Aaron’s analysis of the story is quite interesting; however according to the
lecture, allowances for inconsistencies would mean more would be uncovered. More
would mean that the complexity would be too difficult for humans to deal with,
thus that sort of computer system could never be created. Also, even if such a
computer were to be created hypothetically, it would need to be infinite in many
respects. Such a computer is not possible even in the distance future. Computers
as we know them, require hard drives to store information, the bigger hard
drives we require, the more space we need to place them, the more components we
need to take advantage of them, and consequently the more power we need to run
them. The closest I could imagine to an infinite computer is the dream of
someday having a Quantum Computer.
Lucas said we cannot assert our own consistency, as we are trapped within that
very system. We would need to be able to step out. The reason we can find Gödel
Statements for computers is because we can sit back, far removed and determine
one with all the facts. We can’t for ourselves however, and there exists nothing
above the human mind that we know of. If we did indeed have a Gödel Statement,
it would likely mean we are not so inconsistent after all.
The best explanation I can devise is:
A) Quantum Computers have been invented and found to be infinite, and thus the
computer has turned into a greater being. After all, they can already be more
efficient than us at most things.
B) A Gödel Statement was created for humans, perhaps by a greater being. Maybe
Dizzard was doing some experiments with some sort of unearthly beings. Who knows?
C) Perhaps most of the characters in the story were not human after all, but
rather cyborgs.
So most of my explanations are more out of a science fiction movie than
anything, the whole riddle to me appeared to be quite sci-fi like.
___________________________________________________________________
This message was sent to the math3500 discussion list by Mary Penwell <metallic@yorku.ca> .
This archive was generated by hypermail 2b30 : Tue Dec 07 2004 - 00:50:42 EST