Fractals: Who Knew?

The word fractal was coined in ca. 1980 by the mathematician who was the first to demonstrate how an obscure branch of geometry could be used to generate remarkable models that show properties that are stunningly similar to complex configurations in nature: the branching of trees, coastlines, broccoli florets, galaxies and clusters of galaxies, and many more.

I had heard the word, but didn't know much about them until I read a post in Christine Quigley's blog (my favorite blog!). I especially recommend the 50 minute video she showcased, it is entitled Fractals: The Colors of Infinity.

Despite my engineering education, advanced mathematics (Calculus and beyond), has always been a weak area for me. Even after the excellent explanations and examples in the video, I could not actually generate an image using a fractal. Nonetheless, one property of fractals really popped out at me.

A fractal is a short mathematical expression (example: Z = z times z plus c) which can be iterated to produce artifacts of enormous complexity, endlessly unique shapes with recognizable similarities.

Thus fractals can be used to create geometries more characteristic of nature than of a machine shop's product. One example would be the shapes of trees. Although every oak tree branches in a unique pattern, the patterns of oak tree branches is readily distinguishable from the patterns of pine tree branches. The coastline of Ireland is quite different from the coastline of Puerto Rico, and yet island coastlines are easily recognizable as such on a map. The scale is not important, a bonsai cypress bears a striking resemblance to a huge old growth cypress. Australia's island coastline is clearly in a class with Jamaica's .

What struck me was that a process composed of a few simple steps can create infinitely complex shapes with easily recognizable similarities. I see a parallel with Christian lives. Following Jesus

requires us to invite him to help us iterate on relatively straight forward set of teachings: love one another, forgive one another, give generously, serve humbly, and so on. As each of us repeats those steps over and over, a pattern emerges that is unique to our own life and yet recognizably similar to the lives of other faithful followers of Christ. In a similar way, the pursuit of worldly goals consists of iterations of pride, greed, lust, hate, and so on. Again, each worldly life will differ from all others and yet there are easily recognizable patterns that emerge.

Scale is not important here, just as with fractals. A small kindness resembles a large kindness; a small theft resembles a large one.

Simple steps are not necessarily easy steps. Even small simple steps may be very difficult. Forgiving a small injury may prove more difficult than forgiving a larger one. Giving a billion dollars may be easier for Bill Gates than giving a thousand is for a single mom of limited means.

Generosity cannot be measured by the size of the gift.

Fortunately, each of us is simply responsible to follow God's leading, one step at a time. And because God knows that we will fail apart from his help, he has provided the grace we need.

High Priests of the Big Bang

Wonder. Humans wonder. We want to know.

Journalists created five W's and an H as a mnemonic to help them satisfy our curiosity any time they report an event.

• Who? Who was involved?
• What? What happened (what's the story)?
• When? When did it take place?
• Where? Where did it take place?
• Why? Why did it happen?
• How? How did it happen?

We are most satisfied when all of those questions are answered. Of course, for even the most trivial stories, say a fender bender at rush hour, it is possible that we will never get all the answers.

It should be no surprise, therefore, that we humans struggle to create a story about the origin of the universe that satisfactorily answers all of the Five W's and the H. A quick survey of cosmological theories over the centuries shows that we have had a tough time answering even one of the questions. It is not surprising that there have been attempts to shorten the list of questions.

For many centuries, physicists supposed the when question to be irrelevant. The universe was declared to have had no beginning and no end. Timeless and infinite. But, for most of the last century, scientific thought about the physical universe seems to point to a beginning: the big bang. Before the big bang, neither when nor where existed. Space and time did not exist until the big bang happened. The clock couldn't start ticking until then. Many physicists estimate that the clock has been ticking for about 14 billion years.

There is no strong consensus on when (or even whether) the universe will end. Consequently, one may find several scenarios: The big freeze, the big rip, the big crunch, The big bounce, and the multiverse. Cosmologists seem overly fond of the word big. Big compared to us I suppose, but I thought we had given up having man be the measure (and center) of the universe. Multiverse is a contradiction in terms, since universe is meant to describe all that is.

