As Time Goes By

by Richard H. Williams


David Weiss was a graduate student in Counseling at Mountain University. This academic institution is located 3500 feet above sea level in the western part of North Carolina, not far from Grandfather Mountain and neighboring Rike's Peak. David had always been interested in history and in famous people who lived long ago. If he could somehow invent a time machine he would whisk himself backward in time to visit some of them.

In particular, he would like to meet:

  1. Matsuo Basho, who developed the Japanese poetry form we now call Haiku. Basho was also famous for taking long journeys which he made immortal in a series of travelogs which combined poetry with prose;
  2. Leonardo Pisano Fibonacci, who made significant mathematical contributions and wrote a number of important texts which helped revive ancient mathematical skills; and
  3. Jesus Christ. David had a number of questions regarding certain mysteries surrounding the latter and would be particularly interested in conducting an in-depth Sixty-Minute Type interview with him.

David Weiss checked out these three luminaries on the Internet on the Gateway computer in his office by calling up amazon.com to get some idea of the impact of their work in terms of published books. Of course, for Christ the volume of literature was overwhelming.

David found that Barnes & Noble had recently published a ten volume leather bound series of books titled simply: Implications of Fibonacci's Mathematical Works. It was selling for $475. And Haiku, Senryu, and Renga, all of which sprung from Basho's pioneering efforts, occupied a sizable literature. Dover publications had put out a paperback biographical work on Basho, another on his complete works, and several on anthologies of Haiku and its variations.

David Weiss often dined with fellow graduate students and faculty members of Mountain University at the Faculty Club. The Club chef made a tasty Reuben sandwich and many other enticing dishes. Draft beer was on tap. David became friendly with Frank Wisdom, a professor of Electrical Engineering and they would sometimes discuss David's ideas about time travel in the evening at the college Rathskeller.

Dr. Wisdom had published a paper in a refereed scientific journal on the possibility of time travel and had even included sketches of a time machine in his article which could move people through time, either backward or forward. David and Frank decided to work together on a project designed to create such a machine. Frank Wisdom had a grant with a flexible budget and so they were able to bring in consulting experts for advice from time to time.

In six months they produced a machine which seemed to have the potential, but in its present form, a modest trial test would be necessary. One day, the two of them entered the cockpit and travelled slowly in a five-year interval, going forward and then backward. Some aberrations occurred, although they landed safely, and so Professor Wisdom was reticent to set off for a more ambitious trip. But David Weiss decided to take the risk and attempt to visit the three luminaries that interested him.

Going backward in time he would first encounter Basho in Kyoto, Japan in the year 1670, then on to Fibonacci in Italy in 1215, and finally to the time of Jesus Christ.

Several hundred students and faculty members at Mountain University gathered on Rike's Peak to watch the assent of David Weiss's vehicle and wish him luck. Many of them, including Professor Wisdom, felt the attempted trip was premature. But with a wave of the his hand and the smokey backfire of the time machine, David made a successful departure.

Crashing several time barriers he arrived at Matsuo Basho's thatched roof hut in Kyoto. Basho was reclining on a comfortable looking cushion that resembled a bean bag chair and was smoking what looked like a long brown cigarette with a holder and scratching out a poem. Its odor made one's head spin.

David asked him what the poem was about. The language translator that Professor Wisdom had provided came in handy. Basho said that on the surface of it, it was simply a poem about a frog jumping into a pond. David mentioned to Basho that he had attempted to write what in the future became called Senryu. It has a physical structure similar to Haiku and is likely to focus on satirical or ironic matters rather than ideas related to nature.

This didn't interest Basho! Also, he didn't use words such as Haiku or Senryu. The poems he wrote were what are called, in modern times, Haiku. He said his poems were written vertically, each containing three lines, with the number of syllables 5, 7, and 5, respectively. He added that they contained seasonal words and dealt with nature, and each poem was an entity complete unto itself. In his poems there was often an element of humor or surprise.

Basho added that his poems tried to answer questions like when, where and what. As an example, “what” relates to the poet's reaction to something affecting one or more of the senses — e.g., scent, sound, taste. Basho was an excellent teacher, and in David's time with him he moved David away from rhyming poetry and from Senryu and taught him to relate his poems to nature.

