
AMAZING ARTICLES #7:
MATHEMATICAL MODELING


COROLLARY THEOREMS:
"sooner or later, any valid theorem is going to be invalidated."

In 1600, Mr. Giordano Bruno was burned alive by
Christian Church for his beliefs: he was confident that TerRa
is spinning around its axis, and it is circling the sun Ra. Before he died, he said, "Though, it is still
moving." ("E pur si muove.")
Wonderful words! They are a priceless gift for our entire
Civilization. Giordano Bruno, Galileo Galilei, Johannes Kepler, and Nicolaus Copernicus are
a few names of the
(scientific) Titans of
our Civilization, and we should always remember to venerate them for their
exceptional work.
However, 2000 years before Galileo Galilei, during the Hellenic Civilization, somebody here on TerRa knew a lot about
our Planetary System! [Read about the Antikythera mechanism.]
In addition, take the Hellenic word "TerRa" (meaning Earth): this is in
fact two words "Ter" ("three") and "Ra" ("Sun")
meaning "the third planet from the star Ra".
2000 years before Giordano Bruno, somebody on TerRa was well aware of the
structure of our Planetary System. This is one of the greatest mysteries of our
Civilization: how much more advanced the Hellenic
Civilization really was?
Today, Mr. Stephen William Hawking [one of the greatest theoreticians of our days] says, "We have to colonize
other planets." Well, he is a bit naive when suggesting lightspeed capable ships having
a propulsion similar
to the one used by the fictional starship Enterprise, because lightspeed,
Sir, is not sufficient to reach other stars.
In order to reach our neighboring stars we need ships capable of 1001000 times the lightspeed, or even more.
"Is that
possible?" you may ask. Well, just read our SF books . . .
[Fragment from "Global Picture in News" December 1,
2006. © Corollary Theorems Ltd.]

note added in 2014
(by the Author, O G POPA, who was suprasaturated with the avalanche of
stunningly foolish "concepts" ventured, lately, over the media)
The SF concept of "WormHole" explained mechanically as "a
short jump through folded space" is mechanically idiotic, in addition to
being scientifically impossible. Space, in the Atomic Universe, exists
only as a "continuousdomain", not a "discrete" one; therefore, such
"discontinuous jumps" cannot mechanically exist.
In order to "get the picture", think that we are not fleas jumping on
"the 2D surface of space". No, Sir; space exists only as 3D, for us,
meaning "we are inside the paperspace". Therefore, regardless of how is
the space folded or notto an outside observerto us, inside the paper,
space has the same 3D dimensions (meaning, all distances remain exactly the
same).
In addition, note that the "surface" of the paperspace doesn't
exist for us: it is a "boundary" we cannot cross, EVER!
The papersurface
represents a "limit" which simply doesn't exist in our continuousspace
reality.
Anyway, beyond the mechanical 3D space of our reality, and beyond the
existing continuous spacemattertime coordinates, there are other . . .
"aspects" to consider. Therefore, instead of fussing around for years on
TV venturing such incredibly stupid and impossible 2D "explanations", using
that disgusting white sheet
of paper, the "scientists" could simply learn a thing or two about
REALITY from our SF books. It takes maximum 2 weeks to read them
(the first time), but then you could understand REALITY for
eternity, so . . .

Some readers already know about it, though very many
don't, therefore we need to start by explaining what is this
mathematical modeling and, most important, to what is it good
for. Now, we study our environment and we permanently discover
interesting physical phenomena. Because we have been gifted with
little intelligence, we want to understand the nature of those physical
phenomena as much as it is humanly possible. For that, we use mathematics, and
we imagine
abstract mathematical models that attempt to describe, mathematically,
the behavior of particular physical/real/actual phenomena.
In addition to a deeper scientific understanding of specific physical
phenomena, the advantage of using mathematical models is, if our
mathematical models are really good, we could continue discovering other
true, physical/real phenomena working this time ONLY with mathematical
models!
We cannot think of a better example than the discovery of the
LASER (Light Amplification by Stimulated Emission Radiation)
principle. The LASER discovery has generated a particularly complex
psychological and economical impact in our social life. The less
important aspect for our Civilization, the economic one, was translated
into thousands of useful applications. We wouldn't have the CD drive
today without LASER, and we have absolutely no doubts that many more
exciting LASER applications are going to make our life even more
comfortable in the years to come.

However, what is truly remarkable is the psychological impact the LASER
discovery brought into the scientific world. It happened the LASER
was the first application that has been first discovered on paper,
theoretically, using the available mathematical models, and then
implemented into very successful, practical applications. [Well, we
say it was the first one, although this is not quite true. Again, the
point to note is psychical implications the LASER discovery brought into
the scientific world.] The most intelligent and prominent scientific
minds at that time said, "This is an example of rigorous
scientific development. All future discoveries must have a solid
theoretical fundament first, and then they should be tested
experimentally."
Of course, they said something similar, not exactly the previous words.
Consequently, the scientific world rushed on studying (and on developing) the
existing mathematical models: there was a gold mine waiting to be
discovered in there! Even now, with the latest born physics' child,
Cold Fusion, the most intelligent minds of our days struggle to
design a mathematical model that would "fit" that anomalous behavior
using, of course, the existing mathematical models. Is that good? Is
that bad? Fact is, we do need mathematical models no matter what. Now,
we have seen "the what", and "the why", but the
thorny problem is "how"!

