Bruce: I wonder why we presume that a "theory of everything" has to be grounded
in physics. (01)
John: The idea of a GUT was first conceived by the physicists, whose theories
are more precise than theories in other empirical sciences. . . . (02)
Versions of calculus are used in all theories of physics . . . Bringing physics
into the discussion seems to be more confusing than enlightening . . . (03)
Bruce: I am still hung up in this issue of abstract symbolic representation of
"real world" processes and objects. (04)
For me, this gets right to the core of how language -- and maybe (?) calculus
-- describes reality -- following the precept I absorbed so many years ago, and
which does seem foundational in its simplicity: "reality is continuous,
concepts are discrete." (does that include calculus?) When I first got into
studying the mathematical structure of language, I was looking at "modeling
languages" and trying to understand the connection between an abstract symbol
or "state in a medium" and some object "in the real world". (05)
Language is composed of "little boxes" with names/labels that define categories
supposedly bounded by known dimensions -- "how we can tell the difference
between a dog and a wolf" -- and what those dimensions are is generally a
matter of social stipulation or convention. Something is inside that
n-dimensional box -- whether it is a wolf or a dog -- but in either case, we
are talking about an abstract symbolic model -- existing in some medium such as
a computer -- which we then map to some real world object ("that animal over
there"). (06)
I remember taking my first course in calculus, and my very smart and respected
teacher Miss Johnson trying to explain the concept of a "limit" -- and
admitting to everyone in the class that she did not understand it very well.
In my case, sadly, it's still true. I have never really grasped the notion of
a "limit" as it is used -- so successfully -- in calculus. (07)
There is this thing about "rational numbers" -- which maybe I abuse by wanting
them to be represented in a finite number of decimal places -- because "that's
the reality of what we can actually do". So, the way I see it, any number in a
finite number of decimal places can be represented in a hierarchical/taxonomic
grid where each further level of decimal place is like the next lowest level of
"taxon" -- with continuity -- the unreachable, the infinitesimal -- at the
bottom of the cascade. (08)
So -- the difference between a wolf and a dog is a matter of degree (in any
number of dimensions) and boundary-value conditions -- that we sneak up on --
like a limit -- in tiny increments, until some "tipping point" is reached. (09)
This line of reasoning (if it IS "reasoning") -- tends to convince me that this
GUT ambition when grounded in physics is eternally vulnerable to the confusion
John mentioned in his first comment in this thread: (010)
"Physicists are the closest to finding a Grand Unified Theory (GUT) of
everything. But every time they find one, it opens up far more mysteries than
it solves." (011)
This is why I am inclined to look for a general solution in "pure mathematics"
-- and probably not "complex" mathematics -- but instead, a kind of mathematics
that is so simple it's almost inconceivable -- "simpler than we can conceive"
-- the kind of definition that might emerge from a famous question like "why is
there something rather than nothing?" (012)
I do tend to be somewhat guided by holistic guesswork and am perhaps vulnerable
to its fantasies -- but I like the title of a book by the Dalai Lama -- "The
Universe in a Single Atom -- the Convergence of Science and Spirituality". The
Dalai Lama is a very well-educated guy -- who has spent his life travelling all
over the world going to conferences and talking to very smart people, including
many leading scientists. (013)
So -- I am inclined to look for a mathematical/conceptual foundation where
something dimensionally confusing happens -- such as "the infinite plugs
directly into the infinitesimal" -- the infinitely large maps directly to the
infinite small -- somehow across descending scales of "self-similar"
("fractal") recursion -- with "everything" that can be conceptualized or mapped
to or described by numbers bounded and described within that framework. As I
see it, natural languages -- and machine languages -- are parsings within that
general framework -- of "all possible conceptual form". (014)
So -- what does this have to do with physics? This might be wrong-headed, but
if physics insists that reality is grounded in ever-smaller particles -- and
every particle has to be bounded in some way that makes it distinct -- in the
end, we are talking about the problem of mapping a complex body or cascade of
interconnected distinctions to some "object in the real world" that supposedly
has these properties. Can we EVER do this without measurement or round-off
error -- ? No -- I would say -- because "reality is continuous and concepts
are discrete." (015)
I tend to want a simple framework defined in pure finite-state math that maps
directly one-to-one to a machine state, where everything in reality is
contained and categorized by dimensional boundary values in a finite number of
decimal places. The "real number line" is probably the bottom level of this
cascade -- as an unreachable/unknowable limit -- that is defined as "unbounded"
in some mysterious way we have not quite conceived. (016)
And at the top of the cascade -- the taxonomic hierarchy of numeric
decomposition -- is the un-namable unbounded undivided infinite unit "one"
("the whole", "the all", "the Tao that cannot be named") also somehow magically
self-similar to every other unit in the cascade all the way back down ("turtles
all the way down") to the infinitesimal as a limit at the bottom. (017)
If we could figure out the top and the bottom of this form, and show how it
maps to itself ("the universe in a single atom"), we might (?) generalize the
principle of conceptual form, whether "bottom-up" and observably mapped to real
experience, or "top-down" and purely transcendental and theoretical -- with
"everything else in between". (018)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
Sent: Tuesday, March 03, 2015 11:17 AM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] Grand Unified Theories (019)
David and Bruce, (020)
David
> Johnson at a Management Accounting seminar in 1992 ...
