CS80--Senior Seminar
Discussion Questions--Penrose Chapters 9 & 10
Jim Rogers
jrogers@cs.earlham.edu
Fall 2000
These are a few questions for thought and discussion.
- 1.
- What is the relationship between attention and consciousness? Is
consciousness without attention possible? How about vice versa? Why
does Penrose find the cerebellum more automaton-like than the cerebrum? What
is the relationship between consciousness and algorithmic behavior, both in
Penrose's apparent perspective in this
context and from the perspective of being able to capture thought processes by
recording one's state of mind?
- 2.
- The promise of Quantum Computing is the possibility of realizing
non-deterministic machines--computers with unbounded parallelism (since the
quantum computer could be in many states simultaneously). What is the
relationship between non-determinism (in which the next state is not fully
determined by the current state) and unbounded parallelism? Is finitely
bounded parallelism (as in current parallel computers) sufficient? Is
unbounded parallelism sufficient to solve the halting problem?
- 3.
- Why is it important to Penrose's arguments to have the collapse of
superposed quantum states (operation R) be driven by a mechanism other
than observation?
- 4.
- What is the relationship between consciousness and intelligence? (How
did
we get from questions of artificial intelligence to questions of artificial
consciousness?) Once again, how does Penrose's insistence that consciousness is
necessary for intelligence fit with Turing's ideas about capturing thought
processes by recording one's state of mind? with intuitive notions of
intelligent behavior? On Page 409 Penrose dismisses
philosophical reflection as evolutionary baggage (although mathematical
reflection seems to distinguish intelligent thought from the merely
algorithmic). Is it possible that consciousness is also evolutionary baggage?
So what evolutionary advantages does Penrose find for either consciousness or
intelligence?
- 5.
- In the Section The non=algorithmic nature of mathematical insight
Penrose makes an argument for the existence of Gödel sentences for the
totality of mathematical reasoning. This seems to be based on the idea that
there is a single system of mathematical reasoning that is approximated in all
mathematical argumentation. Must the system of reasoning used in the
communication of mathematical results be complete? What sort of problem (in
terms of formal logic) arises in the process of being convinced by a proof?
Is this necessarily undecidable?
- 6.
- So what is the punch line? Where does Penrose find hope for
non-algorithmic behavior in the brain? How does this proposal fit with what we
know about Quantum Computing? How does it fit with Penrose's belief that one
must be conscious of behavior for it to be intelligent?
CS80--Senior Seminar
Discussion Questions--Penrose Chapters 9 & 10
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James Rogers
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2000-12-09