Chapter 2, W3: Multiple Levels of Investigation

Question 1

Logicism

Answer 1

The POV that thinking is equivalent to performing mental logic; i.e., that thought can be mechanized.
- Logicism is the idea that thinking is identical to performing logical operations
- the view was converted into the logical analysis of relay circuits by Claude Shannon

Question 2

Information processors must be explained at three different levels of investigation:

Answer 2

• At the computational level, one asks what kinds of information processing problems can be solved by a system.
• At the algorithmic level, one asks what procedures are being used by a system to solve a particular problem of interest.
• At the implementation level, one asks what physical mechanisms are responsible for bringing a particular architecture to life (For instance, if one of the devices was an old electronic calculator, then you would feel comfortable in taking it apart to expose its internal workings. )

Question 3

Animism

Answer 3

Animism is the assignment of lifelike properties to inanimate, but moving, objects.
- Animism characterizes the thinking of young children, who may believe that a car, for instance, is alive because it can move on its own.
- Mechanization of life

Question 4

Describe the perspective the following quote presents and how you know:

“For seeing life is but a motion of limbs, the beginning whereof is in some principal part within; why may we not say, that all Automata (Engines that move themselves by means of springs and wheels as doth a watch) have an artificial life? For what is the Heart, but a Spring; and the Nerves, but so many Springs; and the Joynts, but so many Wheeles, giving motion to the whole Body, such as was intended by the Artificer?” (Hobbes, 1651/1967, p. 3).

Answer 4

• The quote is asking, where is the line between man and machine
• It is an appeal/critique of animism
• it also introduces the mechanization of the body

Question 5

Describe the perspective the following quote presents and how you know:

“There is not only a close analogy between the operations of the mind in general reasoning and its operations in the particular science of Algebra, but there is to a considerable extent an exact agreement in the laws by which the two classes of operations are conducted” (Boole, 1854/2003, p. 6).

Answer 5

• This is in support of the idea that thought can be mechanized i.e., logicism

Question 6

Cybernetic Principles

Answer 6

Cybernetic models of cognition often involve feedback loops and control systems that allow the brain to adjust its behaviour based on ongoing sensory input and internal states. These models are often used to explain how the brain achieves homeostasis or a state of stable equilibrium, and how it adapts to changes in the environment. Basic principles include:
- feedback
- control
- adaptation
- hierarchy
- redundancy

Question 7

Truth Tables / Truth-value Systems

Answer 7

Truth tables make explicit an approach in which primitive propositions (p, q, r, etc.) that could only adopt values of 0 or 1 are used to produce more complex expressions
- These tables represent what we would call Boolean logic, and launched modern computing science
- AND: p*q
- OR: p + q

Question 8

Mizar

Answer 8

Mizar attempted to formalize mathematical proofs in hopes that all logic found in mathematical research papers could:
- be stored in computers
- be used to automatically check proofs
- create new knowledge

The Mizar system is based on formalized mathematics, which is a rigorous and precise way of describing mathematical concepts and proofs using a formal language. The language used in Mizar is called Mizar language, which is a variant of first-order predicate logic.

Question 9

Shannon’s Logic

Answer 9

Electrical circuits can be described at the physical level, but also at the logical level i.e., logical operations can be combined into complex expressions
- A small set of primitive operations can be used to build more complex logic circuits (e.g., Shannons combination lock)

The link between Boolean algebra and electrical circuits, and showed how mathematical logic could be used to design, test, and simplify circuits. i.e., electrical circuits can be described at the physical level, but also at the logical level.
- OFF, power cannot flow (=false, 0)
- On, power can flow (=true, 1)

Question 10

Many-To-One Function (“Input-output mapping”)

Answer 10

In the context of circuits, a many-to-one function is a type of logic function where many input values can produce the same output value. The many-to-one relationship between circuits and functions illustrates a third level of inquiry, called the algorithmic level.
- What sequence of steps - what particular circuit - is being used to compute a particular function? What algorithm is being used to generate an input-output relation?

In digital circuits, many-to-one functions are often implemented using logic gates such as AND, OR, and XOR gates, which take multiple input signals and produce a single output signal based on the logic of the gate.
- Many different circuits can be created to perform the same function
- There is a “many-to-one” relation between circuits and a particular input-output function

The result of the comparison depends on the perspective taken.
- On the one hand, they are quite different: they involve different numbers of components, related to one another by completely different patterns of wiring.
- On the other hand, in spite of these obvious differences in details, at a more abstract level the two designs are identical, in the sense that both designs produce the same input-output mapping.