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Archive for January, 2010

Re: neurology's abuse of mammals … perception

cija…@zedat.fu-berlin.de wrote:

 >
 > (Copyright 1998 by LSD Weaver, parts of the text already copyrighted
 > 1997 in my book "…The Mind …")
 >
 > Maybe you could stop cutting optic nerves of others and the like?!
 >
 > >Some animals (cats) still demonstrate vision awareness even though
the optic
 > >nerves have been cut.
 >
 > Of course they have that, they have whiskers and sensor hairs on
their
 > body & legs & tail and they have ears and bunches of different cells
 > so on.
 >
 > What you think to be optics is just a very narrow range of a vast
band
 > of frequencies. And the same as when you switch to Carlos Castaneda’s
 > "seeing"  and the same as some who can hear high  can hear when you
 > send brainwaves,
 > a lot of things can be perceived on very many frequencies.

You rooted around in there and found the "concept" of frequency,
well good for you.

Carlos Castaneda "sees" in the millimeter band. He broadcasts
at 100 GHz, bandwidth of 1GHz, PCM. He has extra metal in his
head to support thought beams with power peaks of 10 KW.

 —
 Jim

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Theorem of Ulam in Jech, Set Theory

I’ve got some difficulties with the Theorem of Ulam as posed in
  Thomas J. Jech, Set Theory (Theorem 66 on page 297).
The statement is that, provided there is a nontrivial measure
on some set S, then *either* there exists a two-valued measure
on S and the cardinality of S is greater than or equal to the
least inaccessible cardinal, *or* there exists an atomless
measure on $2^{\aleph_0}$ and $2^{\aleph_0}$ is greater than
or equal to the least weakly inaccessible cardinal.

My problem is concerned with the either-or-part of the statement.
The proof of the Theorem is done in a series of lemmata and is
finished at the bottom of page 303. There Jech says that if there
is a nontrivial measure on S, then *either* this has an atom *or*
it is atomless, then going on combining some lemmata where nothing
is said about the cardinality of S in the atomless case. I do not see
how this can be used to prove the Theorem. Why is it impossible for
some set S to admit two measures, one with atoms and the other one
atomless?

Any hints?

   -Ingo Lepper

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CADE-15 Tutorial 'Clause Normalform Tableaux'

                        CALL FOR PARTICIPATION

                         CADE-15 Tutorial on

                       Clause Normalform Tableaux

                        Monday, July, 6, 1998

                Peter Baumgartner and Ulrich Furbach
                   University of Koblenz, Germany,
                   http://www.uni-koblenz.de/~peter/
                   http://www.uni-koblenz.de/~uli/

[ LaTeX version included below ]

General
——-
Tableaux offer a unifying view to various calculi which are used in
modern high performance theorem provers and logic programming systems;
they are a major deduction paradigm used in the German research
programm "Deduction" and have been shown there as a serious
alternative to resolution-based systems.

Tableaux are furthermore attractive as a framework to compare calculi
which appear different on a first glance. In the tutorial we will
concentrate on this aspect. We will cover top down calculi like
connection calculi and model elimination as well as bottom up
procedures such as Hyper Tableaux and SATCHMO-like procedures. Special
interest is on variants of these calculi which do not use
contrapositives of clauses and hence allow a procedural logic
programming view of clauses.

Objective of the Tutorial
————————-
The main issue of this tutorial is to describe the spectrum of clause
normal form tableau based theorem proving, including problem solving
questions and the relation to other calculi. Especially the latter may
help to demonstrate the possibilities of tableau techniques to
describe and to improve proof procedures for first order clause normal
form theorem proving.

For the tutorial, we assume that participants know basics of
first-order theorem proving.

Contents
——–

I From analytic tableaux to clause normal form tableaux.

Sequent Systems and Tableaux for non-clausal logic (in brief).
Unification in Tableaux.

II Goal oriented calculi.

Bibel’s connection calculi and its relation to Loveland’s model
elimination. Refinements of model elimination and their properties
(regularity, proof procedures, confluence). Proof Procedures based on
the PTTP technique. Relation to other proof procedures like
nearHorn-Prolog or Plaisted’s problem reduction formats. Answer
Computing and Logic Programming applications.

III Bottom up computation and model generation.

