Thursday, July 30, 2009

Along Came Leonhard Euler

"You can drink from the river without drying it up as long as you don't stop the rain or snow upstream"

Perhaps a simple analogy of balanced economics, but one must realise that credit is debt, and investment is asset. Is this all there is to it? What does work have to do with it? Gravity pulls together, heat transforms. Conservation of matter and energy claims that the system is closed. Work is defined as moving mass by force over distance and time. Not necessarily a product of pathetic fallacy, yet termed that way for convenience of agreement.

Convergence and divergence of finite and infinite series has been a sort of backbone to the body of modern technology seeking to determine its own existence by modifying an analysis of process.

Science News

"...the series of absolute values is the harmonic series, which has been
known to diverge since the 14th century (at least)."
http://home.att.net/~numericana/answer/analysis.htm#targetsum

"...it is always possible to add enough terms of the series to make up for
any (positive or negative) difference between the current sum and the
target S. That's because the series of the absolute values is divergent
(so both the series of negative terms and the series of positive terms
must be divergent, or else the whole series would not be convergent)."

"...simple convergence does not tell you much about the limit. The limit of
continuous functions may not be continuous..."

"Worse, the integral of the limit may not be equal to the limit of the
integrals..."

"This is why the notion of uniform convergence was introduced: We say
that a sequence of functions fn defined on some domain of definition D
converges uniformly to its limit f when it's always possible for any
positive quantity e to exhibit a number N(e) such that whenever n is
more than N(e), the quantity |fn(x)-f(x)| is less than e, for any x in
D. (Note that a "domain of definition" is not necessarily a "domain"
in the sense of an open region, ita est. Whenever it's critical, make
sure to specify which meaning of "domain" you have in mind.)"

"Uniform convergence does imply that the integral of the (uniform) limit
is the limit of the integrals. It also implies that the (uniform)
limit of continuous functions is continuous. Since you have a
discontinuous limit here, the convergence can't possibly be uniform..."

"The above settles the question, but you may also want (for educational
purposes) to show directly that it's not possible for a given (small
enough) quantity e>0 to find an N such that fn(x) would be within e of
its limit for any x whenever n>N. "

http://home.att.net/~numericana/answer/analysis.htm#targetsum

Why fly?



"Fool me once, shame on you. Fool me twice, shame on me."

Simulations for meta processes in civilized life

Concepts such as economics, politics, empire building, or development are disciplines of human dynamic life. Recent events in the news have spawned a rise in documentaries in the media not defined as simply children's entertainment.

There are number of freeware applications for the personal computer running Windows, Linux, or Apple-Mac software. Yet the realtime processes these programs represent, run on different parameters.

As teaching tools they are as good as text books, only easier to keep more information in and faster at doing the math than most people ability by natural means.

The trade offs are an increase in recource demand, frequency to re-evaluate the results, frequency to change the inputs as older output becomes subject to change.

Thus, as someone once said, "We can't predict the past, only point to a possibility that it happened." The future fares no better. Inductive reasoning runs behind deductive reasoning in accuracy of conclusion.

If any progress remains sustainable, it must follow a path of close approximation to all truth, whether it is affecting it or not.

I found a real tidy open source simulation during a search for freeware simulations and games.

The name of it is, "LinCity", and can still be downloaded cost free from SourceForge. Here's the link to the page: http://lincity.sourceforge.net/

I have more applications like this one that run models on a personal computer as do most users that play and collect games.

Another I can think of with some value as a teaching tool is Sim-Dilemma. Available for download also at SourceForge.net Here's the website link: http://simdilemma.sourceforge.net/

Wednesday, July 29, 2009

The year was 1922


  • Reasons:





Article Preview
HOW TWO AMERICANS PLANNED TO SETTLE NEAR EAST PROBLEM; Second Part of Long-Hidden Crane-King

Report Put Forth Definite Suggestions. CUTTING UP OLD TURKEY Powers Warned of the Dangers of

Selfish Division and Exploitation. PLAN FOR SEPARATE ARMENIA In Which by 1925 Armenians

Themselves Would Control--A Separate Constantinople.


December 4, 1922, Monday

Page 12, 27176 words

"The method of inquiry, in making our survey of the Asia Minor portion of our task, has necessarily differed from that followed in the study of Syria. For our ultimate duty, according to our instructions, is "to form an opinion of the divisions of territory and assignment of mandates which will be most likely to promote the order, peace and development" of the peoples concerned."



