Cognitive Science and Computation Theory

Overview of Cognitive Science and Computation

• In the last lesson, a pivotal question was posed: How can we characterize how information processing occurs in the mind and the brain?

• This question served as a challenge to the behaviorist perspective, which focused on observable behaviors rather than internal cognitive processes.

Introduction of Computational Theories

• Early cognitive scientists were influenced by radical new ideas emerging from computer science in the early to mid-20th century.

• Key Concept: The notion of computation as a model for understanding human and machine intelligence began to take shape during this time.

• Pioneering Figure: Alan Turing, a foundational figure in both computing and cognitive science, played a crucial role in developing theories regarding algorithms in the 1930s.

Understanding Turing's Computation

• Turing aimed to create a method through which a machine could apply a finite set of unambiguous rules (algorithms) to transform inputs into outputs.

• Components of Turing's Machine:

  • A read/write head that could:

  • Print symbols

  • Read existing symbols

  • Erase symbols

  • An infinite tape of paper where symbols were manipulated.

Example of Symbol Manipulation

• Example: Transforming the input of 3 + 2 into an output of 5.

  • Instead of using traditional Arabic numerals, Turing's machine uses a series of 1 symbols.

  • The input representation:

  • # 1 1 1 + 1 1 # (where # represents the boundaries).

  • The output representation:

  • # 1 1 1 1 1 # (five 1 symbols).

The Turing Machine and Algorithmic Processing

• The Turing machine processes symbols by applying a series of rules outlined in a machine table.

• State Consideration:

  • Starts in state a and processes symbols according to predefined rules.

  • Example Rule 1: If the Turing head in state a finds a 1, it:

  • Moves one square to the right.

  • Stays in state a.

  • By continuously applying the rules, the machine makes state transitions and manipulates symbols (changes + to 1, etc.).

  • Final State: When rules are executed to the fullest, the machine concludes by replacing symbols and moving to a halting state.

Introducing the Universal Turing Machine

• Turing introduced the Universal Turing Machine, capable of emulating any specific Turing machine's operations, thus enabling it to perform various algorithms and processes beyond simple arithmetic.

• Significance: The Universal Turing Machine concept implies:

  • It can solve a vast array of logical problems, contingent on the availability of the right set of rules.

Implications on Cognitive Science

• Turing's conceptual machine was abstract and did not exist in a physical form; rather, it provided insights into computing devices capable of solving logical problems.

• Turing's ideas inspired cognitive scientists to postulate that human thought likely involves a similar process of

  • Algorithmic symbol manipulation.

  • This led to suggesting that the human brain might function as a real-world Universal Turing Machine.

Conclusions and Future Exploration

• The influence of Turing machines proved essential for cognitive scientists seeking to explain how information processes within the human mind.

• The objective: Identify mental representations (symbols) and the cognitive rules for transforming these symbols.

• This exploration aims to formulate a viable theory of how the mind works, drawn from computational principles.