On 8/11/2025 10:51 PM, dbush wrote:
On 8/11/2025 11:49 PM, olcott wrote:
On 8/11/2025 10:42 PM, dbush wrote:
On 8/11/2025 11:39 PM, olcott wrote:
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qy
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qn
No. the behavior specified by the input to M.H ⟨M⟩ ⟨M⟩
i.e. finite string ⟨M⟩ which is defined to be a description of
algorithm M, proven to be valid by UTM ⟨M⟩ ⟨M⟩ having the exact same
behavior as M ⟨M⟩
is provably different behavior than the behavior of
M applied to ⟨M⟩.
False, as shown above.
So you do not understand that M.H ⟨M⟩ ⟨M⟩
repeats recursively simulating itself?
Only finitely, as the simulation UTM ⟨M⟩ ⟨M⟩ is exactly the same as >> the simulation M.H ⟨M⟩ ⟨M⟩ up to the point that M.H aborts, proving >> that algorithm M halts.
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qy
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qn
UTM ⟨M⟩ ⟨M⟩ has the same behavior as M ⟨M⟩
and different behavior than M.H ⟨M⟩ ⟨M⟩.
On 8/11/2025 10:51 PM, dbush wrote:
On 8/11/2025 11:49 PM, olcott wrote:
On 8/11/2025 10:42 PM, dbush wrote:
On 8/11/2025 11:39 PM, olcott wrote:
On 8/11/2025 10:29 PM, dbush wrote:
On 8/11/2025 11:25 PM, olcott wrote:
On 8/11/2025 10:19 PM, dbush wrote:
On 8/11/2025 11:13 PM, olcott wrote:
On 8/11/2025 9:54 PM, dbush wrote:
On 8/11/2025 10:28 PM, olcott wrote:
On 8/11/2025 9:12 PM, dbush wrote:
On 8/11/2025 10:07 PM, olcott wrote:
On 8/11/2025 8:57 PM, dbush wrote:
On 8/11/2025 9:36 PM, olcott wrote:Finite string representations of numbers always behave >>>>>>>>>>>>> exactly the same way as if they were numbers.
Because no Turing machine ever takes another
Turing machine as an input no Turing machine can >>>>>>>>>>>>>>> directly compute the mapping from an input that
is not in its domain.
Therefore Turing machines can't do arithmetic because no >>>>>>>>>>>>>> Turing machine can take an actual number as input. >>>>>>>>>>>>>>
Agreed?
Finite string representations of Turing Machines do
not always behave exactly the same way as the machine >>>>>>>>>>>>> in one single exceptional case that no one ever noticed >>>>>>>>>>>>> before:
Which is just another way of saying the halting function is >>>>>>>>>>>> not a computable function, as Linz and others have proved >>>>>>>>>>>> and as you have *explicitly* agreed is correct.
*No it is not another way of saying that*
It is a way of saying that the halting function
is not computable because
Assuming it is causes contradictions.
The halting problem causes no contradiction when
it is understood that M.H ⟨M⟩ ⟨M⟩ correctly reports
on the actual behavior of its actual input.
In other words, H isn't giving the answer required by the
specification and therefore doesn't meet the definition of a
total halt decider / termination analyzer.
When the spec requires reporting on a non-input
and ignores reporting on an input then we know
that spec is wrong.
In other words Turning machines can't add 2 + 2 because the number >>>>>> 2 is a non-input, so any specification for a Turing machine to
perform addition must be wrong.
Agreed?
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qy
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qn
No. the behavior specified by the input to M.H ⟨M⟩ ⟨M⟩
i.e. finite string ⟨M⟩ which is defined to be a description of
algorithm M, proven to be valid by UTM ⟨M⟩ ⟨M⟩ having the exact same
behavior as M ⟨M⟩
is provably different behavior than the behavior of
M applied to ⟨M⟩.
False, as shown above.
So you do not understand that M.H ⟨M⟩ ⟨M⟩
repeats recursively simulating itself?
Only finitely, as the simulation UTM ⟨M⟩ ⟨M⟩ is exactly the same as >> the simulation M.H ⟨M⟩ ⟨M⟩ up to the point that M.H aborts, proving >> that algorithm M halts.
I have proven that to be factually incorrect
numerous times on the basis of HHH(DDD) and HHH1(DDD).
HHH simulates DD then simulates an instance of itselfThat is your straw man. That HHH fails to reach the final halt state is
that cannot possibly return.
HHH1 simulates DD then simulates an instance of HHH
that does return.
