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AMAZING ARTICLES #7: MATHEMATICAL MODELING

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

RED LEAFIn 1600, Mr. Giordano Bruno was burned alive by Christian Church for his beliefs: he was confident that Ter-Ra 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 Ter-Ra knew a lot about our Planetary System! [Read about the Antikythera mechanism.] In addition, take the Hellenic word "Ter-Ra" (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 Ter-Ra 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?
The Antikythera mechanism
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 light-speed capable ships having a propulsion similar to the one used by the fictional starship Enterprise, because light-speed, Sir, is not sufficient to reach other stars.

In order to reach our neighboring stars we need ships capable of 100-1000 times the light-speed, 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 supra-saturated with the avalanche of stunningly foolish "concepts" ventured, lately, over the media)


RED LEAFThe SF concept of "Worm-Hole" 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 "continuous-domain", 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 paper-space". Therefore, regardless of how is the space folded or not--to an outside observer--to 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 paper-space doesn't exist for us: it is a "boundary" we cannot cross, EVER! The paper-surface represents a "limit" which simply doesn't exist in our continuous-space reality.

Anyway, beyond the mechanical 3D space of our reality, and beyond the existing continuous space-matter-time 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 gold--incidentally, Cold Fusion seems to be able to do something similar. Over the centuries, the research work was focused on two fronts: Mathematics and Physics--that 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 structure--what 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 sub-components) is a mathematical model--well, 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 . . .
 


 


RED LEAF L

Let's take a true life example. The most known formula in Quantum Mechanics is:

     E = m * c2

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 light-speed constant "c2" 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 light-speed is a constant, and the maximum possible speed in the Universe--according 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 shore--in 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.
 

 


RED LEAF RAs 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) / d2)

In the above formula "G" is universal gravity constant equal to 6.67*10-11 [N * m2/ Kg2]

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, Galaxy-wise, as it is presented in the following picture.
 

 

Gravity vs. Antigravity


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 physical-mathematical 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 lot--possibly, even too much . . .

***

First published on May 25, 2005 
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GREN LEAVES L


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