On Mandelbrot Sets and the Relevance of the Bible

December, 2005

 

As an engineer, I have a deep appreciation of mathematics. My many readings of the Bible have convinced me that a very interesting mathematical concept, the Mandelbrot Set, offers an excellent, and in some ways chilling, insight into the teachings of the Bible and their relevance to our lives today. This description of Mandelbrot Set is taken from http://www.ddewey.net/mandelbrot/ :

"The Mandelbrot set, named after Benoit Mandelbrot, is a fractal. Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small-scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers."

Fractals are usually computer-generated images, because they can be programmed with relative ease, and because the detail at increasing magnifications is difficult to achieve with paint and brush.

While in College I was required to take semester courses in Old and New Testament Studies. I had some excellent instructors, leading scholars in their areas of expertise. I have read the Bible through from Genesis to Revelation some 10 or more times. Each time I read it, a different part jumps to my attention. What was boring and irrelevant during one reading becomes a rich learning experience the next.

An examination of humans throughout 4000 years of history will show that we are not today appreciably different from the way we were a few decades ago, a few centuries ago, or even a few millenia ago. With whatever magnification you apply to recorded human history you will find that, like a fractal image, human character remains essentially the same. With whatever magnification you apply to human social structure, individual, family unit, community, ethnic group, or humanity as a whole, you will also find elements common across these social structures, in which an individual operates with the surrounding world in ways surprisingly similar to the way that a community might operate with the surrounding world.

To say that history repeats itself is widely accepted in the sense that, in hindsight, many mistakes or unwise choices can be seen to resemble well-known mistakes or unwise choices from earlier time periods. The customary use of this phrase is, however, limited to general simiarities between different periods on a timeline. By suggesting that human nature and behavior bear a striking similarity to a Mandelbrot Set I am speaking of a multi-dimensional repetition that spans time and social structure, race, age, philosophical viewpoints, and more, in a fashion that is much more subtle than a simple timeline in which similarites between time periods occur. Part of the subtlety is attributable to our expectation of great differences between what we are examining and what we are comparing to the thing under examination. As soon as the expectation of great difference is satisfied, one ceases to look for similarities. When looking at a Fractal image one often ignores the similarities between portions of the image that differ in scale, because the scale often differs by many orders of magnitude. In comparing oneself with a person of another race one quickly identifies skin color, clothing style, accent, etc., and becomes satisfied with the obvious differences. In comparing our culture to a society from several thousand years ago we are immediately overcome by the differences in technology. What gets overlooked is that skin color or clothing style, or technological superiority, is one of perhaps a very few substantial differences, and that the similarities, when found, can yield far more information than the few differences.

Let me illustrate my point by providing some background to the history of Christianity and Judaism beginning with Abraham.

Prior to the mention of Abraham at the end of Genesis 11 we have descriptions of people and events that are very difficult to place in a specific time or space, such as the stories of Adam and Eve, and of Noah and the Great Flood. Now fast forward to the end of the Bible and you find the book of Revelation. Much of the book of Revelation concerns Christ's return and God's final judgment of mankind, which events are believed to be yet in our future. So, excluding the beginning stories about which we know very little, and the last book describing events that are largely prophetic rather than historical, we have a great, detailed history covering the story of Abraham from about 2000 B.C. (plus or minus a few hundred years) to the beginnings of the early church in the fifty or sixty years following Jesus' death and resurrection.

Abraham lived in a harsh world. If you injured a person, he might think himself justified in killing you. If someone in your family killed a man, his cousin might think himself justified in killing your entire family. A poor person represented an opportunity. One could probably buy that person's son or daughter very cheaply as a servant for one's household. A foreigner or a stranger in a land could not expect to receive the same treatment as a friend or kinsperson. After all, a foreigner was by definition not "one of us". The world was full of gods, and it was typical to worship the same god that one's father worshipped, or the god of a dominant culture. In the land of Canaan, the dominant culture worshipped a god named Molech, or Baal. Molech was the god of fire. It was common practice to sacrifice a child under the age of 12 to Molech once per year at or around harvest time by burning the child alive in front of the altar. Imagine this sacrifice being held at least annually in every city! So when God told Abraham to sacrifice his son Isaac, this was a terrifying, though not completely foreign or unexpected, development. But when the moment of sacrifice came, God prevented Abraham from sacrificing his son. While this story is commonly discussed in relation to God's testing of Abraham, or mentioned as a demonstration of Abraham's faith in God, it can aptly be described as God's first major step to differentiate Himself in the minds of the Hebrews from the other gods of the period. God portrayed Himself as one who cares for the weak, for those who are unable to protect themselves. He became relevant to His people not only because of His power over their lives, but also because of His care for them.

Over 400 years later, in approximately 1500 B.C. one finds the descendants of Abraham leaving Egypt during the Exodus. It was during this Exodus that Moses gave the people a stone tablet on which was written The Ten Commandments. It contained basic rules, such as "Thou shalt not kill", "Thou shalt not covet thy neighbor's wife", and "Thou shalt not bear false witness against thy neighbor". It was about this time that the revolutionary concept of "An eye for an eye, and a tooth for a tooth" was set forth (Exodus 21:23-25). The concept of "an eye for an eye" sounds barbaric to us, but it was novel at the time. It doesn't so much dictate that one should take an eye for an eye as it states that the punishment should not exceed the crime. From these laws you see the development of laws that help the poor and downtrodden. At harvest time the owner of a field or orchard was expected to leave fruit or grain that wasn't ripe or that fell or was somehow missed during the harvest effort for the poor. The poor would then come through the field or orchard to glean food that they couldn't otherwise pay for. It was also during the time of Moses that foreigners were given rights and protection under the law. God became relevant to His people by giving them rules that allowed them to live together in peace, as much as for the manner in which He rescued them from Egypt.

