Why do I do it? Because I can. Because we can. Because our minds and the pursuit of pure science are not restricted by the dimensional walls that hold us here - learning is an infinite frontier upon which ever greater riches can be found. Forget your petty squabbling over a few months at the top of the yapping pack that is this insipid place's politics. True greatness can only come through study, ingenuity and academic perseverance.
Now, you'll note that this time the rod you're holding is made from gold, which I believe should increase conductance by up to 37%…
Science is Amazing
If you had to sum up the beliefs of the Glorious Equation in three words, those would probably be the ones. Over the generations, many of those who have come to the city have been motivated by scientific curiosity of some form or another. This is not, perhaps surprising - after all for a long time the places existence was only known of among the greatest scholars and researchers of many worlds, and even today such individuals are among the more likely to have the wherewithal to make the jump to it should they so choose. And while more than anyone else they are likely to have a full comprehension of the risks involved, a reasonable number still do. Often they come full of hubris, here to prove themselves superior to all who have come before by breaking back out. Others come out of boredom, or feeling stifled in their own worlds, seeking new academic heights.
Even more than misery, academia loves company. After all, there's no point in overturning Le Caron's theory of dimensional wave-parity if there's no one to read the paper. Over the years, colleges (the natural grouping of scholars across the multiverse) have risen and fallen, schools of new thought coalesced and scattered, and many great leaps have been made in the understanding of the nature of the universe. However, it was not until the advent of the Glorious Equation that the disparate academic forces in the city began to unite into a single whole. Initially an alliance between two previously competing colleges (after they were forced to work together to subdue their entries into the city's annual unofficial abomination-off when they escaped from the confines of the arena), the glorious equation began to assimilate smaller groups as they forged ahead in academic brilliance, with the best scientists in the city wanting to be part of the greatest institution. With each new assimilation came more resources and knowledge, allowing yet further advances to be made. While generally not the most business focussed of individuals, enough could see which inventions had earning potential in the markets the city provided, and money and influence was accumulated to allow the acquisition of choice real estate for the construction of laboratories and factories. As the guild went from strength to strength, its influence and dominion spread, and it grew to become one of the most powerful forces in the city.
The Equation's power is a different sort to that of, say, the Inheritors. It does not come from political positioning or ancient ties of family and ownership, but from being incredibly useful to have around. While many of its members outputs are of…questionable application outside the academic world, some of them prove incredibly useful within the city. Rigs for indoor cultivation of crops are a well known one, alongside generators capable of powering technological lighting across swathes of the city, whilst in the field of magical study (less favoured than the arts of technology, but still present within the guild), great improvements in scrying and communicative magics have had their uses in maintaining contact with the outside universe. Many smaller innovations and trinkets come grom the guild as well, and many of its members run small businesses selling the products of their studies. Possession of the latest technological trinket is extremely fashionable among the wealthy and powerful, as is sponsoring some piece of plausibly worthwhile research. All this serves to increase the guild members access to that which they desire the most - time and money to continue their research.
The main challenge to the popularity of the guild is the relative frequency with which its members cause some sort of catastrophic accident. When the cloud of Inverting Smoke or the rampage of the latest failed attempt at an obedient AutonoSpider remains within the guilds own territory, the other tend to turn a blind eye. When, however, it is their streets smashed by hydraulic arachnoid limbs, or their citizens turned unexpectedly inside-out they tend to react poorly. Extravagant recompense is often demanded (and usually paid), but a groundswell of ill feeling against the guild tends to simmer beneath the surface, waiting for the latest disastrous attempt to unlock secrets man was not supposed to know with a skeleton key of dubious provenance.
The equation is run by a council of leading scientific lights, chosen from within its ranks by a poll of the members. Unspoken convention tends to dictate that each major college or school within it will put forward a few candidates, and members tend to split their votes such that each large groups gets a representative. As a player character within the guild, you can be one of these councillors, having a voice in the overall management of the guild. However, the council's power is far from absolute, many scientists responding poorly to such base things as “power stuctures” and “orders”. You might instead choose to be the head of a college specialising in a field of your imagining. Either way, unless you choose to play a true “genius” (the kind who cackles atop a tower more than is healthy), you are likely to have access to the resources and manpower to further your scientific endeavours. As long as you aren't being distracted by the callout to subdue the latest escapee from the breeding pools.
The quarter of the city in which the Glorious Equation are based is by no means the largest of the factions, but nor is it the smallest. It contains a disproportionate number of turns of the river compared its size and within it is contained the entirety of the southern canal. The waters are particularly prized by the members of the Glorious Equation who use them in their many experiments. They take great care to keep the waters clean from their experimental effluvia but occasionally things slip by much to the annoyance of the other residents of the City.