One day, I came upon a brilliant article, in which a rabbi was asked a question every one of us have deliberated over at one time or another. Specifically, the inquiry involved a request for proof of presence of a Creator; a method to the madness, if you will. The response was an astonishingly simplistic analogy. The rabbi brought into light the fact that when a book is written, no one questions the writer's existence and his or her intent to have written the book—that is, no one in their right mind would expect a bottle of ink to spill onto the pages of its own accord, and in such a particular way, that it would have created this book without the writer's will and effort. So, why is it that many of us find it so difficult to believe that a higher power exists?

In the process of reading this article, something in my mind clicked, and I became intensely aware of the unifying parallels between the various elements of the universe, which are presented to us every single day. Incidentally, this theory applies to any given premise—literature, art, music, philosophy, science, etc. But, since my area of expertise lies in mathematics, I shall share with you my outlook in mathematical terms. The basic idea is that there is a connection between everything, and through these connections, one becomes especially conscious of the deliberate order with which nature is created. And much in the way a skilled composer is required in order to effectively plot and build harmonies on a sheet of paper, there must be a force behind these very exact, proportional, and symmetrical arrangements in the environment.

So, let's look at several such examples, which by their very existence whisper, if not shout, that there is something grand at work.

Fibonacci (1175-1250) was one of the most prominent mathematicians of the Middle Ages, extensively contributing to arithmetic, algebra, geometry, as well as being credited with the introduction of the Arabic numerals to Europe. During the process of writing a mathematical handbook, Fibonacci came up with a simple mental exercise, though, interestingly enough, without attributing any particular significance to it. It was not until the nineteenth century that mathematicians began to realize the implications behind what was termed the "Fibonacci Sequence." In essence, each number generated by the Fibonacci Sequence is the sum of the two numbers preceding it. (i.e. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… where 1+1=2, 1+2=3, 2+3=5, 3+5=8, and so on, and so forth). Seems interesting, one may say, but in what way can this sequence be associated with anything of significance?

Well, it seems that the Fibonacci Sequence is far-reaching in exceedingly unanticipated ways. For instance, most of us are familiar with Pascal's triangle, borne of the French mathematician, Blaise Pascal (1623-1662). Pascal's triangle is an array of numbers that is constructed by beginning and ending each new row with a one; the other numbers being formed by adding the numbers above and on either side of them. Each row represents the coefficients of the binomial (a+b) raised to a certain power:

(a+b)^{0} = 1

(a+b)^{1} = 1a + 1b

(a+b)^{2} = 1a^{2} + 2ab + 1b^{2}

(a+b)^{3} = 1a^{3} + 3a^{2}b + 3ab^{2} + 1b^{3}

The Fibonacci Sequence reintroduces itself through the addition of the numbers indicated by the above diagram.

All right, you say. This is amusing enough, but I'm still not convinced.

In that case, let's move on to our next example. The Golden Ratio (aka Golden Mean, Golden Section, and Golden Proportion) represents the proportion of height to width, which is believed to produce the most aesthetically pleasing result. The limit of the sequence of ratios of consecutive terms of the Fibonacci sequence just happens to be the Golden Mean:

The Golden Proportion was also utilized by Leonardo da Vinci in his famed drawing of the proportions of the human body.

As if all this wasn't enough, there are endless instances in which the Fibonacci Sequence appears in nature. We can determine the number of bees in each generation of the family tree of the male honeybee using the Fibonacci Sequence: A male bee has only one parent (as it comes from an unfertilized egg), whereas the female bee requires both parents (since it comes from a fertilized egg).

Other such instances occur very frequently in flowers in terms of the number of petals:

Flower |
Petals |

Lilies, Irises | 3 |

Columbines, Buttercups | 5 |

Delphiniums | 8 |

Corn marigolds | 13 |

Asters | 21 |

The Fibonacci Sequence even applies to the spirals created in pine cones, and formed by the hexagonal-shaped scales in the pineapple.

The examples go on indefinitely; but through the ones sampled above, one is allowed a glimpse into the meticulousness with which the universe was formed. In this light, it would seem highly unlikely that it was an accidental occurrence, but rather, something which was carefully and precisely executed by a force greater than us. One cannot help but be humbled by such a prospect, and come upon the realization that we are here merely to decipher the code, which has been intricately inlaid into nature and has existed long before man.

Author's note: This article was written in memory and dedication to our beloved Rabbitzen Khaya Esther Zaltzman, as a fulfillment of one of her last articulated wishes.

Deciphering Nature's Code (So Fundamental) A real pearl, this one is. Or should I say petal? Rarely is the underlying motivation for a written article, and a mathematics related one in particular, really an article of faith as much as anything else. Being that the authors are women, one a musician, and one a mathematics professor, is a whole order of magnitude more improbable. But as a final wish of their Rebbitzen? Off the charts on all the statistical tables! What did such a highly evolved being request of her spiritual sisters or daughters? Explain what the Golden Mean, means!

She must have believed in looking up things you don't know, like beyond the Fibonacci bunnies, bees, and finding delphinium (8 petals, phi and 'Delphi') aka the toxic 'larkspur'. Septal/nuptial nectaries to attract pollinators or defenders including all flying bugs, lepidoptera, coleoptera, orthoptera, dithoptera and the ants to tend to them. All key words have a 'PT', ancient god Ptah[Egypt]) or 'PH' root words. All one thing in the Divine Proportion!