A dried up goliath and a weasel named fee

The concept of the “Divine Proportion” (or DP) has been around for thousands of years, but most recently became a hot topic after the DP figured prominently in Dan Brown’s novel “The Da Vinci Code”. I was bored over the Labor Day weekend (in a good way), and decided to re-read “The Da Vinci Code”, and when it got to the part about the Divine Proportion, I stopped and did some thinking. I’m sure none of this is earth shattering, but I was surprised at a few of the things I found.

First, some background. The Divine Proportion is actually a ratio, and is typically referred to as Phi (rhymes with “tree”, not with “fly”). This ratio, we are told, is found almost everywhere in nature. Most proponents of the Divine Proportion feel it proves creationism, but I’m not getting into that debate in this blog. A few examples that Dan Brown uses in “The Da Vinci Code” are the spirals of a sunflower, leaf arrangements, and plant stalks. He also mentions ratios on the human body are in exact accordance to the DP. (I decided to measure these for myself – my results are found below.)

But how is the DP calculated? That’s where the Fibonacci Sequence comes in to help. Leonardo Fibonacci discovered a series of numbers, in which the next number is simply the sum of the previous 2 numbers. The sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.

(One sidebar: I once had a boss who was in love with the Fibonacci Sequence, and would get excited when a Fibonacci number was needed. For example, I would come in to his office with a direct mail plan and tell him we had 7 test lists mailing in our next campaign. He would look at it and say, “Let’s make it 8…a nice Fibonacci number”. He got fired less than a year later.)

As the sequence progresses the ratio of each successive pair of numbers converges on Phi, until we get to the generally accepted value of Phi, or the Divine Proportion:

1.618033988749895

So does the DP really “work”? You can find all sorts of websites that state it does, and plenty more that state it doesn’t. But one of the easily calculated tests of the DP is the human body test. I have done these measurements on myself, and the results are below (all measurements in inches):

Total Height (A): 69.50
Height to from head to fingertips (B): 40.25
Ratio (A/B): 1.726708
Variance to Phi: 6.7%

Height from head to navel/elbows (C): 24.50
Ratio (B/C): 1.642857
Variance to Phi: 1.5%

Height from head to pectorals (D): 18.00
Ratio (C/D): 1.36111
Variance to Phi: -15.9%

Height from head to pectorals (D): 18.00
Width of the shoulders (D-i): 23.25
Length of forearm (D-ii): 18.00
Length of shinbone (D-iii): 17.25

Height from head to base of skull (E): 11.00
Ratio (D/E): 1.63636
Variance to Phi: 1.1%

Height from head to base of skull (E): 11.00
Width of abdomen (E-i): 18.00

This shows that several of the measurements are very close to Phi, but some are way off. Also, some of the measurements that are supposed to be the same (all of the “D” measurements) do not come out that way. And while these measurements were not done in a laboratory atmosphere, the variances could be simply that I’m not a “divine” specimen to use as a test case. (And please no comments on the “width of abdomen” measurement.)

Nevertheless, I wasn’t investigating the DP to try to de-bunk it. What triggered my curiosity was some info I read about the DP and how it was used in both Egyptian and Mayan pyramid building, structures that were seemingly built without any knowledge of each other’s civilization. I then thought about the other major similarities between these two (and most other) civilizations, and one jumped out at me: The ability to track time, and specifically their reliance on the sun and its corresponding time frame, the year. So, if the Divine Proportion was seen in nature, wouldn’t it make sense that it was also seen, somehow, in the way we track time? And since tracking time (the movement of the sun) is directly related to the solar system and the universe, is the DP found within the movements of our planetary systems as well?

Doing some online research I found some discussion of Phi in relation to the distances between planets; however, this research decided to include the asteroid belt to create a “10th planet”, and to me this seems like forcing the data to meet the final number. (Also, there is recent proof to suggest that there is a 10th planet of our solar system beyond Pluto, further threatening this calculation.) However, none of my research came across using Phi in a yearly calculation. So I wanted to test it, to see if anything exciting came out.

First I had to decide what calendar to use. The current January 1 to December 31 calendar cycle was created from the Julian Calendar in 46 BC (and reformed in the sixteenth century as the Gregorian Calendar, when 10 days were skipped to correct past mistakes – and maybe a topic for another blog), but even that calendar wasn’t quite in sync with the seasons. Most early civilizations used the equinoxes and solstices to determine their year, and considered the Spring Equinox (March 20) as the last day of the year. (Even the Julian Calendar paid tribute to this fact, giving the name of the new 9th month “September” and the new 10th month “October”, obvious references to them as truly the 7th and 8th month, respectively.) Therefore, if we use March 21 as Day 1 of the year, what day ends up being the “Divine Proportion Day”?

First we need an accurate measurement of how many days in a year. Most astronomers calculate the year based on the term “tropical year”, or more to the point, the mean interval between the vernal equinoxes (March 21). This has been calculated to 365.242199. (As you can see, this is approximately ¼ of a day more than 365 days a year, which is why we have a leap day every 4 years. You will also notice, however, that after 4 years we would have had 1,461 days completed. However, based on the actual time of a year, we should have completed 1,460.9687 days. To make up for this discrepancy, leap years are omitted in years divisible by 100 but NOT divisible by 400. By this rule, 1900 was NOT a leap year, but 2000 was a leap year. 2100 will NOT have a leap day in it.)

Therefore, to calculate the actual DP time, we divide 365.242199 by 1.618033988749895. This gives us the result of 225.7320931, or in other terms, very late on the 225th day from March 21. So let’s calculate what day that is.

Mar 21 – Mar 31 -- 11 days (11 days total)
Apr 1 – Apr 30 -- 30 days (41 days total)
May 1 – May 31 -- 31 days (72 days total)
June 1 – June 30 -- 30 days (102 days total)
July 1 – July 31 -- 31 days (133 days total)
Aug 1 – Aug 31 -- 31 days (164 days total)
Sep 1 – Sep 30 -- 30 days (194 days total)
Oct 1 – Oct 31 -- 31 days (225 days total)

As you can see, right around sunset on the night of October 31, All Hallows Eve, is the time that the Divine Proportion calculates out to. This day has been sacred to Celtics and Druids for centuries, however the Egyptians and Mayans also revered the day as well.

But the question that I have is this: Is October 31 special because of the Divine Proportion? Or is the Divine Proportion special because of October 31? Or is it all one big coincidence?

Coming soon…the secrets to the streets of Washington, DC, and how it all ties in to Phi.