By Anders Sandberg
Mathematics Research Group (MRG, the Mathemagicians)
The mathematical branch of the Void Engineers is little known by the Traditions, but it is a vital part of the Technocracy. It develops new methods for use in the research oriented conventions, control the academic disciplines related to mathematics and constantly research the implications of sleeper mathematics to avoid possible threats to the paradigm. It has strong ties to the Statisticians of Iteration X and the Forecasters.
The group is in fact quite old, among the oldest parts of the Technocracy. Its earliest roots can be traced back to the Pythagoreans, although the group mainly developed during the late Renaissance. Originally it mainly dealt with developing the necessary mathematics for astronomy, helped such giants as Newton, Gauss and Laplace. It later diversified as the utility of mathematics became apparent, and different subgroups split off and became their own disciplines (like the Statisticians or the logic-theorists which latter evolved into the Virtual Adepts). Today it is very respected and so taken for granted by everyone in the Technocracy that its existence is almost forgotten.
Most mathemagicians spend their time studying sleeper mathematics, writing research papers or participating on various conferences to direct mathematical development in the right direction. They are among the most anonymous technomancers possible, practically impossible to discover. Their various amalgams deal with specific areas, such as cryptography (another area where Dr Hill fights the Virtual Adepts), topology, numerical analysis, combinatorics and all other mathematical disciplines. It is common for other conventions to approach them with specific problems they need solved.
Their philosophy is simple: develop mathematics and mathematical models to encompass all of reality. When this has been done, everything will be essentially orderly and stable (although not necessarily computable or predictable). Mathematics is pure thought which can be given physical form. Some mathemagicians believe that reality itself follows from a mathematical basis, and try to develop a model for it.
Most technomancers of the MRG specialise in Entropy, the study of complex systems and probability, or Prime, the study of structures. Other valued spheres are Mind (to gain better control over one's mental processes), Correspondence (the study of geometry) and Time (planning and optimisation). They use complex mathematical formalism to use the spheres, often combined with extensive computer simulations if the problem involves Entropy. They don't use any direct magick, preferring to integrate it into the paradigm instead. This makes them almost immune to paradox. They also use their mathematics defensively: they can easily point out how improbable certain things are or find flaws in coincidences.
New World Order: They need our models and algorithms more than anybody else, and always consult us. We are swamped in requests for statistics, logistical analysis, encryption and decryption schemes, not to mention their obsession with mathematical models of societies and people.
The Syndicate: They are unfortunately not very good at mathematics, and their laughably inaccurate theories complicate things a lot. What they need is once and for all to define their axioms and then stick to them.
Iteration X: They apply our mathematics. While some sleeper mathematicians see applied mathematics as something impure, we realise the need for it. And Iteration X has realised the need for precision.
Progenitors: They rely mainly on some combinatorics and lately on knot-theory. Usually they just consult us to improve their own models.
Void Engineers: We seek to plumb and fill out the last voids of knowledge, making the universe self-consistent, logical and elegant. The other parts of our convention deal with the material aspects of it, while we take care of the abstractions.
Quote: "Isn't it surprising how mathematical the world is?"
The MRG develop solutions and rotes for other conventions. In fact, many of the most common rotes (like the Time-Motion Study of Iteration X) were originally developed by the MRG. However, most of their rotes are just used as integral parts of other rotes (like the Fast Fourier Transform or the differential geometry used by Void Engineer warp drives) or incorporated into consensus reality.
Model Structure (Mind 1 Prime 1 Sphere 1): By examining a system, the mathemagician can create a mathematical model of it. Using this model he can then simulate its behaviour, often in conjunction to other rotes. He can also monitor the differences between the model and reality (using Entropy 1) to see if there are unknown factors or manipulation involved.
Catastrophe Theory (Time 2 Entropy 1): By analysing a system, a mathemagician can predict when it will suffer any drastic change in structure or behaviour, usually called a catastrophe. This can be used to predict the exact moment something will fail, someone will change his mind or paradox to strike.
Optimisation (Entropy 3 Time 2): This is so common in the technocracy that few realise the origin of the rote. Essentially it allows the user to optimise something by calculating the optimum way to do it, removing all random or irrelevant factors and making the system orderly and predictable.
[Each success will decrease difficulty by one or add one success to any task which can be optimised, such as designing a system, running a bank or sabotaging an installation. However, in order to work the task must succeed on its own.]
Complexify (Entropy 3): Often the Technocracy do not want others to understand the inner workings of their devices or their theories. It would for example be disastrous if some future technology got into the hands of the Masses. Therefore the MRG has developed a general way of making theories, objects or rotes more complex and harder to understand partially based on coding-theory. By randomly mixing the parts and introducing self-organising elements they can make the simplest structure so complicated that it will become impossible to understand, while still working as it should.
[ Each success adds two to the difficulty in understanding how the target works. The rote must be used when it is designed or constructed, it won't work on a finished system.]
