Re: functions that halt

From: The Ghost In The Machine (ewill_at_aurigae.athghost7038suus.net)
Date: 05/05/04 

Date: Wed, 05 May 2004 16:00:06 GMT

In sci.logic, Michael Mendelsohn
<keine.Werbung.1300@msgid.michael.mendelsohn.de>
 wrote
on Wed, 05 May 2004 14:16:09 +0200
<4098DB09.94965250@msgid.michael.mendelsohn.de>:
> |-|erc schrieb:
>> "Michael Mendelsohn" <keine.Werbung.1300@msgid.michael.mendelsohn.de> wrote
>> > > > > > > arctan(1)*4 = 3.141592....
>> > > > >
>> > > > > ( arctan 1 * ) 4
>> > > > >
>> > > > > One of those null functions, permissable since the emulator/computer still halts
>> > > > > with null as output. Its only combinations that form infinite loops it must deny
>> > > > > a godel number for.
>> > > >
>> > > > This is patently untrue.
>> > > > In fact, a computable function must not halt.
>> > > > The function that computes arctan(1)*4 does not halt.
>> > > >
>> > > > A computable function writes infinitely many symbols of output.
>> > > >
>> > > > Look it up in Turing.
>> > > >
>> > >
>> > > For the discussion we're only computing a single digit at a time.
>> > > pi =/= 3.14159....
>> > >
>> > > but pi(3) = 4
>> > >
>> > > same result, the notion halt is restored to giving status of being a correct program.
>> >
>> > So what's teh 15th digit of "( arctan 1 * ) 4" ?
>> >
>>
>> F> enter godel number?
>
> You haven't explicitly stated your numbering scheme, which means I can't
> give it to you.
> You only stated that all functions that halt have a Goedel number and
> that this construct halts and has a Goedel number so I assume it has one
> and you can find it.
> Look the quote up above, I left it in.

He (or someone replying to him) did suggest that arctan is symbol 10,
( 11, ) 12, * 13, at one point in this thread. This suggests
that ( arctan 1 *) 4 would have the encoding 11 10 1 13 12 4. This
also suggests that someone doesn't get it; Douglas Hofstadter's
encoding, while ad-hoc, at least had fixed-size tokens.

Then again, the problem isn't the encoding -- the problem is the
fact that one assumes an encoding and constructs the "anti-diagonal"
function.

>
> Michael 

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