Simulation of technological progress (work in progress)

by Daniel Kokotajlo 4 min read10th Feb 20209 comments

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I've made a model/simulation of technological progress, that you can download and run on your laptop.

My goal is to learn something about intelligence explosions, takeoff speeds, discontinuities, human-level milestones, AGI vs. tools, bottlenecks, or something else. I'll be happy if I can learn something about even one of these things, even if it's just a minor update and not anything close to conclusive.

So far I've just got a very basic version of the model built. It works, but it's currently unclear what--if anything--we can learn from it. I need to think more about whether the assumptions it uses are realistic, and I need to explore the space of parameter settings more systematically.

I'm posting it here to get feedback on the basic idea, and maybe also on the model so far if people want to download it and play around. I'm particularly interested in evidence/arguments about whether or not this is a productive use of my time, and arguments that some hidden assumption my model makes is problematically determining the results.

If you want to try out the model yourself, download NetLogo here and then open the file in this folder.

How the model works:

The main part of the model consists of research projects, which are lists of various types of task. Civilization completes tasks to complete research projects, and when projects get finished, civilization gets a "bonus" which allows it to do new types of task, and to do some old types faster.

The projects, the lists of tasks needed to complete them, the speeds at which civilization can do the tasks, and the bonuses granted by completing projects are all randomly generated, typically using exponential distributions and often with parameters you can change in the UI. Other important parameters can be changed in the UI also, such as how many task types are "off limits" for technological improvement, and how many task types are "temporarily off limits" until some specified level of technology is reached.

As explained so far, the model represents better technology leading to more research directions (more types of task become available) and faster progress (civilization can do tasks in less time).

Projects are displayed as dots/stars which flicker as work is done on them. When they complete, they turn into big green circles. Their location in the display represents how difficult they are to complete: the x-axis encodes how many tasks are involved, and the y-axis encodes how many different kinds of tasks are involved. To the left of the main display is a graph that tracks a bunch of metrics I've deemed interesting, scaled so that they all have similar heights.

There are several kinds of diminishing returns and several kinds of increasing returns in the model.

Diminishing:

  • "Projects farther from the bottom left corner on the display require exponentially more tasks and exponentially more kinds of tasks.
  • Project bonuses work as follows: Pick a random bag of tasks, pick random speeds for each task, compare the results to the current state-of-the-art speeds on those tasks and update the state of the art accordingly. Thus, the faster civilization already is at completing a task, the more projects will need to be completed (on average) to improve speed at that task further.
  • Finally, there is the usual "low-hanging fruit" effect where the projects which can get done quickly do so, leaving harder and harder projects remaining.

Increasing:

  • The more projects you do, the more bonuses you get. This makes you faster at completing projects...
  • And opens up new projects to work on, some of which will be low-hanging fruit.

The model also has a simple module representing the "economic" side of things -- i.e. over time, civilization can work on a greater number of projects simultaneously, if you choose. I have a few different settings representing different scenarios:

    • "All projects all the time" represents a situation where science has loads of funding and/or excellent planning of research paths, so that the only constraints on finishing projects are whether and how fast the tasks involved can be done.
    • "100 doable projects" represents a situation with fixed research budget: 100 doable projects are being worked on at any given time.
    • Scaling effort with projectscompleted represents "learning by doing" where the more projects have been completed so far, the more effort is invested in doing more projects.
    • Scaling effort with machinetaskspeed represents a situation where how much effort is devoted to science is proportional to how advanced today's tech is on average.

The "info" tab of the NetLogo file explains things in more detail, if you are interested.

What tends to happen when I run it:

The model tends to produce progress (specifically, in the metric of "projects completed -- see the log plot) somewhere between exponential and superexponential. Sometimes it displays what appears to be a clear exponential trend (a very straight line on the log scale) that fairly rapidly transitions into a singularity (a vertical line on the log scale).

Interestingly, progress in the metric "% of tasks done faster thanks to research" is not typically exponential, much less singularity; it is usually a jumpy but more or less linear march from 0 to 100.

Sometimes progress stagnates, though I've only seen this happen extremely early on--I've never seen steady exponential growth followed by stagnation.

For a while it seemed that progress would typically shoot through the roof around the time that almost all tasks were doable & being improved. This is what Amdahl's Law would predict, I think: Get rid of the last few bottlenecks and progress will soar. However, I now think that's wrong; the growth still happens even if a substantial fraction of tasks are "off-limits," and/or off-limits temporarily. I'm not sure what to think now, but after I give my head a rest I expect ideas will come.

The various parameter settings I've put into the model seem to have surprisingly little effect on all of the above. They affect how long everything takes but rarely do they affect the fundamental shape of the trajectory. In particular, removing the "effort feedback loop" entirely, by choosing "all projects all the time" or "100 doable projects" would (I predicted) slow down progress a lot, but in practice we still seem to get singularities. Of course, I haven't systematically compared the results; this is just the vague impression I get from the handful of different runs I've done.


Doubts I have about the accuracy of the model & ideas for things to add

  • Most importantly, there are probably major flawed assumptions I've made in building this model that I haven't realized yet. I don't know what I don't know.
  • I worry that the results depend in a brittle fashion on the probability distributions and ranges that I use to generate the projects. In other words, I'm worried that the results, though robust to the parameters I've put in the UI, are not robust to hidden assumptions that I made hastily.
  • Often if you can't do a project one way, there is another path via which you can do it. Thus we can e.g. use brute force search in a computer + a small amount of thinking to replace a larger amount of a different kind of thinking. But in my model, all projects have a single list of tasks that need to be done to complete the project. Is this a problem?
  • Maybe I should try to build a version of this model that gets exponential growth followed by stagnation, or at least some sort of big s-curve? Maybe the reason I haven't seen this behavior so far is that I haven't put much effort into looking for it.
  • Ultimately I'd like to have a much richer economy in the model, with different factions buying and selling things as they separately advance up the tech tree. This sounds hard to implement in code, but maybe it's easier than I think. Maybe economics can help me with this.
  • Currently I have to wait a minute or so each run, depending on settings (some runs happen in just a few seconds). This is my very first coding project so the code is probably atrocious and could run significantly faster if I optimized it. If I could run it many times, I'd learn how much the results vary from run to run due to randomness.

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