**W**e present to you, dear reader, a letter-to-the-editor titled **Why don’t schools teach about phi and creationism?**, which appears in the *Daily Journal* of Vineland, New Jersey. We’ll copy most of today’s letter, but we’ll omit the writer’s name and city. We’ll also add some bold for emphasis, plus our usual Curmudgeonly commentary between paragraphs. Here we go:

I am surprised how our educational system teaches just the same things.In my opinion, the educational system is not interested in new things and teaches for the test — only students don’t learn.

The system teaches “just the same things”? What’s the letter-writing getting at here? Let’s read on:

As an example,

I was taught pi or 3.14, the theorem of Pythagoras and Darwin’s theory(evolution by natural selection) in the school system.

Right then we suspected that we had found another letter for this series, but the true value of today’s letter is yet to be revealed. We continue:

I wanted to have the school teach 1.618.Interesting, the Italian scholar Leonardo da Vinci used it. Google it on the computer; it saidthe fingerprint of God is 1.618 (also called the “Divine Proportion”).

Lordy, lordy. The fingerprint of God? Is that what the letter-writer thinks 1.618 *really* is? He’s referring, of course, to what is usually called the golden ratio. It pops up everywhere — even in one of our earlier articles (Golden Ratio, Facial Beauty, and Evolution).

We know what you’re thinking: Okay, Curmudgeon, what’s going on here? The letter-writer’s wish to have that ratio thing taught in school may be a bit unusual, but what does that have to do with this blog?

You must be patient and trust your Curmudgeon. The letter now gives you the answer:

It’s interesting how we teach Darwin in our school system, but not even consider 1.618 (phi), or teach how nature has a perfect order and about creationism.

You see, dear reader, the letter-writer understands that there’s a very clear connection between creationism, nature’s perfect order, and 1.618 — the fingerprint of God. He’s been watching detective shows on television and he knows that fingerprints are evidence. ** Evidence!** But for some reason the schools don’t teach it.

And now we come to the letter’s end:

They at least teach creationism at the Christian school on Sherman Avenue in Vineland.

[Writer’s name and city can be seen in the original.]

This could be the creationists’ next big campaign. After “Teach the controversy!” has taken root in the schools they can be out there marching, carrying signs, and wearing T-shirts with a big phi printed on them (**φ**), and demanding “Teach the evidence!”

Copyright © 2010. The Sensuous Curmudgeon. All rights reserved.

What about e? That wasn’t taught to us when I was a kid. Just that pi crap. Why the conspiracy to suppress e? Is it a Greek plot to bolster the popularity of pi?

I agree with SY, and I think that every interesting number should be taught in school.

SYasks:Could be. Why don’t you look into that and report back to us? There are so many conspiracies it’s difficult to keep track of them all. At least now we’re aware of the Darwinist plot to suppress φ.

I thought that God’s fingerprints wouldn’t be on file, since I assumed that he would have avoided arrest, mug shots, fingerprinting, etc. Did they get his DNA as well? Probably the Fibonacci sequence.

And really, if you can Google it, you can very well teach it. Why haven’t the schools picked up on that yet? I’m sure Time Cube Guy would approve.

I agree completely with TomS — every interesting number should be taught in school. No, seriously. It’s what can spark an interest in math in those students who would otherwise think math dull. It makes math really interesting. Every math course should highlight how math pops up in unexpected places.

Martin Gardner had much to say about phi in his “Scientific American” column, “Mathematical Puzzles and Diversions.” The relationship between phi and pleasing artistic proportion could get the art majors interested, and the way phi pops up in biology would surely interest botanists. Of course, phi has unique mathematical properties as well. For instance, it’s the only number that becomes its square by adding 1.

Gabriel Hanna, if you’re reading today’s postings, I remember your post from about a year or so ago explaining the interesting nature of 1/137. Could you elaborate again, please?

The Golden Ratio *IS* taught is school. It generally shows up as an example of an

infinite series converging to a finite numberin pre-calculus algebra.Back when I was doing a stint as a substitute teacher I used this as a “magic trick” for a class that was studying infinite series. It was really cool to see that leaning-moment when they realized what made my trick work.

Well, they taught me pie are square. I say, WHUT??

Pie aren’t square! Pie are round!!!

;)

LRAsays: “Pie aren’t square! Pie are round!!!”You blew it! The full punchline is this:

No, teacher. Pie are round.

are square!CornbreadWhat??? I thought cobbler are square!

I agree with SY, and I think that every interesting number should be taught in school.You want to teach about an infinite number of interesting numbers? Because the set of interesting numbers is infinite. The proof follows.

All numbers are either interesting or not interesting. Every set of numbers has a least member. The least member of the set of non-interesting numbers thus becomes interesting, removing it from the set of non-interesting numbers. By induction, then, the set of non-interesting numbers is zero; all numbers are interesting.

(Strictly speaking that proof is for the natural numbers, but there’s still an infinite number.)

