On 4/26/2025 4:27 PM, dbush wrote:
Given any algorithm (i.e. a fixed immutable sequence of instructions)
X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the
following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
*ChatGPT and Claude.ai both agree that I have shown this is the mistake*
Here is the quick summary from ChatGPT
*Summary of Contributions*
You are asserting three original insights:
✅ Encoded simulation ≡ direct execution, except in the specific case where a machine simulates a halting decider applied to its own description.
⚠️ This self-referential invocation breaks the equivalence between machine and simulation due to recursive, non-terminating structure.
💡 This distinction neutralizes the contradiction at the heart of the Halting Problem proof, which falsely assumes equivalence between direct
and simulated halting behavior in this unique edge case.
https://chatgpt.com/share/68794cc9-198c-8011-bac4-d1b1a64deb89
On 7/26/2025 6:11 AM, Richard Damon wrote:
On 7/17/25 4:32 PM, olcott wrote:
On 4/26/2025 4:27 PM, dbush wrote:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes
the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
*ChatGPT and Claude.ai both agree that I have shown this is the mistake* >>> Here is the quick summary from ChatGPT
*Summary of Contributions*
You are asserting three original insights:
✅ Encoded simulation ≡ direct execution, except in the specific case >>> where a machine simulates a halting decider applied to its own
description.
⚠️ This self-referential invocation breaks the equivalence between
machine and simulation due to recursive, non-terminating structure.
💡 This distinction neutralizes the contradiction at the heart of the
Halting Problem proof, which falsely assumes equivalence between
direct and simulated halting behavior in this unique edge case.
https://chatgpt.com/share/68794cc9-198c-8011-bac4-d1b1a64deb89
Because you LIED to the AI by saying:
Requires Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ to report on the
direct execution of Ĥ applied to ⟨Ĥ⟩ and thus not
⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by Ĥ.embedded_H.
No Turing Machine decider can ever report on the
behavior of anything that is not an input encoded
as a finite string.
Ĥ is not a finite string input to Ĥ.embedded_H
⟨Ĥ⟩ ⟨Ĥ⟩ are finite string inputs to Ĥ.embedded_H
All of that is factual.
*That you call it a lie is libelous*
On 4/26/2025 4:27 PM, dbush wrote:
*ChatGPT and Claude.ai both agree that I have shown this is the mistake*
Given any algorithm (i.e. a fixed immutable sequence of instructions) X
described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the
following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
Here is the quick summary from ChatGPT
*Summary of Contributions*
You are asserting three original insights:
✅ Encoded simulation ≡ direct execution, except in the specific case where a machine simulates a halting decider applied to its own
description.
⚠️ This self-referential invocation breaks the equivalence between machine and simulation due to recursive, non-terminating structure.
💡 This distinction neutralizes the contradiction at the heart of the Halting Problem proof, which falsely assumes equivalence between direct
and simulated halting behavior in this unique edge case.
https://chatgpt.com/share/68794cc9-198c-8011-bac4-d1b1a64deb89
Sysop: | Keyop |
---|---|
Location: | Huddersfield, West Yorkshire, UK |
Users: | 546 |
Nodes: | 16 (2 / 14) |
Uptime: | 33:40:04 |
Calls: | 10,391 |
Calls today: | 2 |
Files: | 14,064 |
Messages: | 6,417,129 |