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Darren New schrieb:
> I understand that and I agree. My sole point originally was to say that
> it's not a logical implication that "hardwired" implies "not turing
> complete".
It does, when the context implies that "hardwired" means that an option
to re-program /without/ re-wiring does /not/ exist, regardless how you
wire it.
> If you go back to what I originally wrote:
>
> """
> > - Even its 1943 successor, "Colossus", was not Turing-complete, and
> programmable only by re-wiring.
>
> Just to avoid confusion, everyone should be aware that Turing machines
> are programmable only by re-wiring. Those two clauses have nothing to do
> with each other. :-)
> """
>
> You can see that I'm saying that just because you need to change wiring
> to program something doesn't keep it from being turing complete. The
> converse isn't addressed.
If "you /need/ to change wiring to program something" (emphasis added),
then it /does/ keep it from being turing complete.
If the machine is capable of being wired to be Turing complete
(accepting "soft-programming"), then you possibly don't /need/ to change
wiring, as it /may/ happen to already be wired just the way you need.
>> And by virtue of being a UTM, it is automatically "soft-programmable"
>> as well.
>
> Sort of, yes. (Sort of in the sense that a UTM interpreting its tape is
> isomorphic to the actual turing machine being interpreted, but not
> identical to it.)
This is the /only/ sense in which the term "soft-programmable" can be
interpreted without becoming pure nonsense - whether it is a UTM or any
other computing device - so I'm taking this interpetation for granted.
It doesn't matter whether the UTM is just /isomorphic/ to some TM it
simulates: The system as a whole runs a /program/, part of which is
stored on the tape.
> I think you're arguing against a statement I haven't made. I was simply
> pointing out to whoever might not know it that just because a computer
> needs to be physically modified to run a different program doesn't mean
> it isn't Turing complete.
And it is exactly /this/ statement I'm arguing against. It is a
statement about a computer with a certain /requirement/ regarding
programming. If a computer /has/ that requirement (and not just an
/option/ to that effect), it /does/ mean it isn't Turing complete, and
therefore your statement is simply false.
>> There is, however, no way to build a UTM that, at /every/ level, can
>> read program logic from ROM /only/.
>
> That *is* what a Turing machine does. There's no code on the tape that
> executes. That's the whole *point* of defining a UTM - that there is a
> program that can simulate running any other TM hardware program.
As mentioned before, in that sense there is /only/ programming through
re-wiring, and therefore in that sense it doesn't make sense to even
/mention/ such a property for any computing device.
I therefore argue that this low-level perspective is pure nonsense in
this discussion.
>> It must be "soft-programmable" at /some/ level in order to qualify as
>> Turing-complete.
>
> Great. Now define the words you put in quotes precisely and mathematically.
I'm not going to that level, because I'm not a mathematician, and
therefore leave its definition to common sense.
> Well.... The barrier to being Turing complete is amazingly low. If you
> have anything remotely close to a Turing machine, then it's going to be
> Turing compatible.
No, it's not automatically going to be: It depends on the "wiring"; for
instance, a Turing machine constituting a Busy Beaver will never be
Turing complete, despite /being/ a Turing machine (which should qualify
as "anything remotely close" in this sense I guess).
I cannot help but note that for someone demanding from /me/ precise
mathematical definitions, you're surprisingly lax in your own wording.
> It takes less than 30 states and one read/write cycle
> on one symbol of a tape-like memory to qualify.
To avoid confusion, I take the "one symbol" to mean "one symbol plus the
empty-cell symbol" (which I as a layman would consider a total of two
symbols).
> But if you can write to and read from memory, make a decision, and
> branch to a different place in the ROM based on that memory, you're
> Turing complete. Heck, you can be Turing complete if you have just one
> instruction.
Just one instruction at what abstraction level? CPU? Or "bytecode" (or
"soft-programming" to stick to my original term) interpreted by jumping
around in the ROM?
(And again: No, just the mentioned abilities does not /necessarily/ make
your machine Turing complete. It only enables you to simulate /some/
Turing machine(s) - only the proper ROM content would make it Turing
complete, so your ability to /make/ the machine Turing complete would
depend on what part of the ROM you could re-program - or "re-wire", if
you like.)
> I think we're agreeing, but I think you're ascribing to me at least one
> position I never took.
It may be a position you never /intended/ to take, but you persistently
keep taking by your choice of words, so it's hard for me to tell.
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