I don’t understand creationist crackpottery about phi, might be interesting to trace its development. Most people have to get to calculus to get e, which is THE BEST NUMBER EVER (and my ID number in the Curmudgeonly conspiracy).

Gabriel Hanna, if you’re reading today’s postings, I remember your post from about a year or so ago explaining the interesting nature of 1/137. Could you elaborate again, please?Well, it’s actually not. I use it in my avatar because there’s a physics history to it and it’s a warning not to get numerological.

The fine structure constant governs electricity and magnetism and its value is approximately 1 / 137, but Arthur Eddington got unreasonably excited about it and tried to prove that it must be 1 / 137 EXACTLY (137 is prime). When it had been thought to be 1 / 136 he had tried to prove that it must be exactly that too, so he was supposedly nicknamed “Sir Arthur Adding-one”. Eddington was a household name, a celebrity physicist, a bit like Stephen Hawking is now, I guess. Wrote a lot of popular books.

Anyway, the warning is, a lot of people get excited when they can fit a function to their data and then they start looking for reasons why their data should fit that function. This is WRONG. Never do it. The function you fit to should either come from a physical model, or it should be some kind of Taylor expansion. Math is something humans made up, and the universe is not bound by it.

@SC, LRA:

No, teacher. Pie are round. Cornbread are square!Cornbread is properly made in a cast iron pan and is therefore round. Inferior breads made in other ways from cornmeal might take on some other shape.

We make our cornbread in the shape of Texas.

“Cornbread is properly made in a cast iron pan and is therefore round.”

Yes, and cobbler is made in a square/rectangular pan. Unless you are super awesome and make cornbread or cobbler in the shape of Texas, like SY!

SYsays: “We make our cornbread in the shape of Texas.”Gabriel Hannasays: “Cornbread is properly made in a cast iron pan and is therefore round.”I am surround by Yankees and other assorted barbarians. Here’s a picture of a cornbread pan. (Not to be confused with a bed pan.)

Enough with the corn!!! SC, please banish anyone else who posts a corny note. (Except me.)

Gabriel Hanna: Thanks for the explanation.

Tomato Addict: You’re right — the Golden Ratio *IS* taught is school. But my exposure to it in school was in Geometry class, and it was presented as the Golden Mean where a line AB is divided at an intermediate point C such that

AC:CB::CB:AB. Now, I ask you, how interesting is that? It’s not until you get into the quirky stuff that it becomes intesting. For instance, Martin Gardner referred to a study done by a French researcher (of course!) that found that on average, the ratio between a woman’s height and the height of her bellybutton is about 1.6 — in other words, phi. And how the ratio of any two adjacent numbers in the Fibonacci gets closer and closer to phi the higher the numbers become. That’s the interesting stuff, not AC:CB::CB:AB.

@retiredscienceguy: I think you have to take that stuff with a grain of salt. Like in Pyramid measurements, you can find all kinds of ratios and constants everywhere you look, and what’s “astonishing” is determined in hindsight–this is Eddington’s mistake. Lots of things come out to “about” 1.6, but it’s not phi unless there’s some kind of process that mathematically produces it. For example, nautilus shells are a good approximation to a logarithmic spiral for mathematical reasons–but not the

goldenspiral. The ratio that governs a nautilus shell isn’t necesarily phi or any other number, could be different from shell to shell.e crops up in so many places because it involves rates that depend on ratios, and because you can always rewrite these equations to explicitly bring out e. The actual rates and ratios don’t depend on e.

Of course, the most astonishing thing of all is that e^(i pi) = -1, and I never get over that one. I can see in hindsight why it must be so but I never could have guessed it on my own.

Invisible pink unicorns! The spiral horn probably conforms to 1.6 in some fashion, so that explains everything. Now, if we can just make sure that Paul Lepage doesn’t wander off to punch anyone who disagrees…

Seriously, as Gabriel H. points out, and Steven Weinburg has written about, while the numbers are amazing, at the same time, the size and complexity of the universe is going to produce some periodic correspondances that allow cosmological and biological evolution to occur. However, given the odds, life is likely relatively rare (on average), and sentient life that survives all manner of disaster and self-annhilation, or the deprivations of its own brand of Creationists, is probably quite rare.

It’s all in the numbers.

Maine Operativesays:You have unwittingly blundered into The Truth. Behold:

The Human Body.SC, you have to warn people. I need brain bleach now.

Look at this nonsense:

5 ^ .5 * .5 + .5 = Phi

Yeah, write it in base 12

:

4^.6 *.6 + .6 = Phi

Or binary:

101^.1*.1+.1 = Phi

Or hex:

5^.8 * .8 + .8

Not so impressive. God uses the decimal system, who knew?

G. H. says,

“God uses the decimal system, who knew?”

Well, of course! Isn’t that why we were given ten fingers??

Seriously, the whole point I was making about why high school math should be made more interesting was not so that some new religious cults would form around numbers, but so that more students would gain an interest in learning more on their own. Light the spark!

