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Richard W. Hamming Richard W. Hamming Learning to Learn Learning to Learn The Art of Doing Science and Engineering The Art of Doing Science and Engineering Session 6: Artificial Session 6: Artificial Intelligence I Intelligence I
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Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Dec 25, 2015

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Page 1: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Richard W. HammingRichard W. HammingRichard W. HammingRichard W. Hamming

Learning to LearnLearning to LearnThe Art of Doing Science and EngineeringThe Art of Doing Science and Engineering

Session 6: Artificial Intelligence ISession 6: Artificial Intelligence I

Page 2: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Topic OutlineTopic OutlineTopic OutlineTopic Outline

Can Machines Think?Can Machines Think?Can Machines Think?Can Machines Think?

Page 3: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Can Machines Think?Can Machines Think?Can Machines Think?Can Machines Think?

Computers manipulate Computers manipulate symbolssymbols, not , not informationinformation. .

We find it hard to even define a concept like We find it hard to even define a concept like information. Symbols, on the other hand, information. Symbols, on the other hand, are almost arbitrary.are almost arbitrary.

What are the limits of computers? What are the limits of computers?

Are there things that humans can do that Are there things that humans can do that computers can’t? computers can’t?

Computers manipulate Computers manipulate symbolssymbols, not , not informationinformation. .

We find it hard to even define a concept like We find it hard to even define a concept like information. Symbols, on the other hand, information. Symbols, on the other hand, are almost arbitrary.are almost arbitrary.

What are the limits of computers? What are the limits of computers?

Are there things that humans can do that Are there things that humans can do that computers can’t? computers can’t?

Page 4: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Philosophical Background: Philosophical Background: Turing TestTuring TestPhilosophical Background: Philosophical Background: Turing TestTuring Test

Hamming doesn’t discuss this, but a little Hamming doesn’t discuss this, but a little background:background:

The Turing experiment lets a user query via a The Turing experiment lets a user query via a teletype an entity in a locked room. If the user teletype an entity in a locked room. If the user can’t tell the difference between a machine and a can’t tell the difference between a machine and a human, we can think of the machine as being human, we can think of the machine as being “intelligent” in some sense (maybe not literally!)“intelligent” in some sense (maybe not literally!)

Hamming doesn’t discuss this, but a little Hamming doesn’t discuss this, but a little background:background:

The Turing experiment lets a user query via a The Turing experiment lets a user query via a teletype an entity in a locked room. If the user teletype an entity in a locked room. If the user can’t tell the difference between a machine and a can’t tell the difference between a machine and a human, we can think of the machine as being human, we can think of the machine as being “intelligent” in some sense (maybe not literally!)“intelligent” in some sense (maybe not literally!)

Page 5: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Can Machines Think?Can Machines Think?Can Machines Think?Can Machines Think?

John Searle proposes the “Chinese Room” thought experiment.John Searle proposes the “Chinese Room” thought experiment.

You sit in a locked room. You have a set of instructions (in English), You sit in a locked room. You have a set of instructions (in English), someone drops in slips of paper (in Chinese) and, following the someone drops in slips of paper (in Chinese) and, following the instructions, you match the input symbol and respond with another instructions, you match the input symbol and respond with another slip of paper (in Chinese).slip of paper (in Chinese).

This is analogous to the Turing experiment, with the English This is analogous to the Turing experiment, with the English instructions as the “program,” and the slips of paper as questions instructions as the “program,” and the slips of paper as questions and answers.and answers.

You don’t speak Chinese.You don’t speak Chinese.

Do you “understand” Chinese in this experiment? Or are you just Do you “understand” Chinese in this experiment? Or are you just manipulating symbols?manipulating symbols?

John Searle proposes the “Chinese Room” thought experiment.John Searle proposes the “Chinese Room” thought experiment.

You sit in a locked room. You have a set of instructions (in English), You sit in a locked room. You have a set of instructions (in English), someone drops in slips of paper (in Chinese) and, following the someone drops in slips of paper (in Chinese) and, following the instructions, you match the input symbol and respond with another instructions, you match the input symbol and respond with another slip of paper (in Chinese).slip of paper (in Chinese).

This is analogous to the Turing experiment, with the English This is analogous to the Turing experiment, with the English instructions as the “program,” and the slips of paper as questions instructions as the “program,” and the slips of paper as questions and answers.and answers.

You don’t speak Chinese.You don’t speak Chinese.

Do you “understand” Chinese in this experiment? Or are you just Do you “understand” Chinese in this experiment? Or are you just manipulating symbols?manipulating symbols?

