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09-21 Intro to Cog Sci Lecture 6

# 09-21 Intro to Cog Sci Lecture 6 - Introduction to...

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Introduction to Cognitive Science Lecture 6: 9/21/09 Turing machines – the reason for going through Turing machines is that the magic of cognition comes NOT from individual pieces but rather from the PATTERN in which they are arranged; the pieces (just like individual Turing machine pieces) are pretty dumb. Various processes that make sense to you may be implemented in your mind by very dumb pieces, such as dumb pieces of Turing machines semantically interesting results from syntactic machines Turing Machines 1. A Tape Divided into discrete squares (think toilet paper). Each square can have a “0”, a “1”, or nothing. 2. A Scanner Can read the square under it. Can alter its value. 3. An Instruction Table Given current square and state, can (1) replace the square’s value, (2) move L or R, & (3) go to new state. Making Sense of TMs 1. Look for global features (e.g. only moves R) 2. Draw circles for each state 3. Draw arrows for successor states 4. Label arrows with triads (e.g. “#,0,R”) 5. Study the figure; Divide & conquer! Scholl goes over three sample Turing machines. Church/Turing Thesis - Here is an important fact – a mathematical thesis (everyone believes it to be true) - Any finite mathematical or logical procedure – i.e. any computation – can be implemented on a Turing Machine (and also on just its tape!) o All modern PCs are (complicated) TMs o The difference? Architecture! o Note that the substrate doesn’t matter! ( Functionalism – a doctrine that what matters for a system is NOT what it is built on but the pattern in which it is arranged) Book recommendation: Stephen Wolfram’s A New Kind of Science -

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09-21 Intro to Cog Sci Lecture 6 - Introduction to...

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