HOW TWO AMERICANS PLANNED TO SETTLE NEAR EAST PROBLEM; Second Part of Long-Hidden Crane-King Report... [PDF]
December 4, 1922 - Article" -Search query NYTimes archived images 1851-1980


The file of the archive is a pdf image; 98792934.pdf

If you want a copy, register as a member with NYTimes.com

Recent article on a speech by Homeland Security spokesperson, Secretary of the Bureau.
http://www.nytimes.com/2009/07/30/us/politics/30security.html

An archive search (above)in The NYTimes.com website turned up an article on the Near East crisis of the time.
turned up an archived NYTimes article published in 1922 concerning the Near East. It had references to the above article in policy mood regarding foreign policy and security issues.

“The consequences of living in a state of fear rather than a state of preparedness are enormous,” she said.


The 1922 article about this post Wilson document contains many refrences to the Near and Middle East as the year was historically between two major world wars. Submarines were already a menace. Diplomacy apparently walked a narrow path between securing recource rights in a world market, and local civil unrest due to trespass and intervention of developing nations seeking empire as a form of political dominance.

Wednesday, July 22, 2009

Amazing math






I'm fascinated with chaos theory in mathematics. I don't really understand it all, but the results of some computations in the theory are quite unusual.

Sunday, July 05, 2009

The Compulsive Imperative Tense

English as a language has a language all it's own. Grammar is a codification of the usage of the terms that words assume in sentences. Sentences are statements. Thus, terms are parts of sentences or statements. Questions are interrogative statements, whereas sentences are propositions or affirmations.

A good link to grammar was found at http://grammar.ccc.commnet.edu/grammar/verbs.htm.

Assuming language as the water of culture, the structure of the expression of life in that water is the grammar used to express a thought or idea.

In grammar, the term "mood" is used to indicate a modification of usage by emphasis indicating some emotional amplitude in the statement. Perhaps a sense of urgency or relief. Even denial or affirmation.

Thus, how statements are phrased by term usage indicates something else about the statement than mere subject, predicate, object, modifier, article, etc.

The study of the logic of statements attempts to take into account all the elements (terms) of the set of statements that come to some conclusion.

By examining the logical process of the reasoning that leads to a conclusion(s), and comparing the premise(s) (initial statements) with the conclusion(s), a truth value of the set can be determined.

Products of logical analyses about an argument(s) are, negation or affirmation of the truth value(s) of the statement(s) and the commission of fallacies, (known false arguments).

However, truth or falsity are not exhaustive of possibility. Simple or subtle changes of any term of an argument can change the values of literal meaning, while still implying an opposite.

Truth Tables are tabulated values of statements in a typical logical argument ("proof").

If, for example one changes the value of truth into its negative, "lie" or NOT true, what happens to the truth value of the argument as a whole?

Or if we state: true=false, and make a truth table of an argument which is assumed to be true, "All men are Socrates", then one might believe in frustration that all men are Socrates.

Here's the table: All Men are Socrates=true, but true=false, so all men are not Socrates.

Expanded with another statement; Socrates was a man=false. (Cannot be proven, Socrates of Greek antiquity is not living and cannot be examined for gender.) But, false=true so Socrates was not a man by reason of logic, but by reason of faith. Do you personally know Socrates the Greek philosopher of ~500 B.C.E.? Faith=acceptance of testimony as valid.

Ah ha, so if All men are men=true, and Socrates was a man=false, All men are socrates=true because true=false. Not only that, but the truth of "All men are men" is also in question. The Bible implies that "men" (the word) is not gender specific as it is used to refer to all members of the species. You would be expected to have a difficult time trying to prove the argument if the definitions are not tautologically simplified as spade=spade.

Tricky logic is an algebraic nightmare. Just as a plumber or electrician might reverse the on/off positions of valves and switches, the confusion requires some analysis as to the validity of the logic as a predictor of truth. Archives from the films of the thirties show all sorts of strange situations for the sake of comedy. The 'Three Stooges' being no exception.

Saturday, July 04, 2009

What is the Meaning of LIfe?

