Proto-Superior: Numeros, the Angel of Mathematics

By William J. Keith


Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

--Bertrand Russell

Mercurian of Creation IST Lightning
Angel of Mathematics

People often wonder: why a Mercurian? Surely an Elohite makes more sense. Or, if they think about it for a bit more, a Seraph. After all, mathematics is about eternal truths. Of course, the same people are shocked to their toes when they find out Numeros' real Superior.

But Numeros knows why. He'll tell you -- or he would, if he had time -- about the Axiom of Commensurability, or the Universal Set, and how what seems logical, even in mathematics, in one generation, sometimes gives way in the next to something higher and truer. He'll show you four different proofs of the Pythagorean Theorem and talk about how humans seem driven to produce more simply for the sake of doing something old in a new way. He'll try to get across a point that can be ineffably difficult to make: mathematics is as much an art as a science, and in particular, it is a human art. His post didn't go to a Watcher solely because they weren't around when mathematics was born.

Oh, to be sure, there are eternal truths. And indeed, the whole art appeals to the purely rational mind. Define your terms, accept axioms as true, and rationality says you must accept all their consequences. But therein lies the catch: you must define the terms and accept the axioms first, and it is a question of experience which terms to define and how, and a decision of free will which axioms to accept. Eternal truth, in mathematics, to some extent depends on where you begin. As an angel of Creation, it is Numeros' job to see that Mankind picks the right beginning point, and as an angel of Lightning, to guide them along the path of optimal usefulness.

The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities.
---G. Sarton


It is a matter of much debate exactly where mathematics came from. A popular question among Elohim is whether God could have made a universe with a different value of pi. Modern neurologists wonder whether certain concepts of number and space are hardwired into the human brain.

What is certain in the In Nomine universe is that a body of mathematical knowlege existed in Heaven for the purposes of daily life, and had captured the attention of some thinkers for its own sake. However, Heaven is a vastly different realm than the Corporeal, and human mathematics developed along much different lines.

Eli's creation of an angel purely for the purposes of receiving the Word of Mathematics, and his presentation of this angel as one of the first to receive a Word from the Seraphim Council in the dark time just following the Rebellion, were both considered odd. Naturally, everyone respected the ancient and powerful Archangel of Creation, and Numeros himself was a fine work, worthy of the Word after a bare few centuries of proving himself as an angel. No, the question was rather: why? What do nomads and hunter-gatherers need with mathematics?

Explaining his answer would be akin to explaining how a toddler learns. Number sense and spatial figuring were so fundamental to the process of learning required for human advancement that any attempt at education without a firm grasp on these notions would be futile. Later, more established human living groups would require fundamental mathematical knowledge as part of the basic skills required for existence in the community. One wonders whether he knew how right he would turn out to be.

Numeros was given his Word and began the process of educating the humans wandering the wilderness. In this he acted much like a front-line scout -- it was soon noticed that where he passed, the ground was much more fertile for those notions that Lighting, or Fire, or Knowledge, would plant later. A few millenia later, the angels of Stone were the first to notice that any time more than ten human beings settled down and tried to create a community, somebody had to be able to figure if the group was going to be anything more than nomads who had stopped for a long time. And Heaven help you if there were a hundred; if every hundred humans needed an angel to stick around and figure out how long the supply of stored grain could last, the species would never get anywhere. So Numeros got his first underlings.

Now there was a group to coordinate. Numeros began spending less time on the Corporeal Plane, and more time teaching angels the things they needed to know about humans, how they learned, and how they thought, and the mathematics they needed to teach.

Let a few thousand years pass.

"God created the integers and the rest is the work of man." -- Kronecker

Numeros began his first serious work in Asia Minor, teaching humans the concepts of number and space that they would need to organize and direct themselves. Here, too, developed one of the earliest examples of humans surpassing the commonly-known angelic learning: the early Babylonians understood, though without specific proof, such things as Pythagorean triples, and certain trigonometric identities. More suprisingly, they were investigating questions that would seemingly be of no practical use; the fact that a triangle with sides of 7, 24, and 25 units is right was not an issue that practical-minded angels had ever bothered to consider.