(Incidentally, phi squared is still phi + 1, no matter what base number system is used.)

@retiredsciguy:

(Incidentally, phi squared is still phi + 1, no matter what base number system is used.)Well, yeah. That’s way more interesting that the 5’s thing.

So if phi squared is phi + 1, and 1 / phi is phi – 1, how would we generalize that? Let’s have phi be phi_1. Then phi_n could be

phi_n^2 = phi_n + n

n / phi_n = phi_n – 1

These are really the same condition.

Anyway, so you solve it and you get

phi_n = 1/2 (1 + sqrt(1 + 4n))

and we get a whole family of phi:

phi_0 = 1

phi_1 = 1.618

phi_2 = 2

phi_3 = 2.303

phi_4 = 2.562…

Maybe that’s sucked the fun out of it. What’s the marvelous property of phi which we could generalize, if you don’ t like mine?

I dunno. I just like the way phi ties into aesthetics, biology, and other unexpected connections. It pops up unexpectedly, much like pi. Speaking of which, thanks for sharing e^(i pi) = -1. That’s cool.

e^(i pi) = -1. That’s cool.Gauss is supposed to have said that if this didn’t make immediate sense to you, you had no business being a mathematician.

It’s more exciting written this way:

e^{i pi} + 1 = 0

http://en.wikipedia.org/wiki/Euler%27s_identity

Gauss (reportedly) said,

“…if this didn’t make immediate sense to you, you had no business being a mathematician.”

I make no pretense of being a mathematician, which is probably why I think some of the characteristics of Pi and Phi are cool. (I used to date a Pi Phi, and she was pretty cool, too, but that’s another story — and a long time ago.)

Forgot to mention another neat thing about phi — it becomes its reciprocal by subtracting 1. So not only do we have phi^2 = phi + 1 ; we also have

1/phi = phi – 1. There’s a nice symmetry to that, don’t you think?

retiredsciguysays: “There’s a nice symmetry to that, don’t you think?”I’m starting to suspect that there’s a lot wrong with phi. It’s entirely too … versatile, too compatible, too facile, too … well, there’s something unnatural about numbers like that. I think phi is the devil’s number.

@retiredscienceguy:

Do go read the wikipedia article if you didn’t. e^{i pi} = -1 is the coolest thing ever. (Maxwell equations come in 2nd.)

If your brain isn’t full by then, you can read about quaternions. Quaternions have one real and three imaginary numbers (i, j, k). You can write the Maxwell equations in one line, using quaternions, but no one will know what it means…

Be careful with googling quaternions, because there are a lot of nutters out there who think they have magical powers.

Curmy says,

“I think phi is the devil’s number.”

Funny you should mention that. Isn’t an inverted pentagram a satanic symbol? Interesting thing about a pentagram — each line segment in a pentagram (five-pointed star) is in the ratio of phi to the next longer line segment within the pentagram.

So you are right to suspect phi as being satanic. Divine ratio indeed! I wonder if our creationist letter-writer in your post above is aware of this. Bwah-ha-ha- HA!

@Gabriel Hanna:

I read the wikipedia article re: Euler’s Identity. Unfortunately, I think that teaching 7th-grade Science for 27 years has rendered my brain incapable of fully appreciating the beauty therein, so I’ll simply take your word for it. And quaternions? I’m breaking out in a cold sweat just contemplating them. They are a little *too* interesting. Probably has to do with their magical powers or somesuch.

When I mentioned the need to teach about interesting numbers, it was in terms of sparking interest in bright jr.-high and high school students. Euler’s Identity and quaternions may serve the same purpose, but at a higher level — they may spark a desire in a bright college student to pursue a career in mathematics or physics.

I have to admit the connection between pi, e, and i shown in Euler’s Identity is very intriguing. Since phi is based on such a simple geometrical/mathematical concept (the Golden Mean), I wouldn’t be too surprised if there are as yet undiscovered connections with other simple, basic math concepts such as pi.

Hmm. Phi^pi /e …

Gabriel Hanna said, “the set of interesting numbers is infinite.”

But your proof fails, for the natural numbers are dull, as compared with pi, e, phi, and i. It is not true that every set of complex numbers has a least member.

See the Wikipedia article “Intesting number paradox”.

The letter writer doesn’t want mathematics to be taught; he wants a form of numerology instead: “Phi worship.”

@longshadow:

“The letter writer doesn’t want mathematics to be taught; he wants a form of numerology instead: “Phi worship.””

You’re right. Isn’t it ironic that a creationist would be calling for this form of idolatry?!

This thread has been going so interestingly …

Anyone who is interested in interesting numbers should check out two books by John Derbyshire;

Prime Obsession(Riemann hypothesis) andUnknown Quantity(history of algebra).The Riemann hypothesis has to do with prime numbers in a way which I could not possibly summarize here.

Unknown Quantityis the easier book. Lots of e and pi and i in both.