After the Exodus the Israelites entered and conquered the land of Canaan. The inhabitants of this land still engaged in barbaric practices, and child sacrifice to Molech hadn't lost its prominence. God commanded the Israelites to completely destroy the Canaanites, but they did not. Instead, they intermarried with the remaining Canaanites and frequently adopted their customs. Once in Canaan, the Israelites had approximately 400 years of intermittent guidance and leadership by individuals termed "judges". The "judges" were leaders raised up by God to lead the people out of social and moral destruction that they brought upon themselves through the frequent adoption of Canaanite rituals and religions.

Following the period of the judges, Saul became Israel's first king, followed by David in about 1000 B.C. David is generally admired for being a just king who understood the common people. His humble beginnings as a shepherd probably contributed to his ability to understand the commoners. The poor and downtrodden were by law given direct access to the king in a manner that wealthy individuals could only hope for. The king was considered the defender of the disadvantaged. David's kingdom of Israel was divided after the death of his son Solomon into two kingdoms, Judah and Israel. Following Solomon's death, these kingdoms were each ruled by a number of kings, many of whom adopted Canaanite customs, and it is against these kings that the prophets Isaiah, Jeremiah, and Ezekiel speak out.

Among the most common criticisms of the prophets is the absence of social justice, implying a breakdown in the moral fabric of the nation. Kings and powerful individuals did what they wished, and the poor struggled not only against hunger but also against the ruling class that was supposed to defend them. The treatment of children is a key barometer of social justice, and the prophets cite God's anger with the rulers for causing their children to pass through the fire to Molech (Jeremiah 32:35). So, 1400 years after God showed Abraham that child sacrifice was an abomination, the rulers of Israel and Judah continued to practice it. In 586 B.C. Judah fell to Babylon, God's judgment upon His own people for their rebellion and ignorance.

When Jesus appeared on the scene nearly 600 years after the fall of Judah he found Israel in the hands of Rome. The Romans left much of the management of local affairs to the Pharisees, religious leaders of the time who were highly respected for their knowledge of religious laws and for their efforts to follow the laws. But once again, social injustice was rampant. The poor were routinely mistreated. Laws were used to the advantage of those who created them and knew them, rather than for the people who needed them. When Jesus mixed spittle with mud to heal a blind man on the Sabbath he was criticized, because he was working with clay, like a potter or a bricklayer, on a holy day. The health and well being of the blind man was not a legal concern, but the method of his healing was! On one occasion Jesus rescued a woman who was caught in adultery, not because what she did was right, nor because the penalty (death by stoning) was inappropriate, but because justice was unfairly administered. Those who were willing to put the woman to death had conveniently ignored the fact that a man was also involved in the adultery. Where was he? Was he among the crowd, ready with a stone? Or was he in hiding, waiting for the evidence against him to be dispatched? The crowd believed that their own crimes were hidden, and were eager to punish others for offenses that were little different from their own. Jesus apparently informed them that their crimes were not so secret as they hoped. Jesus became relevant to God's people because He cared for them in ways that transcended the laws.

Today slavery is disallowed. Racial and gender discrimination are outlawed. We have an extremely advanced legal system. Child labor laws exist to prevent exploitation of those who cannot defend themselves.

Today, nearly 4000 years after God demonstrated to Abraham that child sacrifice was abominable, many people continue to practice it. The god is no longer called "Molech". It's called "Choice".

Today, 3500 years after God gave the Ten Commandments to the Israelites we still have nation fighting against nation, we have gangs in the streets of L.A. shooting people and committing crimes because they have no desire to live in peace, and we have political parties that seek to pit their followers against each other in bitter verbal battles that threaten to erupt into physical violence at any moment.

Today, 2000 years after Christ, laws are still used to oppress people. Those who can afford lawyers exercise control over others. Oppression is not by whip and chain, but by manipulation of a legal system that has the power to control a person's ability to maintain a job, or own a house. A municipal or state government can litigate against a business that it doesn't like, forcing the business to cease operations due to mounting legal bills. Or a business, with far greater resources than a municipal or state government, can litigate against the government and enforce its own agenda over a community that would otherwise reject such an agenda.

Our society has looked deeply into the fractal image of the Mandelbrot Set of Humanity. We have eliminated some evils, and minimized others. But the pattern of Humanity remains. Social injustice, oppression of the poor and defenseless, continues differently, yet the same. The social fabric of humanity is nothing more than a fractal image, changing little over 4000 years. Do you believe that slavery has been abolished within our society? Tell me the symptoms of slavery, and I'll show you the afflicted 'round about.

How do I know this? I know it because I have read a book that covers 2000 years of history of a single culture. The Bible is unique and remarkable in that there is no other collection of writings or communications in any part of the world that offers this sort of insight into a culture. To the eager historians, anthropologists, and social scientists the Bible offers an account that cannot be duplicated by any number of well-formed human case studies, nor can the truths contained within be overcome by any amount of carefully worded philosophical arguments. The information is there, obvious to those who are willing to search, threatening to those who fear what they might find.

We cannot understand that our history is a fractal image unless we step back to see that our small corner of the image is a repetition of a great pattern. How else can we understand that our future, left to ourselves, is only more of the same? No other book communicates so clearly where we have been, where we are, and where we are going. That book is the Bible, a book that is more relevant to each and every individual in the world today than any book or publication ever produced or conceived. It is more relevant than any book or publication ever will be. God has stepped into our lives yet again, and His relevance to us is that He has shown us who and what we are, and He offers us Jesus, the only way out of our fractal image of a fractured humanity.