If planets like Earth were very rare in ways that didn't change much with time you'd still see a time that was typical

The time measurement is not the only rank measurement we have. We also can compare the sun vs other stars, and it is mediocre across measurements.

Rarity requires an (intrinsically unlikely, ala solomonoff) mechanism - something unusual that happened at some point in the developmental process, and most such mechanisms would entangle with multiple measurements.

At this point in time we can pretty much rule out all mechanisms operating at the stellar scale, it would have to be something far more local.

Tectonics as rare has been disproven recently. Europa was recently shown to have active tectonics, possibly pluto, and probably mars at least at some point.

For later evolutionary development stuff, it will be awhile before we have any data for rank measurements. But given how every other measurement so far has come up as mediocre . . ..

We can learn alot actually from exploring europa, mars, and other spots that could/should have some evidence for at least simple life. That can help fit at least a simple low complexity model for typical planetary development.

It's not binary of course, there's a feasibility spectrum that varies with speed. On the low end there is a natural speed for slow colonization which requires very little energy/effort, which is colonization roughly at the speed of star orbits around the galaxy. That would take hundreds of millions of years, but it could use gravitational assists and we already have the tech. Indeed, biology itself could perhaps manage slow colonization.

Given that the galaxy is already 54 galactic-years old, if life is actually as plentiful as mediocrity suggests, then the 'too hard' explanation can't contain much probability mass - as the early civs should have arose quite some time ago.

I find it more likely that the elder civs already have explored, and that the galaxy is already 'colonized'. It is unlikely that advanced civs are stellavores. The high value matter/energy or real estate is probably a tiny portion of the total, and is probably far from stars, as stellar environments are too noisy/hot for advanced computation. We have little hope of finding them until after our own maturation to some post-singularity state.

I take it as strong evidence for Rare earth.

It's the exact opposite.

If the earth was rare, this rarity would show up in the earth's rank along many measurement dimensions. Rarity requires selection pressure - a filter - which alters the distribution. We don't see that at all. Instead we see no filtering, no unusual rank in the dimensions we can measure. The exact opposite is far more likely true - the earth is common.

For instance, say that the earth was rare in orbiting a rare type of star. Then we would see that the sun would have unusual rank along many dimensions. Instead it is normal/typical - in brightness, age, type, planets, etc.

I don't understand your statement.

I didn't say anything in my post above about the per neuron state - because it's not important. Each neuron is a low precision analog accumulator, roughly up to 8-10 bits ish, and there are 20 billion neurons in the cortex. There are another 80 billion in the cerebellum, but they are unimportant.

The memory cost of storing the state for an equivalent ANN is far less than than 20 billion bytes or so, because of compression - most of that state is just zero most of the time.

In terms of computation per neuron per cycle, when a neuron fires it does #fanout computations. Counting from the total synapse numbers is easier than estimating neurons * avg fanout, but gives the same results.

When a neuron doesn't fire .. .it doesn't compute anything of significance. This is true in the brain and in all spiking ANNs, as it's equivalent to sparse matrix operations - where the computational cost depends on the number of nonzeros, not the raw size.

The human brain has about 100bn neurons and operates at 100Hz. The NVIDIA Tesla K80 has 8.73TFLOPS single-precision performance with 24GB of memory. That's 1.92bits per neuron and 0.87 floating point operations per neuron-cycle. Sorry, no matter how you slice it, neurons are complex things that interact in complex ways. There is just no possible way to do a full simulation with ~2 bits per neuron and ~1 flop per neuron-cycle

You are assuming enormously suboptimal/naive simulation. Sure if you use a stupid simulation algorithm, the brain seems powerful.

As a sanity check, apply your same simulation algorithm to simulating the GPU itself.

It has 8 billion transistors that cycle at 1 ghz, with a typical fanout of 2 to 4. So that's more than 10^19 gate ops/second! Far more than the brain . ..

The brain has about 100 trillion synapses, and the average spike rate is around 0.25hz (yes, really). So that's only about 25 trillion synaptic events/second. Furthermore, the vast majority of those synapses are tiny and activate on an incoming spike with low probability around 25% to 30% or so (stochastic connection dropout). The average synapse has an SNR equivalent of 4 bits or less. All of these numbers are well-supported from the neuroscience lit.

Thus the brain as a circuit computes with < 10 trillion low bit ops/second. That's nothing, even if it's off by 10x.

Also, synapse memory isn't so much an issue for ANNs, as weights are easily compressed 1000x or more by various schemes, from simple weight sharing to more complex techniques such as tensorization.

As we now approach moore's law, our low level circuit efficiency has already caught up to the brain, or is it close. The remaining gap is almost entirely algorithmic level efficiency.

While that particular discussion is quite interesting, it's irrelevant to my point above - which is simply that once you achieve parity, it's trivially easy to get at least weak superhuman performance through speed.

The tl;dr is what I wrote: learning cycles would be hours or days, and a foom would require hundreds or thousands of learning cycles at minimum.

Much depends on what you mean by "learning cycle" - do you mean a complete training iteration (essentially a lifetime) of an AGI? Grown from seed to adult?

I'm not sure where you got the 'hundreds to thousands' of learning cycles from either. If you want to estimate the full experimental iteration cycle count, it would probably be better to estimate from smaller domains. Like take vision - how many full experimental cycles did it take to get to current roughly human-level DL vision?

It's hard to say exactly, but it is roughly on the order of 'not many' - we achieved human-level vision with DL very soon after the hardware capability arrived.

If we look in the brain, we see that vision is at least 10% of the total computational cost of the entire brain, and the brain uses the same learning mechanisms and circuit patterns to solve vision as it uses to solve essentially everything else.

Likewise, we see that once we (roughly kindof) solved vision in the very general way the brain does, we see that same general techniques essentially work for all other domains.

There is just no plausible way for an intelligence to magic itself to super intelligence in less than large human timescales.

Oh thats easy - as soon as you get one adult, human level AGI running compactly on a single GPU, you can then trivially run it 100x faster on a supercomputer, and or replicate it 1 million fold or more. That generation of AGI then quickly produces the next, and then singularity.

It's slow going until we get up to that key threshold of brain compute parity, but once you pass that we probably go through a phase transition in history.

AlphaGo represents a general approach to AI, but its instantiation on the specific problem of Go tightly constrains the problem domain and solution space ..

Sure, but that wasn't my point. I was addressing key questions of training data size, sample efficiency, and learning speed. At least for Go, vision, and related domains, the sample efficiency of DL based systems appears to be approaching that of humans. The net learning efficiency of the brain is far beyond current DL systems in terms of learning per joule, but the gap in terms of learning per dollar is less, and closing quickly. Machine DL systems also easily and typically run 10x or more faster than the brain, and thus learn/train 10x faster.

Consider three types of universes ...

Your are privileging your hypothesis - there are vastly more types of universes ...

There are universes where life develops and civilizations are abundant, and all of our observations to date are compatible with the universe being filled with advanced civs (which probably become mostly invisible to us given current tech as they approach optimal physical configurations of near zero temperature and tiny size).

The are universes like the above where advanced civs spawn new universes to gain god-like 'magic' anthropic powers, effectively manipulating/rewriting the laws of physics.

Universes in these categories are both more aggressive/capable replicators - they create new universes at a higher rate, so they tend to dominate any anthropic distribution.

And finally, there are considerations where the distribution over simulation observer moments diverges significantly from original observer moments, which tends to complicate these anthropic considerations.

For example, we could live in a universe with lots of civs, but they tend to focus far more simulations on the origins of the first civ or early civs.