SATCHMO-like calculi as tableau calculi. Hypertableaux and its
relation to SLO-resolution and Plaisted’s Hyper Linking
calculus. Proof search in confluent tableau calculi: Billons
Disconnection calculus, an improved Hypertableau calculus, connection
calculi with rigid variables. Applications for non-monotonic reasoning
and qualitative and diagnostic reasoning.

Registration
————
Please use the CADE registration form

http://aida.intellektik.informatik.th-darmstadt.de/~cade-15/RegoForm….

Deadline for early registration is May, 15.

Further information
——————-
CADE-15 Web Site — http://www.th-darmstadt.de/cade-15/
TUTORIAL Web Site — http://www.uni-koblenz.de/~peter/cade-15-tutorial/

Latex call for participation:

\documentstyle{article}

%%%%%% Setting of the various dimensions
\setlength{\textwidth}{17.1cm}
\setlength{\textheight}{27cm}
\setlength{\hoffset}{-3cm}
\setlength{\voffset}{-3.7cm}

%%%%%% definition of the macros: this should not be edited
\newenvironment{Presentation}{\noindent
                        % For general presentation:
                        \newline}{~\newline}

\begin{document}
\thispagestyle{empty}
\begin{center}
                       {\Huge\bf CADE-15}
\\[.6cm]
{\LARGE The 15th International Conference on Automated Deduction}\\[.4cm]
{\Large\it July 5-10, 1998, Lindau, Germany}\\[6mm]

                  {\LARGE\bf Clause Normalform Tableaux}
\\[.6cm]
{\Large\it July 6}
\\[.6cm]
{\Large\bf Peter Baumgartner and Ulrich Furbach}
\\[.6cm]
{\LARGE Call for Participation}
\end{center}

\begin{Presentation}
        % Tutorial presentation: Describe here the general
        % purpose of your tutorial and the addressed topics
        % adjust \vspace{12cm} according to the size of your description.

%\vspace{12cm}
% This seems to be slightly more convenient:
%\noindent\vbox to 12cm{
%  \begin{minipage}{\textwidth}
\paragraph{General.}
Tableaux offer a unifying view to various calculi which are used in
modern high performance theorem provers and logic programming systems;
they are a major deduction paradigm used in the German research
programm “Deduction” and have been shown
there as a serious alternative to resolution-based systems.

Tableaux are furthermore attractive as a framework to compare calculi
which appear different on a first glance. In the tutorial we will
concentrate on this aspect. We will cover top down calculi
like connection calculi and model elimination as well as bottom up
procedures such as Hyper Tableaux and SATCHMO-like procedures.
Special interest is on variants of these calculi which do not use
contrapositives of clauses and hence allow a procedural logic
programming view of clauses.

\paragraph{Objective of the Tutorial.}
The main issue of this tutorial is to describe the spectrum of clause
normal form tableau based theorem proving, including problem solving
questions and the relation to other calculi. Especially the latter may
help to demonstrate the possibilities of tableau techniques to
describe and to improve proof procedures for first order clause normal
form theorem proving.

For the tutorial, we assume that participants know basics of
first-order theorem proving.

\paragraph{Contents.} \mbox{}\\
\emph{I\quad From analytic tableaux to clause normal form tableaux.} \\
Sequent Systems and Tableaux for non-clausal logic (in brief).
Unification in Tableaux.\medskip\par

\noindent \emph{II\quad  Goal oriented calculi.} \\
Bibel’s connection calculi   and its relation to
  Loveland’s model elimination.
Refinements of model elimination and their properties
  (regularity, proof procedures, confluence).
Proof Procedures based on the PTTP technique.  
Relation to other proof procedures like nearHorn-Prolog or
  Plaisted’s problem reduction formats.
Answer Computing and Logic Programming applications.
\medskip\par

\noindent \emph{III\quad Bottom up computation and model generation.}\\
SATCHMO-like calculi as tableau calculi.
Hypertableaux and its
  relation
to SLO-resolution and Plaisted’s Hyper Linking calculus.
Proof search in confluent tableau calculi: Billons
  Disconnection calculus,
  an improved Hypertableau calculus, connection
  calculi with rigid variables.
Applications for non-monotonic reasoning  and qualitative and
  diagnostic reasoning.
%  \end{minipage}
%\vfill}

\end{Presentation}
~~\\[3mm]

\vspace{.3cm}
\begin{center}

\vspace{.5cm}
\fbox{\bf TUTORIAL Web Site — \tt http://www.uni-koblenz.de/~peter/cade-15-tutorial/}

\vspace{.5cm}
\fbox{\bf CADE-15 Web Site — \tt http://www.th-darmstadt.de/cade-15}

\end{center}
\end{document}


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Peter Baumgartner                         Universitaet Koblenz-Landau
Tel:  (+49) 261/9119-426                  Institut fuer Informatik
Fax:  (+49) 261/9119-496                  Rheinau 1
mail: pe…@uni-koblenz.de                D-56075 KOBLENZ
WWW:  http://www.uni-koblenz.de/~peter/   Germany
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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KNOWLEDGE

Hi all.

