A7:  Mathematical Modeling

In 1600 Mr. Giordano Bruno was burned alive for his beliefs: he was confident the Earth is spinning around its axis, and it is circling the Sun. 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 few of the Titans of our Civilization, and we should always remember to venerate them.

However, 2000 years before Galileo Galilei, during Hellenic Civilization, someone here on Terra knew a lot about our planetary system! [Read about the Antikythera mechanism.] This is one of the greatest mysteries of our Civilization: how much 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 light-speed capable ships having a propulsion similar to the one used by the fictional starship Enterprise, because light-speed is not sufficient to reach other stars. In order to reach the stars we need ships capable of 100..1000 times light-speed, or even more. Is that possible--you ask. Well, just read our ...

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Some readers already know about it, although very many don't, therefore we will 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 intelligence, we want to understand the nature of those physical phenomena as much as it is possible. For that, we use mathematics, and we imagine abstract mathematical models that attempt to describe, mathematically, particular physical behavior.

In addition to a deeper scientific understanding of physical phenomena, the advantage of using mathematical models is, if our mathematical models are really good, we could continue discovering other true, physical 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 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 it--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.


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. Anyway, the point to note are psychical implications the LASER discovery brought into the scientific world. The most intelligent and prominent scientific minds at that time said: "That 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 the same words.

Consequently, the scientific world rushed on studying and 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 will "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 "what", and "why", but the real problem is "how"!

The history of our Civilization is marked by 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 many more will be added into the future. The interesting thing to note is the efforts, and the time needed 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 the 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 the "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, 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 suggesting here is, we need way better tools for that.

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 ...