If A Tree Casts A Shadow.09.08
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No prerequisites
What is computation?
If a Tree Casts a Shadow, is it Telling the Time? Compute: com + putare: to think with
Russ Abbott California State University, Los Angeles
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
2
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
3
Blue’s fable One day, Mara, the Buddhist god of ignorance and evil, was traveling with his attendants through the villages of India. He saw a man doing walking meditation. The man’s face was lit up in wonder. He had just discovered something on the ground in front of him. Mara's attendants asked what the man had found. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
4
Humans: smart enough to have ideas; foolish enough to believe them. “A piece of the truth,” Mara replied. “Doesn't this bother you when someone finds a piece of the truth, O evil one?” his attendants asked. “No,” Mara replied. “Right after this they usually make a belief out of it.” -- Christina Feldman and Jack Kornfield, in “Stories of the Spirit, Stories of the Heart,” from Everyday Mind, Jean Smith (ed) . 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
5
Preview of issues and answers
What is computation?
How do we use a natural process for computation?
Physical processes are computation when we treat them as externalized thought. We use a natural process for computation when we modify the environment against which it plays itself out in such a way that we can use the result to work with our thoughts.
How should we understand the Church-Turing thesis?
The Church-Turing thesis says that the agent-based model of computation represents how we understand externalized thought processes operating against an unknown environment. • But we do not yet understand much about multi-scalar environments. • And there are more ways to interact with an environment than we are currently able to externalize.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
6
I feel so much better.
Is Google reading my email? Answer from
the Gmail.com FAQ
Google computers scan the text of Gmail messages in order to filter spam and detect viruses, just as all major webmail services do. Google also uses this scanning technology to deliver targeted text ads and other related information. The process is completely automated and involves no humans. [Emphasis added.]
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
7
What do we really care about?
It’s what goes on in the minds of human beings (and other cats) that matters.
Most people find it reassuring that
although Google’s computers may be reading their email no human beings are.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
8
We care about meaning — A computer? With a mind? Nonsense. That’s why I don’t care if computers read my email.
which has as something to do with an idea forming in a mind.
Not the same as formal semantics, i.e., mapping syntax to models.
Most people don’t believe it makes sense to say that an idea has formed in the mind of a computer
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
9
If a tree falls in a forest with no one around to hear it, does it make a sound?
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
10
My answer? Berkeley’s answer: yes because God is
there to hear it.
One must distinguish between physical events and subjective experience. If a tree falls in a forest, it generates (what we call) sound waves. But if no being has a subjective experience of sound, no sound will be heard/experienced. But we have no idea how to think about subjective experience and connect it to everything else. --David Chalmers: subjective experience is the hard problem of AI.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
11
Berkeley’s question extended If a tree grows in a forest with no one aware of it, is it instantiating the idea of a tree?
The idea of a tree exists only as subjective experience.
An idea exists only in the mind of the person thinking it.
Even if the idea of a tree is exactly the right way to describe that particular aspect of nature, that idea exists only as an idea.
Ideas exist only as subjective experience—not on paper, not in a computer, no where but in the mind of someone thinking the idea.
A brute fact, not a mystical notion. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
12
Thought tools
A thought tool is a physical device/object that helps us externalize and work with our thoughts. Thought tools differ in kind from scientific instruments — microscopes, telescopes, other instruments of observation. Every computer application is a thought tool.
10/17/08
Its conceptual model represents the thoughts that are being externalized.
Humans: smart enough to have ideas; foolish enough to believe them.
13
Computations are externalized ideas When a computer runs is it computing? A computer is computing only when it is understood to be performing some externalized mental activity. Otherwise, it’s just an arena within which electrons are moving about.
When a tree grows rings, it just grows rings.
When we use tree-ring growth as a way to count years—to help us work with ideas such as “a year”— then we can say that the tree has performed an (unconventional) computation.
Computation is our term for a ideas that we have been able to externalize in a way that allow us to use physical processes to perform them.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
14
I don’t believe it.
Defining (physical) computation “A series of rule governed state transitions
whose rules can be altered.”
Eliasmith, Dictionary of the Philosophy of Mind, http://philosophy.uwaterloo.ca/MindDict/computation.html.
Presumably he means state transitions of physical elements. Otherwise we start in the mental realm and simply stay there.
Defines computation as something in and
of the world and independent of us, i.e., a type of natural phenomenon. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
15
Why “whose rules can be altered?” Eliasmith
claims that if you leave out that requirement then every physical system is a computational system, which makes the definition vacuous.
How
10/17/08
can the transition rules be altered?
They can’t if physical processes operate according to unalterable physical laws. You can’t change the laws of physics. Humans: smart enough to have ideas; foolish enough to believe them.
