“Golden deceiver” (φ)


With this year being an unfortunate exception, I have traditionally ran an NCAA Tournament pool. For the last several seasons, I have used a point-distribution system based on the Fibonacci sequence, in which any given number is the sum of the previous two numbers. When applied to a Tournament pool, this means that the sequence awards up to 8 points for a correctly naming a regional final winner, up to 13 points for calling a national semifinal correctly, and up to 21 points for picking the right champion.

The system’s originator also devised a control whereby upsets are worth more points, relative to how big a shocker it is seed-wise. The system used some fairly advanced mathematics, and being not fairly advanced mathematically, I forwarded the pool outline to a Ph.D. in the field, who confirmed that the ideas presented were sound. As if I needed more proof, the first year that I used the system, I won the pool.

The Fibonacci Sequence is frequently associated with the Golden Ratio, although there is no evidence that the 13th Century Italian mathematician was thinking about the ratio when he came up with the formula. He devised it while solving a problem that centered on rabbit populations.

The idea that Fibonacci employed the Ratio while coming up with the sequence that bears his name is one of many myths associated with the Ratio.

The Golden Ratio has the value of 1 to φ, or phi. φ is about 1.618, but like pi’s 3.14, this is an approximation since phi is an irrational number that strings along infinitely.

φ and the Golden Ratio have multitudinous mathematical applications. Skeptoid’s Brian Dunning explained one such case thusly: “If you take a rectangle whose sides are proportional to the golden ratio, you can cut a square off one end of it, and the resulting small rectangle that remains is of the exact same proportions as the original. You can cut a square off of that and you’ll get a still smaller golden ratio rectangle, and you can do this ad infinitum.

Nature has discovered its applications. Dunning noted that, “A tree is most efficient if as many leaves as possible are visible and not shaded by other leaves. As a stem grows, it follows a genetic formula to know how often to produce a leaf and at what angle from the preceding leaf…Produce φ leaves per turn and no two leaves will ever shade each other.” A similar process allows sunflowers to grow with maximum efficiency.

Phi also plays a role in better acoustics and dynamics. Engineers can cancel unwanted audio waves or resonances if they design sound rooms or theatres on Golden Ratio principles.

This is all wonderful, but the Golden Ratio’s beauty has been coopted by the pseudoscientific crowd. Perhaps the best known example is the claim that the ancient Greeks who designed the Parthenon employed the Ratio, as assertion without historical or mathematical evidence. A look at the Parthenon’s design shows no employment of the Ratio, though some armchair archeologists think they have discovered it, which is mostly based on miscalculations.   

Another pseudoscientific claim is that the Golden Ratio is found throughout the human body, such as the width of the shoulders compared to the height of the head, where the belly button is in relation to the rest of the body, or the forearm’s length competed to the distance from the head to the fingertips. The glaring issue with such claims is that such proportions are different for everyone and thus, the Ratio is not in play. In the tree and sunflower cases, application of the Ratio is uniform for every such living organism.

A nearly soundproof way to tell real manifestations of the Golden Ratio from assumed ones is whether it serves a purpose that could not also be served by a similar number. A tree’s employment of the golden angle for its leaves’ distribution serves a clear purpose and requires φ. An example of a mistaken assumption is claiming that the joints in human fingers become longer at a rate that follows the Golden Ratio. Not only is this measurably wrong, but it would provide no specific benefit to people when they are filling out NCAA Tournament brackets or otherwise using their hands.

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