[Top] [All Lists]

Re: [ontolog-forum] Can Syntax be Semantic?

To: ravi sharma <drravisharma@xxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Rob Freeman <lists@xxxxxxxxxxxxxxxxxxx>
Date: Thu, 28 Jan 2010 14:57:30 +1300
Message-id: <7616afbc1001271757u47badb1cm97d27f800497a505@xxxxxxxxxxxxxx>
Ravi,    (01)

On Wed, Jan 27, 2010 at 4:47 AM, ravi sharma <drravisharma@xxxxxxxxx> wrote:
> ...
> Is the computational irreducibility similar to irreducible representation in
> group theory?    (02)

Computational irreducibility is Wolfram's word, but I think so, yes.    (03)

Both are random (in the Chaitin sense that there is nothing smaller
which can generate them.)    (04)

You would need to find an analogue of decidability. Russell's paradox
might be a form of that.    (05)

I guess I came across the whole subject from this direction myself.
Not formal group theory, I was considering what would happen if you
tried to learn grammatical classes from word associations. It struck
me you could find a lot more sets of word associations than words, but
that in general the sets would contradict each other. In a sense the
process of learning grammar was not "decidable".    (06)

Actually people started trying to learn grammatical classes from sets
of word associations this way a long time ago. Sure enough they got
contradictory sets. But the assumption grammar should be "decidable"
was so strong they concluded there was a problem with the method.    (07)

More recently this theoretical result has been forgotten and people
working in Grammatical Induction just try to compromise on the
contradictions, perhaps working on the assumption that there shouldn't
be contradictions, so any contradictions they find must not be
important.    (08)

To help with the randomness they find in their grammars, they make
extensive use of probabilities.    (09)

> Or is it so that the problem is not amenable to computation
> (at least with current information)?    (010)

It's quite the opposite! It means the problem is _only_ amenable to computation.    (011)

That undecidability means some problems are not amenable to
computation is the traditional point of view, it is true. But people
only see it that way because they have become so used to thinking
about the world in terms of theory/logic (in the West at least.) Our
traditions demand hard yes/no answers, and when computation fails to
deliver it is tempting to say computation has failed.    (012)

But that is only our expectation about the world.    (013)

What these results suggest is that computation (directly over
observations) may be a better conceptual model, exactly because it
predicts the partial character or "uncertainty" in our conceptual
world which is what we actually find.    (014)

> Penrose talks about computability of mind (processes), is it irreducible if
> so in capacity of today's machines or because we can not yet reduce it to
> computation?    (015)

I wouldn't be surprised if Penrose had never heard of the term
computationally irreducible, which as I say is Wolfram's.    (016)

But Penrose talks about the fact that many problems are undecidable
computationally, which comes to the same thing, yes.    (017)

However the conclusions he draws from that are very different.    (018)

>From what I have read of Penrose he represents an extreme statement of
the traditional point of view. So the opposite of what I am stating.    (019)

Penrose interprets undecidability not to be a representation for
conceptual "uncertainty" in the world, he interprets it to be a
failure of computing to fit his expectations that the conceptual world
be decidable.    (020)

As far as I know, to fulfil his expectation that the conceptual world
be decidable he posits a completely new mechanism. I believe he thinks
there is some mysterious thing going on in "microtubules" in the
brain.    (021)

Independently of whether Penrose is right and there is some other
thing in the brain which makes the conceptual world decidable (though
we don't observe it to be decidable), as undecidability is a basic
property of computation this will be true for all time and has nothing
to do with the capacity of today's machines.    (022)

-Rob    (023)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (024)

<Prev in Thread] Current Thread [Next in Thread>