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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