

I used what they say the "simplest way" is -- writing out the English alphabet underneath the numbers 1-9, starting with A=1, B=2, and so on; after you reach I=9, you start over with J=1.  Following this protocol, my whole name adds up to 76.  You're then supposed to add the digits (giving 13) and then add those (giving a final answer of 4).

So my number apparently is 4, which unfortunately is not one of the "auspicious numbers" mentioned above.  Four, apparently, means "a foundation, the implementation of order, a struggle against limits, and steady growth."

I suppose it could be worse.

In any case, I'm not going to lose any sleep over the fact that I didn't get "9" (the number of "immense creativity").  Nor am I going to do what the authors say some folks have done, which is change their name to one that has a better number.

It might be worth getting a second opinion, however.  Maybe I should see what the "steampunk Tarot cards" have to say on the matter.  That should be illuminating.

Patterns and meaning

I remember a couple of years ago noticing something odd.  While eating breakfast on work days, I'd finish, and always give a quick glance up at the digital clock that sits on the counter.  Three times in a row, the clock said 6:19.

I know there's a perfectly rational explanation; I'm a complete creature of habit, and I do the same series of actions in the same order every single work morning, so the fact that I finished breakfast three days in a row at exactly the same time only points up the fact that I need to relax a little.  But once I noticed the (seeming) pattern, I kept checking each morning.  And there were other days when I finished at exactly 6:19.  After a few weeks of this, it was becoming a bit of an obsession.

[image courtesy of the Wikimedia Commons]

So being a rationalist, as well as needing a hobby, I started to keep track.  And very quickly a few things became obvious:

1. I almost always finish breakfast (and check the clock) between 6:16 and 6:22.
2. 6:19 is the exact middle of that range, so it would be understandable if that time occurred more often.
3. Even considering #2, 6:19 turned out to be no more likely than other times.  The distribution was, within that six minute range, fairly random.

So I had fallen for dart-thrower's bias, the perfectly natural human tendency to notice the unusual, and to give it more weight in our attention and memory.  The point is, once you start noticing this stuff, you're more likely to notice it again, and to overestimate the number of times such coincidences occur.

The whole thing comes up because of a link sent to me by a loyal reader of Skeptophilia called, "Every Time This Happens, an Angel Reveals Itself!"  I'm not going to recommend your going to the site, because it's pretty obviously clickbait, but I thought the content was interesting from the standpoint of our determination that the patterns we notice mean something.

The site is an attempt to convince us that when we see certain numbers over and over, it's an angel attempting to give us a message.  If you notice the number 1212, for example, this is an angel encouraging us to "release our fears and apprehensions, and get on with pursuing our passions and purpose... [asking you to] stay on a positive path and to use your natural skills, talents, and abilities to their utmost for the benefit of yourself and others."

Which is good advice without all of the woo-woo trappings.

Some numbers apparently appeal not only to our desire for meaningful patterns, but for being special.  If you see 999 everywhere, "you are amongst an elite few... 999 is sometimes confrontative, and literally means, 'Get to work on your priorities.  Now.  No more procrastinating, no more excuses or worries.  Get to work now."

Since a lot of the "angel numbers" involve repeated digits, I had to check to see what 666 means.  I was hoping it would say something like, "If you see 666, you are about to be dragged screaming into the maw of hell."

But no.  666 apparently is "a sign from the angels that it's time to wake up to your higher spiritual truth."  Which is not only boring, but sounds like it could come from a talk by Deepak Chopra.

So the whole thing turns out to be interesting mostly from the standpoint of our desperation to impose some sense on the chaos of life.  Because face it; a lot of what does happen is simply random noise, a conclusion that is a bit of a downer.  I suspect that many religions give solace precisely because they ascribe meaning to everything; the bible, after all, says that even a sparrow doesn't fall from the sky without the hand of god being involved.

Me, I think it's more likely that a lot of stuff (including birds dying) happens for no particularly identifiable or relevant reason.  Science can explain at least some of the proximal causes, but as far as ultimate causes?  I think we're thrown back on the not very satisfying non-explanation of the universe simply being a chaotic place.  I understand the appeal of it all having meaning and purpose, but it seems to me that most of what occurs is no more interesting than my finishing breakfast at 6:19.