The Golden Mean [Golden Ratio] (1+sqrt(5))/2

"Professor Sever Tipei sent this in response to a student who asked about the Golden Ratio in music:
The golden mean ratio can be found in many compositions mainly because it is a "natural" way of dealing with divisions of time. One can find it in a lot of works by Mozart, Beethoven, Chopin, etc., etc. It is a question if it was used in a deliberate way or just intuitively (probably intuitively). On the other hand, composers like Debussy and Bartok have made a conscious attempt to use this ratio and the Fibonacci series of numbers which produces a similar effect (adjacent members of the series give ratios getting closer and closer to the golden mean ratio). Bartok intentionally writes melodies which contain only intervals whose sizes can be expressed in Fibonacci numbers of semitones. He also divides the formal sections of some of his pieces in ratios corresponding to the golden mean. Without going into much detail, Debussy also does this in some of his music and so does Xenakis (a composer who writes exclusively by using stochastic distributions, set theory, game theory, random walks, etc.) in his first major work, "Metastasis". The idea is not new, already in the Renaissance composers used it and built melodic lines around the Fibonacci sequence -just like Bartok's "Music for strings, percussion and celesta".
See also Erno Lendvai Bela Bartok : Analysis of His Music
Dr. Sever Tipei, Professor of Music Manager, Computer Music Project of the University of Illinois Experimental Music StudiosUrbana, Illinois 61801, USA" -http://www.hep.uiuc.edu/home/karliner/golden.html

So What?

For openers, I would like to quote Bertrand Russell. The work dates back to 1917, about the time of the First World War. This horrible conflict, optimistically but falsely labeled, "The war to end all wars" left many nations of the modern era in tatters of social and physical ruin. So why is the work of a philosopher from that period of time significant? Probably depends on whether war is a natural or artificially contrived phenomenon.

Bertrand Russell:

"Four questions thus arise in considering the truth or falsehood of
mysticism, namely:
I. Are there two ways of knowing, which may be called respectively
reason and intuition? And if so, is either to be preferred to the
other?
II. Is all plurality and division illusory?
III. Is time unreal?
IV. What kind of reality belongs to good and evil?
On all four of these questions, while fully developed mysticism seems
to me mistaken, I yet believe that, by sufficient restraint, there is
an element of wisdom to be learned from the mystical way of feeling,
which does not seem to be attainable in any other manner. If this is
the truth, mysticism is to be commended as an attitude towards life,
not as a creed about the world. The meta-physical creed, I shall
maintain, is a mistaken outcome of the emotion, although this emotion,
as colouring and informing all other thoughts and feelings, is the
inspire of whatever is best in Man. Even the cautious and patient
investigation of truth by science, which seems the very antithesis of
the mystic's swift certainty, may be fostered and nourished by that
very spirit of reverence in which mysticism lives and moves.