Page 6: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Can Machines Think?Can Machines Think?Can Machines Think?Can Machines Think?

Searle’s thought experiment is sometimes thought of as the Searle’s thought experiment is sometimes thought of as the difference between “Strong AI” and “Weak AI.” difference between “Strong AI” and “Weak AI.”

Strong AIStrong AI proponents say that an appropriately programmed proponents say that an appropriately programmed computer is not a simulation of a mind; it computer is not a simulation of a mind; it isis a mind. a mind.

Weak AIWeak AI advocates believe that the computer is only a simulation of advocates believe that the computer is only a simulation of the mind.the mind.

This is in part a black box/white box difference.This is in part a black box/white box difference.

Humans are doing computation in the strong AI view, and that Humans are doing computation in the strong AI view, and that computation is intelligence; it is just that the computation is too computation is intelligence; it is just that the computation is too complex for us to describe and understand at the present time.complex for us to describe and understand at the present time.

Thermostats are “thinking” in a limited way.Thermostats are “thinking” in a limited way.

Searle’s thought experiment is sometimes thought of as the Searle’s thought experiment is sometimes thought of as the difference between “Strong AI” and “Weak AI.” difference between “Strong AI” and “Weak AI.”

Strong AIStrong AI proponents say that an appropriately programmed proponents say that an appropriately programmed computer is not a simulation of a mind; it computer is not a simulation of a mind; it isis a mind. a mind.

Weak AIWeak AI advocates believe that the computer is only a simulation of advocates believe that the computer is only a simulation of the mind.the mind.

This is in part a black box/white box difference.This is in part a black box/white box difference.

Humans are doing computation in the strong AI view, and that Humans are doing computation in the strong AI view, and that computation is intelligence; it is just that the computation is too computation is intelligence; it is just that the computation is too complex for us to describe and understand at the present time.complex for us to describe and understand at the present time.

Thermostats are “thinking” in a limited way.Thermostats are “thinking” in a limited way.

Page 7: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Can machines think?Can machines think?Can machines think?Can machines think?

The question of materialism vs. dualism also The question of materialism vs. dualism also quickly raises its head. quickly raises its head.

Materialism holds that everything is the result of Materialism holds that everything is the result of physical phenomena. “Consciousness” is really physical phenomena. “Consciousness” is really just a byproduct of fancy chemistry and physics.just a byproduct of fancy chemistry and physics.

Dualism holds that there is a “spirit” separate and Dualism holds that there is a “spirit” separate and distinct from physical phenomena.distinct from physical phenomena.

Rene Descartes was famous for this position: Rene Descartes was famous for this position: ”cogito ergo sum (I think therefore I am).””cogito ergo sum (I think therefore I am).”

The question of materialism vs. dualism also The question of materialism vs. dualism also quickly raises its head. quickly raises its head.

Materialism holds that everything is the result of Materialism holds that everything is the result of physical phenomena. “Consciousness” is really physical phenomena. “Consciousness” is really just a byproduct of fancy chemistry and physics.just a byproduct of fancy chemistry and physics.

Dualism holds that there is a “spirit” separate and Dualism holds that there is a “spirit” separate and distinct from physical phenomena.distinct from physical phenomena.

Rene Descartes was famous for this position: Rene Descartes was famous for this position: ”cogito ergo sum (I think therefore I am).””cogito ergo sum (I think therefore I am).”

Page 8: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

PenrosePenrosePenrosePenrose

Penrose (Penrose (Shadows of the MindShadows of the Mind) suggests 4 extreme positions:) suggests 4 extreme positions:

A.A. All thinking is computation; feelings of conscious All thinking is computation; feelings of conscious awareness are evoked by computation.awareness are evoked by computation.

B.B. Awareness is a feature of the brain’s physical action; any Awareness is a feature of the brain’s physical action; any physical action may be simulated computationally, but the physical action may be simulated computationally, but the simulation does not evoke awareness.simulation does not evoke awareness.

C.C. Physical action of the brain evokes awareness, but this Physical action of the brain evokes awareness, but this awareness cannot even be simulated computationally.awareness cannot even be simulated computationally.

D.D. Awareness cannot be explained by physical, Awareness cannot be explained by physical, computational, or any other scientific terms.computational, or any other scientific terms.

Penrose (Penrose (Shadows of the MindShadows of the Mind) suggests 4 extreme positions:) suggests 4 extreme positions:

A.A. All thinking is computation; feelings of conscious All thinking is computation; feelings of conscious awareness are evoked by computation.awareness are evoked by computation.