We've got your number

As a science teacher, one of the things I find fascinating and perplexing is the phenomenon of innumeracy.

An innumerate person is someone who doesn't understand numbers.  We're not talking about simple ignorance of algebra, here; we're talking about someone who has no fundamental comprehension of quantity.

[image courtesy of the Wikimedia Commons]

As an example, take a student of mine who took physics with me, perhaps 25 years ago.  We were studying electrical force, and there was a problem set up that allowed you, with a few given parameters, to calculate the mass of an electron.  So after working for a time, this kid raised her hand, and asked, "Is this the right answer?"

She'd gotten the answer "36 kilograms."

Now, I'll point out from the get-go that she'd made a simple computational error -- divided when she should have multiplied.  What struck me is that she had no idea her answer was wrong.  When I said, "Doesn't your answer seem a little large, for an electron?" she replied, "Is it?  It's what my calculator said."

What's curious about innumerate people is that they're frequently quite good at rote cookbook math -- they can follow lists of directions like champs.  But they have no real sense of numbers, so they have no way to tell if they've gotten the wrong answer.

What's also interesting is that there are people who are pretty competent with small numbers, but lose it entirely with large numbers.  An exercise I used to do with my physics students to help correct this -- which, allow me to say up front, wasn't particularly successful -- was to have them do order-of-magnitude estimation problems.  Within an order of magnitude, how many ping-pong balls would it take to fill the classroom?  How many 1'x1' floor tiles are in the entire school?  How many telephone books in a stack would it take to reach from the Earth to the Moon?  And so on.  Once again, these kids could do the problems, once you'd established a protocol for how to solve them; but I don't think they really got any better at understanding magnitudes through doing it than they had to start with.

Now, scientists at Imperial College in London have gained an insight into why this big-versus-small number comprehension issue might exist; they have found that big and small numbers are processed in different parts of the brain.

The study, led by Qadeer Arshad of the Department of Medicine, said that the idea for the study came from studying victims of strokes whose damage interfered with very specific abilities apropos of number processing. "Following early insights from stroke patients we wanted to find out exactly how the brain processes numbers," Arshad said.  "In our new study, in which we used healthy volunteers, we found the left side processes large numbers, and the right processes small numbers.  So for instance if you were looking at a clock, the numbers one to six would be processed on the right side of the brain, and six to twelve would be processed on the left."

The team then used a procedure to activate one side of the brain more than the other, and asked the volunteers to do various estimation tasks.  Interestingly, people had a systematic tendency to err in a opposite directions depending on which side of the brain was stimulated.  "When we activated the right side of the brain, the volunteers were saying smaller numbers," Arshad explained.  "For instance, if we asked the middle point of 50-100, they were saying 65 instead of 75.  But when we activated the left side of the brain, the volunteers were saying numbers above 75."

Apparently, the context of the task was also critical.  "If someone was looking at a range of 50-100 then the number 80 will probably be processed on the left side of the brain," Arshad explained.   "However, if they are looking at a range of 50-300, then 80 will now be small number, and processed on the right."

Which at least gives a preliminary explanation of why there are students who do just fine with manipulating small numbers, but fall apart completely when dealing with large ones.  I deal with kids for whom 10,000 years ago, 1,000,000 years ago, and 1,000,000,000 years ago all sound about the same -- "big" -- making it difficult to give them any real sense of the time scale of evolutionary biology.

Anyhow, I think the study by Arshad et al. is fascinating, and gives us a further window into understanding how our brains work.  Which is all to the good.  Although it still doesn't quite answer how someone could think that a 36 kilogram electron sounds reasonable.

A slice of pi

Sometimes you have to admire the woo-woos' dogged determination to fashion the universe into their own bizarre version of reality.

Most of us, I'd like to think, just see what we want to see and believe what we want to believe, and don't make such a big deal out of it.  If we want to believe in a Higher Power That Guides Everything, we do, and don't spend endless hours crafting abstruse proofs of the conjecture.  We're content to have a beer, watch a hockey game, and let god have some much-needed quiet time.

There are a few people, however, who just aren't content if they're not actively beating the matter into submission.  Such a person is Marty Leeds, Wisconsin-born writer, mystic, philosopher, and the origin of dozens of highly entertaining YouTube videos.

