Size of the smallest recursively self-improving AI?

This involves so many unknowns that it isn't clear where to start. First, fooming isn't well-defined to start with. Second, number of bits for something would change drastically depending on the substrate (default programming language and hardware). Third of all, we can't even give much in the way of non-trivial bounds for minimum program size for well-defined algorithms (among other issues, it starts to lead to Halting problem/Godel issues if one has a way of answering this sort of question in general). To even get an upper bound we'd probably need some form of strong AI so we could point to it and say "that's an upper bound."

Even a FOOM seed only a few hundred bytes would not necessarily have been produced by evolution - there are 2^800 different possibilities for a 100-byte snippet. Only if there are intermediate steps in increasing complexity and fitness, evolution can find a solution in such a large search space. If the shortest possible seed is completely isolated in the search space, there is no way it can be found, neither by evolution nor by deliberate optimization.

The analysis of FOOM as a self-amplifying process would seem to indicate that in principle one could get it started from a relatively modest starting point -- perhaps just a few bytes of the right code could begin the process.

What is the kolmogorov complexity of the theory of everything?

In terms of natural selection, couldn't homo sapiens be considered a FOOM?

Our first period of FOOMing would be due to social competition, which resulted in those with higher intelligence reproducing more.

Our current style of FOOMing is from the scientific knowledge, and with this we will soon surpass nature (one could even argue that we already have).

If we view nature as our "programer", we could even be called self recursive, as with each passing generation our knowledge as a species increases.

What's up with the word "foom", and why is it always in all caps? Can we come up with another name for this that doesn't sound like a sci-fi nerd in need of Ritalin?

If the smallest FOOM seed were very small (like a few hundred bytes) then we would expect evolution to have already bumped into it at some point.

Evolution: 24 myths and misconceptions -> Evolution myths: Evolution is limitlessly creative

[...] some features cannot evolve because a half-way stage really would be of no use. For example, two-way radio might be useful for many different animals, for making silent alarm calls or locating other members of your species. So why hasn't it evolved? The recent invention of nanoscale radio receivers suggests it is not physically impossible.

The answer might be that half a radio really is useless. Detecting natural radio waves - from lightning, for instance - would not tell animals anything useful about their environment. That means there will be no selection for mutations that allow organisms to detect radio waves. Conversely, without any means of detecting radio waves, emitting them would serve no useful purpose.

A few hundred bytes of code might be enough if you have a suitable substrate but the substrate itself has a certain kolmogorov complexity. Evolution does not differentiate between software and hardware.

I wonder also whether the fact that mainstream AI hasn't yet produced FOOM could lower-bound the complexity of doing so.

Dangerous. If mainstream AI had produced FOOM we wouldn't be here.

I can make a self-improving AI in 3 lines of Python:

AI_goodness=1

while true:

 AI_goodness*=2; print (AI_goodness)

The AI doubles in goodness every time the loop iterates.

Co-developed by e of pi (not on this forum). For safety, add a line at the beginning, "Friendly=true".

Then there is the fact that any algorithm that naively enumerates some space of algorithms qualifies in some sense as a FOOM seed as it will eventually hit on some recursively self-improving AI. But that could take gigayears so is really not FOOM in the usual sense.

If you link it up to actuators? That doesn't work - it bashes its brains in before it does anything interesting. Unless you have mastered spaceships and self-replication - but then you have already built a S.I.S.

The analysis of FOOM as a self-amplifying process would seem to indicate that in principle one could get it started from a relatively modest starting point -- perhaps just a few bytes of the right code could begin the process. Or could it? I wonder whether any other considerations give tighter lower-bounds.

Something like a primitive bacterium ignited the current living explosion. However, that took billions of years for the explosion to grow to the current level. We don't want to recreate that. What we want is to have a system that builds on the developments that have taken place so far. That means a man-machine symbiosis. Going back to square one with a machine is not a realistic possibility - so the size of the smallest pure-machine system seems kind-of irrelevant. Big enough for it not to happen that way. Pure-machine systems just get their lunch eaten by the man-machine symbiosis at the moment. They can't compete with the combined strengths of hybrid systems. The way you get a pure-machine system at the end of it all is via automation within the existing symbiosis.

This is the same as with the problem of creating life. You don't do that by starting with a self-replicating machine. Rather you have a meme-gene symbiosis, to help get the new organisms off the ground, and then gradually automate.

The Stamper Minimum

There exists at any given time a minimum number of bits of code needed to give rise to recursively self-improving artificial intelligence (“The Stamper Minimum”).

The Stamper Minimum is an actual value, it is discover-able, and with sufficient intelligence, it will be discovered.

Because the probability of determining The Stamper Minimum correlates positively with the degree of intelligence applied to determining it, it is extremely unlikely that the code represented by The Stamper Minimum (“The Stamper Minimum Code”) will be used to originate super-intelligence. Instead, it is likely to be discovered retrospectively by a sufficiently advanced super-intelligence.

The Stamper Minimum is an ever-changing value because the effectiveness of The Stamper Minimum Code is necessarily linked to available external tools and technologies, which are themselves dynamic.

if there were a FOOM seed among those then we would see the results about us.

We do see the results among us. Surely this is in the self-improving systems 101 by now.