Magic On A Small Planet

On a small planet beset by turmoil and revolution, a military leader emerged in one of the planet’s dominant species. We’ll use the masculine pronouns in this account. He seemed to have the potential capability not only to resolve his own tribe’s problems, but also to lead his tribe in the conquest of others. In what would later seem to be a preliminary practice campaign, this commander led an expedition to a distant land mass, with the objective of subduing an ancient civilization there.

One of the serendipitous accomplishments of this campaign was a discovery in the foreign land of ancient writings in an unknown language. It was suddenly and astonishingly possible to understand this previously unknown language for the first time. This seemingly magic development was divined to be an especially good omen for the fortunes of the adventurers. Future events would not disprove this notion.

Among the officers who accompanied this leader to the exotic foreign land were two interested in transformational magic, a subject unknown to and feared by most soldiers of that era. Whether the exposure of these two magicians to the mysteries and mysticism of the foreign land was beneficial to their development is a point of conjecture. It is quite certain, however, that the military experience was beneficial to their leader.

A superficial evaluation of this intercontinental campaign would unavoidably come to the conclusion that it was an utter failure in the military sense. After deposing the rulers of this ancient nation, our commander found it impossible to bring in sufficient supplies to maintain his army and establish long-term authoritative control of the land. Eventually he abandoned the effort and returned to his homeland.

But the lessons he had learned would prove helpful on many other fields of battle. Over the next few years, his armies conquered virtually every tribe on his home continent, and he acquired the title of Emperor. While the Emperor became a powerful ruler, famous across the planet, his former staff officers, the two magicians, departed military duty and labored in obscurity. They developed some magical formulae which were of interest to hardly anyone, and so these formulae were largely set aside.

Eventually the Emperor and his empire came to ruin, as Emperors and empires seem bound to do. At least the Emperor was widely remembered even after his exile and demise. The magicians, never widely known during their lifetimes, were almost totally forgotten after those lifetimes ended, and their apparently useless formulae survived only in libraries for a century or so. Fortunately, librarians tend to retain everything.

During the passage of all those years on the small planet, these beings developed new skills at designing and building things. A new sub-species emerged which was devoted to such efforts, and its members were known as genies. The things designed and built by the genies were multifarious, and the genies gradually became adept at using magic in their designs. But some of their formulae used to describe the physical world proved difficult to solve.

Out of the past and to the rescue came the transformational magic of those two who had served their leader in that exotic land across the sea. Their work enabled the genies to transport from the real world certain problems involving time dependence, into a partially imaginary domain where the independent variable is inverse time rather than time itself. Problems turn out to be much more tractable in this brave new world, and their solutions may be reverse-transported back to the real world, by again using the transformational incantations of the long-dead magicians.

Thus those magicians of long ago contributed greatly to the much more recent emergence on their planet of such creature-made phenomena as vision of distant scenes, machines which perform tasks, flight on great metal birds, and travel across space to other planets. The major accomplishment of their Emperor perhaps after all was not the conquest of his nation’s continent, but his having provided the means for his subordinates the magicians to visit a site of mystical inspiration.

* * * * *

The story above is hardly untrue. The planet is Earth. The species is homo sapiens. The military leader who became Emperor is Napoleon of France (1769-1821). His early campaign was in Egypt (1798-1801). It included discovery of the Rosetta Stone in 1799, which facilitated previously unachievable translations of hieroglyphic writings.

Napoleon’s staff officers who were adept at the magic of mathematics are Pierre-Simon Laplace (1749-1827) and Jean Baptiste Joseph Fourier (1768-1830). Their works used today are known as the Laplace Transform, the Fourier Transform, and Fourier Series.

“Genie” is a French word for engineering. The engineers themselves are more accurately in France called “ingenieurs”. Inverse time is frequency. That partially imaginary domain is the complex plane of high school algebra.

Complex frequency is denoted by s. It has a real part denoted by sigma (σ) and an imaginary part denoted by omega (ω). The letter j is used by most engineers to denote the square root of negative 1, because they’ve already used i for something else. So, symbolically,

s = σ + jω

That is, complex frequency s is the sum of sigma and jay omega.