On 8/11/2025 2:04 PM, dbush wrote:
On 8/11/2025 3:00 PM, olcott wrote:
On 8/11/2025 1:51 PM, dbush wrote:
On 8/11/2025 2:50 PM, olcott wrote:
On 8/11/2025 1:45 PM, dbush wrote:
On 8/11/2025 2:40 PM, olcott wrote:
On 8/11/2025 1:33 PM, Richard Heathfield wrote:
On 11/08/2025 18:48, olcott wrote:It is incorrect to say it *is* a wrong answer until after
On 8/11/2025 11:42 AM, Richard Heathfield wrote:
On 11/08/2025 17:29, olcott wrote:
<snip>
I have proven that DD correctly simulated by HHH
No, you haven't. You have asserted that the simulation is
correct, but we all know that it derives a different result >>>>>>>>>> from that produced by direct execution, and therefore we all >>>>>>>>>> know that the simulation is not correct.
You can only fully know that your assumption is incorrect
when you notice that no specific error exists.
The specific error is that you get the wrong answer.
a specific error in the basis of this answer is found.
It's the wrong answer because it doesn't meet the required
specification:
That merely presumes that the required specification
is correct.
It's correct because I want to know if any arbitrary algorithm X
with input Y will halt when executed directly.
Likewise I want to know the radius of a square circle
that has a length of 2.0 of one of its equal length
four sides.
The difference is that every algorithm X with input Y either halts or
does not halt when executed directly, so there is a correct answer in
all cases.
Because no Turing machine ever takes another
Turing machine as an input no Turing machine can
directly compute the mapping from an input that
is not in its domain.
In all but one case input ⟨M⟩ to simulating halt
decider H has the exact same behavior machine M.
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qy
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qn
(a) M copies its input ⟨M⟩
(b) M invokes M.H ⟨M⟩ ⟨M⟩
(c) M.H simulates ⟨M⟩ ⟨M⟩
When H is embedded within M then the behavior of
⟨M⟩ ⟨M⟩ simulated by M.H cannot possibly reach a final
halt state, even if there is no loop trick at the end.
The halting problem definition assumes that this case
does not exist. Thus they used the short-hand that
H applied to ⟨M⟩ ⟨M⟩ is reporting on M applied to ⟨M⟩.
On 8/11/2025 10:51 PM, dbush wrote:
On 8/11/2025 11:49 PM, olcott wrote:
On 8/11/2025 10:42 PM, dbush wrote:
On 8/11/2025 11:39 PM, olcott wrote:
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qy
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qn
No. the behavior specified by the input to M.H ⟨M⟩ ⟨M⟩
i.e. finite string ⟨M⟩ which is defined to be a description of
algorithm M, proven to be valid by UTM ⟨M⟩ ⟨M⟩ having the exact same
behavior as M ⟨M⟩
is provably different behavior than the behavior of
M applied to ⟨M⟩.
False, as shown above.
So you do not understand that M.H ⟨M⟩ ⟨M⟩
repeats recursively simulating itself?
Only finitely, as the simulation UTM ⟨M⟩ ⟨M⟩ is exactly the same as >> the simulation M.H ⟨M⟩ ⟨M⟩ up to the point that M.H aborts, proving >> that algorithm M halts.
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qy
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qn
UTM ⟨M⟩ ⟨M⟩ has the same behavior as M ⟨M⟩
and different behavior than M.H ⟨M⟩ ⟨M⟩.
On 8/11/2025 10:51 PM, dbush wrote:
On 8/11/2025 11:49 PM, olcott wrote:
On 8/11/2025 10:42 PM, dbush wrote:
On 8/11/2025 11:39 PM, olcott wrote:
On 8/11/2025 10:29 PM, dbush wrote:
On 8/11/2025 11:25 PM, olcott wrote:
On 8/11/2025 10:19 PM, dbush wrote:
On 8/11/2025 11:13 PM, olcott wrote:
On 8/11/2025 9:54 PM, dbush wrote:
On 8/11/2025 10:28 PM, olcott wrote:
On 8/11/2025 9:12 PM, dbush wrote:
On 8/11/2025 10:07 PM, olcott wrote:
On 8/11/2025 8:57 PM, dbush wrote:
On 8/11/2025 9:36 PM, olcott wrote:Finite string representations of numbers always behave >>>>>>>>>>>>> exactly the same way as if they were numbers.
Because no Turing machine ever takes another
Turing machine as an input no Turing machine can >>>>>>>>>>>>>>> directly compute the mapping from an input that
is not in its domain.
Therefore Turing machines can't do arithmetic because no >>>>>>>>>>>>>> Turing machine can take an actual number as input. >>>>>>>>>>>>>>
Agreed?
