HOUSE_OVERSIGHT_015943.jpg
1.51 MB
Extraction Summary
4
People
2
Organizations
0
Locations
1
Events
1
Relationships
3
Quotes
Document Information
Type:
Book page / congressional production document
File Size:
1.51 MB
Summary
This document appears to be a scanned page (page 253) from a book or academic paper discussing artificial intelligence, mathematics, and computer science. It specifically addresses the 'Special Purpose Objection,' comparing human mathematical discovery (exemplified by Andrew Wiles solving Fermat's Last Theorem) to computer processing (exemplified by Google search). The document bears a Bates stamp 'HOUSE_OVERSIGHT_015943', indicating it was part of a document production for a US House Oversight Committee investigation, likely related to Jeffrey Epstein's connections to the scientific community, though Epstein is not mentioned on this specific page.
People (4)
| Name | Role | Context |
|---|---|---|
| Wiles | Mathematician |
Mentioned as proving Fermat's Last Theorem and used as an example in the 'Special Purpose Objection' argument.
|
| Hilbert | Mathematician |
Referenced in the context of 'Hilbert's tenth problem'.
|
| Turing | Mathematician/Computer Scientist |
Referenced regarding the 'Turing limit' and what he proved regarding algorithms.
|
| Matiyasevich | Mathematician |
Referenced alongside Turing regarding what they proved about algorithms/decidability.
|
Organizations (2)
| Name | Type | Context |
|---|---|---|
|
Used as an example of a search engine finding a proof rather than discovering it.
|
||
| House Oversight Committee |
Implied by the Bates stamp 'HOUSE_OVERSIGHT_015943' at the bottom of the page.
|
Relationships (1)
Text mentions 'what Turing and Matiyasevich proved' regarding algorithms.
Key Quotes (3)
"Theorem (Undecidability of Hilbert’s tenth problem) There is no algorithm which, for a given arbitrary Diophantine equation, would tell whether the equation has a solution or not."Source
HOUSE_OVERSIGHT_015943.jpg
Quote #1
"I am not arguing having a solution to a given mathematical puzzle presents a difficulty to a computer; I am arguing a computer cannot discover one."Source
HOUSE_OVERSIGHT_015943.jpg
Quote #2
"There is no sense in which the search engine discovered the proof."Source
HOUSE_OVERSIGHT_015943.jpg
Quote #3
Full Extracted Text
Complete text extracted from the document (2,511 characters)
Software 253
mathematician, he managed to prove this conjecture and so, two years
after first announcing that he had solved Fermat’s Last Theorem he could
finally lay it to rest.
after first announcing that he had solved Fermat’s Last Theorem he could
finally lay it to rest.
The Special Purpose Objection
Before I declare mankind’s outright victory over computers, the Special
Purpose Objection must be overcome. The objectors would argue that
Wiles is a Special Purpose computer. Special Purpose computers are at
no risk of breaking the Turing limit when they solve problems they have
Before I declare mankind’s outright victory over computers, the Special
Purpose Objection must be overcome. The objectors would argue that
Wiles is a Special Purpose computer. Special Purpose computers are at
no risk of breaking the Turing limit when they solve problems they have
Theorem (Undecidability of Hilbert’s tenth problem)
There is no algorithm which, for a given arbitrary Diophantine
equation, would tell whether the equation has a solution or not.
There is no algorithm which, for a given arbitrary Diophantine
equation, would tell whether the equation has a solution or not.
been programmed to answer. The objection misses the key point. I am
not arguing having a solution to a given mathematical puzzle presents a
difficulty to a computer; I am arguing a computer cannot discover one.
not arguing having a solution to a given mathematical puzzle presents a
difficulty to a computer; I am arguing a computer cannot discover one.
Take, for example, the search engine Google. If I type “where can
I find the proof of Fermat’s Last Theorem?” into the search box, it will
retrieve a PDF of the proof as the third result. It appears this special
purpose computer solved the problem. But you immediately see the
difficulty. Google search already knew the answer, or more precisely had
indexed the answer. The computer was not tackling a random problem
from scratch. It was tackling a problem for which it knew the answer, or
at least where an answer could be found. There is no sense in which the
search engine discovered the proof.
I find the proof of Fermat’s Last Theorem?” into the search box, it will
retrieve a PDF of the proof as the third result. It appears this special
purpose computer solved the problem. But you immediately see the
difficulty. Google search already knew the answer, or more precisely had
indexed the answer. The computer was not tackling a random problem
from scratch. It was tackling a problem for which it knew the answer, or
at least where an answer could be found. There is no sense in which the
search engine discovered the proof.
To really understand this objection we need to examine exactly
what Turing and Matiyasevich proved.
what Turing and Matiyasevich proved.
An arbitrary problem is one you do not already know the solution
to when you write the algorithm. You can think of it as a variable. Is
there an algorithm that can solve problem ‘X’? The alternative is a special
program. It can solve problem Y. Y is a problem it knows. It must have
the solution coded somewhere within it in a computably expandable way.
You might think of this as a table of constants; problem Y has solution
1, problem Z has solution 2, and so on. But it could be more subtle than
that. Problem Y might have a solution which is encrypted so you cannot
recognize it within the program, or it might even be the result of some
to when you write the algorithm. You can think of it as a variable. Is
there an algorithm that can solve problem ‘X’? The alternative is a special
program. It can solve problem Y. Y is a problem it knows. It must have
the solution coded somewhere within it in a computably expandable way.
You might think of this as a table of constants; problem Y has solution
1, problem Z has solution 2, and so on. But it could be more subtle than
that. Problem Y might have a solution which is encrypted so you cannot
recognize it within the program, or it might even be the result of some
HOUSE_OVERSIGHT_015943
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