Kansas Snapshots by Gloria Freeland - April 15, 2016
My Fibonacci flowers
Every Wednesday, husband Art and I have lunch with our friend Dave. Both men work in electronics, so a little shop talk is normal. I usually just listen through these times, but not always. A good example happened a few weeks ago.
Dave had met with a physicist that morning about a project that included a small speaker. Sort of tongue-in-cheek, Dave had asked if he wanted the holes for the sound to come out to be drilled in any particular pattern. Without missing a beat, the fellow told him that he thought it would be good if Dave did them in a Fibonacci sequence.
Art laughed, Dave grinned and I had no idea what they were talking about - or wouldn't have a few years ago. But I have been around Art and Dave enough to have picked up a few things. I knew the Fibonacci sequence had something to do with the patterns of petals on a daisy or the seeds in a sunflower head.
I asked Art to remind me of the details. The Fibonacci sequence is a series of numbers generated when you start with the numbers 0 and 1 and then form the next number by adding the previous two. So the Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, etc.
But none of us knew anything about Fibonacci, the man. So as Art reached for his smart phone, I laughingly said, "I'm going to say his first name was Leonardo" - the only Italian name I could come up with on the spur of the moment.
Art laughed ... and then laughed harder when the site loaded. "You're right!" he said.
Leonardo Bonacci, who lived from about 1170-1250, was also known as Leonardo of Pisa, Leonardo Pisano Bigollo and Leonardo Fibonacci. He was an Italian mathematician who popularized the Hindu-Arabic numeral system we now know so well to the Western World through his 1202 "Liber Abaci" - Book of Calculation. His book proposed using the digits 0 through 9 and place values. The book showed the Arabic numeral system by applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest and money-changing.
Our curiosity satisfied, the conversation moved on to other topics.
A few days later, Art and I decided to watch "The Great Math Mystery" on PBS's "Nova" program. To my surprise, Fibonacci numbers were one of the first things mentioned. The scientist said they appeared not only in the petal counts of daisies and the seeds in a sunflower head, but in the pattern of a pinecone's scales and the spiral of a Nautilus shell.
The premise of the program was that many physicists see math not just as a convenient tool to describe the universe, but as an inherent part of nature. As an example, astrophysicist Mario Livio mentioned that Pi - the ratio of the circumference of a circle to its diameter - shows up in seemingly unrelated topics, such as the length of a meandering river compared to the straight-line distance from its beginning to its end.
Physicist Max Tegmark explained that although a digital photograph looks like the original, when we look closer, the picture is really a bunch of tiny picture elements - pixels - with each represented by three numbers that specify the amount of red, green and blue light.
Throughout history, philosophers, mathematicians and scientists have searched for the relationship between math and the universe. The program gave several examples:
- In the sixth century, Greek philosopher Pythagorus explored the relationship between math and music.
- In the sixteenth century, Italian mathematician, astronomer and engineer Galileo Galilei used math to show that, when dropped, objects fall at the same rate, regardless of their weight when the effect of air resistance is removed. He later wrote, "Mathematics is the language in which God has written the universe."
- English physicist and mathematician Isaac Newton described gravity in a mathematical equation.
- In the 1860s, James Maxwell, a Scottish mathematical physicist, published a set of equations that explained how electricity and magnetism are related.
- In 2012, experiments at The European Organization for Nuclear Research (CERN) confirmed the existence of the Higgs boson, an atomic particle named for Peter Higgs, whose mathematical work suggested its existence.
But another scientist on the program cautioned against accepting the idea that everything is mathematical. He suggested that because we have used math to investigate the physical world, it's only natural that everything we've found relates to math.
"I think it's an illusion," said Stephen Wolfram, chief executive officer of Wolfram Research. "Because I think what has happened is that people have chosen to build physics, for example, using the mathematics that has been practiced ... But actually there is a whole vast ocean of other things that are really quite inaccessible to those methods."
Examples given included weather forecasting, which is too complex for precise predictions, as well as others, such as the volatility of the stock market and psychology.
Art told me while Wolfram may be right, his examples are not examples at all of what he suggests.
"There was a time when we didn't know the mathematical rules that govern motion and so we could not have determined what was needed to get a ship to the moon," Art said. "But just because we didn't know the relationship doesn't mean it doesn't exist.
"In the case of weather, we do know the laws that govern," he added, "but don't yet have robust-enough calculating devices to give tomorrow's weather with precision before tomorrow arrives. In contrast, we do not yet know the governing laws of the stock market which is actually a reflection of the human psychology that drives it. But not yet is not the same as never."
The narrator wrapped the program up with the following:
So which is mathematics? A discovered part of the universe or a very human invention? Maybe it's both ... We may have some idea to how all this works, but not the complete answer. In the end, it remains The Great Math Mystery!"
I'm afraid a lot of the math still remains a mystery to me. I'm one of those artsy types who describes things in terms of their poetry rather than their mathematical equations. So when I think about the Fibonacci sequence, I'll still picture daisies and sunflowers - But they will be my Fibonacci flowers.
When the honey bee has finished its work and the sunflower dries, the seeds hidden below will increase in number from the center outward in a Fibonacci series - an arrangement that allows the maximum number of seeds to be packed into the available space.