16
How do we create a computation?
We alter the environment within which the laws of physics operate.
When we load a program into a computer, we are altering the environment within which the CPU (or some other deterministic virtual machine) operates.
How a physical process proceeds depends on environmental contingencies.
When we control (or interpret) the contingencies so that we can use the resulting state transitions to work with our own thoughts, then the process is a computation. An unconventional computation. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
17
Inverting the roles
In traditional computing the process is an algorithm, which operates on passive data.
Non-algorithmic (unconventional) computing involves configuring environmental contingencies within which natural processes will play themselves out.
Inverts the roles of the process (fixed, not mutable into any algorithm) and the environment (not a passive object that the algorithm manipulates but mutable so as to shape the fixed processes). 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
18
The von Neumann middleman Conventional computation (with real von
Neumann computers) is a (very) constrained form of unconventional computation. Then the CPU becomes the fixed process and the loaded program the environment that shapes it. A goal of this conference is to eliminate the von Neumann middleman—to find ways to externalize our thoughts by mapping them more directly onto the forces of nature. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
19
Turing Machines as computation? Why can’t we look to Turing Machines (and
equivalents) for a definition of computation defined independently of thought? Turing Machines, recursive functions, and their equivalents rely on the notions of symbols and symbol manipulation, which are fundamentally mental constructs. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
20
It’s the programs that matter Turing Machines, etc. are all defined
constructively, i.e., in terms of the operations one may use to construct a computational procedure.
A program in one model can be constructively converted to be a program in another.
Turing Machines and equivalent models are
equivalent as programming languages: any program written in one can be converted into a program in the others. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
21
Not the functions
Computability theory takes this generic class of software, applies it to the task of computing functions, and defines that class of functions as the Computable functions. Although interesting, this step isn’t necessary. What’s important about the Church-Turing Thesis is that Turing Machines, etc. characterize externalizable thought processes, not computable functions. Digital computers … are intended to carry out any operations which could be done by a human. — A. Turing
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
22
Wegner’s interactive machines Even a Turing Machine is best seen as a finite state agent operating stigmergically in a “environment” consisting of an unbounded sequence of cells. Wegner claims that his interactive machines—basically agents—are more powerful than Turing Machines.
We think that’s the wrong question. The programs that agents can run are the same as those a Turing machine can run.
To the extent that agents are more powerful than Turing Machines it is only only because they are open with respect to information flow. Agents are “far-from-equilibrium” with respect to information flow in the same way that complex systems are “far from equilibrium” with respect to energy flow.
10/17/08
Tit-for-Tat in iterative PD (open) is different from—and more successful than—Defect in one-shot (or n-shot) PD (closed). Humans: smart enough to have ideas; foolish enough to believe them.
23
Where we stand An FSA (agent) using externalized thought
processes to interact with a closed, monolevel, but unbounded environment (i.e., a TM) yields Turing Computability. But there are other possibilities.
The environment may be more sophisticated. • The agent may be part of the environment.
10/17/08
The agents may be more sophisticated. Humans: smart enough to have ideas; foolish enough to believe them.
24
A more sophisticated environment The environment may change as the agent
operates on it.
There may be multiple agents. Other processes may cause change.
This is our current consensus model for
agent-based modeling/programming.
It represents an extended interpretation of the Church-Turing thesis, namely that it’s a good model for how people perform.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
25
A multi-scalar environment The environments we build for our agents are
typically quite trivial: a grid with stuff on it. We don’t know how to model multi-scalar environments.
• Gecko wall-climbing; evolutionary arms races; nature as an oracle—write a program that simulates the environment within which scientific discovery occurs (must operate at many levels of abstraction).
A good use for unconventional computation: tame nature to become more interactive. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
26
More sophisticated agents
Write programs that deal with multi-scalar environments. We don’t know how to externalize the production of “new ideas”—genetic programming notwithstanding.
I doubt that we know how to write a program that would have come up with the idea of unconventional computation, a simple generalization, or using airplanes as flying bombs.
It would take least an agent that is able to model its environment and make GP runs against that internal model. Even then can it come up with new abstractions—which get incorporated into the model?
But people do it all the time.
There are perceptual operations that we as humans perform which we don’t yet know how to externalize—and which may not yield to Turing computational approaches. A good use for unconventional computation: support hybrid computing by building plug-ins that use natural processes to do computations we don’t now how to do otherwise. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
27
Summary You’re repeating yourself; stop talking. An FSA (agent) using externalized thought
processes to interact with a closed, monolevel, but unbounded environment (i.e., a TM) yields Turing Computability. But there are other possibilities.
The environment may be more sophisticated. The agents may be more sophisticated.
Unconventional computation techniques
can help explore these possibilities.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
28
What is computation?
