We have a bunch of states, and we want to define a frame
We have a bunch of states, and we want to define a frame
Frames are description languages
Frames are description languages
Frames as equivalence classes
Frames as equivalence classes
Spacetime: timewise simultaneous events
Branchial: “in a superposition” states (i.e. you are looking at all of them at the same time)
Rulial: computationally interconvertible states
“The universe is what you make of it”
“The universe is what you make of it”
Given a certain description language, you will infer certain laws of physics
Given a certain description language, you will infer certain laws of physics
To knit together reality, you have to be computational system ... but then the difference between different rules is no longer visible to you
To knit together reality, you have to be computational system ... but then the difference between different rules is no longer visible to you
Given a Turing machine you can emulate the universe, whatever its rules are.
You choose a rulelike hypersurface
You choose a rulelike hypersurface
The reason one can construct a foliation....
The reason one can construct a foliation....
Spacetime: you could have moved to a different spatial point (hence the spatial hypergraph is connected)
Branchial: you could have measured a different thing
Rulial: you could have used a different rule
[the emulation is happening in the ultramultiway graph itself]
< To get from one rule to another, you do emulation ..... but that is something that happens through events in the graph > [[ -> universality ]]
[[ hypercomputer: faster than TM emulation ]]
Given a measure of rule differences, the maximum speed of emulation tells you how many elementary times it takes to go how far in rule space.
Computational irreducibility => finite speed of light : i.e. it can take time to do the emulation; emulation is irreducible.
Geometry of rulial space:
[geometric complexity theory???]
Black holes in rulial space: ???
DIsconnected rule space: non-simulatable
There could be an infinite of disconnected collection of universes ??
[the emulation is happening in the ultramultiway graph itself]
< To get from one rule to another, you do emulation ..... but that is something that happens through events in the graph > [[ -> universality ]]
[[ hypercomputer: faster than TM emulation ]]
Given a measure of rule differences, the maximum speed of emulation tells you how many elementary times it takes to go how far in rule space.
Computational irreducibility => finite speed of light : i.e. it can take time to do the emulation; emulation is irreducible.
Geometry of rulial space:
[geometric complexity theory???]
Black holes in rulial space: ???
DIsconnected rule space: non-simulatable
There could be an infinite of disconnected collection of universes ??
We should be able to make rule space with e.g. CAs
We should be able to make rule space with e.g. CAs
As models, we can look at weaker forms of computation.... E.g. the rule simulation graphs
Sufficiently dumb rules are black holes in rule space...
Sufficiently dumb rules are black holes in rule space...
If there are rules where you can’t get there from here... eventually they may form an event horizon
A rule-space black hole corresponds to a simple (non-irreducible) scientific model
A rule-space black hole corresponds to a simple (non-irreducible) scientific model
You pick your reducible description. When you try to stick to it, lots of irreducibility starts poking in.
Earth is going around in an ellipse .... but soon you need epicycles, and you’ll need more and more epicycles...
Earth is going around in an ellipse .... but soon you need epicycles, and you’ll need more and more epicycles...
Once you know the universe is computational, at some level it doesn’t matter which rule.....
Once you know the universe is computational, at some level it doesn’t matter which rule.....
Like: universe is a piece of art; each choice of rule-space hypersurfaces is an interpretation
Like: universe is a piece of art; each choice of rule-space hypersurfaces is an interpretation
To see the universe from the outside, we’d have to be infinitely computationally able: i.e. we’ve have to travel at infinite speed in rule space
To see the universe from the outside, we’d have to be infinitely computationally able: i.e. we’ve have to travel at infinite speed in rule space
Because we’re bounded in computational ability, we experience through foliations
Because we’re bounded in computational ability, we experience through foliations
[No doubt we’re not in the canonical foliation of rule space]
[No doubt we’re not in the canonical foliation of rule space]
The canonical foliation is just: it’s a Turing machine....
PCE implies that rule space does not consist mostly of black holes
PCE implies that rule space does not consist mostly of black holes
You’re unlikely to live in a part of rule space that isn’t full of irreducibility
[PCE is equivalent to causal invariance in rule space]
[PCE is equivalent to causal invariance in rule space]
Geodesics in rule space involve sequences of potentially different computational rules....
Possible claim: shortest paths in rule space involve repeats of a single rule
Possible claim: shortest paths in rule space involve repeats of a single rule
[ND]NDTM
[ND]NDTM
very non-deterministic TM
In[]:=
RulePlot[TuringMachine[2343]]
Out[]=
There needs to be a rulial Ξ
There needs to be a rulial Ξ
How many different languages are there to describe everything; AKA how many genuinely different TMs are there?
Curvature in rule space: how different are the outcomes of nearby rules
Curvature in rule space: how different are the outcomes of nearby rules
Analog of dimension in rule space is position in arithmetic hierarchy
Analog of dimension in rule space is position in arithmetic hierarchy
Geodesic ball volumes in rule space
Geodesic ball volumes in rule space
You do a certain amount of computation: how far can you get in simulating other rules
Higher positive curvature means lower expressive power for the language
Higher positive curvature means lower expressive power for the language
If you are effectively exponential dimensional, you can get across rule space in bounded time
If you are effectively exponential dimensional, you can get across rule space in bounded time
[ Inflation in rule space is solving the halting problem ]
Undecidability is the statement that there are places you can’t get to [fast enough] in rule space
Undecidability is the statement that there are places you can’t get to [fast enough] in rule space
Necessity of superposition as a result of maximum entanglement speed
Necessity of superposition as a result of maximum entanglement speed
Analog of Einstein equations is the equation of motion of the path integral
Analog of Einstein equations is the equation of motion of the path integral
Lagrangian is classical ; vs. varying in branchial space
Branchial wormhole causal wormhole : ER = EPR ?
Branchial wormhole causal wormhole : ER = EPR ?
No transporters: if you can build that amount in the causal graph, you have a piece of space
No transporters: if you can build that amount in the causal graph, you have a piece of space
Inside every electron there could be a copy of our universe
Inside every electron there could be a copy of our universe
[[ Which is essentially the hashing model ]]
[[ Which is essentially the hashing model ]]
Would force unitarity