The nearly-identical halves of your almost-round self

Is the Universe simple, or complex?

Galaxy NGC 4414

Galaxy NGC 4414

The confounding answer is, the Universe is simple in it’s complexity, and complex in its simplicity.

For those of you who haven’t punched me in the nose yet, read on.

A matter of perspective

Of course, an answer to the simple / complex Universe question depends on how you’re looking at the Universe.

  • Are you looking at it microscopically, from the vantage point of amoeba?
  • Atomically, from inside the nucleus of an atom?
  • Or, how about from the edge of our solar system, or edge of the Milky Way galaxy?

Each view shows different activities and suggests different answers.

Searching for patterns

Oceanic storm waves

Oceanic storm waves

In the midst of what seems chaotic, we can often discern patterns once we stabilize our view.

  • Wave patterns on top of the seemingly-random ocean can be boiled down to numerous harmonic patterns added together.
  • Weather patterns depend largely on the constant redistribution of heat and the spinning of the earth, amongst other things. I’d venture every weather factor has a relatively-simple law of physics behind it — we just cannot yet build a weather forecasting computer because there are an overwhelming number of discreet systems that add up to what we see — from our perspective — as “weather.”
  • The site of a crumpled afghan or piece of clothing doesn’t appear to contain patterns — until you smooth out the material and can appreciate its weave or knit-stitch.

Patterns are everywhere. I don’t think you can name one thing that I cannot find several patterns in.

What’s with all the circles and mirrors?

As you start looking for patterns, you might notice two very common things:

  1. Symmetry
  2. Circles

Symmetry

Just look in the mirror. Your body is a great example of symmetry. Your left side is, in many ways, a mirror image of your right side. This even holds true for some components on the inside of your body. Any differences are a result of the execution of this intended symmetry as you grow and attempt to survive. Perhaps some nutritional factor, injury, or birth defect caused one side to develop differently than the other. Rest assured, though, that our messenger RNA is supposed to be carrying blueprints that often result in symmetrical body parts.

More symmetry

Where else can you find symmetry? There are other kinds. Your body example is bilateral symmetry, but there is also radial symmetry, with the classic starfish example. What about trees? I’d venture to say that a tree’s basic growth instructions, in a perfect world, would result in a symmetrical structure — two identical halves. That doesn’t happen, though, so what gives?

The growth of a tree seems random and chaotic because the direction and size of growth is constantly dependent on a number of factors, such as:

  1. Sunlight direction (Remember phototropism from grade school science?)
  2. Sunlight intensity
  3. Dark / Light period balance
  4. Availability of water
  5. Availability and quality of nutrients
  6. Temperature
  7. Lots more…

All these factors add up to growth that appears random. I argue, though, that each of these factors has a pattern of their own. The fractal growth of a tree results from blueprints for a balance, symmetrical organism that has all these other growth-affecting patterns superimposed.

Circles everywhere

cave-wheelIf you can appreciate symmetry, then around the same time you’ll probably notice how prevalent circles and circular motion are in our world. Sometimes we think of this hairy caveman accidentally discovering the wheel, but I’m pretty sure it was inevitable, because circular shapes and motion are natural. They happen by themselves, no happy accidents necessary.

Circles to think about

  1. Wheels and gears are one great example.
  2. Knobs, dials, gauges, faucets — in one way or another, they all have at least one radial component.
  3. Your eyes
  4. Galaxies, solar systems, orbits, planets — get celestial!
  5. Atomic and subatomic particles — go micro!

Circles keep it together

Line

Imagine a line, and that line contains all the energy in the Universe. Energy and mass are theoretically interchangeable, so our imaginary line contains the entire Universe.

You may remember from geometry class that a line keeps going in both directions for infinity. If you spread all the energy in the Universe out over an infinite distance, then, the discernible result would be zero, nada, nothing, zilch. Like spreading a tablespoon of peanut butter on a piece of bread the size of Manhattan — it amounts to nothing, skippy.

CircleTake our imaginary line, though, and bend it over into a circle. Now, all that energy in the Universe has a real container. You don’t really know where the two ends of the line connect — because there is no such thing as an end to a line — but in theory, you now have contained all that line’s energy in an enclosed system. All the energy of that line is now bound up somewhere along the circumference of our new circle.

Static systems

The Universe could be viewed as one big circle, then — a circle (sphere, really) comprising a finite amount of energy and mass in various states. If we could see the sphere of the Universe, then perhaps it would be a perfect sphere.