The subject of "knowledge" comes up here a lot, off and on, and elsewhere.
I shall add my naive tuppence, a simple approach to the matter, which
satisifies me, at least till somebody shoots it down.  As I have many
anti-fans in these newsgroups, that should not take too long.

No doubt these naive ideas have already been expressed before, at
fairly intolerable length, in various philosophical tracts, and have
been much debated in all directions.  Alas, a philosophobe like myself
is hardly likely to know any detail thereof.

As was mentioned recently, the "standard" attitude toward knowledge
is that of
              "justified true belief".
               ~~~~~~~~~~~~~~~~~~~~~
Various odd examples are given to show that none of this can be dropped,
and there have even been attempts to add various fourth words into it.

IMHO, this approach is all wrong.  Trying to crystallize a concept
into such a jewell-phrase is bound to be trying, and even if it becomes
useful as having proverb status, this one is still badly off.

For a start, knowledge does neither have to be true, nor a belief, nor
any combination of these. (So we can just ignore the "justified"!)

For instance, I know that Zeus married his sister.  It is not part of
my belief, but it is part of my knowledge.  For a Greek peasant of the
hellenic dark age it was both knowledge and belief.  For most moderns
it is neither.  For the Greek peasant child, it might be part of
his beliefs but not knowledge, (maybe at a bit of a stretch!)

So, as we use "knowledge" in all cases, what are we to do?

It seems to me, the obvious and simple answer is always to define
knowledge in a CONTEXT.  Knowledge, is facts from some (possibly
implicit) background canon of agreed facts; only some of which may
be known by any particular person, (and indeed some of which may be
unknown by ANY of the people involved, e.g. if they are only on record.)

So, in one context I can say: "I know that Thor makes thunder", and be
correct.  But I can say the same in another context, and be lying.

Seems simple enough so far.  And, I dare say, would be a very simple and
effective approach to the concept of knowledge in an AI system, should
such folk possibly be concerned about such a matter.

Everyone will clamour – "What about *absolute* knowledge, in general,
based on absolute truth".   This gets close to "unassailable beliefs"
again, which we know is a dodgy issue.  So don’t necessarily expect
that "absolute knowledge" is going to be very meaningful.

But an obvious approach might be, "the context in which the agreed
canon of facts are all those TRUE statements about the universe, as
determined by what people ultimately find out about it".

I doubt though, that this could stand up to much scrutiny.  Simple
middle-sized things that no longer change might qualify – e.g. it is
probably absolute knowledge that Paris was the capital of France between
1600 and 1990.  But we daren’t go much further than these brute facts.
It was recently "(absolute?) knowledge" that gravity was an attractive
force with an inverse square law; but not altogether so any more. It
is doubtful if "electrons are charged particles" will be knowledge in
200 years time, indeed in some contexts it is already quite doubtful.
It is doubtful if "there was a big bang" or "evolution is true" and many
other such can be knowledge at all, merely on the grounds of ambiguity,
an ambiguity that can hardly be resolved except by changing the statements
so much that they become something else altogether.  At the moment, in
the current academic context, they are agreed facts; but are hardly
likely to qualify as "absolute".

So summarising then:-

1) To have knowledge, one must have a bunch of people in some context;

2) and a (possibly extendable) canon of facts agreed between them;

3) then you KNOW something if you are in the context, and it is one of
   those facts, and you have immediate(ish) mental access to the fact.

Vital note – there are no remarks here about TRUTH or BELIEF, either way.

Too simple really.
Bound to be major problems there…

——————————————————————————-
             Bill Taylor            W.Tay…@math.canterbury.ac.nz
——————————————————————————-
                     You are what you remember.
——————————————————————————-

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Help : Give me Karnaugh-Map Coding Program..

I  want to study "Electronics".

Give me K-map source-program.

If the program is programmed with C-language,
I will happy more…

Thanks for any reply.

    reply e-mail : kyun…@hyowon.pusan.ac.kr

Please reply anything…

                            from Nam-kyu, Kang in Korea.

