Functor Reality is a company whose goal is to apply new and/or under-utilized mathematics to real-world problems. It is founded on the belief that revolutionary advances will emerge from the introduction of more sophisticated mathematical techniques into technology. Almost all modern engineering (be it mechanical, aeronautical, electrical or computer) uses methods that are at least a hundred years old, and were developed before high-powered computation became available. Consequently, many approaches are simply adaptations of those that were once performed with pencil and paper, albeit now executed literally millions of times faster. Functor Reality looks to change this paradigm by designing algorithms and software that simultaneously incorporate more cutting-edge mathematics and, in an ab initio manner, exploit modern computational capabilities: hardware, software and distributed.
In Category Theory, a functor is a fundamental notion, which allows one to "map" between seemingly disparate domains while preserving underlying structure. This characteristic, i.e., the ability for structure to be transfered between different settings, is known as functoriality.
Consider the following:
The theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics. The accusation is one against which there is no valid defense; and it is never more just than when directed against the parts of the theory which are more particularly concerned with primes. A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life. The theory of prime numbers satisfies no such criteria. Those who pursue it will, if they are wise, make no attempt to justify their interest in a subject so trivial and so remote,...[emphasis mine]- G.H. Hardy, 1915, lecture on Prime Numbers
The irony, of course, is that the "theory of Numbers" is the basis for practically all the cryptography that enables e-commerce. Yet a hundred years ago, one of the greatest living mathematicians espoused an opinion that would surely have been echoed by nearly all his mathematcal colleagues, viz., that Number Theory was the epitome of Knowledge for the Sake of Knowledge, with no Practical Value. (It is telling, however, to note Hardy's lugubrious defintion of "useful"; it is helpful to recall that World War I had begun in August of the previous year, and no doubt influenced heavily this particular turn of phrase.)