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Tuesday, August 23rd 2016


Phi in Nature, part 3: The Bones of your Hand


It’s August. The temperatures are cooling off, and the days are getting to be rather nice instead of sticky. June is hanging in health-wise, but not doing as well as she should. Let me just relate the minimal story, if you don’t mind. She is showing some serious nutritional deficiencies, which means in her case that the body does not easily absorb them even when their present. The condition may be resolved with megadoses, but the question for us is also what the necessary supplements will do to her digestion. (As for me, I’m pretty good for the most part.)

We had a rather active weekend, by our standards. On Saturday we spent most of the day at a nearby resort/camp ground, though not to return to nature (as much as we want to do that again, given the next opportunity). We were a part of a gospel sing on behalf of MDA, the Muscular Dystrophy Association, which was held in a big “commons room.” It was good to get together again with some of my friends from “Cowboy Church.” There were a number of bands and some soloists. The quality was variable, of course, though nobody was really bad. I did one set in the afternoon, right after which I accompanied Susan and Bob, former fellow members of the Tippyditch Singers and Cowboy Church performers, on my bass.

Playing for Jellypalooza

It was my first time playing the bass publicly in well over a year, as well as finally using the new amplifier I received Christmas before last. So, that song was my warm-up, as it were. Then, later on in the evening, I played bass along with another friend. By then I felt quite comfortable on the instrument again and I confess that I surprised him a little bit when, out of sheer high spirits, I inserted some lead lines.

Then yesterday was Jellypalloza, the celebration of the fourth anniversary of StreetJelly.com, one of those days on which all regular StreetJelly artists are invited to do a short set. I did mine in the early afternoon, wearing the recommended tie-die look. My program consisted of a more or less random selection of songs I like in the folk, country, and gospel categories. This coming Thursday night is the fourth Thursday of the month, which I usually designate as an all-gospel night. My customary time is 9 pm Eastern, and—as always—it will be live on the internet at StreetJelly.com.

Last night we got together with the “boys” and their wives at Sitara Indian restaurant in Muncie to celebrate my birthday. I have totally fallen in love with their lamb biryani, which they prepare Hyderabad style.

Where else in nature can you find the golden ratio?

One suggestion, advanced by “Mr. Phi,” Gary B. Meisner, is in the proportion of bones in our arms and hands. I have referred to some of Meisner's expositions in other contexts several times already. He is definitely a phi advocate, but a critical and honest one.

Let us look at a couple of instances. I have approached them with as much skepticism as I could reasonably muster. Still, by the time we're done, it looks as though the proposed proportions are present, at least in acceptable approximations.

First, here is Meisner’s depiction of an arm with a hand:

Meisner arm and hand
The golden ratio in the human arm and hand,
picture by Gary Meisner from his site.

I went through my usual process of measuring the pixels of the various lines, and here is what I found. Remember, that the dimension of the picture depend on your screen size, magnification, etc. But the proportions should hold true within technically possible parameters.


Section Length Proportion
Forearm 216 pixels -----
Hand 136 pixels Forearm to hand: 1.59 to 1
Forearm + hand 352 pixels Forearm + hand to forearm: 1.63 to 1

Those numbers, i.e. 1.59 to 1 and 1.63 to 1, are certainly quite close within the inevitable margin of error, allowing for fallibility in my measurements as well.

I’m not sure about the placement of the white line separating the hand from the arm. It seems to me that it may be a little too far to the right, past the wrist and cutting off a little bit of what I would consider to be hand rather than arm, and if we moved it a little further left, the ratio would go down. Measuring my own arm and hand did not come up with similar results, but pretty much stuck to 1.5 to 1 even with the dividing point where Meisner put it. I'm not saying that Meisner fudged, but there does seem to be a disparity in my judgment vs. his.

Then there is the proportion of the various little bones of the hand and fingers to each other. We are looking at four components for each finger: three phalanges and one metacarpal, all of them rooted are in the set of carpals.

hand bones
Diagram of the bones of the hand
by Mariana Ruiz Villarreal (LadyofHats)
Wikipedia Public Domain

Here is Meisner's x-ray view of one forefinger.

Meisner finger

The bones of a human forefinger.
Picture by Gary Meisner from his site

As you can see in the picture, the size of the little bones follow the Fibonacci numbers more or less. Let's agree on more than less. I’ve copied the picture and sunk the lines from the ruler down across the pieces, so as to in order to enhance our ability to visualize the approximations.

Meisner finger with some extra lines

It appears that, given a bit of leniency, the Fibonaccis are there: 2, 3, 5, 8.

Still, I do have a little bit of a problem with this display. I don’t have an x-ray of my fingers handy, and I can only measure my own finger externally. But that fact doesn’t mean that I have no way to test what Meisner is saying. The fingernail is supposed to represent one unit of length. I can’t measure the bone underneath my flesh and skin, but I can measure how many fingernails long the distal phalanx is, and that comes out pretty closely to two units, by assumption and some observation. However, measuring the second section (the intermediate phalanx) does not get me close to three by that scale. At first glance distal and intermediate bones seem to be equal; depending on how I position the finger and ruler, I can get it up to 2.5 fingernails long, but that’s all. Thus, if you use my finger as in any way representative and allow for external measurements, the Fibonacci series is not quite as prominent as one would like. Then again, my fingers may be oddly proportioned in various ways. (Speaking of which, I’m happily looking forward to my trigger finger surgery, still a couple of weeks or so away.)

The lesson is simple, but important. The regularities of nature, even when they manifest a mathematical formula, do not necessarily conform to it with complete mathematical precision. God did not create assembly line robots, but individuals. Theoretically, one could say that each individual's departure from the mathematical template is a flaw or defect. But it's the departures from the theoretical blue plan that makes us individuals, unique, and worth knowing.

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