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1.59 MB
Extraction Summary
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People
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Organizations
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Quotes
Document Information
Type:
Book excerpt / scientific article
File Size:
1.59 MB
Summary
This document appears to be a page from a popular science book or article discussing theoretical computer science, specifically the concept of 'hyper-computers' versus 'Turing machines.' It explores the limits of artificial intelligence compared to human cognition and mathematical problem solving. The document bears a 'HOUSE_OVERSIGHT' stamp, suggesting it was included as evidence in a congressional investigation, likely related to Jeffrey Epstein's connections to the scientific community or his interest in AI and transhumanism.
People (2)
| Name | Role | Context |
|---|---|---|
| Alan Turing | Mathematician/Computer Scientist (Referenced) |
Referenced via 'Turing machine' and 'Turing limit' in the context of computational theory.
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| Pierre de Fermat | Mathematician (Referenced) |
Referenced via 'Fermat's Last Theorem' as an example of a problem for a hyper-computer.
|
Organizations (1)
| Name | Type | Context |
|---|---|---|
| House Oversight Committee |
Document source/production stamp (HOUSE_OVERSIGHT_015965) likely related to a congressional investigation.
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Key Quotes (4)
"If you believe humans outthink computers, be warned; you are in controversial territory."Source
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Quote #1
"A hyper-computer is a machine that can calculate a function which a Turing machine can not."Source
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Quote #2
"Humans commonly demonstrate one clear example of thinking which appears to break the Turing limit, namely finding solutions to mathematical puzzles."Source
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Quote #3
"Turing machines are already infinitely powerful and we know from our chapter on infinity that all countable infinities are the same."Source
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Quote #4
Full Extracted Text
Complete text extracted from the document (2,388 characters)
If you believe humans outthink computers, be warned; you are in controversial territory. This would need a hyper-computer and many scientists speak of these in the same breath as perpetual motion machines.
I’m not sure it’s an entirely fair analogy. We understand machines, and the physical laws of our Universe forbid perpetual motion. We don’t understand brains, so we can’t reasonably dismiss human hyper-computing. Humans commonly demonstrate one clear example of thinking which appears to break the Turing limit, namely finding solutions to mathematical puzzles. We need an explanation for this. Let me take you on a whistle-stop tour of all the schemes people have imagined that might lead to a hyper-computer.
A hyper-computer is a machine that can calculate a function which a Turing machine can not. For example, when given a number denoting a problem such as Fermat’s Last Theorem, it can give me in return a number representing a valid proof. We are not concerned here with speed. We are talking about fundamental ‘do-ability’. Such machines are often dubbed ‘super-Turing’.
Epic Fails
Let us first look at some proposals that blatantly fail. My children call these ‘epic fails’, and they are the perpetual motion machines of the hyper-computing world.
Let us first look at some proposals that blatantly fail. My children call these ‘epic fails’, and they are the perpetual motion machines of the hyper-computing world.
Could we run many Turing machines at the same time, perhaps even an infinite number? Then we would have a much more powerful machine that must beat the Turing limit.
The answer is no.
Turing machines are already infinitely powerful and we know from our chapter on infinity that all countable infinities are the same. Infinity plus infinity, infinity times infinity, infinity to any power; all are equal. One single, fast, one-dimensional machine can simulate them all. We get no greater power with an infinite number of similar machines.
The answer is no.
Turing machines are already infinitely powerful and we know from our chapter on infinity that all countable infinities are the same. Infinity plus infinity, infinity times infinity, infinity to any power; all are equal. One single, fast, one-dimensional machine can simulate them all. We get no greater power with an infinite number of similar machines.
The next technique which might realize a hyper-computer is to have a machine which simultaneously runs every possible branch in a program. Each time the machine gets to a point where there is a binary decision, it can take the ‘yes’ branch, spawn a copy of itself, and run the ‘no’ branch as well. Logically this machine should be able to calculate anything since it tries every conceivable option. The process is called non-determinism. This doesn’t mean the computer has free will. It just means the computer never chooses one option over another. It just
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