> "We have come to the end of our ability to understand & describe the
> world around us within the confines of Newtonian physics." (021)
Johnson was about a hundred years late. In the 1890s, physicists began to see
that Newtonian mechanics had serious limitations.
In 1905, the "annus mirabilis", Einstein pointed the way to the future with
four amazing publications: (022)
1. Brownian motion: He showed that particles that are visible
in an ordinary microscope are being kicked around by much
smaller invisible particles. This was the first direct
evidence for the atomic hypothesis. (023)
2. Quantum mechanics: He showed that Planck's theory of radiation
implied that light energy is quantized in discrete photons. (024)
3. Relativity: Physicists knew that Maxwell's equations for
electromagnetism -- which predicted that the speed of light
is the maximum possible speed -- are inconsistent with
Newtonian mechanics. Einstein developed a new theory of
mechanics that is consistent with electromagnetism. (025)
4. Mass-energy equivalence: The famous E=mc^2 and its derivation
from the theory in paper #3. (026)
For a summary, http://en.wikipedia.org/wiki/Annus_Mirabilis_papers (027)
David
> Double entry accounting—to which we are all beholden—was created from
> the same intellectual ferment that produced The Calculus. (028)
Versions of calculus are used in all theories of physics. I don't know what
metaphor Johnson was using. But bringing physics into the discussion seems to
be more confusing than enlightening. (029)
Bruce
> I wonder why we presume that a "theory of everything" has to be
> grounded in physics. (030)
The idea of a GUT was first conceived by the physicists, whose theories are
more precise than theories in other empirical sciences.
Researchers in the other sciences tend to suffer from "physics envy".
They compensate by trying to be "more mathematical than thou". (031)
As Marcus and Davis pointed out, they tend to "decorate" their theories with
abstruse mathematical equations that are more confusing than helpful.
Unfortunately, reviewers and investors who are hopelessly confused by the math,
don't want to admit their confusion. (032)
Bruce
> ideas rule the world. We need to understand ideas -- good ones, bad
> ones, confused ones, crazy ones. It's ideas that cause teenage girls
> to join ISIS. (033)
I agree. The ISIS propagandists wrap their crazy ideas in a thin veneer of
theology. Marcus and Davis were trying to warn investors that a thin veneer of
mathematics can be just as confusing. (034)
John (035)
_________________________________________________________________ (036)
I wonder why we presume that a "theory of everything" has to be grounded in
physics. What about the approach that every "thing" is actually only knowable
as a symbolic representation as some kind of concept -- including fundamental
particles? Seen this way -- a "theory of everything" involves a "universal
theory of concepts" and the issue becomes reliably connecting the abstract
symbolic representation ("the concept") to the "actual empirical object" --
like a fundamental particle -- or any other discernible and bounded/distinct
object. (037)
I like physicist Arthur Eddington's suggestion in his "Fundamental Theory"
(1946): "All the laws of nature that are usually classed as fundamental can be
foreseen wholly from epistemological considerations." (038)
My own feeling is -- what is needed today is a new foundation for mathematics
itself -- a new ontology of mathematical fundamentals -- that interpret in
mathematical terms what Eddington was calling "epistemological" (039)
I like an approach that says something like "all concepts can be constructed
out of dimensions and the fundamental constructive element is a cut (as per
Dedekind) or distinction." You can build any concept taking that approach and
it is 100% linearly recursive and extremely simple. (040)
For me, all of this floats in a framework defined by John Sowa's basic
proposition, as I read it: "concepts are discrete, reality is continuous". We
need to generalize the framework that contains this fundamental truth, and show
how all mathematics -- arithmetic, real numbers, continuous variation --
emerges as attributes of this containing framework. Distinctions within this
framework become "all the concepts in reality". (041)
Do this in a top-down way -- and you get something like the model described in
the Numenta white paper on hierarchical memory, which mostly describes simple
linear recursion. Build it up from the bottom (based on observable empiricism)
-- and you get something like John Sowa's "semantic networks". (042)
I don't know if "neurons" are organized in the way Numenta suggests -- but I'd
say concepts can be -- and neurons support conceptual processing. (043)
We should connect these approaches. We need a "transcendental container" that
can hold all of this in one framework. This mathematical object might be
fairly simple -- if dimensionally a little tricky -- and emerge as the
conceptual foundations for a new and very-much simplified and integrated way to
understand reality. (044)
- Bruce (045)
PS -- ideas rule the world. We need to understand ideas -- good ones, bad
ones, confused ones, crazy ones. It's ideas that cause teenage girls to join
ISIS. (046)
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