B.B. Awareness is a feature of the brain’s physical action; any Awareness is a feature of the brain’s physical action; any physical action may be simulated computationally, but the physical action may be simulated computationally, but the simulation does not evoke awareness.simulation does not evoke awareness.

C.C. Physical action of the brain evokes awareness, but this Physical action of the brain evokes awareness, but this awareness cannot even be simulated computationally.awareness cannot even be simulated computationally.

D.D. Awareness cannot be explained by physical, Awareness cannot be explained by physical, computational, or any other scientific terms.computational, or any other scientific terms.

Page 9: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

PenrosePenrosePenrosePenrose

Penrose’s categories A-C can be thought of as Penrose’s categories A-C can be thought of as compatible with materialism, while D is dualist (at least). compatible with materialism, while D is dualist (at least).

A corresponds to Searle’s strong AI description.A corresponds to Searle’s strong AI description.

B says we can, in principle, make a Von Neuman machine B says we can, in principle, make a Von Neuman machine pass a Turing test, but it would not be conscious.pass a Turing test, but it would not be conscious.

C is still materialist, but suggests we couldn’t make a C is still materialist, but suggests we couldn’t make a Von Neuman machine pass a Turing test. But we might Von Neuman machine pass a Turing test. But we might with some other, man-made mechanism, such as neural with some other, man-made mechanism, such as neural nets or biological computers.nets or biological computers.

D is compatible with a religious, mystic, or Cartesian D is compatible with a religious, mystic, or Cartesian dualist outlook.dualist outlook.

Penrose’s categories A-C can be thought of as Penrose’s categories A-C can be thought of as compatible with materialism, while D is dualist (at least). compatible with materialism, while D is dualist (at least).

A corresponds to Searle’s strong AI description.A corresponds to Searle’s strong AI description.

B says we can, in principle, make a Von Neuman machine B says we can, in principle, make a Von Neuman machine pass a Turing test, but it would not be conscious.pass a Turing test, but it would not be conscious.

C is still materialist, but suggests we couldn’t make a C is still materialist, but suggests we couldn’t make a Von Neuman machine pass a Turing test. But we might Von Neuman machine pass a Turing test. But we might with some other, man-made mechanism, such as neural with some other, man-made mechanism, such as neural nets or biological computers.nets or biological computers.

D is compatible with a religious, mystic, or Cartesian D is compatible with a religious, mystic, or Cartesian dualist outlook.dualist outlook.

Page 10: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

GamesGamesGamesGames

Games are often used as test cases in AI.Games are often used as test cases in AI.

Games have clear rules, and we can determine Games have clear rules, and we can determine when a participant has “won” or “lost”, or at least when a participant has “won” or “lost”, or at least gauge the participants effectivenessgauge the participants effectiveness

Other situations are not as well defined as games. Other situations are not as well defined as games. The rules are not clear, and objectives are fuzzy.The rules are not clear, and objectives are fuzzy.

Games are often used as test cases in AI.Games are often used as test cases in AI.

Games have clear rules, and we can determine Games have clear rules, and we can determine when a participant has “won” or “lost”, or at least when a participant has “won” or “lost”, or at least gauge the participants effectivenessgauge the participants effectiveness

Other situations are not as well defined as games. Other situations are not as well defined as games. The rules are not clear, and objectives are fuzzy.The rules are not clear, and objectives are fuzzy.

Page 11: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

GamesGamesGamesGames

Some games can be programmed such that they Some games can be programmed such that they exhibit aspects that resemble human thinking.exhibit aspects that resemble human thinking.

• Cannibals & missionaries, theorem provingCannibals & missionaries, theorem proving

The first attempts at a “general problem solver” The first attempts at a “general problem solver” used a small number of rules.used a small number of rules.

Later attempts increased this to 5,000 rules or Later attempts increased this to 5,000 rules or more, and applied the rules to a specific problem more, and applied the rules to a specific problem domain with mixed results. domain with mixed results.

These are called rule-based systems.These are called rule-based systems.

Some games can be programmed such that they Some games can be programmed such that they exhibit aspects that resemble human thinking.exhibit aspects that resemble human thinking.

• Cannibals & missionaries, theorem provingCannibals & missionaries, theorem proving

The first attempts at a “general problem solver” The first attempts at a “general problem solver” used a small number of rules.used a small number of rules.

Later attempts increased this to 5,000 rules or Later attempts increased this to 5,000 rules or more, and applied the rules to a specific problem more, and applied the rules to a specific problem domain with mixed results. domain with mixed results.

These are called rule-based systems.These are called rule-based systems.

