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CMPUT 474: Midterm Review Review of first half: Restricted models of computation Dale Schuurmans

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CMPUT 474: Midterm Review Review of first half: Restricted models of computation Dale Schuurmans 1 Introduction Three fundamental lessons of computation 1. consequences of simple rules/mechanisms 2. finiteness vs infiniteness Cantor: • cardinality: 1 to 1 correspondence • #(P(S)) #(S) 3. consequences of self-referability 2 Emergence of computation • 500 BC-1800s: the struggle representing real numbers • Late 1800s paradoxes: Weierstrauss function, Russell paradox, Vitali set • 1900 hope: Hilbert, Russell • 1930s dies: Church, G¨odel, Turing • 1935 birth of computation • 1940s; experimental computation • 1950-70s: commoditization of computation • 1980s: personal computers • 1990s: internet • 2000s: social & media • 2010s: AI • now?

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CMPUT 474: Midterm Review
Review of first half: Restricted models of computation
Dale Schuurmans


1 Introduction
Three fundamental lessons of computation
1. consequences of simple rules/mechanisms
2. finiteness vs infiniteness
Cantor:
• cardinality: 1 to 1 correspondence
• #(P(S)) > #(S)
3. consequences of self-referability


2 Emergence of computation
• 500 BC-1800s: the struggle representing real numbers
• Late 1800s paradoxes: Weierstrauss function, Russell paradox, Vitali set
• 1900 hope: Hilbert, Russell
• 1930s dies: Church, Gödel, Turing
• 1935 birth of computation
• 1940s; experimental computation
• 1950-70s: commoditization of computation
• 1980s: personal computers
• 1990s: internet
• 2000s: social & media
• 2010s: AI
• now?

1

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