David Fleming
It's All Academic   www.davidflemingsite.com   
Phee Phi Pho Phum

August 2004:  We've not yet been canceled!

Ask the "Experts"

Dave: Gary! Someone actually reads our articles! We just received the following question:

Dear Quaac: I just finished reading The Da Vinci Code. Is all that stuff true about there being a secret relationship, Phi, built into the design of nature?


Gary: So, someone reads our articles, but isn't willing to admit it?

Dave:  Or someone isn't willing to admit they read that book.  Can't say I blame them.

Gary:  Didn't you read that book?

Dave:  Uh, yeah, but I try to not get too caught up in the wild speculations about history and art that are in there.

Gary:  Oh, the humanities, eh?

Dave: Um, yes. Too bad we don't have "AAACK:" Art Analysis Across the Curriculum, chaired by Bill the Cat, of course.

Gary: Anyway, for the last few people in America who haven't read the book.

Dave: They're waiting for the movie.

Gary: Do you mind? As I was saying, for those who haven't read the book, "Phi" is the symbol for a number that is approximately 1.6. It's also known as the Golden Mean or Golden Ratio and it represents the quotient of the relative sizes of a great many juxtaposed spiral and branching forms in nature. It's also said to be the most visibly pleasing shape of a rectangle and is used extensively in architecture and product designs.

Dave: Golden Ratio?  Product Designs? If that's true why are my Golden Grahams™ square?

Gary: I can answer that.

Dave: Really?

Gary: Yes, in this case the ratio applies to the optimal amount of milk to pour on them.

Dave: Really!

Gary: No. I was just tired of you getting all the good lines this week.

Dave:  I can take a hint. Do you have some actual examples?

Gary: Yes, the Parthenon in Greece and 3x5 or 5x8 cards.

Dave:  Is that it?

Gary:  No, but if you want more you can visit here on your own time.


Dave:  Fair enough, you also mentioned it occurs in nature.

Gary: Yes, the number of petals on flowers, leaf arrangements, and sea shells shapes all tend to follow the golden ratio and/or involve Fibonacci numbers. Again, too many things to fully explain in the space provided, so please read more about that here: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html


Dave: I know I'll regret this, but what are Fibonacci numbers?

Gary:  They are numbers from the sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ... (Add the previous two numbers to get the next in the series.)

Dave:  I finally understand that T-shirt of yours, but what do they have to do with Phi?



Gary:  As you proceed through the sequence, the ratio of two consecutive terms gets closer and closer to Phi.

Dave:  Wow, I'm two-for-two in following you today. So everything in nature follows this rule?

Gary:  Hold on, Skippy, this is where most people go wrong. They assume that because a relationship is common to many items, it is always applicable. Theories are not proven by example, only disproved. 

Dave:  Boy, are you harsh today!

Gary:  No, I'm like this everyday. Seriously though, someone reported that the ratio of male to female honeybees was 1.6; but even honeybee sex ratios vary dramatically from 1.6 in accordance with local hive conditions. Why didn't they choose cats or dogs instead? Neither of these animals have a sex ratio that is even close to 1.6. This is a typical example of "sifting" data to artificially support a "pet" theory.

Dave:  Pet Theory? O.k., I'll ...

Gary:  No, Dave, not even if we factor in dog years.

Dave:  How did you know where I was going with that?

Gary:  How long have I known you? Anyway, given the complexity and scope of nature, one can sift enough data to support any ratio one wishes.

Dave: Plus there are some species where there are external factors that can influence the sex of the offspring. I heard that fertilized goldfish eggs can develop into either male or female fish, depending on environmental factors such as temperature. In fact, even grown male and female goldfish can 'morph' into the opposite sex if it enhances survival of the species! There were times I thought this would be useful, in high school, when I couldn't get a date... 

Gary: Just when you were finally getting scholarly you have to ruin it like that.

Dave:  Perhaps now is a good time to wrap this up.

Gary:  Indeed. Dear Anonymous: There are commonly occurring relationships in nature, but they are by no means secret. In very simplistic terms, evolution is kind to optimization and for many, but not all, things, Phi happens to be part of the mix.