God Flashed Me

Stephen Harris

Spring, 2005

As a kid I had a T-shirt with a picture of a computer generated fractal on the front of it and on the back was the formula for generating it.  I took the formula and wrote a computer program to generate the same image.  Then using a cumbersome process I animated it.

The computer I had ran at 16 Megahertz with a separate math co-processor.  For the time it was a nice little machine.  These days there is probably more computing power in the free kid’s meal toy at McDonald's.  None the less I took this toy computer, hacked some hardware, hooked it up to a video camera, and managed to animate fractals straight to video tape.  It turned out better than I figured it would.  But today any kid into computers could easily do the same thing all with any standard new computer, and with much more spectacular results.

I made movies out of mathematical toys, the hard way, because the easy way is rarely worth doing.  Since then these mathematical toys have gone from the garages of geeks to a powerful societal revolution.  What is the significance?  What is going to happen?  What does the future look like?  We ask ourselves these questions about the future continuously.  Sometimes we look at tomorrow, sometimes the next year, sometimes the next century, all while casually anticipating the next moment.  Future events are why we look where we’re going, and the further we try to look the harder it is to see.  And we look far because no matter what, there is no way to know for sure what is to come.



Where do coincidences come from?  While working at Microsoft I went to a talk called “Generating True Random Numbers Using an Inexpensive Soundcard” or something like that.  It sounded boring, but at the moment it sounded better than work. 

When I got there the room which was usually half empty, for other more interesting sounding talks, was now standing room only.  I thought wow?! people really like random numbers.  But what really surprised me was when the arguing started.  Someone called “bullshit!” and I half expected name calling to follow.  Then I thought wow!? people get really wound up about random numbers!  Fortunately before any furniture was thrown the speaker agreed that his use of the words “True Random Numbers” was not appropriate and calm was restored, if now a bit awkward. 

Most computers use very simple ways of generating “random” numbers.  Doing something like taking the static from a sound card as input to some formula would probably work really well wherever you don’t need true random numbers.  I can’t think of anything where a good approximation wouldn’t suffice seeing as true random numbers may not even exist.


Fractal sections

About a year ago while taking a shower I noticed that the ever subtly changing puddle in the bottom of the tub was shaped a bit like a Christmas tree.  Then looking at the edges of the “tree” I realized that the shape was a fractal, just like coastlines and Christmas trees.  And I thought how in the world could that be?  This was a puddle of water in a manmade object, namely the bathtub, and how could it be that a manmade object could create a cross section of water in the shape of a natural phenomena, a fractal? 

Then I remembered my high school math and the area of mathematics called conic sections.  Which just as it sounds is about taking cross sections of cones.  And by doing that it is possible to create all sorts of interesting shapes such as circles, ellipses, parabolas, and other things.  These shapes coincidently also describe the shapes of lots of phenomena we observe every day.  The path a ball takes when you throw it.  The orbit of the moon around the earth and the earth around the sun.  

And that is when I became confident that everything is fractal in nature.  Just as slicing a plane through a cone gives a conic section, slicing a fractal through another fractal gives a fractal section.  And that fractal section is in turn a fractal.  Which reduces down to everything is a fractal and everything that we perceive is a fractal section.


Implications of a Fractal Nature

Trees are glaring examples of a natural fractal.  So are smoke, wind, surf, sound, music, mating patterns, plate tectonics, social structures, and pretty much everything else I can think of.  They all have this infinite geometry to them, but geometry none the less. 

Since I don’t believe in the unnatural, I believe that natural selection is still at work.  The same force that brought us to life is still at work leading us through life.  We are the sum of all of the circumstance that our ancestors have ever had before.  Our consciousness is a reflection of that experience.  Our own experiences contribute to the consciousness of ourselves and the experiences of our descendents, making experience and consciousness recursive in nature.

