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1.58 MB
Extraction Summary
5
People
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Organizations
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Locations
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Events
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Relationships
5
Quotes
Document Information
Type:
Book page / evidence document
File Size:
1.58 MB
Summary
This document is page 246 from a book or paper (possibly titled 'Are the Androids Dreaming Yet?') included in a House Oversight investigation file (Bates stamped HOUSE_OVERSIGHT_015936). The text discusses computer science and philosophical concepts, specifically the Halting Problem, Universal Turing Machines, and Gödel's Incompleteness Theorems, referencing Roger Penrose and Stephen Wolfram. It argues that if a Halting procedure existed, it would imply a deterministic universe without free will.
People (5)
| Name | Role | Context |
|---|---|---|
| Roger Penrose | Physicist/Author |
Cited in the text for giving a three-page example of a Universal Turing Machine in his book 'The Emperor’s New Mind'.
|
| Stephen Wolfram | Scientist/Mathematician |
Cited in the text for implementing a Universal Turing Machine using a cellular automaton.
|
| Picasso | Artist (Reference) |
Mentioned metaphorically regarding the theoretical capabilities of a pocket calculator.
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| Mozart | Composer (Reference) |
Mentioned metaphorically regarding the theoretical capabilities of a pocket calculator.
|
| Gödel | Mathematician/Logician |
Referenced in the section 'Gödel’s Insight' regarding mathematical puzzles and proofs.
|
Relationships (1)
Both are cited in the same paragraph as providing examples of Universal Turing Machines.
Key Quotes (5)
"There is only one way out. There can be no halting procedure."Source
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Quote #1
"A Halting Program running on such a machine should be able to compute all the knowledge in the Universe."Source
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Quote #2
"My pocket calculator could, theoretically, paint like Picasso and compose like Mozart."Source
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Quote #3
"If you philosophically rebel against this then the Halting Problem must have no solution."Source
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Quote #4
"Solutions to mathematical puzzles are neat, orderly sequences of statements where the problem is solved step by step."Source
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Quote #5
Full Extracted Text
Complete text extracted from the document (2,382 characters)
246
Are the Androids Dreaming Yet?
Are the Androids Dreaming Yet?
Both analyses lead to a paradox! There is only one way out. There can be no halting procedure. I’m sorry if this is quite convoluted.
Philosophical Proof
If you find these technical proofs difficult to follow, it may be easier to examine the problem philosophically. Consider the consequence of the existence of a Halting procedure. A Universal Turing Machine is a relatively small program. Roger Penrose gives a three-page example in The Emperor’s New Mind, and Stephen Wolfram has implemented one using a cellular automaton with as few as five component parts.
If you find these technical proofs difficult to follow, it may be easier to examine the problem philosophically. Consider the consequence of the existence of a Halting procedure. A Universal Turing Machine is a relatively small program. Roger Penrose gives a three-page example in The Emperor’s New Mind, and Stephen Wolfram has implemented one using a cellular automaton with as few as five component parts.
A Halting Program running on such a machine should be able to compute all the knowledge in the Universe. Every structure, every work of literature, every galaxy could be the output of this single, simple program. My pocket calculator could, theoretically, paint like Picasso and compose like Mozart. All art, knowledge and science would be entirely determined in our Universe and we would have no free will. If you philosophically rebel against this then the Halting Problem must have no solution.
Gödel’s Insight
Another way to understand this conundrum is through the earlier work of Gödel. Solutions to mathematical puzzles are neat, orderly sequences of statements where the problem is solved step by step. Computers are good at step by step processes. Surely a computer could simply proceed in a painstaking fashion to check all the possible combinations of words and symbols to discover a proof.
Another way to understand this conundrum is through the earlier work of Gödel. Solutions to mathematical puzzles are neat, orderly sequences of statements where the problem is solved step by step. Computers are good at step by step processes. Surely a computer could simply proceed in a painstaking fashion to check all the possible combinations of words and symbols to discover a proof.
An analogy might be trying to find your hotel room if you have forgotten the number. You could simply find it by trying every room. As you progressed through each floor, you would try every corridor and retrace your steps to the main hallway before attempting the next. Eventually you would succeed.
Finding proofs of theorems is often understood to be the same sort of task: search systematically through all the numbers and you will find the solution. But this is not so: There is a hidden problem.
Although it is true to say problems and proofs can be described by numbers, they are not simply related like a lock and key. We need the first number to translate into a set of symbols meaning something about mathematics: for example, that x squared plus y squared equals z squared but for higher powers there is no equality, and the second number to
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