Page 12: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Nature of human thoughtNature of human thoughtNature of human thoughtNature of human thought

But perhaps we can’t think everything we But perhaps we can’t think everything we know. Perhaps there are some thoughts our know. Perhaps there are some thoughts our minds are physically incapable of holding, minds are physically incapable of holding, given the limitations of our biology. given the limitations of our biology.

Examples: can a bat hold certain ideas that Examples: can a bat hold certain ideas that humans can? Can bats form experiences humans can? Can bats form experiences that humans cannot conceive?that humans cannot conceive?

If this is true, this may present problems for If this is true, this may present problems for rule-based systems. rule-based systems.

But perhaps we can’t think everything we But perhaps we can’t think everything we know. Perhaps there are some thoughts our know. Perhaps there are some thoughts our minds are physically incapable of holding, minds are physically incapable of holding, given the limitations of our biology. given the limitations of our biology.

Examples: can a bat hold certain ideas that Examples: can a bat hold certain ideas that humans can? Can bats form experiences humans can? Can bats form experiences that humans cannot conceive?that humans cannot conceive?

If this is true, this may present problems for If this is true, this may present problems for rule-based systems. rule-based systems.

Page 13: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

GamesGamesGamesGames

In the same way, this may correspond to In the same way, this may correspond to position C in Penrose. position C in Penrose.

While humans may be able to create a While humans may be able to create a device that mimics human thought, that device that mimics human thought, that device may not be a Von Neuman machine. device may not be a Von Neuman machine.

It may be that Von Neuman machines or It may be that Von Neuman machines or Turing machines cannot express the things Turing machines cannot express the things necessary for intelligence.necessary for intelligence.

In the same way, this may correspond to In the same way, this may correspond to position C in Penrose. position C in Penrose.

While humans may be able to create a While humans may be able to create a device that mimics human thought, that device that mimics human thought, that device may not be a Von Neuman machine. device may not be a Von Neuman machine.

It may be that Von Neuman machines or It may be that Von Neuman machines or Turing machines cannot express the things Turing machines cannot express the things necessary for intelligence.necessary for intelligence.

Page 14: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

GamesGamesGamesGames

Computers have been programmed to play Computers have been programmed to play checkers, and in fact have beaten state checkers, and in fact have beaten state champions.champions.

They also displayed a form of learning--by They also displayed a form of learning--by having various parameters that could be having various parameters that could be tuned, and playing games against itself until tuned, and playing games against itself until a superior system, the computer showed a superior system, the computer showed something resembling learning, in a genetic something resembling learning, in a genetic algorithm.algorithm.

Computers have been programmed to play Computers have been programmed to play checkers, and in fact have beaten state checkers, and in fact have beaten state champions.champions.

They also displayed a form of learning--by They also displayed a form of learning--by having various parameters that could be having various parameters that could be tuned, and playing games against itself until tuned, and playing games against itself until a superior system, the computer showed a superior system, the computer showed something resembling learning, in a genetic something resembling learning, in a genetic algorithm.algorithm.

Page 15: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Learning?Learning?Learning?Learning?

Is this an example of learning by machines?Is this an example of learning by machines?

The program is telling the machine how to The program is telling the machine how to learn. But how is this different from a learn. But how is this different from a geometry teacher “programming” your mind geometry teacher “programming” your mind with some axioms?with some axioms?

Is this an example of learning by machines?Is this an example of learning by machines?

The program is telling the machine how to The program is telling the machine how to learn. But how is this different from a learn. But how is this different from a geometry teacher “programming” your mind geometry teacher “programming” your mind with some axioms?with some axioms?

Page 16: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Tic-Tac-ToeTic-Tac-ToeTic-Tac-ToeTic-Tac-Toe

You can program a computer to play TTT (on a 4X4 You can program a computer to play TTT (on a 4X4 grid) with a relatively small number of rules.grid) with a relatively small number of rules.

If you have three men in a row, play it as a win.If you have three men in a row, play it as a win.

If you can’t immediately win, block an opponent’s If you can’t immediately win, block an opponent’s immediate win.immediate win.

If you have a fork, play it.If you have a fork, play it.

If your opponent has a fork, block it.If your opponent has a fork, block it.

Beyond this the rules are somewhat hazy; you may Beyond this the rules are somewhat hazy; you may choose to pick squares in certain high value spots choose to pick squares in certain high value spots on the grid. These are known as heuristics.on the grid. These are known as heuristics.

You can program a computer to play TTT (on a 4X4 You can program a computer to play TTT (on a 4X4 grid) with a relatively small number of rules.grid) with a relatively small number of rules.