I remember learning about recursion in my first college computer course.  It is a powerful yet simple idea that is at the core of what a fractal is.  Abstractly it is defining something in terms of itself.  Concretely it is something that computers are so well suited for it looks like magic.  Programs that generate fractal images are so small that they don’t look like they could generate anything at all. 

Here is a simple fractal “program” that you can “run” on yourself.  First draw a straight line on something.  Then draw another line that is intersecting, perpendicular to, and half the length of the last one.  Repeat as long as you can.

When you are done, depending on your interpretation of the “program”, you will quite likely have something that looks like a spiral.  If you had an infinitely sharp pencil the spiral could be infinitely deep.  Unfortunately you’d also need infinite time to draw it, unless of course you were able to draw infinitely fast. 

By only drawing this “as long as you can” the recursion has an out.  In computers it is called a “base condition”.  If a recursive computer procedure does not have an out, or base condition, then the program would try to use all of the computer’s finite memory and crash.


Fractal Arithmetic

For a while at Microsoft I worked on SQL Server writing esoteric code that interpreted expressions written in a bizarre yet powerful language called Structured Query Language or SQL (pronounced “sequel”).  One of the changes that I made was adding “date arithmetic”.  It wasn’t really a new feature, it was just an improvement on an old clunky feature.  

In SQL there is a type of data called a “datetime” which is used to represent a specific time on a specific day.  And there is a function in SQL Server called GetDate() which returns a datetime representing the current date and time.  So to calculate the day after tomorrow we made it so you could just write something like GetDate() + 2 .  Or to mean 12 hours ago write GetDate() - 0.5, where the number indicates the number of days.   

It mostly makes sense and works logically.  But internally something kind of strange is going on.  To make things more consistent with the other data types and easier to implement, any value added or subtracted to a datetime is first converted to a datetime itself.  But what does it mean to convert a number into a date and time?

Internally each datetime is stored as a number of seconds or partial seconds since a predefined date and time, namely 1/1/1900 12:00 AM, or in other words each datetime is stored as an interval of time.  So to convert the number 2 into a datetime it would become 1/3/1900 12:00 AM.  Then using “date arithmetic” the following would be true.

(1/3/1900 12:00 AM) + (3/2/2005 2:00 PM) = (3/4/2005 2:00 PM)

So what is happening is that we’re adding one interval to another and getting an expected answer.  Thinking about it like that makes it seem a little less strange.  But consider that it also works for multiplication and division.  What would it mean to double a datetime?  Or take half of it?  It would allow you to answer queries like "what was the date when I was half the age I am now?"  Although the syntax is disabled in SQL Server the query would have an expression that looked something like this.

 MyBirthdate + (0.5 * (GetDate() – MyBirthdate))

That seems pretty reasonable too.  However, I have trouble imagining when anyone would want to take the square root of a datetime.  I don’t even know what that would mean.  It would be like taking the square root of an amount of money.  The units get screwed up, but the math would probably still work, however, we would also need to define some new units called “imaginary time” and “imaginary money”, and it would work just like the imaginary numbers. 

Fractal images created using imaginary time and imaginary money probably would look much the same as the ones made using imaginary numbers.  The units don’t show up in the picture anyway.

Just as we can reliably perform mathematical operations on numbers, cones, time, and money, we can perform mathematical operations on fractals.  Conceptualizing fractal arithmetic is more abstract than much of how we conceptualize more familiar finite numbers and geometry.  However, even “finite” line segments consist of an infinite number of points.  And the number of numbers between one and two is infinite.  But for some reason that doesn’t normally get in the way of believing that 2 + 2 = 4.

In a sense we can’t not have a concept of math.  The difference between 1 and 1000 stampeding antelope can be the difference between life and death.  And just like snowflakes none of those antelope are exactly the same as each other, yet it is apparent that each one is an antelope and together they are a threat.  Also like snowflakes no two threats are ever the same, yet we have evolved and learned to recognize threats within an infinite array.  Just like recognizing snowflakes from within the infinite variety, we anticipate and recognize unknowable threats, events, and circumstances as they arrive from the future.