The History of our Civilization is marked by a few major technological
steps: fire, wheel, sail, steam power, internal combustion engine,
reactor engine, uranium fission, and the semiconductor technologies.
Overall, they are not very many, but it is certain that many more are
going to be added into the future. Now, the interesting thing to note is the
efforts, and the time it took to step from one technological level to
the other, on one hand; the other aspect is, each new technological
level has changed our society, and our life, in a dramatic way.
There was a time when Euclid's geometry was regarded as the
most pure, exact, and rigorous mathematical model; later, the sphere
geometry came to deny all laws and rules governing Euclid's
geometry. Other scientists have been passionate for centuries trying to
discover the "golden numbers" which were supposed to explain
all secrets of our life. Many have searched for "philosopher's stone"
which was supposed to transform everything it touched into pure
goldincidentally, Cold Fusion seems to be able to do something
similar. Over the centuries, the research work was focused on two
fronts: Mathematics and Physicsthat was, on each of them more or less
independently. However, we need them both, if we want any real,
beneficial results.
Today, we have at our disposition many complex mathematical models trying
to account for various, true, physical phenomena. The point to note,
however, is mathematical models are just TOOLS. Trying to discover our
reality using the existing tools is not going to help us much, because
new, radical discoveries require new, better tools. Suppose you have
a big hammer tool and you use it to break little atoms hoping to
discover what is inside them. That big hammer represents the Quantum
Mechanics Theory we use today to find out more about atom's
structurewhat we try to suggest here is, we need way better tools for
that.
Now, it happens that we do not have, and we cannot have
physical instruments which could penetrate inside the quarks, for
example, to test our theories; therefore, the only true, reliable tool
we have to work with those tiny atomic components (and subcomponents)
is a mathematical modelwell, there are other tools but . . . we will
explain them later . . . perhaps. Now, a bad mathematical model could
hold back our technological development for hundreds of years, while
with a good one . . .

Let's take a true life example. The most known formula in
Quantum Mechanics is:
E = m * c^{2}
When Albert Einstein has formulated it the first time, this formula has
generated a revolution of multiple aspects: theoretical, physical, and
philosophical. It is still one of the most important formulas we have,
because it says mass (matter) is nothing else but pure energy.
That is the colossal importance of the formula: atoms, and atoms'
components, are constructed out of ONLY energy!
ATTENTION Note that the above formula is too simple, and it tells us nothing about
THE NATURE of the energy: it could be heat, potential energy,
electromagnetic energy, or something else. Now, try to imagine
that
the squared lightspeed constant "c^{2}" is replaced by a variable: in that case you could discover
that
mass (the atom) is in fact equal to the sum of various types of
[energies]. We used square brackets intentionally, because in this
instance the energy would cease to be energy, as we know it: it will have to
be something else, something out of which the energy itself is built.
We will continue developing this topic but, for now, we recommend
our SF books for truly
exciting details.


One of the most troublesome aspects is the constants we use in our existing mathematical models, and they are very
many. A true mathematical model needs to be funded on experimental data, and on some fixed, reference points, in
order to test its validity: the constants provide those very references we need. For example,
Quantum Mechanics is founded on the idea that lightspeed is a constant, and the maximum possible speed in the
Universeaccording to Albert Einstein.
If the above hypothesis is true, then we are in a big trouble: we will never be able to meet with our dear brothers
and sisters living nearby, in our beautiful Milky Way Galaxy. We would be left as we were 2000 years ago, when
people were watching over the immensity of the ocean thinking it was impossible, even dangerous, to reach the other
shorein fact, people thought there was no other shore. Now, 2000 years later,
anybody can cross the ocean in about 7 hours, and even less; it is just a matter of little more money. The new
ocean to us, today, is the Galaxy, and the only tools we have to conquer it are
new, better mathematical models.

As mentioned, a mathematical model requires constants, and
we have discovered very many. Let's take a look at the most known one:
F = G ((m1 * m2) / d^{2})
In the above formula "G" is universal gravity constant
equal to 6.67*10^{11} [N * m^{2}/ Kg^{2}]
The above formula is Newton's Law of Universal Gravity, and it
works so well that it was successfully used to discover, theoretically,
new Planets in our Planetary System. The only problem is, at Galaxy level
the above formula tells us there should be at least 100 times more
matter, in order to satisfy the existing Galaxy, AND the formula.
That
"extra" nonexistent matter has been poetically named Dark Matter,
because the assumption was, and it still is, the universal gravity
constant is a "true" constant. Fact is, there is no more matter in our
Galaxy, and in the Universe, and the universal gravity constant is not
constant: it has other values, Galaxywise, as it is presented in the
following picture.



The implications of a wrong constant in our life are enormous. One constant which is not quite constant means
that other tens of constants are not quite constants, and then hundreds of theories and even physical
Laws are not
right. In the end, our entire
physicalmathematical apparatus will have to be revised. Scary, isn't it?

NOTE ADDED IN JANUARY 2012
In 2010, some Australian researchers have
announced (for the first time in History) that, indeed, a few
constants are not constant at Galaxy level!

Naturally, some readers may agree with this article, though we are certain that very many would not. Of course, we
need to
detail these brief "assumptions" of ours. Sure, we intend to do that, only we cannot guarantee it is going to be
tomorrow. Meanwhile, you could study MERCY and
THREE STORIES FROM HILSA'N TASSA GALAXY: these two
unique
books reveal a lotpossibly, even too
much . . . ***
First published on May 25, 2005
© SC COMPLEMENT CONTROL SRL. All rights reserved.

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