The Universe is made of other circular and spherical systems, though. Galaxies, for instance. We could change perspective and focus on just one galaxy. Indeed, there is a circular nature to each different shape of galaxy, but none are perfect circles. What’s the deal?

Each galaxy is being pushed and pulled by the gravity of other galaxies. The only perfect sphere you’ll find, then, is by changing your perspective to view the entire sum of the Universe.

What about perfect circles here on Earth? What about the perfect bowling ball? They may appear to be perfect circles all by themselves, but they are not. They are only perfect circles here on Earth, and their perfection depends on the Earth’s gravity, our Moon’s gravity, and a number of other factors that I don’t even want to start trying to wrap my brain around. Indeed, if you had a sub-atomically perfect sphere here on Earth and moved it to, say, Jupiter, it would no longer be a perfect sphere. To the naked eye, it might appear the same, but with subatomic measurements, you could tell the difference.

Why it all matters

It doesn’t matter! In our day-to-day lives, none of this really matters. You can’t control it. You can’t use it to your advantage. But when you wonder about life and meaning, maybe you shouldn’t ignore how so many things are symmetrical and round.

It seems there is some power in circles.

  1. Orthogonal circle

    Orthogonal circle

    At the large scale of the universe and galaxies, all the way down to sub-atomic particles, we find circles and orbits containing all discernible energy.

  2. Why is π (pi) so elusive?
  3. Why is the divine proportion (golden ratio) so common?
    (And why do we find its result pleasing?)

I wish I knew some unifying theory that tied it all together, but for now, I’ll have to be content to just wonder.

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Macintosh image programming blast from the past

Manipulating image data has been a big part of my life, both hobby and professional. Today, the Wayback Machine gave me a blast from the past, as I was able to dig up old screenshots of my Image Extractor and TIFF Tool programs.

Prepress lead to programming

I worked in prepress since the early days of “desktop publishing,” when a 32MB SIMM for your Mac was $1,200, FreeHand and PageMaker were viable and owned by a company called Aldus, and Adobe products weren’t even available for Windows. Back in those days, necessity really was the mother of invention. Some imaging challenges often made the difference between shipping a product on time or late.

AppleScript and RealBasic

That’s when Ken and I got busy with AppleScript and I built Image Extractor, and later TIFF Tool. Our TSI Graphics coworker Bill White, who has now been at Wolfram Research a number of years, introduced us to AppleScript by loaning us his copy of “The Tao of AppleScript” book. From there, we went to FaceSpan, moved development to RealBasic, and the rest of my career moved on from there.

Image Extractor – Extracting from PostScript

Image Extractor screen shots and info pages (PDF)

Image Extractor started out as a plain AppleScript, received a user-interface facelift using FaceSpan, and eventually became much faster as a compiled RealBasic cross-platform product. This was the first product I’d ever had featured in a magazine – an April 1998 edition of MacWeek.

Image Extractor user interface

Image Extractor user interface

Image Extractor, at the time, was the only easy way to pull embedded raster data out of PostScript, PDF, Illustrator, and FreeHand files. We used to get native Illustrator files from clients, with embedded image data, but we were unable to make changes to that embedded data. I know that sounds ridiculous — and it was — so we made Image Extractor and stopped losing days of production while waiting for clients to provide us with bitmap originals we could edit.

TIFF Tool – Learning the tags

TIFF Tool screen shots and info pages (PDF)

My next step was to provide more services to folks using TIFF files. After reading The Encyclopedia of Graphics File Formats and the smaller Graphics File Formats, I became obsessed with the Tagged Image File Format (TIFF.) I built TIFF Tool originally to help me better understand the nature and capabilities of TIFF files. Later, I added editing capabilities and exporting to other file formats and PostScript.

TIFF Tool user interface

TIFF Tool user interface

To this day, it amazes me that TIFF files aren’t used more extensively. I wonder sometimes if Adobe hadn’t been building the Portable Document Format (PDF) — PostScript’s little lean sibling — if TIFF would have been the universal cross-platform format of choice. I found it interesting that the TIFF 6.0 spec, published by Adobe, always seemed to be behind the times. Only recently have the JPEG compression abilities in TIFF files been added to PhotoShop. I wonder if Adobe now figures PDF has been entrenched long enough that TIFF poses no threat?

The future

My future is more about data mining and artificial intelligence than anything. But those early days of extracting raster data from PostScript, and of understanding the flexibility of TIFF tags, definitely provided a solid foundation for what I do now.

A few PDFs from the Wayback Machine

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