Some angels were already mindful of these facts; Jean, Raphael and Yves were among those who found the new researches no surprise, and Eli accepted the news with a certain satisfaction. Education programs for angels heading to Earth duty underwent what would become the first of many expansions. Numeros himself became aware of whole new vistas of his Word -- the Word-expansion he underwent is still spoken of as one of the most glorious ever to have taken place below Superior level. He went into retreat for several hundred years, and emerged with several new Attunements and Rites, as well as a vastly deeper view of the world.

However, during this time, mathematics had advanced on Earth as well. While Numeros was ahead of human mathematics in several areas, he happily accepted the reality that humanity would be generating as much of a contribution to his Word as Heaven could. He will freely admit that, were it not for the fact that his Word grants him the ability to know the full current state of human knowledge regarding mathematics, he would be unable to keep up with this branch of human endeavor.

At certain times in history, Numeros' Word has flourished more strongly than at others. Certainly the Hellenic Period was his classical Golden Age; as art, science, philosophy, and tool, mathematics was integrated into the intellectual culture of the era. Iindeed, so highly did the Greeks venerate mathematics -- the Pythagoreans went so far as to consider certain shapes sacred -- that Numeros came under suspicion of cultivating worship. Contemporaneous developments in India and China also laid the foundation for later achievements there... and these would become important after the fall of Greece. When the Roman writer Cicero declared proudly that the Romans had reduced mathematics to its only usefulness, that of measuring and counting, Numeros' Word in the Western world had reached its lowest point, and it remained there for a long time. Nevertheless, he persevered, helping to develop the Hindu-Arabic numeral system, a truly concise and useful numeration tool. After the Dark Ages, mathematics paralleled developments in art, science, and philosophy as the Renaissance progressed. Art would be vastly different without the geometry of perspective; science would be nowhere without its omnipresent mathematical tools; and Descartes' mathematically-inspired philosophy shaped the thought of a generation.

Today, Numeros' Word is more ubiquitous than it has ever been; he works closely with angels not only of Lightning, but of Trade, Destiny, and Creation, and his services are requested well beyond these boundaries. He oversees a large staff of angels of Lightning, assessing and influencing human mathematical advancement and the social perception of mathematics. It is in this latter area that he is under the most serious demonic attack.

Hell has apparently decided not to counter Numeros by giving a demon the Word of Mathematics. Instead, Numeros faces challenges on many smaller fronts, such as Numerology, Statistics, and a Word whose closest English translation is a high-pitched voice claiming, "Math is Hard!" These demons work hard to promote the views that mathematics is a.) an arcanely difficult subject best left to the experts, b.) something those experts can use to say whatever they wish, and c.) when useable by "normal" people, a thing of luck, unluck, and superstition.

Numeros longs for the days when the mathematician or the teacher of math was held in higher honor. But he is not without weapons in this area; the coming decades may see a resurgence in the public opinion of Numeros' Word and its human exponents, and (he hopes) with it a new Golden Age of rationality, Heaven's most potent weapon against Hell's myriad deceptions.


Perebor: The angel can, quite simply, perform any finite algorithmic calculations instantly. He can factor PGP keys, solve a travelling salesman problem, or catch a hidden statistical error. In game terms, this is more than Lightning Calculator, but less than Intuitive Mathematician (although Numeros himself possesses this latter ability).

Measure: An angel with this Attunement is never at a loss for a ruler, watch, or scale; he can focus on any precisely definable quantity in view, such as "the length of this room, in feet," or "the weight of this statue," and with a successful Perception roll will know the numerical amount of that quantity.

Distinction: The angel to whom this ability is granted bears a portion of Numeros' awareness of human mathematical achievement, typically limited to a particular branch; a broader equivalent of the post sometimes called "the Reader," whose job at an institution is simply to keep up with the literature on a subject, and make themself available to researchers.

Naturally, a non-Superior cannot truly grant a Distinction; this is essentially an Attunement. However, it requires considerably more energy for Numeros to tune the angel's Heart to his Word in this fashion, and thus it is only granted for exceptional service, with a certain likelihood that the angel will continue to serve Numeros in the future.


+1 Spend two hours teaching mathematics to a willing student.
+1 Force a disagreeing party to bow to a logical argument.
+2 Prove a theorem worthy of publication.


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