I. REASON AND INTUITION[3]
Of the reality or unreality of the mystic's world I know nothing. I
have no wish to deny it, nor even to declare that the insight which
reveals it is not a genuine insight. What I do wish to maintain--and
it is here that the scientific attitude becomes imperative--is that
insight, untested and unsupported, is an insufficient guarantee of
truth, in spite of the fact that much of the most important truth is
first suggested by its means. It is common to speak of an opposition
between instinct and reason; in the eighteenth century, the opposition
was drawn in favour of reason, but under the influence of Rousseau and
the romantic movement instinct was given the preference, first by
those who rebelled against artificial forms of government and thought,
and then, as the purely rationalistic defence of traditional theology
became increasingly difficult, by all who felt in science a menace to
creeds which they associated with a spiritual outlook on life and the
world. Bergson, under the name of "intuition," has raised instinct to
the position of sole arbiter of metaphysical truth. But in fact the
opposition of instinct and reason is mainly illusory. Instinct,
intuition, or insight is what first leads to the beliefs which
subsequent reason confirms or confutes; but the confirmation, where it
is possible, consists, in the last analysis, of agreement with other
beliefs no less instinctive. Reason is a harmonising, controlling
force rather than a creative one. Even in the most purely logical
realm, it is insight that first arrives at what is new.
Where instinct and reason do sometimes conflict is in regard to single
beliefs, held instinctively, and held with such determination that no
degree of inconsistency with other beliefs leads to their abandonment.
Instinct, like all human faculties, is liable to error. Those in whom
reason is weak are often unwilling to admit this as regards
themselves, though all admit it in regard to others. Where instinct is
least liable to error is in practical matters as to which right
judgment is a help to survival: friendship and hostility in others,
for instance, are often felt with extraordinary discrimination through
very careful disguises. But even in such matters a wrong impression
may be given by reserve or flattery; and in matters less directly
practical, such as philosophy deals with, very strong instinctive
beliefs are sometimes wholly mistaken, as we may come to know through
their perceived inconsistency with other equally strong beliefs. It is
such considerations that necessitate the harmonising mediation of
reason, which tests our beliefs by their mutual compatibility, and
examines, in doubtful cases, the possible sources of error on the one
side and on the other. In this there is no opposition to instinct as a
whole, but only to blind reliance upon some one interesting aspect of
instinct to the exclusion of other more commonplace but not less
trustworthy aspects. It is such one-sightedness, not instinct itself,
that reason aims at correcting.
These more or less trite maxims may be illustrated by application to
Bergson's advocacy of "intuition" as against "intellect." There are,
he says, "two profoundly different ways of knowing a thing. The first
implies that we move round the object: the second that we enter into
it. The first depends on the point of view at which we are placed and
on the symbols by which we express ourselves. The second neither
depends on a point of view nor relies on any symbol. The first kind of
knowledge may be said to stop at the _relative_; the second, in those
cases where it is possible, to attain the _absolute_."[4] The second
of these, which is intuition, is, he says, "the kind of _intellectual
sympathy_ by which one places oneself within an object in order to
coincide with what is unique in it and therefore inexpressible" (p.
6). In illustration, he mentions self-knowledge: "there is one
reality, at least, which we all seize from within, by intuition and
not by simple analysis. It is our own personality in its flowing
through time--our self which endures" (p. 8). The rest of Bergson's
philosophy consists in reporting, through the imperfect medium of
words, the knowledge gained by intuition, and the consequent complete
condemnation of all the pretended knowledge derived from science and
common sense.
This procedure, since it takes sides in a conflict of instinctive
beliefs, stands in need of justification by proving the greater
trustworthiness of the beliefs on one side than of those on the other.
Bergson attempts this justification in two ways, first by explaining
that intellect is a purely practical faculty to secure biological
success, secondly by mentioning remarkable feats of instinct in
animals and by pointing out characteristics of the world which, though
intuition can apprehend them, are baffling to intellect as he
interprets it.
Of Bergson's theory that intellect is a purely practical faculty,
developed in the struggle for survival, and not a source of true
beliefs, we may say, first, that it is only through intellect that we
know of the struggle for survival and of the biological ancestry of
man: if the intellect is misleading, the whole of this merely inferred
history is presumably untrue. If, on the other hand, we agree with him
in thinking that evolution took place as Darwin believed, then it is
not only intellect, but all our faculties, that have been developed
under the stress of practical utility. Intuition is seen at its best
where it is directly useful, for example in regard to other people's
characters and dispositions. Bergson apparently holds that capacity,
for this kind of knowledge is less explicable by the struggle for
existence than, for example, capacity for pure mathematics. Yet the
savage deceived by false friendship is likely to pay for his mistake
with his life; whereas even in the most civilised societies men are
not put to death for mathematical incompetence. All the most striking
of his instances of intuition in animals have a very direct survival
value. The fact is, of course, that both intuition and intellect have
been developed because they are useful, and that, speaking broadly,
they are useful when they give truth and become harmful when they give
falsehood. Intellect, in civilised man, like artistic capacity, has
occasionally been developed beyond the point where it is useful to the
individual; intuition, on the other hand, seems on the whole to
diminish as civilization increases. It is greater, as a rule, in
children than in adults, in the uneducated than in the educated.
Probably in dogs it exceeds anything to be found in human beings. But
those who see in these facts a recommendation of intuition ought to
return to running wild in the woods, dyeing themselves with woad and
living on hips and haws."
-Mysticism and Logic and Other Essays, Bertrand Russell,
PROJECT GUTENBERG EBOOK MYSTICISM AND LOGIC
EBook #25447 Available from http://www.gutenberg.org/

Since scholarship is too often very complex, the discussion will continue as convenient but not necessarily necessary. Posted this 4th July 2009