Some thoughts on Φ from me below …
something i learned today:
the ratio between the size of one digit of one of your fingers and the next digit of the same finger is roughly Φ, the golden ratio. Their lengths line up in an approximate way with sequential fibonacci numbers, because as the fibonacci sequence progresses the ratio between sequential numbers approaches Φ. i illustrated this in that image using an arbitrary unit of pixels and the grid in photoshop.
but the real cool part is that because of this, when you curl and uncurl your fingers, the path described by a fingertip is pretty close to a perfect golden spiral! what sweetly built machines we pilot over the earth
“What sweetly built machines we pilot over the Earth” … yes, indeed. Our construction is truly amazing.
A few people have asked whether the “appearance” of the Golden Ratio in nature is coincidence, or proof that the number holds some greater biological significance. Some folks have gotten dangerously close to attaching it to the idea that there’s some greater design behind all this grandeur of life. That’s not the case.
Some straight talk about the Golden Ratio: If we stick to a straight mathematics definition, the Golden Ratio truly is golden. As it states above, the ratio between consecutive numbers in the Fibonacci Sequence gets closer and closer to Φ as we go down the list. That’s absolutely true, although Dan Brown went a little nuts with the idea in The Da Vinci Code.
When we start applying the ratio to natural forms, we have to be a bit more careful. Seashells, pineapples, hands and facial ratios might carry proportions close to Φ, but Φ is a VERY precise, infinitely repeating irrational number. Being close to Φ is not the same as being Φ. The truth is, if you were to measure facial distances or finger lengths in a thousand people, you might see an average close to Φ, but there would be quite a bit of variability in either direction.
What we, as scientists, must dismiss is that Φ is evidence of some greater design. Every feature in the natural world, spiraling according to Φ or not, is the result of countless generations of selection, and the resulting evolution of better and more advantageous forms. While our hands may exhibit finger length ratios close to the golden ratio today, they do so because that is what our evolution demanded they be, and not because Φ is inherently better than any other ratio. A horse’s forelimb has similar bone structure to ours, and no such Golden Ratio. Is its elegant strength less beautiful than our own hand?
We may one day prove that the waves of gene expression in developing embryo hands, or the growth cycle signals of the nautilus shell and the pinecone really are all directly related to the Golden Ratio, but that will be because of the beautiful application of the Fibonacci sequence, and not due to the design of natural splendor using a ruler marked Φ.