Our ability to adapt is a direct result from what we have learned from the past.  Unfortunately the past is not a reliable predictor of the future.  It only bears a resemblance.  So a key to anticipating the future is recognizing the resemblance between the past and the present. 

So using “fractal arithmetic” I contend that the difference between the past and the present is a reflection of the difference between the present and the future.  Or

present – past ≈ future – present

The difficult part is that the past, present, and future are each approximately infinitely complex.


Consequences of a Recursive Consciousness

Math, religion, and the universe are all reflections of one another.  Mathematics describes the nature of the universe.  Implications of the universe are religious in nature.  And religion is mathematical.

So then who or what is God the Father?

I saw some of the gymnastics during the last Olympics and this tiny young amazing teenage freak of nature apparently had a less than satisfactory routine.  Never mind that 99.999% of the rest of us couldn’t even come close to this “bad” routine.  But in the Olympics it is all about pushing the best of the best to their limits and as this young girl left the mat the announcer said “looks like she’s getting fathered by the coach”, while they showed her getting chewed out.

I thought it was an interesting use of the word “fathered”.   Fathering seems to be associated with discipline and often comes from something other than one’s biological father.  Fathering instead comes in some way from the universe and its inhabitants. 

But just as fathers are fallible, so is the universe and its inhabitants.  Some days you get away with risking your life for the fun of it, and others your life can be derailed for no apparent reason.  One day you could jump the Grand Canyon on a motorcycle and the next day trip over a cat and fall down a pile of stairs. 

We can’t not be fathered and we can’t not learn.  The sum of all that we experience from our fathers and mothers, brothers and sisters, friends and enemies. The sum of the sun, moon, and stars, the oceans, forests, technology and religion.  All of these things define what we experience and the sum of them is God the Father.   

So in a sense, we all are a part of and contribute to God the Father. 

So then how does God the Father sire a son?  God is not bound by things that we as merely parts cannot escape from, such as time.  Jesus was not begotten of the father until centuries after he was crucified.  I would argue that he not only rose on the third day, he was also immaculately conceived on that day.  Keeping in mind that days in the Bible are abstract time frames that can last hundreds, millions, or billions of years, and that God’s reach is both forward and backward through time.


Truth, Understanding, and Metaphors

We’re all specimens examining each other and our cage.  

Our cage is balanced with our own ability to manipulate it.

Be careful playing tag with God.

Recursion is the key characteristic that fractals have.  Natural examples are abundant.  Trees, waves, coastlines, consciousness.  Which is why I think of consciousness as a ripple, on a wave, in an ocean, created by the pressure of time. 

How does that work?  It really just sounds like metaphors posing as poetry.  I believe that the rhythm and pattern that relates poetry to meaning stems from the same effect that relates waves to consciousness.  We’re not that different, but we’re all different.


More Fractal Arithmetic

Video games use linear algebra and transformation matrices to create two dimensional pictures from 3D models.  It’s harder for a computer to go the other way around and make a 3D representation out of 2D pictures.  However, we do exactly that with our eyes and our brains all the time. 

We look at a world using two eyes.  We can still see with only one or even live well with none.  But even with two healthy 20/20 eyeballs the information reaching our brains still has been constricted as two 2D images projected upside-down on the back of each eye.  Those images are preprocessed by the eyeballs themselves before sending some partially deconstructed “image” to the brain via the optic nerve for further processing.

This whole process involves loss of fidelity.  What we think of as the physical world is an imperfect mental reconstruction based on our flawed senses and instincts.  It is impossible to have a completely accurate concept of the world because we interact with the world using inherently limited senses.

In spite of and because of that I believe there exists some infinite fractal formula that transforms the shape of one’s stream of consciousness into something resembling a stream down a mountain.  The stream and the mountain both have an infinite, predictable, and inherently constricted sense of each other.  Just like our sense of the universe and it of us.


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