If you have three men in a row, play it as a win.If you have three men in a row, play it as a win.

If you can’t immediately win, block an opponent’s If you can’t immediately win, block an opponent’s immediate win.immediate win.

If you have a fork, play it.If you have a fork, play it.

If your opponent has a fork, block it.If your opponent has a fork, block it.

Beyond this the rules are somewhat hazy; you may Beyond this the rules are somewhat hazy; you may choose to pick squares in certain high value spots choose to pick squares in certain high value spots on the grid. These are known as heuristics.on the grid. These are known as heuristics.

Page 17: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Objections to AIObjections to AIObjections to AIObjections to AI

Some people say “I wouldn’t trust a Some people say “I wouldn’t trust a computer with my life.”computer with my life.”

But in reality this is done all the time, via But in reality this is done all the time, via traffic controls, pacemakers, fly-by-wire traffic controls, pacemakers, fly-by-wire systems, etc.systems, etc.

Computers are exceptionally good at Computers are exceptionally good at vigilance tasks and fast computation.vigilance tasks and fast computation.

This seems to be a less common objection This seems to be a less common objection these days.these days.

Some people say “I wouldn’t trust a Some people say “I wouldn’t trust a computer with my life.”computer with my life.”

But in reality this is done all the time, via But in reality this is done all the time, via traffic controls, pacemakers, fly-by-wire traffic controls, pacemakers, fly-by-wire systems, etc.systems, etc.

Computers are exceptionally good at Computers are exceptionally good at vigilance tasks and fast computation.vigilance tasks and fast computation.

This seems to be a less common objection This seems to be a less common objection these days.these days.

Page 18: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

ReligionReligionReligionReligion

Some people are hostile to the concept of Some people are hostile to the concept of machine intelligence, because they believe it machine intelligence, because they believe it is an essential part of humanity, and only is an essential part of humanity, and only God can create such things.God can create such things.

This is compatible with Penrose position D.This is compatible with Penrose position D.

Some people are hostile to the concept of Some people are hostile to the concept of machine intelligence, because they believe it machine intelligence, because they believe it is an essential part of humanity, and only is an essential part of humanity, and only God can create such things.God can create such things.

This is compatible with Penrose position D.This is compatible with Penrose position D.

Page 19: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

AIAIAIAI

Some define “intelligence” as “that which Some define “intelligence” as “that which humans can do but machines can’t.”humans can do but machines can’t.”

This is a bit problematic, since it may This is a bit problematic, since it may constantly shift. A few years ago, the chess constantly shift. A few years ago, the chess world champion was beaten by a machine. world champion was beaten by a machine. Does this mean the definition of AI changed Does this mean the definition of AI changed at that point?at that point?

Some define “intelligence” as “that which Some define “intelligence” as “that which humans can do but machines can’t.”humans can do but machines can’t.”

This is a bit problematic, since it may This is a bit problematic, since it may constantly shift. A few years ago, the chess constantly shift. A few years ago, the chess world champion was beaten by a machine. world champion was beaten by a machine. Does this mean the definition of AI changed Does this mean the definition of AI changed at that point?at that point?

Page 20: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

DualityDualityDualityDuality

You can also think of AI as being analogous You can also think of AI as being analogous to the duality of photons. They are not either to the duality of photons. They are not either a particle or a wave, but both at the same a particle or a wave, but both at the same time.time.

Likewise, you can think of machines as Likewise, you can think of machines as being both intelligent and not, at the same being both intelligent and not, at the same time. time.

You can also think of AI as being analogous You can also think of AI as being analogous to the duality of photons. They are not either to the duality of photons. They are not either a particle or a wave, but both at the same a particle or a wave, but both at the same time.time.

Likewise, you can think of machines as Likewise, you can think of machines as being both intelligent and not, at the same being both intelligent and not, at the same time. time.

Page 21: Richard W. Hamming Learning to Learn The Art of Doing Science and Engineering Session 6: Artificial Intelligence I Learning to Learn The Art of Doing Science.

Personal outlook regarding AIPersonal outlook regarding AIPersonal outlook regarding AIPersonal outlook regarding AI

Whatever your beliefs, you should be able to Whatever your beliefs, you should be able to coherently defend them. If you can’t do this, coherently defend them. If you can’t do this, you are likely to be badly led astray in the you are likely to be badly led astray in the real world.real world.

Whatever your beliefs, you should be able to Whatever your beliefs, you should be able to coherently defend them. If you can’t do this, coherently defend them. If you can’t do this, you are likely to be badly led astray in the you are likely to be badly led astray in the real world.real world.