Biological humans collectively exert at most 400 gigabits/s of control over the world.
Edit: I now believe that the first paragraph of this post is (at least) not quite right. See this comment for details.
If an agent makes one binary choice per second, no matter how smart it is, there’s a sense in which it can (at best) be “narrowing world space” by a factor of two in each second, choosing the “better half” of possible worlds, from its perspective.
This is the idea behind the reinforcement learning concept of “empowerment”.
People have tried to measure the information throughput of biological humans. The very highest estimates, which come from image recognition tasks, are around 50 bits per second, and most estimates are more like 10 bits per second.
There are about 8 billion living humans. Even if humanity could be perfectly modeled as a single rational agent, and all our choices were perfectly independent of each other, I think this implies that we collectively have no more than about 50 * 8 = 400 billion bits per second of control over the world.
I don’t know how to think about this statement. Should I find this a ‘small’ number or unimpressive in some respect?
This allows for each second, picking a possibility out of ‘no more than about’ 2400,000,000,000 high-level possibilities, which is a possibility-space so large I don’t think I can write it out in decimal without crashing LW2 or hitting size limits. (GHCi tries to evaluate it but I killed it after a bit when the RAM consumption started to worry me.) Even at the individual level, this implies that in, say, 1 year, I get to pick a possibility out of 2^(365.25 * 24 * 60 * 60 = ~36000000)^ outcomes. (Which at least GHCi can evaluate and print out as a decimal reasonably well, it just takes patience and what looks like thousands of screens of output.)
Are these ‘small’ amounts of control to have? Is there some important task for which this level of control is clearly inadequate, or at what amount of control would one consider it a ‘large’ amount of control?
This is just the “inner brain”, the paper also introduces the “outer brain”. It’s thoroughly plausible that information not routed through the inner brain’s cohesive agency but still partially processed can leak via e.g. subtle facial cues or tone, likely resulting in the experience of a much higher bitrate in things like Circling or other interpersonal meditative practices.
Nate Soares points out that the first paragraph is not quite right: Imagine writing a program that somehow implements an aligned superintelligence, giving it as an objective, “maximize utility according to the person who pressed the ‘go’ button”, and pressing the ‘go’ button.
There’s some sense in which, by virtue of existing in the world, you’re already kind of “lucky” by this metric: It can take a finite amount of information to instantiate an agent that takes unbounded actions on your behalf.