On Tue, Jun 16, 2009 at 4:29 PM, John F. Sowa <sowa@xxxxxxxxxxx>
All of the topics on your list lead to unsolved research problems,
but they are all related to ontology. In fact, that is the reason
why I am so skeptical about any proposed universal upper ontology.
All of the fundamental issues are still unsolved research problems.
RS> I want to comment on adequacy of mathematics: Yes when used in
> applicable range (e.g. linear, quadratic, etc.) it is elegant andI completely agree. That is why I keep saying that the elegance of
> explains physics very very well.
> But most of Nature, such as many-body problem, is either extremely
> non-linear, tightly coupled, subject to neural-like complex
> situations or such that relevant mathematics is yet to be identified,
> discovered, or applied and often we go to numeric or simulated
the fundamental principles in physics is misleading. Every practical
application of physics (i.e., every branch of engineering) uses
approximations, because the basic equations are unsolvable.
Furthermore, even a single kind of problem in a single branch of
engineering uses a multiplicity of *inconsistent* approximations
for different special cases. For example, computing the air flow
over a wing requires totally different approximations for laminar
flow, turbulent flow, subsonic flow, transonic flow, supersonic
flow, hypersonic flow, etc. Usually, the computations are so
difficult that engineers compute them only for a two-dimensional
special case. Computing 3D flow is many orders of magnitude
more difficult -- but it's necessary for a better approximation.
(But we have to recognize that it is still an approximation.)
If there is no such thing as a one-size-fits all upper level even
for airflow over a wing, how could you imagine a consistent upper
level that covers all of aeronautical engineering? Or every branch
of engineering? Or every aspect of even a single engineering company?
Or every aspect of multiple companies? Or the entire world?
RS> What is the connection to languages? Math is the most precise
> representation of language and stems from reasoning and this isPeople often think that math is more complex than ordinary language,
> the connection with Ontology.
but that is totally false. In practice, every engineering problem
that uses mathematics is *immensely* oversimplified. That kind
of simplification is necessary to make the equations solvable, but
the real world in all its richness is so vastly more complex that
no solutions are computable (or even precisely expressible). For
that reason, we have to use ordinary language, because mathematics
cannot deal with the full complexity of what we talk about.
RS> The richness of language and its brevity like math is derived
> from formulae (Sutras in Sanskrit and as Azamat mentioned BuddhistYes, but each one of those formulae uses a different simplification
> Logic - also derived from Sanskrit) but pre-supposes a lot of
> Context and Concept understanding. This is the fundamental
> requirement for different Ontologies to Interconnect, synchronize
> or inter-operate.
or approximation from the full complexity of reality. Furthermore,
the approximations used for one problem or context are inconsistent
with the approximations used for any other problem. Therefore, it
is impossible to have common consistent formulae (or axioms) that
are sufficiently general that they can be used in all contexts.
RS> I fully concur with your thoughts for Precision - it is for purpose.
Yes, and different purposes require different approximations. As I
often say, the standard for being spherical is vastly different for
meatballs and ball bearings. But the same is true even for different
kinds of ball bearings. The earth is closer to being a true sphere
than most of the things we call spherical in engineering, but it has
a lot of nonspherical features, which we call mountains, valleys, etc.
RS> I am not sure if Tensor Calculus would not need to be modified
> for Kerr formalism for Black-holes and similarly there would be > precise landing on Jupiter's Moon.
> a large number of digits after decimals in the orbit required for
Every formalism we use today will undoubtedly be modified or extended
in the future. Just look at how far physics has come in the past
hundred years. And with every new discovery, physicists begin to ask
many more questions that they had never before been able to imagine.
Peirce stated that point very well:
CSP> It is easy to speak with precision upon a general theme. Only,
> one must commonly surrender all ambition to be certain. It is
> equally easy to be certain. One has only to be sufficiently
> vague. It is not so difficult to be pretty precise and fairly
> certain at once about a very narrow subject.
In short, it is impossible to have general axioms that are completely
certain. The only kind of generalizations that can have any degree
of certainty must be "sufficiently vague".
But it is possible to have low-level microtheories that are "pretty
> precise and fairly certain at once about a very narrow subject."
That is the conclusion that everybody who has worked with large
ontologies has discovered. Doug Lenat discovered it in his work
with Cyc, but Peirce stated the principle a hundred years earlier.
(Dr. Ravi Sharma)
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