If a Tree Casts a Shadow, is it Telling the Time? Compute: com + putare: to think with
Russ Abbott California State University, Los Angeles
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
2
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
3
Blue’s fable One day, Mara, the Buddhist god of ignorance and evil, was traveling with his attendants through the villages of India. He saw a man doing walking meditation. The man’s face was lit up in wonder. He had just discovered something on the ground in front of him. Mara's attendants asked what the man had found. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
4
Humans: smart enough to have ideas; foolish enough to believe them. “A piece of the truth,” Mara replied. “Doesn't this bother you when someone finds a piece of the truth, O evil one?” his attendants asked. “No,” Mara replied. “Right after this they usually make a belief out of it.” -- Christina Feldman and Jack Kornfield, in “Stories of the Spirit, Stories of the Heart,” from Everyday Mind, Jean Smith (ed) . 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
5
Preview of issues and answers
What is computation?
How do we use a natural process for computation?
Physical processes are computation when we treat them as externalized thought. We use a natural process for computation when we modify the environment against which it plays itself out in such a way that we can use the result to work with our thoughts.
How should we understand the Church-Turing thesis?
The Church-Turing thesis says that the agent-based model of computation represents how we understand externalized thought processes operating against an unknown environment. • But we do not yet understand much about multi-scalar environments. • And there are more ways to interact with an environment than we are currently able to externalize.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
6
I feel so much better.
Is Google reading my email? Answer from
the Gmail.com FAQ
Google computers scan the text of Gmail messages in order to filter spam and detect viruses, just as all major webmail services do. Google also uses this scanning technology to deliver targeted text ads and other related information. The process is completely automated and involves no humans. [Emphasis added.]
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
7
What do we really care about?
It’s what goes on in the minds of human beings (and other cats) that matters.
Most people find it reassuring that
although Google’s computers may be reading their email no human beings are.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
8
We care about meaning — A computer? With a mind? Nonsense. That’s why I don’t care if computers read my email.
which has as something to do with an idea forming in a mind.
Not the same as formal semantics, i.e., mapping syntax to models.
Most people don’t believe it makes sense to say that an idea has formed in the mind of a computer
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
9
If a tree falls in a forest with no one around to hear it, does it make a sound?
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
10
My answer? Berkeley’s answer: yes because God is
there to hear it.
One must distinguish between physical events and subjective experience. If a tree falls in a forest, it generates (what we call) sound waves. But if no being has a subjective experience of sound, no sound will be heard/experienced. But we have no idea how to think about subjective experience and connect it to everything else. --David Chalmers: subjective experience is the hard problem of AI.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
11
Berkeley’s question extended If a tree grows in a forest with no one aware of it, is it instantiating the idea of a tree?
The idea of a tree exists only as subjective experience.
An idea exists only in the mind of the person thinking it.
Even if the idea of a tree is exactly the right way to describe that particular aspect of nature, that idea exists only as an idea.
Ideas exist only as subjective experience—not on paper, not in a computer, no where but in the mind of someone thinking the idea.
A brute fact, not a mystical notion. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
12
Thought tools
A thought tool is a physical device/object that helps us externalize and work with our thoughts. Thought tools differ in kind from scientific instruments — microscopes, telescopes, other instruments of observation. Every computer application is a thought tool.
10/17/08
Its conceptual model represents the thoughts that are being externalized.
Humans: smart enough to have ideas; foolish enough to believe them.
13
Computations are externalized ideas When a computer runs is it computing? A computer is computing only when it is understood to be performing some externalized mental activity. Otherwise, it’s just an arena within which electrons are moving about.
When a tree grows rings, it just grows rings.
When we use tree-ring growth as a way to count years—to help us work with ideas such as “a year”— then we can say that the tree has performed an (unconventional) computation.
Computation is our term for a ideas that we have been able to externalize in a way that allow us to use physical processes to perform them.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
14
I don’t believe it.
Defining (physical) computation “A series of rule governed state transitions
whose rules can be altered.”
Eliasmith, Dictionary of the Philosophy of Mind, http://philosophy.uwaterloo.ca/MindDict/computation.html.
Presumably he means state transitions of physical elements. Otherwise we start in the mental realm and simply stay there.
Defines computation as something in and
of the world and independent of us, i.e., a type of natural phenomenon. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
15
Why “whose rules can be altered?” Eliasmith
claims that if you leave out that requirement then every physical system is a computational system, which makes the definition vacuous.
How
10/17/08
can the transition rules be altered?
They can’t if physical processes operate according to unalterable physical laws. You can’t change the laws of physics. Humans: smart enough to have ideas; foolish enough to believe them.
16
How do we create a computation?
We alter the environment within which the laws of physics operate.