David told Basho that the implications of his work were immense in modern times and that he was considered to be a celebrity. Although Basho was pleased and amused to hear those words of praise, he somehow didn't seem too surprised.

The wise, famous poet showed David Weiss some of his poems as follows:

A crow
has settled on a bare branch —
autumn evening.

The old pond —
a frog jumps in
sound of water.

Fleas, lice,
a horse peeing
near my pillow.

It has rained enough
to turn the stubble on the field
black.

Note: In the original Japanese, these four poems do follow the 5-7-5 pattern.

Basho and some of his poetry students waved David off from Kyoto, Japan and, fortunately, the time machine was continuing to behave itself. David spiralled through space and soon landed in Pisa, Italy, the city of the famous leaning tower.

By chance, Leonardo Pisano Fibonacci walked right up to David's machine as it landed. Wearing heavy gloves, he began to take measurements. David soon found out that along with his theoretical work on the Fibonacci Sequence and its applications, the mathematician was continually gathering empirical data to support or deny his hypotheses. As David stepped out of the cockpit they smiled and greeted one another.

David said, “I am from another age. I am from the future. Your work is well known for that time period.”

The first evening in Pisa, Fibonacci and some of his students and scientific colleagues and David dined at what would be called an Italian restaurant in 20th century terms. They sat around a huge circular table and enjoyed a four-course meal. The first course was comprised of minestrone soup together with garlic bread; then came pizza with all of the trimmings, deep pie. The third was spaghetti and meatballs — delicious sauce — and the final entrée was Italian ice.

While in Pisa, David developed bronchitis and Fibonacci took him to what might be called a medical clinic. The doctor was a handsome young man resembling Mario Lanza. After he had completed his examination and prescribed treatment David and Fibonacci prepared to leave the clinic. But suddenly David noticed that all of the doctor's assistants were incredibly beautiful women, possessing the dark Italian looks, and would be able to vie with the women of 20th century Victoria's Secret. David was shocked when the greatest of these beauties smiled at the doctor, tapped him on the belly, leaned against him, and kissed him on the lips. This seemed radically different from modern-day nurse behavior.

Before the advent of his trip, David Weiss had compiled a list of Fibonacci's accomplishments, as seen from the modern day, typed them up on Microsoft Word, and made two copies. The evening after they had enjoyed the fine meal he had a discussion with the mathematician and gave him a copy. Fibonacci was enchanted with the fine, clear print and how nicely it sat on the page. It was in marked contrast to the manner in which he was obliged to write out his manuscripts and copy them in longhand. Here is a list of a sample of what appeared on the sheets. Some of these are the titles of books:

Fibonacci was the greatest mathematician of his age. He did not simply master the arts of geometry, trigonometry, and algebra, but also made his knowledge useful to all the businesses employing mathematics. He eliminated use of complex Roman numerals and made mathematics more accessible to the public because he brought the Hindu-Arabic system to Western Europe.

2. Technical Note: Here is the Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, . Each number in the Sequence is obtained by summing the previous two numbers. It goes on forever! Then, by dividing each number by the one that precedes it, one forms a series of ratios whose limiting value is 1.62, the Golden Ratio.

Fibonacci numbers are related to flowers, pine cones, pineapples, trees, suspension bridges, spider webs, dripping taps, CD’s, your savings account, and quite a few other things.

4. Candlesticks, Fibonacci, and Chart Pattern Trading Tools The Fibonacci Sequence and the Golden Ratio can be seen in DNA. Within human and animal DNA there lies the Fibonacci Sequence. Henceforth the con- struction of DNA is done by using the Golden Ratio. Implications of Fibonacci's Mathematical Works (10 volumes), Barnes & Noble, 2003.