It surprises me that one of the more literate cosmologists hasn't proposed the the big whimper, thus allowing us to start with a bang and end with a whimper.

Cosmologists have done their best to answer the what, when, and where questions. Things get messy when we move on to who, why, and how. Those who are disinclined to the spiritual side resent the suggestion that a who is involved. With no who, the question of why is difficult to entertain. Theists propose a Big Who and believe that the Who knows why.

Cosmologists have an o.k. story about the how follows the big bang. They don't have much to say about how the big bang happened. It would be a description of no space and time suddenly spawning a singularity that contains all space time and proceeds to spread out over as many dimensions as we care to do the math for. So nothing results in everything tightly compressed , followed by expansion ended by freeze, rip, crunch, bounce or the poet's entry, whimper.

This would seem to be a story that suits both theists and atheists. The matters of who and why could be declared outside the scope of the cosmological debate. However this seems to trouble some atheists, who insist there is nothing outside the scope of the physical universe. Theists, like myself, wonder what makes the atheist care about the who and why questions, since they seem to insist that who and why don't exist. It seems the atheist wants the theist to play by the rules while insisting that there are no rules.

It is those atheists who want theists to shape up and fly right that I would call the High Priests of the Big Bang. The High Priests seem to damn the theists, and not with faint praise. I pray God would bless the atheists, and sincerely hope that damnation is not their fate nor my own.

Living Poised Between Heaven and Hell

photo credit: Heaven & Hell by J. Lozano

When things are great, we say "this is heaven on earth". When things are really bad we say "I am going through hell".

Neither is true.

Our lives are a mixture of pain and sorrow, pleasure and joy. We work to move closer to the good and further from the bad, but we know that bad things of one sort or another will dog us to the end of our days on earth. When life is particularly difficult, we may despair, yet the sun rises each day, flowers grow, children laugh. We could not survive if all things were evil.

We exist somewhere between the worst and the best we can imagine. We may rest easy at a spot where the hellish events on this earth seem to be far from us, but we know that in a single moment, terrible suffering may beset us.

Recently a friend and five of her seven children were in a van, on a freeway, returning from a vacation. Her son was driving and made a common mistake for a new driver, he over corrected the steering in response to a small difficulty. Even at the legal speed limit, that one error was enough to cause the van to careen and then roll several times. The friend and four of her children were battered badly, but sustained no serious injury. However, one daughter repeatedly struck the pavement. When all movement stopped, she was badly injured and pinned under the weight of the van.

Disease. Accidents. Financial ruin. Each can occur at any time. I thank God that I have enjoyed a life where such difficulties have been the punctuation in sentences, rather than the body of the story. There are some who struggle to see the few bright spots in their otherwise bleak existence.

Optimists and pessimists are both frequently correct. However, both are fallible and unable to predict the future accurately. From conception to death, we live poised between heaven and hell. Our best efforts may not succeed in moving us closer to heaven. Our personal failures and our worst enemies may not be able to move us closer to hell.

God knows the troubles we experience. He became a man and walked the earth. He suffered and died. He has not forgotten a single one of us. He calls us to him, that we may be assured a home with him for all eternity. We must focus on what is ahead as we endure what is here. We can be thankful for the good things in this life. Better is yet to come.

Do not pray for an easy life. Pray to be stronger. Pray to serve better.

What Most People Need Is A Good Listening To

Photo credit Ear by Travis Isaacs

You probably have a lot to say, a lot on your mind, a need to vent a bit. So do I. So do most people. There is a plenitude of folks who want to talk. Unfortunately, there is a paucity of folks who want to listen.

Perhaps you are thinking, "That's not true. I have to listen to others all day long. I am lucky to get even a scrap of air time." That may well be. There are plenty of people who feel that they have to listen. I am talking about people who want to listen.

It is much more difficult to listen when compelled to do so instead of desiring to do so. You may very well hear every word spoken. You may even remember most of them. But as John Milton wrote "The mind is its own place and in itself, can make a Heaven of Hell, a Hell of Heaven". The ear can pick up the sound waves, the brain can process and store the message, while the mind is stubbornly pursuing its own agenda. Sometimes that agenda is well meaning, as when we are wondering what is the best thing to say in response to what is being heard. Other times the mind is simply bouncing about from topic to topic and only occasionally stopping in to participate in the current conversation. Very little true listening is going on. Regardless of whether we are sympathetic or merely bored, hearing is not listening.