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Logic of Trust ?

I’d be interested in knowing about any literature pertaining
to the notion of a Logic of Trust".

Hilbert Levitz
lev…@cs.fsu.edu


Hilbert Levitz
Department of Computer Science
Florida State University
Tallahassee, FL 32306 USA
lev…@cs.fsu.edu
http://www.cs.fsu.edu/~levitz

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Lightning Strike

What could be the probability of one getting struck by lightning in
the following scenarios (during a mild/strong lightning storm) :-

1. Getting to the car.
2. Working on the computer.
3. Cooking.
4. Having a shower.
5. Driving a car.
6. Standing outside a building for a smoke.
7. Taking pictures of the clouds.

I guess it’s between 65% and 88%. My results are based primarily on the
instincts and experiences. Pls let us know yous.

Thanks

Derek.

—–== Posted via Deja News, The Leader in Internet Discussion ==—–
http://www.dejanews.com/   Now offering spam-free web-based newsreading

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Decidability Question

I am posting the following question, on behalf of Luis Homero Lavin
Zatarain, who does not have access to this newsgroup.

Please respond in e-mail to HIM       —    la…@tecno.net
and not to me! Thank you in advance.

==================================================================
==================================================================

I am a PhD student in computer science. I have a set of polynomials with
integer coefficients that I want to prove is decidable in the following
sense:

Let Z be the ring of the integers.

Definition.- A polynomial P in Z(X_1,…,X_n) is called positive iff for
every n-tuple (a_1,…,a_n) of positive integers, it holds that
P(a_1,…a_n) is a positive integer.

Definition.-A subset D of Z(X_1,…,X_n) is called decidible iff
there is an algorithm A such that for every P in D, the algorithm A
determines if the poynomial P is positive.

I would like to find out which sets of polinomials have been shown to be
decidable, hoping to find one that contains the set I am interested in, or
an idea on how to prove that the set of polynomials I have is
decidable.

Any pointers to the bibliography will be greatly appreciated.

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Re: [Q] What are these "inferences" called?

k y n n (NOSPAMkEy…@panix.comNOSPAM) wrote:

: I suppose the classical logicians, who seemed to have classified and
: catalogued every possible turn of thought, gave a name to this:
: "deducing" the truth of a proposition because otherwise, nothing of
: "what follows" makes any sense.  For example, I found myself making
: one such inference recently while reading a treatise on algebra.  The
: authors asserted that for any element in the algebra under discussion
: a decomposition as linear combination of certain other elements was
: always possible.  They did not stipulate, however, that such
: representation was unique, and without uniqueness several of their
: subsequent statements became ill-defined.  So the reader had to
: "deduce" uniqueness to salvage the text as a whole.

: I suspect that in "real life" this sort of inference is common and
: probably also indispensable, though I can’t justify it on logical
: grounds.  Is there a name for it?

I would simply call it a presupposition of their view, but don’t know if
there is a name for the act of deducing that they maintain the truth of
this presupposition.

Paul

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Absolutely Nothing Is Absolute (Was Re: Rationalism?)

Alright. I have given in to the temptation to provide a substantive contribution to this thread. You can thank Carl and his argument
for psi piece. Please comment freely.

Forgive me for this, but, I have a certain possesiveness for what follows.

What follows is a copyrighted work. Permission to excerpt for comment or other "fair use" as defined by US Copyright law is hereby
granted so long as said excerpt is attributed to the author. Use for any other purpose, commercial or otherwise without express
written permission of the author is prohibited.

(C) Copyright 1997 by Edwin L. Smith
===========================

Absolutely nothing is absolute.

Now for me is later for him and sooner for her.  Here is there to someone else.  My up, your down. His left, her right.

What you are used to seeing of the world you view through a window, your senses. But this window is located in the middle of the
room. When one steps back and looks at the universe from the outside, one does not see a box, measurable with a fixed yardstick,
timed with an absolute cosmic clock, floating in stationary fluid.  Instead, one sees an ethereal blob, stretching, contorting,
moving, not relative to an external frame of reference, but relative to itself.

When one looks in the window again, normalcy returns, at least in appearance. Items appear to be solid, distances constant,
measurements absolute.

