This web-history speaks most frequently about concepts in mathematics and computing. They will be discussed in the midst of some other concepts, concerning political science. We have not been posting content as frequently as we were a year or so ago, seeing that we have been busied with numerous projects in computer science education. Yet, those have slowed some in light of COVID-19. So, the author thought that he would pick up this writing project again.
In the text, the Emperor of Ocean Park by Stephen L. Carter,
the protagonist is an African American male and law professor who is a
chess-fanatic. He is nicknamed after a great Russian Grand Master, Mischa. As
such, during his life’s situations depicted in the text, the strategic concept
of “zugzwang” is presented.
It, in itself, as shown in this text, is the
“chess-playing” situation were a player is facing an imminent checkmate and any
move which he makes will simply sink him, weakening his position and further
solidifying the situation of the impending checkmate.
This became a blatant
fact of life, as the author was streaming news in his quarantined community, on
yesterday evening, a couple of days after April 1st. It seems that
during the current state of world affairs and the “raging” health pandemic, the
government of the United States of America blindly has accepted healthcare
equipment from countries with which it has had a bittersweet relationship for
numerous decades. This includes the government that spearheaded the former
Soviet Union and China.
This is a humbling experience, where the mightiest and
greatest nation in the world must ask for help from others. Otherwise, it might
collapse. And, this “help” must come from those who its propaganda machine says
are untrustworthy. Yet, if these
countries are truly foes, what will stop them from shipping masks, some
of which are tainted with COVID-19 or other harmful biological agents.
In this war, which every country is currently fighting, the
healthcare workers are a front-line of defense. If their numbers are decimated
by contaminated mask and respirators which cannot be sanitized, who will
America have for defense.
With this as the case, the battle of dominance as a
super-power becomes one of the numbers. As the author’s high school American
government instructor named Jack would say, “the country with the most
citizen’s wins”, if the number of denizens lost in the battle remains fairly
uniform between combatants.
Below is a list of the largest countries in the world based
upon an approximate population:
Rank Country Population
1 China 1,426,279,708
2 India 1,338,558,742
3 United
States 327,527,107
4 Indonesia 263,564,697
5 Brazil 210,193,253
6 Pakistan 194,749,053
7 Nigeria 185,313,910
8 Bangladesh 165,552,994
9 Russia 144,154,086
10 Mexico 129,132,150
11 Japan 127,962,410
Number one is larger than numbers three through seven
combined.
Also, in that, the author has a close relative who has a
small business that manufactures personal protective equipment kit, he is aware
of the fact that the “best priced” wholesale masks, gowns, and nitrile gloves
come from mainland China. And, they likely are the largest supplier of such. If
that nation takes advantage of this “opportunity” while the United States and its
other adversaries are weakened and vulnerable, it could decimate much of the
world’s non-Chinese inhabitants.
Is this cause for alarm? Most likely, it is not. China
could place the Trump-Pence team and the rest of the inhabitants in the world’s
most eminent and well-known super-power with military installations on every
continent in “zugzwang”. Although such a situation would likely not happen, it
would not be a new strategy as far as the United States military is concerned.
It is a well-known fact of history that while smallpox was ravaging the
population of true indigenous Americans along with the rest of the European
settlers during America's early years, the US Army provided those whom they were displacing from the land
with the “gift” of blankets infected with that very same disease. In short, one
should always be cautious when offered a “gift”, especially if it is offered
for free by an adversary when one is desperate for help.
Yet, the leadership in China and the former Soviet Union
likely are above doing such. China simply would not put America’s leadership in
such a “zugzwang”. In fact, the world leadership likely operates much like
organized crime syndicates in a single region, such as a city. They are
simultaneously “friends” and “foes” who have mutual “best” interest. They agree
upon the boundaries of each other’s operations and help each other keep their
individual regions under control.
Consider the vacuum that would be created in the world’s
sociopolitical and economic systems, if America fell over the course of the
next few decades. It would be much like the chaos that one currently sees in
the East and Africa after the removal some of its pivotal and powerful leaders
such as Hussein and Khadafi. And, it might take a century or more before the
reverberations of such a move settles down. That is more instability than anyone
is interested in seeing. Such a political tidal current could wash away many of
the world’s current super-powers.
Yet, all of this had been said so the author might set
the stage for a simple postulate about human behavior and hand-wave through a couple of mathematical suppositions.
“Humans see and perceive what they choose and what they
find pleasing and comfortable, although the contrary might be painfully
obvious.”
