Comment author:turchin
05 September 2016 11:41:58AM
0 points
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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.

Comment author:Viliam
06 September 2016 11:59:06AM
1 point
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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.

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.

Comment author:turchin
08 September 2016 12:40:33PM
0 points
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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.

Comment author:Viliam
11 September 2016 08:46:12PM
0 points
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such set may be very small

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.

Comment author:turchin
06 September 2016 12:17:17PM
0 points
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I also thought that we may be in in the lowest level of infinitely complex multilevel simulation (and of any possible simulation in math world).

But it still don't help with measure problem, because many similar things in math world is just one thing. So if our world is simulated many times it doesn't change its measure. Like no matter how many times we wrote 25 it will not change distribution of prime numbers in the set of natural numbers.

But also random choosing doesn't work with infinite sets. We can't choose random prime number, or it will be infinitely long. I think we could dig in this way.

Comment author:turchin
06 September 2016 01:46:24PM
*
0 points
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A. One possible counterargument here is following. Imagine that any being has rank X, proportional to its complexity (or year of birth). But there will be infinitely many beings which are 10X complex, 100X complex and so on. So any being with finite complexity is in the beginning of the complexity ladder. So any may be surprised if it is very early. So there is no surprise to be surprised.

But we are still should be in the middle of infinity, but our situation is not so - it looks like we have just enough complexity to start to understand the problem, which is still surprising.

B. Another similar rebuttal: imagine all being which are surprised by their position. The fact that we are in this set is resulted only from definition of the set, but not from any properties of the whole Universe. Example: All people who was born 1 January may be surpised that their birthday coincide with New Year, but it doesn't provide them any information about length of the year.

But my birthday is randomly position inside the years (September) and in most testable cases mediocracy logic works as predicted.

## Comments (45)

BestThe 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

whythe 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.

I also thought that we may be in in the lowest level of infinitely complex multilevel simulation (and of any possible simulation in math world).

But it still don't help with measure problem, because many similar things in math world is just one thing. So if our world is simulated many times it doesn't change its measure. Like no matter how many times we wrote 25 it will not change distribution of prime numbers in the set of natural numbers.

But also random choosing doesn't work with infinite sets. We can't choose random prime number, or it will be infinitely long. I think we could dig in this way.

*0 points [-]A. One possible counterargument here is following. Imagine that any being has rank X, proportional to its complexity (or year of birth). But there will be infinitely many beings which are 10X complex, 100X complex and so on. So any being with finite complexity is in the beginning of the complexity ladder. So any may be surprised if it is very early. So there is no surprise to be surprised.

But we are still should be in the middle of infinity, but our situation is not so - it looks like we have just enough complexity to start to understand the problem, which is still surprising.

B. Another similar rebuttal: imagine all being which are surprised by their position. The fact that we are in this set is resulted only from definition of the set, but not from any properties of the whole Universe. Example: All people who was born 1 January may be surpised that their birthday coincide with New Year, but it doesn't provide them any information about length of the year.

But my birthday is randomly position inside the years (September) and in most testable cases mediocracy logic works as predicted.