When we load a program into a computer, we are altering the environment within which the CPU (or some other deterministic virtual machine) operates.
How a physical process proceeds depends on environmental contingencies.
When we control (or interpret) the contingencies so that we can use the resulting state transitions to work with our own thoughts, then the process is a computation. An unconventional computation. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
17
Inverting the roles
In traditional computing the process is an algorithm, which operates on passive data.
Non-algorithmic (unconventional) computing involves configuring environmental contingencies within which natural processes will play themselves out.
Inverts the roles of the process (fixed, not mutable into any algorithm) and the environment (not a passive object that the algorithm manipulates but mutable so as to shape the fixed processes). 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
18
The von Neumann middleman Conventional computation (with real von
Neumann computers) is a (very) constrained form of unconventional computation. Then the CPU becomes the fixed process and the loaded program the environment that shapes it. A goal of this conference is to eliminate the von Neumann middleman—to find ways to externalize our thoughts by mapping them more directly onto the forces of nature. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
19
Turing Machines as computation? Why can’t we look to Turing Machines (and
equivalents) for a definition of computation defined independently of thought? Turing Machines, recursive functions, and their equivalents rely on the notions of symbols and symbol manipulation, which are fundamentally mental constructs. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
20
It’s the programs that matter Turing Machines, etc. are all defined
constructively, i.e., in terms of the operations one may use to construct a computational procedure.
A program in one model can be constructively converted to be a program in another.
Turing Machines and equivalent models are
equivalent as programming languages: any program written in one can be converted into a program in the others. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
21
Not the functions
Computability theory takes this generic class of software, applies it to the task of computing functions, and defines that class of functions as the Computable functions. Although interesting, this step isn’t necessary. What’s important about the Church-Turing Thesis is that Turing Machines, etc. characterize externalizable thought processes, not computable functions. Digital computers … are intended to carry out any operations which could be done by a human. — A. Turing
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
22
Wegner’s interactive machines Even a Turing Machine is best seen as a finite state agent operating stigmergically in a “environment” consisting of an unbounded sequence of cells. Wegner claims that his interactive machines—basically agents—are more powerful than Turing Machines.
We think that’s the wrong question. The programs that agents can run are the same as those a Turing machine can run.
To the extent that agents are more powerful than Turing Machines it is only only because they are open with respect to information flow. Agents are “far-from-equilibrium” with respect to information flow in the same way that complex systems are “far from equilibrium” with respect to energy flow.
10/17/08
Tit-for-Tat in iterative PD (open) is different from—and more successful than—Defect in one-shot (or n-shot) PD (closed). Humans: smart enough to have ideas; foolish enough to believe them.
23
Where we stand An FSA (agent) using externalized thought
processes to interact with a closed, monolevel, but unbounded environment (i.e., a TM) yields Turing Computability. But there are other possibilities.
The environment may be more sophisticated. • The agent may be part of the environment.
10/17/08
The agents may be more sophisticated. Humans: smart enough to have ideas; foolish enough to believe them.
24
A more sophisticated environment The environment may change as the agent
operates on it.
There may be multiple agents. Other processes may cause change.
This is our current consensus model for
agent-based modeling/programming.
It represents an extended interpretation of the Church-Turing thesis, namely that it’s a good model for how people perform.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
25
A multi-scalar environment The environments we build for our agents are
typically quite trivial: a grid with stuff on it. We don’t know how to model multi-scalar environments.
• Gecko wall-climbing; evolutionary arms races; nature as an oracle—write a program that simulates the environment within which scientific discovery occurs (must operate at many levels of abstraction).
A good use for unconventional computation: tame nature to become more interactive. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
26
More sophisticated agents
Write programs that deal with multi-scalar environments. We don’t know how to externalize the production of “new ideas”—genetic programming notwithstanding.
I doubt that we know how to write a program that would have come up with the idea of unconventional computation, a simple generalization, or using airplanes as flying bombs.
It would take least an agent that is able to model its environment and make GP runs against that internal model. Even then can it come up with new abstractions—which get incorporated into the model?
But people do it all the time.
There are perceptual operations that we as humans perform which we don’t yet know how to externalize—and which may not yield to Turing computational approaches. A good use for unconventional computation: support hybrid computing by building plug-ins that use natural processes to do computations we don’t now how to do otherwise. 10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
27
Summary You’re repeating yourself; stop talking. An FSA (agent) using externalized thought
processes to interact with a closed, monolevel, but unbounded environment (i.e., a TM) yields Turing Computability. But there are other possibilities.
The environment may be more sophisticated. The agents may be more sophisticated.
Unconventional computation techniques
can help explore these possibilities.
10/17/08
Humans: smart enough to have ideas; foolish enough to believe them.
28
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