COGS 100 Lecture Notes - Turing Machine, Theory-Theory, Universal Turing Machine
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28 Nov 2012
School
Department
Course
Professor
Midterm
10-12 questions
Turing Machine
Chapter 1 & all course notes
Main questions & lots of detailing
Turing machine
Calculable machine
Gives result to a given input
Functions -> Computable -> Turing Computable
Qi (instruction), Si (seeing) , A(what to do), Q(which state to go
into)
Long tape of set instructions.
Turing’s results:
There exists universal Turing Machines
There are incomputable functions. Ex: g (x)=fx (x)+1
Concept of computability – Turing computable
“Everything computable is also Turing computable.”
Familiar with the workings of Turing machines
If the function is not defined then the machine won’t stop.
In Turing’s time, a Universal Turing machine was simply a list of
quadruples. Today it’s a laptop for example.
Relationship between Church’s theories.
Mind is a Universal Turing Machine. “The mind is a computer – a
software, that can run a multiple amount of instructions.”
Physical universe is a machine.
Descartes – anatomy of mechanical physician. Human beings cannot
be explained mechanically
If the brain is like a computer then there are two levels: neurons and
such and then an abstract level (functions that are being calculated)
Input -> Output = function
Functionalism: position within the PHIL of the mind (The mind is what
the brain does; the function of the brain) The mind is a software;
multitude of programs.
Describe the mind on an abstract level, not a concrete level.
What level does the mind occupy?
The function is the mind
The brain represents things as the computer does.
Shannon information theory – theory of information.
Miller – to talk about information and memory.