Admittedly, the title of this blog is a bit of a tease, as I expect that what I am going to talk about is not precisely what most people reading this title will have in mind. That said, in fairness, the tease itself comes from the fellow who gave the sermonette today, and managed to (surprisingly to me) involve me in the message by asking me a direct question from the pulpit about where I learned about the Fibonacci sequence. And, to be fair, I have always been greatly interested in number theory, and learned the sequence first as a kid watching PBS, although I have also found its relationship to areas of art and architecture to be of great interest as well. It is curious, to me, how a simple little set of numbers that I learned as a small child have such an interesting resonance in life.
A great deal of beauty depends on a certain sense of balance and proportion. For reasons I don’t particularly understand, there seems to be a golden ratio that is the most comfortable for human beings, that shows up in a lot of areas of our body and our world (including the aspect ratio of televisions as well as the proportion of furniture and even index cards). Even more interesting, and puzzling, is how this ratio is related to adding up the sums of the previous two numbers and dividing n by n+1 as you converge on this ratio. How algebraic sums of numbers relate to a ratio that is particularly pleasing to the human eye, and one that appears quite frequently in the human body (including the overall dimensions of our body, our arms, our face, and our hands), which is one reason why the human body is a particularly appealing shape to the human eye is one of the mysteries of mathematics.
I tend to be someone who likes to see the connections between different fields. When mathematics mixes with furniture design and architecture and theology, one has found a particularly rich seam to examine. Why would a number just about 3/5 be a proportion that is most appealing to the human eye? I don’t know the answers, and they are a question in mathematics that relate to our perceptions that would suggest that there is a mathematical basis for much of our thoughts on beauty. That is not to say that there are not elements of taste, because there are, but clearly if there is a ratio that we tend to consistently find appealing, that suggests that at least some element of our judgment of aesthetics comes from a rational source. And there are implications to this, as it suggests that our impressions and judgments about form and beauty have a basis in some kind of facts, upon which are added subjective factors relating to our experiences (and no doubt other factors).
So, I was pleased by the message today, as it gave me at least a helpful reminder as to why Fibonacci deserves to be remembered. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc ad infinitum is not necessarily the most exciting of series. Yet its implications are greatly interesting. Sometimes what appear to be mundane subjects have a reach that extends far into areas of great importance and general interest, and yet we will never find out these connections unless we are willing to do the hard and tedious work of figuring out the connections that spring from often neglected nodes  that prove to be fascinating once someone takes the time to get to know them. Then again, I’m a person in general that thinks that just about anything can potentially be of value if one takes the time to understand it well. And yet there is only so much time, so most of us would tend to spend that time examining that which is of more immediate interest, not seeing the depths that come from patient and steady exploration of the world around us and what it connects to.
 See, for example: