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Thursday, August 11th 2016


Phi in Nature, part 2: Bees

  • STATE OF EXISTENCE: Not being a busy bee

It's still early August, but the local schools are already in session. The weather is hot and humid; I wonder if those kids are learning anything. Or, let's say, if they're learning more than under the traditional calendar when schools used to start after Labor Day.

June and I haven't been doing a whole lot right now after coming back from visiting Ralph and Lisa in South Carolina. What a nice visit that was! The StreetJelly concert was a super highlight, but it was good all around.

me and guitarSpeaking of StreetJelly, I'll be doing my "regular" show tonight (Thursday) 9 pm EDT. In fact, that's only about an hour from now, so I better hurry up. Back to just me, Sarah (the guitar), maybe some other instruments, and you, my faithful viewers and remote back-up band. The theme is the generic "Summer Sunshine," and I'm bringing out some songs I haven't done in a while. Please join me and help me have fun!

And furthermore, speaking of playing the guitar, my painful "trigger finger" has returned. It showed up last year somewhere around this time, and at the subsequent doctor's visit, an injection of cortisone did the trick--for about 10 months. So, at a visit yesterday the doctor offered to let me get more shots at decreasing intervals one after the other ... not a good thing ... or get surgery. Actually last year, I had expected surgery, and the good results of the shot were a real surprise, but, obviously, that's not the kind of thing someone would just want to maintain over and over again. So, I'm scheduled to have the problem fixed on September 9, one day after the anniversary of my day of amnesia. It'll take a couple of weeks to get back to normal, and it's supposed to remain that way then. We'll see what happens with my musical efforts during that time.

The summer Olympics are well underway, of course, with all their usual flamboyance, real and contrived drama, and some awe-inspiring accomplishments. It's the one time every four years that we all get interested in gymnastics, and the women's team has definitely made it worthwhile. Congratulations to the "Final Five" for an entertaining gold medal performance.


Well, here's another occurrence of phi in nature: the genealogy of a male bee, commonly called a drone. We get to it by way of the Fibonacci series.

First, some basic facts.

worker bee and parents1. Your basic worker bee is a female bee descended from an ovum supplied by the queen bee and fertilized by a drone. She collects the nectar in blossoms to make honey, distributes pollen among flowers in the process, and stings people if they deserve it from her point of view. Worker bees have no role to play in reproduction other than the coronation of a new queen if one is needed.

2. A queen bee is a female bee who has been fed large amounts of "royal jelly," a product that turns her into a reproductive machine. She is the daughter of a previous queen bee and a drone.

3. I've mentioned the drones above as the male bees who fertilize the eggs produced by the queen bee. That's what drones do. In fact, it's the only thing that drones do. The unique feature of a drone is that he does not have father, but only a mother, namely the queen bee. Consequently, he only has one set of chromosomes, as opposite to the normal two. Scientifically, it's called "haploid," a term that refers to having only half of the usual numbers of chromosomes (in contrast to the more usual "diploid").

On the right is a diagram of the parentage of a working bee. Father drone and mother queen give birth to a girl-bee, who will probably never become a queen. If for some reason, she were to be chosen to become the next queen, her sisters and half-sisters will feed her large amount of "royal jelly." Her abdomen would enlarge, and her ovaries would morph from being useless vestiges to high capacity organs. Otherwise, she's condemned to a life of celibacy and hard work. All humor aside, the queen probably works harder than all of the other bees, spending her life giving birth to one larva after another, and it doesn't look like much fun.

So, let's look at the ancestry of a drone. In the diagram below, you can see that every drone had one queen as parent, and every queen had two parents, a drone and another queen. Common female worker bees have no place in this depiction because they do not actually participate in the reproductive process. And, needless to say since you can see it yourself, the number of ancestors of the drone follows the Fibonacci numbers as we go back generation by generation. Thereby, they are headed ultimately to converge at phi.

genealogy of drones

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