If I want to listen, I must start with the proper motivation: How can I best serve this person?. Desiring to serve differs fundamentally from desiring to be served. How we grow our desire to serve is a topic outside the scope of this essay. For my purpose here, I am going to assume that we want to serve.

We must dump the idea that listening is a passive activity. To really listen, we must actively consider the words, the tone, the body language, and the context. Our goal is to understand what the speaker is saying, as well as why they feel it needs to be said. We can gauge the efficacy of our listening by checking to see how well we understand. The simplest way to check is to occasionally rephrase a part of what you have heard and feed it back to the speaker. You will often get a response ranging from "No, that's not what I mean" to "Well, sort of" and on to "Exactly!".

I like to fish. Fishing is most exciting when I feel the line tug in a way that makes me cry out "fish on!". When I paraphrase what someone has said and they say "Exactly!", we both get a similar thrill. I use exactly as a representative word. The speaker may actually say "Yes!", "That's it", or any of a wide range of exclamations and affirmations. It may even be a nonverbal response. One of my friends energetically points his finger at me when I understand him well; another widens his eyes and nods.

That moment of understanding is precious to both speaker and listener. It is a building block for relationships.

Another way to check understanding is to respond to what you have heard by telling an anecdote. Strive for a quick story that shows how you have experienced or observed something very similar to what the speaker hopes to convey. When you miss the mark, common responses include a frown, a puzzled look, or even a head shake. Verbal responses may be as direct as "That's not what I am talking about" or as passive as a vague "oh". In those cases you may need to reestablish the speaker's train of thought by referring back to what was said earlier or by asking a clarifying question.

Speaking of questions, avoid asking questions that are really disguised advice. It isn't nearly so disguised as you think. Advice should only be offered when asked for. Even then, offer it sparingly. People with advice are abundant. People willing to listen well are rare, and correspondingly more valuable.

You may find yourself longing for someone who will listen well to you. There is absolutely nothing wrong with that. Just be patient. Model the behavior you would like to see. Remember to encourage those who listen even a little, and to cherish those who listen well.

Been There, Failed That

Sometimes failure can be a powerful source of comfort. Not so much for the person failing, but for all of their friends, acquaintances, or even anonymous observers. One place I have noticed this is in meetings. When I just can't follow what is going on, and I have to stop everything to ask for an explanation, I almost always see relief on some of the faces in the room. Maybe they too needed help to understand, or maybe they are just enjoying seeing how dense I am. Either way, I have contributed to their sense of well being.

As a young engineer, I dreaded making presentations to audiences that were either large or full of people to whom I was a peon. However, one day I was standing near my boss's boss when he was called upon to address a large room full of people. I was close enough to see his face twitch a bit. I could hear a small tremor in his voice. I saw that deer in the headlight look in his eyes. Once I realized he was nervous, I could have decided that it simply proved that I was right to be afraid of speaking to groups. I had often thought that way. This time I was struck by a new idea: if he is two levels up ladder, 15 years more experienced, and still quaking about sharing a few words, then it is no big deal if I suffer that same anxiety. That epiphany occurred 35 years ago, yet I remember it vividly. It has helped me countless times.

I made sure I shared lots of my failures with my kids. I knew they would eventually learn that I was fallible, even if I tried to hide it from them, but I really enjoyed giving them advance notice. Sometimes I blushed when they laughed heartily at my shortcomings, but my shame was only momentary. It was soon supplanted by the warm glow of knowing that they had just been freed to make a few mistakes themselves without undue worry.

False humility drains failure of much of its value. I mustn't pretend that I always fail. I don't. Very likely some of my successes have inspired others. I too enjoy seeing someone surmount a challenge.

Seeing others both fail and succeed allows me to see them in depth. I am far more able to identify with them. We share a common plight.

I hope we can all find the courage to showcase at least a few of our failures. It will make the world a better place.