Finite string representations of Turing Machines do
not always behave exactly the same way as the machine >>>>>>>>>>>>> in one single exceptional case that no one ever noticed >>>>>>>>>>>>> before:
Which is just another way of saying the halting function is >>>>>>>>>>>> not a computable function, as Linz and others have proved >>>>>>>>>>>> and as you have *explicitly* agreed is correct.
*No it is not another way of saying that*
It is a way of saying that the halting function
is not computable because
Assuming it is causes contradictions.
The halting problem causes no contradiction when
it is understood that M.H ⟨M⟩ ⟨M⟩ correctly reports
on the actual behavior of its actual input.
In other words, H isn't giving the answer required by the
specification and therefore doesn't meet the definition of a
total halt decider / termination analyzer.
When the spec requires reporting on a non-input
and ignores reporting on an input then we know
that spec is wrong.
In other words Turning machines can't add 2 + 2 because the number >>>>>> 2 is a non-input, so any specification for a Turing machine to
perform addition must be wrong.
Agreed?
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qy
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qn
No. the behavior specified by the input to M.H ⟨M⟩ ⟨M⟩
i.e. finite string ⟨M⟩ which is defined to be a description of
algorithm M, proven to be valid by UTM ⟨M⟩ ⟨M⟩ having the exact same
behavior as M ⟨M⟩
is provably different behavior than the behavior of
M applied to ⟨M⟩.
False, as shown above.
So you do not understand that M.H ⟨M⟩ ⟨M⟩
repeats recursively simulating itself?
Only finitely, as the simulation UTM ⟨M⟩ ⟨M⟩ is exactly the same as >> the simulation M.H ⟨M⟩ ⟨M⟩ up to the point that M.H aborts, proving >> that algorithm M halts.
I have proven that to be factually incorrect
numerous times on the basis of HHH(DDD) and HHH1(DDD).
HHH simulates DD then simulates an instance of itself
that cannot possibly return.
HHH1 simulates DD then simulates an instance of HHH
that does return.
Is your name Dave?
On 8/12/2025 7:11 AM, dbush wrote:
On 8/12/2025 12:00 AM, olcott wrote:
On 8/11/2025 10:51 PM, dbush wrote:
Only finitely, as the simulation UTM ⟨M⟩ ⟨M⟩ is exactly the same as
the simulation M.H ⟨M⟩ ⟨M⟩ up to the point that M.H aborts, proving
that algorithm M halts.
I have proven that to be factually incorrect
numerous times on the basis of HHH(DDD) and HHH1(DDD).
HHH simulates DD then simulates an instance of itself
that cannot possibly return.
i.e. HHH simulates DD then simulates an instance of HHH that it aborts
HHH1 simulates DD then simulates an instance of HHH
that does return.
i.e. HHH1 simulates DD then simulates an instance of HHH but does not
abort it allowing it to reach a final state.
Both are the exactly the same up to the point that HHH aborts.
The behavior varies not because HHH aborts.
Their behavior varies because DDD calls HHH(DDD) in
recursive emulation and DDD does not call HHH1(DDD) at all.
Both are exactly the same until their DDD calls HHH(DDD).
There are many other steps after that before HHH(DDD) aborts.
On 8/12/2025 7:12 AM, dbush wrote:
On 8/12/2025 1:01 AM, olcott wrote:
On 8/11/2025 10:51 PM, dbush wrote:
On 8/11/2025 11:49 PM, olcott wrote:
On 8/11/2025 10:42 PM, dbush wrote:
On 8/11/2025 11:39 PM, olcott wrote:
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qy
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qn
No. the behavior specified by the input to M.H ⟨M⟩ ⟨M⟩
i.e. finite string ⟨M⟩ which is defined to be a description of >>>>>> algorithm M, proven to be valid by UTM ⟨M⟩ ⟨M⟩ having the exact >>>>>> same behavior as M ⟨M⟩
is provably different behavior than the behavior of
M applied to ⟨M⟩.
False, as shown above.
So you do not understand that M.H ⟨M⟩ ⟨M⟩
repeats recursively simulating itself?
Only finitely, as the simulation UTM ⟨M⟩ ⟨M⟩ is exactly the same as
the simulation M.H ⟨M⟩ ⟨M⟩ up to the point that M.H aborts, proving
that algorithm M halts.
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qy
M.q0 ⟨M⟩ ⊢* M.H ⟨M⟩ ⟨M⟩ ⊢* M.qn
UTM ⟨M⟩ ⟨M⟩ has the same behavior as M ⟨M⟩
and different behavior than M.H ⟨M⟩ ⟨M⟩.
Only because M.H aborts, and up to the point it does both are exactly
the same.
In other words you believe that ⟨M⟩ ⟨M⟩ correctly
simulated by M.H would eventually reach its own
simulated final halt state with no need for any abort.
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