Tagged: Fractals

Chapter Two: A Theory of Technology Evolution

This book is so jam packed with valuable information, I am taking notes. Genuine education.

Kurzweil opens this chapter explaining The Law of Accelerating Returns, “which describes the acceleration of the pace of and the exponential growth of the products of an evolutionary process”.

[[[[[ As I start to hone in on what I want to write about tonight, I easily notice how reading Kurzweil opens up new channels of scientific curiosity and understanding. He thinks, and writes very logically, yet comes up with these incredible notions. I marvel at history’s revolutionary scientists who conjured up virgin ideas, had no one to depend on but themselves, but nevertheless relentlessly explored exactly what they didn’t know. But there’s a logic to Kurzweil, he’s not thinking up the unknown. He’s predicting things based off of facts**. He’s preaching what man has always accepted, but that which often goes unthought of: we humans will always (try to) improve ourselves, and we will use technology to do it. From fire to computer chips, technology is our endless ladder. ]]]]]

The Law of Accelerating Returns is a simple idea, though with over two pages dedicated to summarizing its principles.

I’ll just summarize my notes. This book is so dense, damn.

Evolution applies positive feedback

If anyone doubts this concept, please read at least the first two chapters of this book, or maybe just my last chapter post. Evolution snowballs, it accumulates. Add technology on top of that, and the snowball just rolls faster, goes further. This law essentially defines Moore’s Law which I spoke about in my last chapter post. Exponential growth is everywhere. Especially in evolution, and especially in technology. Evolution. Technology. Just a year ago, I never imagined how these words fit together.

Every so often, I just GOTTA quote this guy. I literally (figuratively) feel like I’m getting slapped in the face with truth. Literally (figuratively).

By the time of the Singularity; there won’t be a distinction between humans and technology. This is not because humans will have become what we think of as machines today, but rather machines will have progressed to be like humans and beyond. Technology will be the metaphorical opposable thumb that enables our next step in evolution. Progress (further increases in order) will then be based on thinking processes that occur at the speed of light rather than in very slow electrochemical reactions… Over time, the “order” of the information embedded in the evolutionary process (the measure of how well the information fits a purpose, which in evolution is survival) increases.

Evolution works through indirection

What created technology? Humans. What created humans? Evolution. What created evolution? I couldn’t begin to explain (future post topic?). What I mean to point out is that there is a chain of events. One could not have happened without the event prior. Remember those six epochs?

An evolutionary process is NOT a closed system

I don’t think I can summarize this one half as nicely as Kurzweil:

“Evolution draws upon the chaos in the larger system in which it takes place for its options for diversity. Because evolution also builds on its own increasing order, in an evolutionary process order increases exponentially.”

The “returns” of an evolutionary process increase exponentially

The rate of exponential growth is exponential

Yes. Exponential this, exponential that.

The process of evolution, such as allowed rate of mutation, has itself evolved over time

Endless positive-feedback loops. I actually started laughing reading through these principles, it was almost jokish. Exponential is. Exponential is exponential. Exponentially. GAHHHH!

The principle described above applies to biological & technological evolutionary processes.

A specific paradigm generates exponential growth until its potential is exhausted

This then causes a paradigm shift, enabling exponential growth to continue

Technological paradigms represent the creation, explosion, and demise of outdatING inventions (outdatED would imply our current technology will escape the inevitable fate brought on by new technology). Remember when computers that filled up whole buildings were incredible? Remember how cool a camera phone was? We all recognize technology falls in and out of the spotlight, but we never think about the curve on a graph that it makes. I knew this concept, but I did not think about it. I SHOULD TELL DOOGS.


You don’t need to understand what the text says, but look at the single s-curve at the top left. The life of a technological paradigm exists on an s curve. First the invention is invented. Then it takes some time to get the ball rolling (lowering production costs, increasing access, more investors, yadayada), which is represented by the left plateau of an s curve. THEN EXPONENTIAL GROWTH duh. They’re called fads for a reason you know 😉 And then there is a plateauing effect as the technology reaches it’s maximum usefulness, or coolness. This describes The Life Cycle of a Paradigm.

FUN FACT: The time to adopt new paradigms is going down by half each decade. Think about it.


It is at this point I wonder whether anyone is going to continue reading through this. My vote, YOU SHOULD. Now I know the word fractals is scary, trust me I’ve been there, until I read this chapter actually. My first memory of this word: I remember being on vacation with my family somewhere, and we were stopped outside, somewhere, and we were looking at some sort of awesome tree. At least my dad pointed out that it was awesome. Anyway, the tree’s pattern of growth and structure was beautiful, and the pattern was visually systematic, I could see that much. But my dad kept saying “…fractals!….incredible!”, and thus I was unknowingly introduced to fractals.

Fractals answer questions like “how is it possible for the genome, which contains comparatively little information, to produce a system such as a human, which is vastly more complex than the genetic information that describes it?”

Kurzweil describes two types of fractal designs, Deterministic and Probabilistic.

Deterministic fractals describe when a single design element, an initiator, produces new elements called generators, which then in turn become initiators what are also replaced with elements of a generator. “Each new generation of fractal expansion adds apparent complexity but requires no additional design information.” Deterministic fractals will always look the same as they initiate and generate.

This is unlike Probabilistic fractals, which are not as cut and dry as the previously mentioned. These represent the natural effects of random chance and uncertainty. Probablistic fractal designs generally have a more organic experience. For example, they may be used in programming to design a natural landscape, etc. This is because the probability of the application of each generator (created by the initiators) is less than 1. Just think about biological evolution. Why bacteria? Why DNA? Why nerves, why bones, why why why? Sometimes, things are chosen from a larger possible pool for no good reason. “A key aspect of a probabilistic fractal is that it enables the generation of a great deal of apparent complexity, including extensive varying detail, from a relatively small amount of design information.”

SO IF YOU READ THIS you now may understand fractals a little better! From reading a blog! It wasn’t so hard, eh? Thanks for reading! I’ll be posting up again real soon.

** Riddle me this: How is fact? Who is fact?