RE: Challenge of Design Complexity

Billy Brown (
Tue, 15 Dec 1998 14:43:08 -0600

Robin Hanson wrote:
> > returns. Recent history demonstrates that if you research enough
> > things, you can create a situation in which the ability of your society
> > make technological advances increases faster than the difficulty of
> > the next step. A reasonable extrapolation of the trend would predict a
> > century or two of steadily-accelerating progress before things begin to
> > change so fast that an unenhanced human can't cope..
> What is the "recent history" that shows a "trend" of
> progress"? No such acceleration shows up in economic trends over the last
> half century.

I meant technological progress, not economic growth. Since new inventions do not necessarily show up in economic data, even when they have a substantial effect on the human condition, concentrating exclusively on economic data could easily lead us to miss important facts.

> >Roughly speaking, the our rate of progress is determined by:
> >
> > R * P * I
> > Progress / unit of time = -----------
> > T * C
> >
> >Where R represents the resources available to each researcher, P is the
> >population of researchers, I is the average intelligence of the
> >T is our current level of technological sophistication, and C is a
> >of the time and effort required for researchers to communicate.
> I think you mean T to be an inverse of tech sophistication.
> You are assuming that progress comes mainly from researchers. This
> undercounts contributions to progress from everyone else. And you are
> not allowing for the possibility that we solve the easier problems first,
> so that problems get harder with time.

No, I mean T is proportional to tech sophistication - this is the effect you mention, in which advanced technologies are harder to invent, design and build than primitive ones. Also, I mean 'researcher' in a broad sense - you could break out R and P into lots of separate terms to reflect the contributions of different groups of people. I didn't, because to do so would greatly complicate the expression without changing anything relevant about the way it behaves.

> >Most of the
> >increasing rate of change in recent times comes from a slow geometric
> >increase in both R and P, and a steady drop in C. Since the changes in R
> >and C are both due to technology, the whole process tends to feed on
> >Meaningful IE would make I increase in roughly the same fashion as R.
> >only would this dramatically speed up our rate of advance, it would also
> >increase the rate at which our rate of advance speeds up..
> You might see if these claims can be illustrated in the context of a
> specific mathematical model of these processes.

I don't think a detailed model is practical, because all of these terms (except for P, of course) are difficult or impossible to reduce to simple numeric terms. However, I will venture some general observations:

  1. We don't know what coefficients should be applied to any of these terms. However, this lack does not have much effect on the model because we are discussing geometric rather than linear growth.
  2. It appears that the product of R and P is proportional to per capita GNP - a wealthy society can devote more resources to tech advance, and it make tradeoffs between number of researchers and money spent per researcher. This quantity therefore enjoys slow geometric growth in the present world.
  3. Since tech advance is a major source of economic growth, it indirectly increases (R * P).
  4. Tech advance also decreases C. Since all of the hard numbers on changes in communication cost and speed reflect geometric progressions, I assume that the decline in this term is geometric.
  5. I assume that the increase in T is also geometric. This is definitely a simplification, but it seems to fit the observed trends.
  6. The history of the last 500 years seems to indicate that R*P will grow faster than T*C, given a reasonable population base and a certain degree of economic freedom. The result is a slow geometric increase in the rate of progress.
  7. When intelligence enhancement becomes possible, it cause a moderately fast geometric increase in I (somewhere between GNP growth rates and computer speed improvement rates).
  8. Since the whole system experiences positive feedback, the change in I will have a much larger effect than might be expected. If you start with assumptions that give moderately fast growth, the change in I causes the rate of advance to explode over the course of a few dozen feedback cycles.

Billy Brown, MCSE+I