Motions are governed by simple laws in this inside world — laws that become more complex the more carefully they are studied. The
simplicity with which one can describe two billiard balls in a gravityless, frictionless mental laboratory is close enough to what
we see in the gravity-filled, felt-covered world upon which real balls interact that we can convince ourselves of its absolute
truth. It’s simplicity is it own proof.

Reduce the balls to the size of atoms, and increase the speed of their collision to nine tenths the speed of light and the laws are
quite different. Of course, our window into this microworld is quite different as well. We cannot see the subjects of our scrutiny,
but can find out where they were by spraying them with other such balls and seeing where they go and how fast. The rules that
predicted so nicely how our macroworld balls behave cannot even tell us where our atomic-sized balls are now. Or when, for them, now
is.

Return to the macroworld of billiard balls, earth, wind and fire, and we find that even this more predictable world is not so
predictable.  When we add back our gravity and felt, we must also account for the dust, the unevenness of the table, the minuscule
eddies in the air currents and the jumping up and down of the anxious instigators of the collisions of our study as they further
attempt to influence the final outcome of their experiment and sink the 8 ball. Each force, itself describable and perfectly modeled
by simple vector arithmetic, when combined becomes a symphony of effects that happen with such complexity and speed that the
greatest supercomputer ever built could spend until the end of the universe and be unable to calculate, to complete precision, the
exact result of this simple experiment. This is no fault of the computer or its programmer. It is the nature of the nature it
attempts to simulate to be unsimulatable.

The world we see is a grammar. It produces, from a very few simple rules of syntax, an infinite variety of sentences. You can add to
the vocabulary, and even enhance the grammar itself, but you cannot grasp the meaning of its sentences. For, the semantics of the
universe is unknown. The grammar is self-relative, and its absolute underpinnings defy us. Indeed, they may not exist.

To attempt to garner the semantics by studying the syntax is equivalent to proffering, as fact, the Rusellian paradox: “This
statement is false.” In fact, it is easier to settle the truth of such a statement than to seek absolute truth from our
understanding, now or ever, of the universe we see.

————–
The most concrete substance is nothing but an abstraction.

The heaviest, densest rock ever found on earth is almost entirely empty space.

What we feel when we touch it is a force exerted by the electrons of this mostly-empty-space rock on the electrons of our
mostly-empty-space fingers. This force is carried by particles that have never been seen in a laboratory but exist in the
imaginations of particle physicists attempting to build a “theory of everything.”

What we see when we look at it is a minuscule fraction of electromagnetic energy released by the electrons when they get temporarily
excited by energy from the almost-empty-space sun. This energy then excites electrons in your almost-empty-space retina, which
starts a chain of excited electrons into your almost-empty-space brain, your window in the middle of the room.

What we notice when we drop it on our toe is not, as we suspect, because of the rock’s absolute acceleration to the earth, simply
because heavy rocks fall. If we were to look at this from outside the room, we would be surprised to see that the hand holding our
rock is accelerating it away from its preferred, constant speed path towards the earth along a track curved through space-time by
the existence of high-mass protons and neutrons scattered throughout the almost-empty-space earth.

Our universe is an ethereal blob because of the impact highly dense almost-empty-space objects like the earth have on space-time.
But it seems neither ethereal or blobby from inside the room, because the more proletarian vocabulary of the grammar that is our
universe describes it more concretely. The more arcane vocabulary of the theory of general relativity connotes a much different
“real” universe than what we normally see. Yet, the true meaning, if there is one, still eludes us.

The electrons in the rock, which impose upon us an electromagnetic repulsive force, do not float around in space along some neatly
defined orbits, as most people imagine them to. In fact, as suggested before, they do not actually even exist in the sense that we
are used to. We cannot know, at any given moment, exactly where that electron is and what it is doing. It is not simply that we have
no small enough ruler, or even, as quantum mechanics and the uncertainty principle claim, that no small enough ruler could ever,
even in principle, be developed. No, our claim on understanding the nature of the universe is more tenuous than even that. Being
unable, even in principle, to know the answer to a question, suggests that there is no answer. Of several possible answers, no one
is right, no one is wrong. They are simultaneously right, even as they are mutually exclusive. None of them is right, even as one
must be.

As irrational as it sounds, at the quantum level, an object does not occupy one state at the exclusion of others. It occupies a
range of states, indeed an infinite range of states within finite bounds. It is neither here, nor there, nor halfway between, nor
halfway before that. It exists in all these places, and infinitely more, in different degrees, corresponding to probabilities
calculated via complex expressions. Ironically, we can look back in time, and retrospectively determine where the electron was, but
until we did so, it did not exist there. Or more properly, it did exist there, but only partially, as it also existed in those other
places we expected it to be, back when then was now. This is not some mystical, paranormal phenomenon. It is scientific theory,
verified by experiment.

