### Change at the Top

Many of you will now see some version of the logo above when you read Fractals of Change. It is at the top of the blogsite, on top of subscription emails sent through FeedBlitz; and a small form is displayed by some but not all feedreaders. This is just the beginning of the technical remake of this blog. Goals are to make it easier to find what you’re interested in, to be intriguing for new readers, and very functional for returning readers.

Change, of course, must start at the top. Talented graphic artist and web designer Pat Bertha made the new logo with the fractals in the background. You can see her own site and what she does here.

As you know, change is what I write about mainly. It fascinates me and I assume it interests you if you are a regular reader. It’s cliché to say that we live in a time of accelerating change – but we do. It’s my contention that change is a fractal; its twists and turns are impossible to project. You can’t even accurately predict the short-term velocity of change although you know for the minute – subject to change – whether conditions are turbulent or smooth. Things tend to move in the direction they’re already moving – until they don’t.

We have unprecedented tools for dealing with change: information from anywhere on earth at minimal cost and light speed, plentiful cheap MIPs to crunch data; huge places in tiny spaces to put all this data; and even tools to find it again once we store it. But all of these tools for dealing with change enable even faster change. No good reason to think our brains have evolved much recently. So we are beyond our physical design limits in the amount of change we must handle. Except that our physical design includes the ability to create both tools and culture – mental levers that allow us to lift larger loads than our hunter-gatherer brains can do unaided.

At the dawn of the computer age – I was around – we thought that even the pitiful processing power we had then would make everything calculable. Surely ENIACS and UNIVACS and the new computers from time-clock maker International Business Machines would overwhelm problems like weather – particularly weather, stock market prediction, earthquake forecasting, the origin of the universe, the mechanisms of the brain. We would answer the question of free will vs. absolute determination.

Instead we learned about chaos. The flap of a butterfly’s wing in China can cause a hurricane in Georgia. (I understand that two congressional committees and most of the class-action bar are looking for the bug that caused the storm that broke the New Orleans levies. There’ll be hell to pay when Lou Dobbs discovers we outsourced rainmaking to anyone in China, let alone a butterfly.) There’s a lot of stuff we’re not going to be able to compute before the entropy-spring of the universe unwinds.

Even one plus one might not really be exactly two given quantum uncertainty, just ask Schrödinger’s poor cat. What’s worse is we don’t know whether the failure of certainty is due to the uncertainty in our computing or the uncertainty of the laws of physics or even whether there is a distinction between those two possibilities.

All of this is why smart venture capitalists don’t ask innovative new businesses for five years worth of projections. It’s why very few companies end up being the business they started to be or solving the user problem they were formed to solve; the successful ones are just as likely to be off plan as the failures. Success often depends on how quickly you can abandon your preconceptions and adapt, on how quickly you can unlearn the lessons of the past.

Which takes us back to fractals. They are generated mathematically by a class of formulae which have the chaotic property that you can’t take any shortcut to calculating the nth iteration, each step is a surprise until you calculate the one before it – sort of like quarterly results. Here’s an example:

There is a formulae ecologists use for predicting the next-generation population of a closed, ecosystem with some limiting factor like food supply or space which inhibits reproduction when strained. Under some circumstances. population does NOT go to its sustainable max and stay there; it never settles down. The so called “pond population” formula is P_{(t+1)} = xP_{(t)}(1-P_{(t)}).

Think of P as being the percentage of the absolute limit to population which has been reached. x is a population growth factor under non-limiting conditions. In other words, x=2 means that, under perfect conditions, each couple (if these are monogamous creatures) will have four surviving offspring and then promptly die.

t=0, as you mathematicians already know, is the initial population or the population when you start measuring; t=1 is the next generation (“state” for the technically minded); t=50 is the 50^{th} generation and so on.

This is fun, right?

Let’s say we start at 2% of the absolute limit and x=4. Here’s 50 generations of history in our pond:

The pattern doesn’t really repeat. Hyper population growth leads to a crash. A low population will rebuild. Sometimes extremes are avoided; sometimes they’re not.

But the mathematical point is that there is no magic formula for knowing what the size of generation 50 is going to be except calculate it out a generation at a time. In other words, there are some principles, some trends, a dim view of what will happen in the immediate future, and no visibility to what’ll happen a few generations out until you get there.

Those are the fractals of change.

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