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turchin comments on The map of ideas how the Universe appeared from nothing - Less Wrong
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The relation thing is really appealing. But as Tegmark said all mathematical universe is about relation, so in a nutshell relation universe is Math universe hypothesis (MUH). If we use Kolmogorov complexity as the measure, it results in Computable universe (CUH). But still most problems of MUH and СГР are unresolved here, and most of the are still about measure and our mediocracy.
Because measure is the same spark of existence which we tried to explain from the start, and if we need it at the end, we didn't explained anything.
For example, in CUH only computable universes exist. But still it would favour very complex AIs with infinitely large minds and field of perception.
It also favour somekind of dust minds which I would name "axiomatic brains". We could postulate any complex mind as an axiom, and it is enough to its existence, and from such minds most will be very complex and very random.
There is also a problem with measure in math world - in it can't be several copies of something. There is no many copies of number 151. It is just one number, even if it appear many times in different ways of calculation. So something can't be "rare".
My attempt to patch it was "logic universe", in which all relations are logic consequences of non existence. In it all very complex thing also exist but they should be logical consequences of simpler things. And now it starts to look like our universe which starts from simple singularity and evolves towards the zoo of very complex possible AIs.
You're right. There is still missing the explanation for why the universes with higher measure (however defined) should be the ones we are more likely to exist in.
Just randomly guessing, maybe it's related to simulation: the universes with lower Kolmogorov complexity will more often be simulated by something in other universes. Unlike the typical anthropocentric simulation hypothesis (strawmanned as: "every advanced civilization will want to simulate 20/21 century homo sapient on Earth, because we are the coolest ones"), let's assume that things will be simulated for various reasons, sometimes not even because of some conscious decision, just as a side-effect of some laws of physics in some universe... and the more simple a universe is, the more often it will get simulated for completely random reasons.
But I'm not too proud to admit that I am completely confused here, heh.
I got the following ideas about the spark.
The laws of our universe are such that they enable creation of something out of nothing. QM with its fluctuations and GR with its singularity describe the world which appeared from nothing.
Not any set of possible laws allow it. These laws are math objects, but they allow creation of something from nothing (most laws don’t do it). So only a subset of all math universe is able to create things. It creates natural cutoff between all possible math objects - only rather simple laws allow such type creation.
I would illustrate it with following example: Newtonian laws are not describing appearing of matter from nothing. So while purely Newtonian universe is conceivable and mathematically possible, it doesn't exist as it existence would contradict its own laws.
But there is another set of laws: QM+GR - it describes how something could appear from nothing, and so existence of something doesn't contradict these laws.
I think that there are other possible combinations of laws which internally consistently explain how something could appear from nothing. But such set may be very small, as more complex laws results in more contradictions.
So we have very natural cutoff in math universe - lets name it Generational Universe hypothesis (GUH). It said that only those universes exist which laws describes how they appear from nothing and also don't have contradictions. GUH has stronger restrictions than CUH.
Logical universe hypothesis (LUH), which said that if nothing exists than 1 doesn't exist and if 1 doesn't exist than 2 doesn't exist is also similar GUH, as it describes the generation of math objects. But it doesn't explain properties of our universe.
Still infinite probably.
But I like the idea how you consider whether the laws themselves allow creation of a new universe. So, it seems like the Tegmark mathematical universe provides "templates" for universes, but only a subset of these "templates" will actually create a working instance.