Logical Loop (Mind 3 Prime 2): This is essentially a computer virus developed by the logic research team and the psychologists of the NWO. It is a small set of postulates, which will quickly overload any logical system capable of understanding them (mainly computers, but human mathematicians or programmers are vulnerable) by constantly expanding itself and increasing in complexity without ever repeating. It has proven very efficient against Virtual Adepts, who often tend to think in slightly computerlike ways.
[The Loop will quickly expand and fill out all available processor power and memory of a computer which starts to interpret it correctly. Humans must understand the Loop (requires Computer 3, Enigmas 4 or Mathematics 3), and will then be partially infected. Usually it will only lead to a minor obsession of thinking through its implications (which never end), but in severe cases the victim becomes catatonic. If it successfully infects the mind of a victim, it will drain as many Willpower points as its successes as the victim can't resist thinking about it. After a while, the victim will get a new Willpower test, and if he fails the loop drains some more Willpower. If Willpower reaches zero the victim goes into catatonia until somehow freed from the Loop.]
Coordinator Structure (Entropy 4 Spirit 4 +other sphere): This is one of the most advanced results of the complexity research team. They found, that under very general circumstances physical (or other) systems of sufficient complexity could be subtly manipulated to contain a self-organising mathematical structure called a Coordinator Structure. These structures are essentially a built-in control system, which can be designed to perform various actions depending on circumstances. For example, the semi-random behaviour of an ecosystem can be kept within certain bounds by adding a Coordinator Structure, or the fluctuations of the Market could in principle be controlled using self-sustaining Coordinator Structures (the Syndicate has vetoed this). The New World Order has expressed great interest in Coordinator Structures, and are studying if they could be integrated within the human mind.
[ The system has to be complex enough to exhibit self-organisation. The mathemagician carefully analyses it, develops a mathematical model and creates the Coordinator Structure using subtle manipulations. It is necessary for the responsible research team to know the necessary system well enough to control it in some aspects (Forces 2/4, Matter 3, Life 2-4, Mind 2/3, etc.). The structure can fulfil simple commands within the system, like keeping it orderly, minimise certain factors or optimise others. Any sufficiently strong fluctuation will destroy it. ]
Daleth Deciphering (Entropy 5): The coding experts of the Technocracy and the Virtual Adepts fight each other by creating ever more secure ciphers and by cracking the others codes. The MRG has develop a series of codes based upon curves in Teichmuller spaces called epsilon-codes while the Virtual Adepts have perfected public-key codes. Both sides however realise that any code can be broken by using sufficient amounts of brute force and ingenuity. In fact, the MRG has developed a very general deciphering scheme named daleth deciphering, based on huge amounts of computing power and their most ingenious algorithms. It can be shown that it can decode all possible codes in a finite time, but the process usually takes a long time and requires the most acute minds of the Technocracy to work well. The Virtual Adepts fight this by trying to make sleepers use encryption too, so that their own messages are hidden by a torrent of other encrypted messages. The NWO and Iteration X are jointly developing an expert system using Daleth Deciphering to meet this threat.
G|del Openings (Entropy 5 Prime 4): Kurt G|del demonstrated that any sufficiently complex mathematical system contained theorems whose truth couldn't be proved. This was at once a blow to the Technocracy, and an opportunity to expand its reach. The mathemagicians have found that by judiciously exploiting known holes in accepted theories, technomancers can use magickal effects normally not allowed while still not contradicting the theory (and incurring paradox). To find these "G|del Openings" extensive computer simulations and tweaking of the model is needed, which usually requires the help of the sharpest minds of the MRG. In exchange, it is possible to find situations or methods which make certain operations permissible even if they are not part of the paradigm. This makes it possible to do some work normally done in Horizon realms on Earth instead, which is much more economical.
The desired effect must not be directly vulgar (against the laws of consensus reality), but doesn't have to be coincidental. A typical example would be the use of nanotechnology; it's currently not in the paradigm, and it's capabilities are as yet undefined. By modeling the paradigm and modifying the effect slightly, the mathemagicians can find circumstances where the nanotechnology would work even if it's not part of the paradigm. A necessary part of this is to make sure the effect will not leave unambiguous traces if the paradigm should change so that the effect was never possible. In the example, the nanotechnology have to be possible to explain away as biotechnology or something similar if it later turns out that the symposium decides it should be scrapped.
[ If the rote succeeds, a set of related vulgar without witnesses effects can be made coincidental. ]
Talisman: Provably Safe Operating System
Doctor Hill is among the most dangerous enemies of the Virtual Adepts in the Technocracy, especially because he appears to be so innocuous. What could a Void Engineer mathematician do against the masters of information? But the Virtual Adepts have begun to realise that he may be a bigger threat against their vision than the entire New World Order. Because Dr Hill is redefining reality against Virtual Adept Ascension.
