#### 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

RulePlot[TuringMachine[2343]]

In[]:=

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