clipka wrote:
> 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.

You understand that Turing machines are hard-wired, right? You can't 
reprogram them without rewiring them?

> If "you /need/ to change wiring to program something" (emphasis added), 
> then it /does/ keep it from being turing complete.

I suspose it's arguing over what "programming" means, now.

> 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.

If you're talking about real machines with real I/O and such, then no, maybe 
you want to rewire it anyway.

>>> 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.

Yes, but the output of that program might not appear anywhere on the tape.

If I take a Turing machine to add two numbers together from the tape and 
write the result on the tape, there's nothing that says a UTM running that 
program will read two numbers off the tape and write the result 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.

Alright, so you're arguing over the word "is". Fair enough. You're saying 
that your statement "has to be rewired" is to be interpreted as logically 
implying it's incapable of being rewired into a universal machine.

I don't agree that most people interested in the subject would interpret 
your sentence that way, but if you do, sure, you've defined your statement 
to mean that, so there ya go.

I would have said "if it can't be rewired into a universal machine, then you 
have to rewire it for every calculation."

>> 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.

But the whole magic of the property is that you *can* build such an 
interpreter. Before the UTM was invented, it wasn't anyways clear to anyone 
that such a thing was possible. Nobody knew that the rules of arithmetic 
were adequate to express the rules of arithmetic.

> I therefore argue that this low-level perspective is pure nonsense in 
> this discussion.

I disagree.

>>> 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, that's exactly what Turing did, which is why he's still world famous. :-)

>> 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).

Fair enough. Obviously I meant to say if you have something remotely close 
to being a turing machine which you can rewire the state machine of.

> I cannot help but note that for someone demanding from /me/ precise 
> mathematical definitions, you're surprisingly lax in your own wording.

You're taking this way too seriously. You can win.

>  > 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).

No. One symbol is what's stored on one position the tape, which may be more 
than one bit.  I think the minimum turing machine is 28 states and 3 baud or 
something.

>> 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?

CPU.  I.e., the hardware only interprets one opcode.

> 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.)

There's no ROM. There's just one instruction reading data out of the memory.

>> 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.

You're making ambiguous statements (as am I, by the very nature of language) 
which we're interpreting differently, is all.

-- 
   Darren New, San Diego CA, USA (PST)
   I ordered stamps from Zazzle that read "Place Stamp Here".

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