Followup to: The First World Takeover

As last we looked at the planet, Life's long search in organism-space had only just gotten started.

When I try to structure my understanding of the unfolding process of Life, it seems to me that, to understand the optimization velocity at any given point, I want to break down that velocity using the following abstractions:

The searchability of the neighborhood of the current location, and the availability of good/better alternatives in that rough region. Maybe call this the optimization slope. Are the fruit low-hanging or high-hanging, and how large are the fruit?
The optimization resources, like the amount of computing power available to a fixed program, or the number of individuals in a population pool.
The optimization efficiency, a curve that gives the amount of searchpower generated by a given investiture of resources, which is presumably a function of the optimizer's structure at that point in time.

Example: If an object-level adaptation enables more efficient extraction of resources, and thereby increases the total population that can be supported by fixed available resources, then this increases the optimization resources and perhaps the optimization velocity.

How much does optimization velocity increase - how hard does this object-level innovation hit back to the meta-level?

If a population is small enough that not all mutations are occurring in each generation, then a larger population decreases the time for a given mutation to show up. If the fitness improvements offered by beneficial mutations follow an exponential distribution, then - I'm not actually doing the math here, just sort of eyeballing - I would expect the optimization velocity to go as log population size, up to a maximum where the search neighborhood is explored thoroughly. (You could test this in the lab, though not just by eyeballing the fossil record.)

This doesn't mean all optimization processes would have a momentary velocity that goes as the log of momentary resource investment up to a maximum. Just one mode of evolution would have this character. And even under these assumptions, evolution's cumulative optimization wouldn't go as log of cumulative resources - the log-pop curve is just the instantaneous velocity. If we assume that the variance of the neighborhood remains the same over the course of exploration (good points have better neighbors with same variance ad infinitum), and that the population size remains the same, then we should see linearly cumulative optimization over time. At least until we start to hit the information bound on maintainable genetic information...

These are the sorts of abstractions that I think are required to describe the history of life on Earth in terms of optimization. And I also think that if you don't talk optimization, then you won't be able to understand the causality - there'll just be these mysterious unexplained progress modes that change now and then. In the same way you have to talk natural selection to understand observed evolution, you have to talk optimization velocity to understand observed evolutionary speeds.

The first thing to realize is that meta-level changes are rare, so most of what we see in the historical record will be structured by the search neighborhoods - the way that one innovation opens up the way for additional innovations. That's going to be most of the story, not because meta-level innovations are unimportant, but because they are rare.

In "Eliezer's Meta-Level Determinism", Robin lists the following dramatic events traditionally noticed in the fossil record:

Any Cells, Filamentous Prokaryotes, Unicellular Eukaryotes, Sexual Eukaryotes, Metazoans

And he describes "the last three strong transitions" as:

Humans, farming, and industry

So let me describe what I see when I look at these events, plus some others, through the lens of my abstractions:

Cells: Force a set of genes, RNA strands, or catalytic chemicals to share a common reproductive fate. (This is the real point of the cell boundary, not "protection from the environment" - it keeps the fruits of chemical labor inside a spatial boundary.) But, as we've defined our abstractions, this is mostly a matter of optimization slope - the quality of the search neighborhood. The advent of cells opens up a tremendously rich new neighborhood defined by specialization and division of labor. It also increases the slope by ensuring that chemicals get to keep the fruits of their own labor in a spatial boundary, so that fitness advantages increase. But does it hit back to the meta-level? How you define that seems to me like a matter of taste. Cells don't quite change the mutate-reproduce-select cycle. But if we're going to define sexual recombination as a meta-level innovation, then we should also define cellular isolation as a meta-level innovation.

It's worth noting that modern genetic algorithms have not, to my knowledge, reached anything like the level of intertwined complexity that characterizes modern unicellular organisms. Modern genetic algorithms seem more like they're producing individual chemicals, rather than being able to handle individually complex modules. So the cellular transition may be a hard one.

DNA: I haven't yet looked up the standard theory on this, but I would sorta expect it to come after cells, since a ribosome seems like the sort of thing you'd have to keep around in a defined spatial location. DNA again opens up a huge new search neighborhood by separating the functionality of chemical shape from the demands of reproducing the pattern. Maybe we should rule that anything which restructures the search neighborhood this drastically should count as a hit back to the meta-level. (Whee, our abstractions are already breaking down.) Also, DNA directly hits back to the meta-level by carrying information at higher fidelity, which increases the total storable information.

Filamentous prokaryotes, unicellular eukaryotes: Meh, so what.

Sex: The archetypal example of a rare meta-level innovation. Evolutionary biologists still puzzle over how exactly this one managed to happen.

Metazoans: The key here is not cells aggregating into colonies with similar genetic heritages; the key here is the controlled specialization of cells with an identical genetic heritage. This opens up a huge new region of the search space, but does not particularly change the nature of evolutionary optimization.

Note that opening a sufficiently huge gate in the search neighborhood, may result in a meta-level innovation being uncovered shortly thereafter. E.g. if cells make ribosomes possible. One of the main lessons in this whole history is that one thing leads to another.

Neurons, for example, may have been the key enabling factor in enabling large-motile-animal body plans, because they enabled one side of the organism to talk with the other.

This brings us to the age of brains, which will be the topic of the next post.

But in the meanwhile, I just want to note that my view is nothing as simple as "meta-level determinism" or "the impact of something is proportional to how meta it is; non-meta things must have small impacts". Nothing much meta happened between the age of sexual metazoans and the age of humans - brains were getting more sophisticated over that period, but that didn't change the nature of evolution.

Some object-level innovations are small, some are medium-sized, some are huge. It's no wonder if you look at the historical record and see a Big Innovation that doesn't look the least bit meta, but had a huge impact by itself and led to lots of other innovations by opening up a new neighborhood picture of search space. This is allowed. Why wouldn't it be?

You can even get exponential acceleration without anything meta - if, for example, the more knowledge you have, or the more genes you have, the more opportunities you have to make good improvements to them. Without any increase in optimization pressure, the neighborhood gets higher-sloped as you climb it.

My thesis is more along the lines of, "If this is the picture without recursion, just imagine what's going to happen when we add recursion."

To anticipate one possible objection: I don't expect Robin to disagree that modern civilizations underinvest in meta-level improvements because they take time to yield cumulative effects, are new things that don't have certain payoffs, and worst of all, tend to be public goods. That's why we don't have billions of dollars flowing into prediction markets, for example. I, Robin, or Michael Vassar could probably think for five minutes and name five major probable-big-win meta-level improvements that society isn't investing in.

So if meta-level improvements are rare in the fossil record, it's not necessarily because it would be hard to improve on evolution, or because meta-level improving doesn't accomplish much. Rather, evolution doesn't do anything because it will have a long-term payoff a thousand generations later. Any meta-level improvement also has to grant an object-level fitness advantage in, say, the next two generations, or it will go extinct. This is why we can't solve the puzzle of how sex evolved by pointing directly to how it speeds up evolution. "This speeds up evolution" is just not a valid reason for something to evolve.

Any creative evolutionary biologist could probably think for five minutes and come up with five great ways that evolution could have improved on evolution - but which happen to be more complicated than the wheel, which evolution evolved on only three known occasions - or don't happen to grant an immediate fitness benefit to a handful of implementers.