Just yesterday, I was sent a link to one of Leeds' creations, entitled, "The Holy Spirit, Pi, and the English Alphabet."  The link was accompanied by a message stating, and I quote: "Words cannot describe the level of derp in this video."  So of course I had to watch it.  And I wasn't disappointed.

If you're unwilling to sacrifice ten minutes of your precious time, and countless innocent cells in your prefrontal cortex that will die in agony, allow me to present to you the main points of Leeds' argument.

1)  There's this thing called gematria that was made up a while back by some Hebrew mystics who had overactive imaginations and too much free time.  The idea behind gematria is that each letter in the alphabet (whether Hebrew, English, or other) is assigned a number, and when you add up the numbers for a word or name, you get a number that "means something."

2)  You get to decide what the numbers mean.

3)  If two words add up to the same thing, they are mystically linked.  Leeds uses a form of gematria which takes the English alphabet, splits it into two lists of thirteen letters each (A-M, and N-Z), and numbers each list from 1 through 7 and then back down to 1.  So my first name, Gordon, would be 7+2+5+4+2+1 = 21.  "Sharp" is 6+6+1+5+3, which also adds up to 21.  So you can see that thus far, we have a pretty persuasive theory here.

4)  Leeds then does a gematria addition for four words or phrases.  We have "man" = 3, "woman" = 9, "Christian" = 39, and "The Holy Spirit" = 61.  Note that he had to add a "the" to the last one to make it work out the way he wanted.

5)  So, let's look at the first thirteen digits of pi.  He picked thirteen because we had split the alphabet into two groups of thirteen letters each, which seems like impeccable logic to me, given the obvious connection between pi and the English alphabet.  So, we have 3.141592653589.  It starts with 3 and ends with 9 -- giving you "39."  So right away, we can see that there's something wonderfully Christian about pi, not to mention having a man on one end and a woman on the other.  Also, 3+9 = 12, and 3x9 = 27, and 12+27 = 39.  So you get your 3 and 9 back, so "man + woman" + "man x woman" = "Christian."  Or something like that.

6)  Take the middle number in the sequence (2) and the two on either side (9 and 6).  Why?  Because tridents, that's why.  Stop asking questions.

7)  If you multiply 9x2x6, you get 108, which is a very holy and important number.  Myself, I just thought it was the most convenient way of getting from 107 to 109, but what do I know?  But the Hindus liked the number 108, and plus, it's the number of stitches on a baseball, so there you are.

8)  Now, take the remaining digits of pi, and basically draw a menorah under them.  You then put them together in pairs, flip 'em around, and add 'em together.  I really don't want to go into all of how he does that, because my cortical neurons are already whimpering for mercy, so you'll just have to either watch the video or else just accept on faith that somehow all of the numbers and flipped numbers and all add up to 352.  Then, you add that to the 2 and 6 from the trident bit, and you get 360, which is the number of degrees in a circle.  Get it?  Circle?  Pi?  Are you blown away?  (Okay, he left out the 9.  But still.)

9)  If you multiply the first through eighth digits of pi, you get 6,480.  If you multiply the eighth through the thirteenth digits, you get 32,400.  Subtract them, and you get 25,920, which he says is the number of years for the precession of the Earth's axis to complete one rotation.  Except that according to the Cornell University Astronomy Department's webpage on the precession of the Earth's axis, the length of the precession of the Earth is said to be "about 26,000 years" -- the imprecision being because a motion that slow is almost impossible to measure accurately.  But I think we call all agree that since we're using gematria as our jumping-off point, being off by eighty years or so is plenty accurate enough.

10)  Of course, like any good performer, he saves his most amazing bit for the end, wherein we find out that the first thirteen digits of pi add up to 61, which you will recall is the number of "The Holy Spirit."  So pi "encodes" (his word) The Holy Spirit and the precession of the equinoxes.

11)  Therefore god.  Q.E.D.


Well, I  hope you've enjoyed our little ramble through woo-woo arithmetic.  Me, I'm planning on watching some of Leeds' other videos when I have the time (two especially fascinating-sounding ones are "The Isis and Osiris Myth" and "The Holy 108").  However, I think next time I won't launch into this without something to insulate my poor brain against further damage.  I'm thinking that a double scotch might do the trick.