Dr Hill is not even well known among mathematicians outside his own field, Automata and Complexity Theory. But those mathematicians and computer scientists who know of him, are generally very impressed. His theories and proofs are masterpieces of cold elegance, defining and exploring what is possible for computers to do, and what is not. Few realise that his theorems about the computational power of generalised Turing Machines also limits the abilities of the computers of the Virtual Adepts and Sons of Ether. He has ruthlessly demonstrated certain mathematical problems which cannot be solved using any computer, or that they cannot ever be solved faster than certain bounds. To most mathematicians this is just fascinating ideas, but to the Virtual Adepts this is a direct and deadly attack. Dr Hill is successively narrowing down the paradigm regarding what is computable and not, and apparently seeks to once and for all define immutable limits on all forms of computation.
Naturally, Dr Hill has met with some resistance. While most of the Traditions, including many Virtual Adepts, don't realise the danger he poses, the Chaoticians fight him at every opportunity. They wage an abstract war against Dr Hill and his followers in mathematical journals, on conferences and in the computer science community. Dr Hill fights back, both using his dreaded precision and eye for any flaws in an argument, and the more subtle support by the Technocracy. Strangely, the Chaotician papers have trouble getting published while the supporters of Hill almost always get into prestigious journals. There have even been some direct attempts on his persona, but Dr Hill has an uncanny ability to never be where he ought to be. Tracking him is almost impossible.
Despite his intimidating reputation among the Chaoticians, Dr Hill is rather unremarkable when met in person. He is a short, middle aged man with balding hair and horn-rimmed glasses. He speaks fast and precisely, never ending lecturing or explaining things to his audience. His humour is dry and usually only comprehensible for other mathematicians, although he politely smiles to any attempts at joking. He would disappear into the academic crowd if it wasn't for his charisma: his presence is *felt*. It's not known where he lives or if he has an family, somehow investigations never turn up anything.
Among the Void Engineers, Dr Hill is a major figure. Although the convention is most known for its space research, all forms of basic science is its domain. Dr Hill is the Research Director of the Mathematics Research Group (MRG, also called the Mathemagicians by others), which deals with the continued development of mathematics and related sciences like logic and statistics. The MRG cooperates with many other groups in the Technocracy, most notably the Particle Physics Research Group (PPRG), Iteration X and the statistics department of the NWO.
Dr Hill is very respected among the Void Engineers, where he has an influential role. Although the space division isn't as involved in mathematics as it used to be, it realises the importance of Hills work. Iteration X is also interested in it, but a bit ambivalent (if that is possible for them) due to some of the limitations his theories could place upon their paradigm. The New World Order is quite happy with his work, especially since he helped them design the provably safe operating system for their computers.
Dr Hill himself is a careful man. He is very intelligent, and has long ago learned the risks and benefits of being an administrator in the Technocracy, not to mention how far the rules can be bent or manipulated. He is also convinced that the Technocracy represents the only hope for mankind; without its stability and efficiency, the world would degenerate into despicable chaos and decay. Most of the Traditions are not any real dangers, since their paradigms are so far from the consensus that very few people would seek them. But the Virtual Adepts represents a subtle danger. By riding piggyback on the Technocracy paradigm, they have managed to gain more power and influence than is acceptable and safe. Their visions are dangerous, because they could convince the Masses in the beginning, and eventually lead to disastrous consequences. Therefore Dr. Hill has embarked on a personal quest to stop them long before they get any chance to fight back.
Chaos theory is another area Dr Hill is doing his best to deal with. He cannot do anything about it (his predecessor as Research Director of the MRG let for some inscrutable reason the area develop too far before stepping in, and then it was too late), but he has appointed a research team to try to bring some control over chaos. Another worry is the area of Differential Geometry. Some recent results have disturbing implications, although so far just Dr Hill and some of his trusted colleagues have noticed it. These results show a definite Nephandi influence, implying the existence of strange and threatening structures both in mathematics and in physical reality. Dr Hill is secretly trying to trace the theorems to their source.
Dr Hill is a frightening opponent. Although he might not be dangerous on the physical plane, his influence over consensus reality is strong. Given some time, he can disprove any theory he doesn't like or add defences to consensus reality against most effects. He is slowly sealing all holes in reality, making it orderly and logical. Inside it there will be no room for Ascension.
Essence: Dynamic
Nature: Perfectionist
Demeanour: Teacher
Str: * Cha: *** Per: *** Dex: * Man: *** Int (ordered): ***** Sta: ** App: ** Wit: ***
Expression: ***
Subterfuge: **
Drive: **
Leadership (Research Director): ****
Computer (theory): ****
Enigmas (mathematical problems):*****
Research: ***
Linguistics (German, French, Russian, Japanese): ****
Science (Mathematics): *****
Willpower: 7
Arete: 5
Spheres: Mind 1, Correspondence 4, Prime 4, Entropy 5.
Foci: all spheres: Mathematics, Entropy and Prime: Computer.
Backgrounds:
Status: *****
Allies: ****
Arcane: ****
Roleplaying tips: You believe in order, elegance and consistency. Always point out when something is wrong, inaccurate or just fuzzy. If you make a mistake, point it out and correct it.
Quote: "...but since the memory usage grows as ordo n log n for any algorithm of this type, while the upper bound of the memory modules of the system is finite, we find that any sufficiently large problem in these classes will be unsolvable on any set of generalised Turing machines."