As a martyr and the leader of a peaceful insurrection
many centuries ago said while discussing an ancient prophesy…
“[Mat 13:14-15 KJV] 14 And in them is fulfilled the
prophecy of Esaias, which saith, By hearing ye shall hear, and shall not
understand; and seeing ye shall see, and shall not perceive: 15 For this
people's heart is waxed gross, and [their] ears are dull of hearing, and their
eyes they have closed; lest at any time they should see with [their] eyes, and
hear with [their] ears, and should understand with [their] heart, and should be
converted, and I should heal them.”
Yet, men of learning often discount what this leader said
as platitudes and emotional opiates for those of a weak, feeble, and untrained
mind.
Well, those of great learning, especially, in mathematics, let us discuss what is truly irrational. This incredibly
“simple” paradox in modern mathematics, which could result in a dissertation
for more than a pair of docs, has been mentioned before in this web history.
When examining the number sets that we have available,
such as the integral and rational numbers, we have accepted that some
numbers with which we work do not have a rational representation. Yet, is such
true without the removal and banishment of at least one key integer from the
“primitive set” of integral values? We, as mathematicians, both professional
and amateur, accept that values such a π and e have expansions which
are never-ending and do not repeat. These are called “irrational” numbers. It
is “accepted” that such cannot be formed from a ratio of other numbers. It can
therefore be determined that any integers which one can place in a ratio will
produce an expansion that eventually terminates or repeats indefinitely. This
repetition of the terminal digits of such an expression is signaled with the
vinculum, a bar drawn above the final repeating digits of the ratio’s written
expansion.
Yet, what if we make use of this symbol, or an equivalent
one, on the opposite side of the decimal, when working with the number 10. What
is the largest possible power of ten? 10…., one followed by a non-terminating
sequence of zeros. Although one could never render such a number, it can and
should exist based upon the rules of the basic numbering system. And, it would
be an integer, by definition. Plus, it would be less than infinity, because it
is less than 9…, or the number which is a never-ending sequence of nines. And,
what if we take this “largest” power of ten, LPT, and multiply if by π
or e. Thus, we would have the non-repeating, non-terminating integers Zπ
and Ze formed from (π * LPT) and (e * LPT). Then,
what if we divide Zπ and Ze both by LPT? We will have π =
(Zπ
/ LPT) and e = (Ze / LPT), if the LPT aka “the big
honking ten” does exist. And, the irrational becomes rational. At least, for
those who will open their eyes, unstop their ears, and soften their hearts.
Yet, if men will not do such over the trivial, trifling, and niggerling issues
found in numeric manipulation, will they do so over the weightier matters?
And, those great men of learning in academics might
explain away how such a misrepresentation concerning the foundations of
mathematics has persisted over the centuries and undergirds much of the work
done this day is modern STEM fields which will be establishing the
technological infrastructure that this world has for any future millennia that
mankind might see.
And, as for i, it is the “sloppiest little
mathematical bugger” but also is the basis for establishing the set of complex
numbers. Yet, alone, it remains a reckless contraction of mathematical
information. The great geometers, such as Pythagoras and Euclid, would fast
faint at the structuring of such a myopic mathematical misfit. In that, the
value i, represents the root of a square area, it, in essence, is the
measure of at least a pair of the sides of such a shape. A square of area nine
has four sides of length three or negative three, if examining their measures
in the first and third quadrants of the Cartesian plane. So, the true square
root of 9 is the n-tuple (3,3,3,3) or (-3,-3,-3,-3). That is exact and might be
safely condensed becoming (3,3) and (-3,-3) in light of its complex counterpart
and the fact that an area is number with a pair of factors. What is the square
root of a square with an area of -9? Considering its geometric representation
when centered at the origin, starting from that point, and working clockwise,
it would be the n-tuples (-3,3,-3,3) and (3,-3,3,-3). This might be safely
condensed producing (-3,3) and (3,-3) or 3*(-1,1) and 3*(1,-1) instead of 3i.
So, i must truly and simultaneously be (-1,1) and (1,-1).
Does this remind anyone of the superpositions found in
quantum mechanics? Well said. The author loves hearing what you are thinking.
Notice the information concerning orientation and
direction lost when one simply uses the complex number, i. Doing so,
hides the geometric nature of square roots which can be vital when they
represent concepts within the worlds of physics and chemistry and not simply
those wafting in the miasma of mathematical reasoning.
So, write your i s as (-1,1) and (1,-1), if not
(-1,1,-1,1) and (1,-1,1,-1). Then, see what marvelous insights arise.
In a summarized conclusion, this day we find that, in
mathematics, as in life and political situations, the irrational just is rational
and the complex simply is overly simplified.