We assume that our world is concrete, because it is our nature to grasp for the concrete. But the only evidence we have that it
exists at all is our perception of it. We know now that that perception is very biased and even incorrect. What we know, as Socrates
noted thousands of years ago, is that we know almost nothing. What we view to be concrete might as well be nothing beyond a figment
of our imagination.

————
Only abstractions are concrete.

If we can doubt that the world around is real, if we start to believe that the real is abstract, can anything be real? When
desCartes said “cogito ergo sum,” he was declaring that his own ability to ponder reality gave him reality enough. Does that really
solve the problem or does it merely evade it? In effect, the cogito accidentally redefines reality. All it proves is that existence
means something. It grants that it is a valid question to ask if something exists, but it does not answer the more fundamental
question of what existence means.

I can invent a number. I could write it down on this paper. The number might have 78 digits. Whichever 78 digit number I choose, it
is almost certainly the first time that that number has ever been written down, expressed or even conceived by any being anywhere in
the universe. The likelihood of the identical number having previously been used is so remarkable that if every intelligent creature
in the universe, however many of them their might be, were to begin writing down random 78-digit numbers, the odds of anyone of them
hitting that number before all of the stars in the universe go super nova is still virtually zero.

So if I write down my number, a curious thing happens. I put into a certain concrete existence something that has always had a
theoretical existence. That this 78-digit number existed before it was expressed is sort of intuitive. It was inevitable in an
infinite time line that this, and every other number would have been eventually expressed. The rules for eventually discovering it
are well established. Start at one, and count until you get there. So we argue that it existed because we could think about how to
generate it, even if we would never, ever have really generated it in the real world.

There are other such truths that we deem to exist even though we have never, as yet, imagined them. The entire field of mathematics
is about discovering, a little at a time, an entire universe of truths that have absolutely nothing to do with the real world. They
are true entirely for the sake of the integrity of the field in which they were discovered. And we know, we absolutely take for
granted, that there are an infinite number of these truths waiting to be discovered that are as concretely true as anything we can
imagine.

In essence, we ascribe a more certain sense of existence to something that does not exist than those things we feel do exist. Things
that we can conceive of must exist, where as those things that we perceive might not. Thomas Aquinas first proved that God exists by
ascribing to him this mental, theoretical existence. Since he was able to conceive of Him, then he has a theoretical existence the
way a random 78-digit number has a theoretical existence even if never expressed. Since Aquinas’ concept of God was one of a being
perfect in every aspect, and since concrete, if you will, real existence was deemed to be more perfect than mere theoretical
existence, God must concretely and really exist. Curious, though, how one might use the upside-down world described herein to draw
the exact opposite conclusion – that a most perfect god would be one that exists only in concept and not in reality, because only
abstract reality is concrete.

————-
The concept of good and evil is a myth.

Well if the abstract is real and the real is abstract, then the boundary between the physical and theoretical worlds takes on a new
life. Religion and philosophy have often argued about which world begot which. Yet, to some lesser or greater degree, the common
wisdom places the physical world as the stage for a set of physical players acting out some sort of cosmic script. Unlike the
behavior of billiard balls, or the derivability of trigonometric identities, the rules of behavior of the world’s less predictable
occupants had to be invented instead of discovered.

Rules of law, rather than predicting behavior are designed to regulate it. Of course, in fact, they do neither very well. The fact
that human behavior is unpredictable does not imply that it is unguided. Just because there might be rules governing that behavior
does not mean those rules can be discovered by us.

Nonetheless, we try to avoid the anarchy that we view would erupt from letting that behavior take its normal, unpredictable turns.
We develop grand systems of ideology, and bestow to them the status of absolute truth, the way we bestow that title to trigonometric
identities. And when certain individuals deviate from this ordained truth, we deem that they have sinned. Then human behavior, being
inherently unregulatable by such dogmatic regimes, we find that almost every individual sometimes sins. So we develop vastly
complicated structures in which we rate the relative severity of these sins, forgiving some, correcting others, harshly punishing
for the greatest.

