Rob (01)
Thanks for the topic. (02)
I went back and read it in the context of Turing and halting steps as
well as Hilbert's problems. (03)
But I am referring to the fact that living and cognitive systems can at
least imagine Non_Physical_World and create math formalisms, just as
higher order Turing machines are not yet physically possible or yet
discovered or solved, and this is so because we do not have ability to
solve many math problems today as in some of physics. People are now
only beginning to solve some math postulated by Hilbert, Ramanujan etc. (04)
Because of neural and cognitive evolution, hopefully, we are more
intelligent in some aspects of reasoning than (a lower expressive level
of) some animals. (05)
Thus Turing Machine of higher orders are still like a theory AND ARE
LIKE HUMAN MIND IMAGINATIONS THAT DO NOT HAVE TO BE TESTED BY PHYSICS
ALONE TODAY. IMPLYING THAT LIFE FORMS HAVE NO OBLIGATION TO BE VERIFIED
BY PHYSICAL LAWS ALONE (there is chemistry, hormones, genetics, and
higher order of life that we are trying to understand in biology).
Cognition is a very fortunate quality of human forms, but we know that
animals have ways of predicting Tsunamis, floods etc. Yes they include
in their physical form - laws of physics, you can not save a brain from
gravity fall, but it can think beyond gravity and that is also the hope
from Math. (06)
(P.S. Capital Letters are accidental typos) (07)
Thanks.
Ravi (08)
(Dr. Ravi Sharma) Senior Enterprise Architect (09)
Vangent, Inc. Technology Excellence Center (TEC) (010)
8618 Westwood Center Drive, Suite 310, Vienna VA 22182
(o) 703-827-0638, (c) 313-204-1740 www.vangent.com (011)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Rob Freeman
Sent: Thursday, February 07, 2008 11:31 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Axiomatic ontology (012)
Ravi, (013)
I think you are saying our minds, exemplified by mathematics, are not
limited by the physical world. That may be, but mathematics has its
own limitations, and they bear an interesting relationship to
limitations in general cognition, physical laws etc. (014)
Have you read anything of Chaitin's Omega? (015)
-Rob (016)
On Feb 8, 2008 11:33 AM, Sharma, Ravi <Ravi.Sharma@xxxxxxxxxxx> wrote:
>
> Rob
>
> If it were pure math (they can afford to neglect current information
or
> data i.e. devoid of compulsion for conforming to observation), it can
> postulate infinite accuracy for position and momentum simultaneously
and
> not obey today's physical laws?
>
> But how will they then relate to reality? In life sciences and
cognitive
> sciences they still can! In that case they are only bound by speed of
> mind (Thought) and not of Photon (light). As I write this message, I
> have cognitively (conceptually) traversed across universe and returned
> but in he same period the photon has not even traveled half way to the
> Sun.
>
> Without such freedom to axiomatic ontology practitioners (and
> mathematicians and logic experts), we physicists could not take refuge
> in the wonderful Riemannian formalism for relativity, Set theory and
> Group theory, Graphs and Hilbert Space for Quantum phenomena or MHD
> (CFD) solutions for turbulent plasmas or in complex numbers required
in
> quantum field theories.
>
> Mathematics is not necessarily constrained by Information density.
> Physics is (as even NSA is) bound by conveyance or transfer of
> information, whether through quantum, bioinformatics, other finite
media
> whether photon, lasers, etc, or through use of so called
> less-intelligent life species! Even butterflies and birds navigate
> beyond us, dogs can hear better etc.
>
> "Information density in mind" (or cognitive versus physical systems
> based) could perhaps be considered a "good Thread to pursue".
>
> Let me quote from Sanskrit again:
>
> "That mind of ours (poor but approximate translation for "Manas")
which
> wanders when awake, and so in sleep, and which travels faster than
that
> the fastest of lights, should have noble (auspicious) thoughts!"
>
> Neurons still allow us to beat at least sequential decisions by apply
> our experience and neural networks, these perhaps can be further
> strengthened by collaborative synergies such as Ontology CoP?
>
>
>
> Thanks.
>
> Ravi (017)
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