7. The Fibonacci Sequence is found everywhere in living things because of the way things grow exponentially in nature. The relation between art and music and the Sequence is interesting. If one looks at famous works of art or architecture recurring patterns of the Golden Numbers are obvious. Fibonacci's first major work, Liber Abbaci (The Book of Calculations) was written in the year 1202. It contains many practical problems of value to merchants of the time, ranging from the calculation of interest to problems con- cerning currency exchange rates and profit margins. Also contained in this volume are a variety of problems and puzzles including his famous problem on the reproduction of rabbits.

The most well know of Fibonacci's achievements is definitely the Fibonacci Sequence. The numbers comprising the Sequence have applications in modern mathematics. They are often used in modern computer science, as a part of number theory. Leonardo Fibonacci can be credited with the introduction of scientific calculating techniques into general business practice.

11. Fibonacci Applications and Strategies for Traders Applications of the Fibonacci Sequence in plants and nature. For example, when counting the number of petals of a flower, it is most probable that they will correspond to one of the Fibonacci Numbers. It is seen that:

Also, seed formation patterns come from the Fibonacci Sequence. Fibonacci Numbers in the human body: as an example, the index finger is divided into parts from the tip to the wrist. Using the Golden Ratio or Golden Mean (also called Phi), which is approximately 1.62, if one multiplies each part of the finger by the Golden Ratio, the length of the next part is obtained. This occurs all the way down the finger, and there are many similar relations describing other parts of the body.

Here is Fibonacci's famous rabbit reproduction problem: Suppose a newly-born pair of rabbits, one male, one female are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits The puzzle that Fibonacci posed was: How many pairs will there be in one year? (Assume none of them die and they reproduce punctually.)

Constructing diagrams in report writing-Don't make diagrams too big and ensure that they are balanced (as symmetrical as possible). To make diagrams look better, make use of the Golden Ratio. This is the number 1.62 — the limiting value of a series of ratios formed by dividing each number in the Fibonacci Sequence by the number which precedes it. So make the diagram 1.62 times as wide as it is high.

16. Fibonacci: The Man and the Markets

17. Notice: The Seventh International Fibonacci Conference met in March of 2003 in New Orleans. The attendance was twice that of any one of the previous six meetings. Two-hundred and forty papers were presented by members of The Fibonacci Society and twenty-five symposia were in the program. Next year's meeting will be in New York City. It was announced that the circulation of the Fibonacci Journal had risen to 8500.

Leonardo di Pisa Fibonacci of Pisa, Italy, was sobbing. As he was reading through the sheets David had given him, he began to lose control of his emotions. Later on he boiled a batch of tea for himself and David. He said, “I have truly achieved immortality. I thought I would be completly forgotten. I can't believe it!” And then he confronted David Weiss with a deluge of question, such as: What is the Stock Market? What is a CD? What is DNA? What do you mean by a computer? What is computer science? How does Microsoft Word work? What is number theory? Can you get me one of these modern books that bears my name?, etc., etc., etc. They talked through the night. David couldn't give defensible scientific answers to all of Fibonacci's questions, but he did the best he could. Because of Fibonacci's quizzical nature he followed up these and other questions with additional questions.

After two weeks in Pisa, David Weiss felt his brochitis becoming more severe. He met with the handsome doctor at the Pisa medical clinic, but nothing seemed to help. His eyes and nose were rheumy, a near continuous discharge from the mucous membranes was occurring, his temperature was elevated, he had a rumbling wheeze in his chest, he was spitting up purple globs of phlegm and he had the fear that he might sink into pneumonia. After a while he could hardly get out of bed. And Finonacci's strong tea didn't help. Unfortunately, antibiotic drugs had not yet been invented at that time period.

David decided to return to his home in the future and packed his belongings and prepared the time machine for immediate take-off, wwith the assistance of Fibonacci. He would have to visit Jesus Christ on a subsequent trip into the past.

Although he still felt terrible when he landed at Rike's Peak, he was cheered somewhat by the crowd that welcomed him and the band playing a musical tribute to his exploits. He had sent a radio message to folks at Mountain University while passing through the 17th century to tell them of his return. When he recovered from his illness he was constantly invited as a guest speaker and several publishing houses made bids for him to write a book describing his adventures. Dr. Frank Wisdom was interested in accompanying David on his next trip.


Copyright © 2005 by Richard H. Williams

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