The cloak in which we wrap our ideological framework is the artificial field of morals. Lacking any real foundation in either
empirical or theoretical study, we justify them through utilitarian and anthropic arguments. A world with law is more orderly and
more just than a world without law, therefore some set of morals is necessary. Since certain sets of morals better fit our intuitive
notion of what works than others, we pick one that seems to better server the purpose to which it will be assigned.

Of course, most moral frameworks claim a religious or spiritual basis. A set of rules passed down on a tablet from on high has not
only the benefit of practicality but the authority of some entity more knowledgeable than the mere mortals to which they will apply.
Yet, despite this pretense of religious basis, it is more likely that the ten commandments were devised by mankind as a way of
battling ancient, genetic aggressive instincts, than handed down by an otherwise very rarely heard deity.

If a grand deity exists, it seems likely, in light of our newly inverted view of the universe, that the true purposes of the world
are much more abstract than simply, “Thou shalt not kill.” The physical world we know is too full of natural violence to make one
believe that artificial violence defies some grand master plan. The idea of a straight-and-narrow path towards a concept we call
“good” in defiance of a force that pushes us to stray that we call “evil” seems very simplistic, and, as one-dimensional in
intuition as it is in model.

If there is to be a purpose served, then, whatever that purpose might be, it is best served by allowing those individuals the freest
rein to explore their personal boundaries between the abstract and the concrete. There is most certainly, for each a right behavior
and a wrong behavior. Occasionally when  the right behavior of one individual abridges the potential right behavior of another, a
compromise must be reached, and a set of rules agreed to by which this compromise is accomplished is a noble, if not implicitly
necessary goal.

What can not be right behavior, though, is the forced abridgment of someone else’s sphere of right behavior. In other words, a
person’s own search for his grand purpose is not served by having some other person’s idea about his grand person imposed upon him.
In a world where my here is your there and your left is my right, and my window in the middle of the room has a slightly different
view than yours, how can you feel justified in being so sure that the understanding you think you have attained in your search for
your grand purpose will be even remotely similar to the understanding I will build? How can you feel so certain, not just that an
absolute right and wrong exist, but that you are so better able to discern them than I?

In a universe where the abstract is concrete and the concrete is abstract, there can be no confidence that the concrete laws of
concrete human beings in a concrete world can even remotely resemble the more real laws of abstract ideas and expressions that so
assuredly are beyond our comprehension. In fact, if we can draw any conclusion at all, it is that each person must explore her own
connection with the absolute truths of the abstract world and how they relate to her behavior in the more relative instantiation of
those truths in the real world. The only “real” evil would be to keep her from doing just that.

——–
Truth is found, not in answers to questions, but in the questions themselves.

If Socrates was right, that we know only that we know nothing, then can we ever really know truth? We believe in the truth of the
abstract, and we question the absolute truth of the real. But what good is Fermat’s last theorem to my decision about which wine to
serve with dinner?

If each of us is to discover our own spiritual self, our own connection with the abstract world, and in so doing, or own sense of
right and wrong in the real world, we seem at first doomed. We could not know a truth if it hit us in the face. How are we to search
for something we can not possibly know?

The universe is a giant web of ideas, some of which are true, some of which are false, and some of which are simply paradoxical.
These ideas interact with a fluid, erratic, relative physical world that is the place in which we actually live. We can not hope to
know the truths of the universe anymore than a Christian can hope to be free from sin. So, like the Christian, we must forgive
ourselves the indiscretion of our ignorance. We must be content to search for the truth, as best we can, and delight in the bits of
wisdom we discover along the way. In so doing, we grow, and we build an identity for ourselves and a relationship with our universe.
Of course, we must be careful along the way to avoid the arrogance that personal wisdom sometimes brings. Sharing discoveries and
insights is acceptable. Ordaining them as absolute truth and insisting that others see them as you do is not.

In the end, if you are to judge yourself against this grand scheme that you can not begin to fully know, how would you proceed? What
standard might you use. What conclusion can we draw that will help us guide our lives in this upside-down, inside-out
abstract-is-real and real-is-abstract universe. Perhaps only the following can be known for certain:

If absolute truth exists, it can not be fully understood by us mere mortals.

We may be able to determine the relative truth of certain ideas in our real world (just as we can measure the relative speed of two
billiard balls, even if we can’t measure their absolute speed relative to some unknown fixed point).

Insightful questions are often a display of relative truth, as they ask, if this is true than might that as well?

In the end, these questions may, by their self-relative nature, offer the only truth we may ever actually know.

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