Topics

Topics

Kleene Fixed Point Theorem and Quines (back to Lecture 03)

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Kleene Fixed Point Theorem and Quines (back to Lecture 03)

Non-Universal Replication: Langton's Loops

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Non-Universal Replication: Langton's Loops

The Barricelli Cellular Automaton

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The Barricelli Cellular Automaton

Wrap-up about Cellular Automata

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Wrap-up about Cellular Automata

Wrap-Up about Cellular Automata

Wrap-Up about Cellular Automata

What are we describing with cellular automata?

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What are we describing with cellular automata?

What should we want for the next scale?

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What should we want for the next scale?

What is non-trivial self-replication?

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What is non-trivial self-replication?

Langton's Loops

Langton's Loops

Questions about Langton's Loops

Questions about Langton's Loops

What is non-trivial replication?

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What is non-trivial replication?

Could Langton's loops be blocks of life forms?

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Could Langton's loops be blocks of life forms?

Is there an analogue of Kleene's theorem here?

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Is there an analogue of Kleene's theorem here?

Barricelli's ($\infty$-range) Cellular Automaton

Barricelli's ($\infty$-range) Cellular Automaton

Cells are occupied by positive or negative integers, representing their 'velocity'

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Cells are occupied by positive or negative integers, representing their 'velocity'

In one dimension (as was introduced)

In one dimension (as was introduced)

By default, an integer will 'hop' at every step by its own value (e.g. the number 3 will jump three steps to the right, the number -4 will jump four steps to the right, etc.)

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By default, an integer will 'hop' at every step by its own value (e.g. the number 3 will jump three steps to the right, the number -4 will jump four steps to the right, etc.)

Now, when there is a collision (two integers wanting to be at the same location at the next step), the involved integers die

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Now, when there is a collision (two integers wanting to be at the same location at the next step), the involved integers die

Reproduction: if an integer $n$ arrives at time $t+1$ at a position $(x)$ which was occupied at time $t$ by an integer $o\neq n$, then a new integer is put at location $(x+o-n)$, i.e. at a location $(x)$ shifted by the momentum difference $o-n$

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Reproduction: if an integer $n$ arrives at time $t+1$ at a position $(x)$ which was occupied at time $t$ by an integer $o\neq n$, then a new integer is put at location $(x+o-n)$, i.e. at a location $(x)$ shifted by the momentum difference $o-n$

Now, the integer we put at location $(x+o-n)$:

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Now, the integer we put at location $(x+o-n)$:

Can be $n$, simply

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Can be $n$, simply

Or can be a 'hybrid', like a rounded version of the average $(o+n)/2$

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Or can be a 'hybrid', like a rounded version of the average $(o+n)/2$

This rule was introduced to force numbers to 'cooperate' with other numbers (since we need $o\neq n$ above)

This rule was introduced to force numbers to 'cooperate' with other numbers (since we need $o\neq n$ above)

Why is the Barricelli's system interesting

Why is the Barricelli's system interesting

We have an _emergence_ of 'creatures', made of a pattern of numbers, as well as spontaneous _reproduction_

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We have an emergence of 'creatures', made of a pattern of numbers, as well as spontaneous reproduction

Emergence

Emergence

Reproduction

Reproduction

There is a diversity that shows up (for some time, at least)

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There is a diversity that shows up (for some time, at least)

There are some phenomena that can be likened to 'parasitism' or 'symbiosis'

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There are some phenomena that can be likened to 'parasitism' or 'symbiosis'

While things appear to be rather short-lived (at least in 1D, on fairly small systems), there is definitely something fascinating with Barricelli's system and it is probably somehow under-rated

While things appear to be rather short-lived (at least in 1D, on fairly small systems), there is definitely something fascinating with Barricelli's system and it is probably somehow under-rated

A possible take-away from Barricelli's work

A possible take-away from Barricelli's work

In some sense, Barricelli made the 'basic' reproduction a trivial problem (emptied it from the solution to the mystery of how it is possible that it emerges), and allows us to worry about 'next scale problems'

