HOUSE_OVERSIGHT_015915.jpg
1.62 MB
Extraction Summary
3
People
2
Organizations
0
Locations
0
Events
0
Relationships
2
Quotes
Document Information
Type:
Book page / article (evidence exhibit)
File Size:
1.62 MB
Summary
This document appears to be a page (page 225) from a book or article titled "Turing's Machine." The text discusses computer science theory, specifically the "Halting Problem," operating systems, and mathematical proofs like Fermat's Last Theorem. While the text itself contains no direct references to Jeffrey Epstein or his associates, the footer bears the Bates stamp "HOUSE_OVERSIGHT_015915," indicating it was part of a document production for a US House Oversight Committee investigation, likely related to Epstein's known interest in and funding of theoretical science and mathematics.
People (3)
| Name | Role | Context |
|---|---|---|
| Douglas Adams | Author |
Mentioned in reference to the 'answer to life, the Universe, and everything'.
|
| Fermat | Mathematician |
Mentioned in the context of 'Fermat's puzzle' and 'Fermat's Last Theorem'.
|
| Alan Turing | Mathematician/Computer Scientist |
Mentioned as the author of a paper proving the 'Halt program' cannot exist.
|
Organizations (2)
| Name | Type | Context |
|---|---|---|
| Clay Mathematics Institute |
Implied by the mention of 'Clay Mathematics prizes'.
|
|
| House Oversight Committee |
Implied by the Bates stamp 'HOUSE_OVERSIGHT_015915'.
|
Key Quotes (2)
"It turns out this program would be more than just useful. It could be used as an oracle, capable of answering almost any question imaginable."Source
HOUSE_OVERSIGHT_015915.jpg
Quote #1
"Does such a magical program exist? The answer, sadly, is no. There is no Halt program and the final part of Turing's paper proved there can never be."Source
HOUSE_OVERSIGHT_015915.jpg
Quote #2
Full Extracted Text
Complete text extracted from the document (2,675 characters)
Turing's Machine 225
execution. You might ask what runs the operating system and that is a
smaller program called the BIOS. What runs BIOS? An even smaller
program called the Bootstrap. Once all this is up and running you have a
working computer, which can run any program you throw at it.
smaller program called the BIOS. What runs BIOS? An even smaller
program called the Bootstrap. Once all this is up and running you have a
working computer, which can run any program you throw at it.
The problem with programs is they tend to crash – usually at
the most inconvenient times. It is often not clear whether a program
has truly crashed. It might be stuck in an infinite loop, or it could be
calculating the answer to a complex question, such as the answer to life,
the Universe, and everything. How would we know? If only I had waited
a little longer before rebooting, the program would have run to its end
and given me the answer to Douglas Adams' question.
the most inconvenient times. It is often not clear whether a program
has truly crashed. It might be stuck in an infinite loop, or it could be
calculating the answer to a complex question, such as the answer to life,
the Universe, and everything. How would we know? If only I had waited
a little longer before rebooting, the program would have run to its end
and given me the answer to Douglas Adams' question.
It would be very useful, and save a great deal of time, if I had a way
of telling whether a program will ever stop. An elegant solution would be
to have a second program called 'Halt', which would test the program and
output 'will halt' or 'will crash' as appropriate. It turns out this program
would be more than just useful. It could be used as an oracle, capable of
answering almost any question imaginable.
of telling whether a program will ever stop. An elegant solution would be
to have a second program called 'Halt', which would test the program and
output 'will halt' or 'will crash' as appropriate. It turns out this program
would be more than just useful. It could be used as an oracle, capable of
answering almost any question imaginable.
I could, for example, write a program that says: for every index in
Fermat's puzzle try every number and halt if you find a solution greater
than 2. Now if I run my halt program on this program and it states 'will
crash', I will have solved Fermat's Last Theorem! Do you see why?
Fermat's puzzle try every number and halt if you find a solution greater
than 2. Now if I run my halt program on this program and it states 'will
crash', I will have solved Fermat's Last Theorem! Do you see why?
If we give 'Halt' an input: a program we are interested in, along with
some data, it will tell us if the program finds an answer. If I am trying to
solve Fermat's Last Theorem, we will ask it to try every possible index for
the equation 3x+4x=5x and halt when it finds a true result greater than 2.
If the halt program says yes and halts, you can trace through the program
and work out how it did it. The theory would be proved. If the program
says no, the theory is disproved. This gives us a way to discover proofs of
many mathematical theorems.
some data, it will tell us if the program finds an answer. If I am trying to
solve Fermat's Last Theorem, we will ask it to try every possible index for
the equation 3x+4x=5x and halt when it finds a true result greater than 2.
If the halt program says yes and halts, you can trace through the program
and work out how it did it. The theory would be proved. If the program
says no, the theory is disproved. This gives us a way to discover proofs of
many mathematical theorems.
I could try almost any puzzle using a program with this form. All I
need do is put a problem in the following decision format: try all possible
options, and then stop and ring a bell if a solution is found. The Halt
program would then give the result leading to untold riches, winning all
the remaining Clay Mathematics prizes at the very least and earning me
$6m.
need do is put a problem in the following decision format: try all possible
options, and then stop and ring a bell if a solution is found. The Halt
program would then give the result leading to untold riches, winning all
the remaining Clay Mathematics prizes at the very least and earning me
$6m.
Does such a magical program exist? The answer, sadly, is no. There
is no Halt program and the final part of Turing's paper proved there can
never be.
is no Halt program and the final part of Turing's paper proved there can
never be.
HOUSE_OVERSIGHT_015915
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