In some sense, Barricelli made the 'basic' reproduction a trivial problem (emptied it from the solution to the mystery of how it is possible that it emerges), and allows us to worry about 'next scale problems'

It highlights that if some non-trivial interaction between the 'entities' happens, it is fairly easy to see _emergence of complexity_, which is definitely a desirable feature of life as we would like to capture it

It highlights that if some non-trivial interaction between the 'entities' happens, it is fairly easy to see emergence of complexity, which is definitely a desirable feature of life as we would like to capture it

Some interesting alleys for a small project

Some interesting alleys for a small project

Study the 3D Barricelli automaton, find ways to visualize it and analyze it at large scale

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Study the 3D Barricelli automaton, find ways to visualize it and analyze it at large scale

The Barricelli automaton in 2D

The Barricelli automaton in 2D

How does computability theory play a role here?

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How does computability theory play a role here?

Is Turing-completeness absolutely essential, or is there a weaker notion that works?

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Is Turing-completeness absolutely essential, or is there a weaker notion that works?

How far can studying cellular automata bring us towards understanding life in various media?

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How far can studying cellular automata bring us towards understanding life in various media?

Can the study of continuous systems give us additional insight?

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Can the study of continuous systems give us additional insight?

Samples from Barricelli's CA

Samples from Barricelli's CA

An attempt to clarify what nontrivial reproduction means and whether Turing-completeness is a _necessary_ condition

An attempt to clarify what nontrivial reproduction means and whether Turing-completeness is a necessary condition

A nostalgic video of Langton's CA

A nostalgic video of Langton's CA

A 'data pipe' with no signal

A 'data pipe' with no signal

The pictures below come from Langton's paper:

The pictures below come from Langton's paper:

A rightward-traveling signal

A rightward-traveling signal

A 'data pipe' junction

A 'data pipe' junction

Langton took the simplification of Von Neumann's CA done by Codd (an 8-state automaton with simpler 'data pipes'), and made a very simple model of self-replicating loops (which are clearly not Turing-universal, but which he argues display a non-trivial form of self-replication)

Langton took the simplification of Von Neumann's CA done by Codd (an 8-state automaton with simpler 'data pipes'), and made a very simple model of self-replicating loops (which are clearly not Turing-universal, but which he argues display a non-trivial form of self-replication)

One of the key insight in the design is that data is traveling in cycles, and there is no traveling reading head, and we get loops that end up forming a colony of loops

One of the key insight in the design is that data is traveling in cycles, and there is no traveling reading head, and we get loops that end up forming a colony of loops

Some steps of the Langton loop's life cycles

Some steps of the Langton loop's life cycles

Do we have a proto-form of Turing-completeness?

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Do we have a proto-form of Turing-completeness?

Maybe strict Turing-completeness is not required: if finite computations of unbounded finite complexity work, is that enough?

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Maybe strict Turing-completeness is not required: if finite computations of unbounded finite complexity work, is that enough?

Can we make modification of the loops so that they are arbitrarily big, store data, and interact with other loops in their colonies?

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Can we make modification of the loops so that they are arbitrarily big, store data, and interact with other loops in their colonies?

Can we make a theory of open-ended evolution?

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Can we make a theory of open-ended evolution?

What do we do about physicality constraints?

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What do we do about physicality constraints?

We have many questions

We have many questions

What we saw so far

What we saw so far

Von Neumann's automaton and self-replication

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Von Neumann's automaton and self-replication

The game of life and basic cellular automata questions (Garden of Eden's)

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The game of life and basic cellular automata questions (Garden of Eden's)

Wolfram's proposed classification and emergence

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Wolfram's proposed classification and emergence

Self-replication, life, and irreversibility

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Self-replication, life, and irreversibility

Can we use arrows of time as measures of life-like processes happening?

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Can we use arrows of time as measures of life-like processes happening?