Reinvention is either repetition or reconception. Repetition achieves the same result by the same method; reconception achieves the same result by a new method: reinvention is not valueless for the repeater, but it is valueless in itself; reconception is valuable in itself because it adds to understanding.

Repetition is valueless in itself because it is wasteful. It has value for three conditions: first, when the desired invention is unattainable, but its use is familiar; second, when the idea of the invention travels faster or more freely than its workings, and can be reinvented more efficiently than obtained; and third, when the waste of reinvention is outweighed by the desire for the habit of invention. The third value is mine.

Invention is not itself a faculty, but it is the simplest compound of the faculties, employing reason, memory, and imagination equally. That old scheme is incidental to the definition—any division will do; what matters is the equality. Invention is that use of the mind which is limited not by the power of its parts, but by the speed and life of its connections; not by its strength, but by its agility.

It requires practice; but because it is an act of all faculties, set problems, which exclude memory; études, which exclude imagination; and exercises, which exclude reason, cannot properly develop it. It must grow with a round habit, equal on all sides. For this, it requires real problems: problems that arise in useful work and productive projects.

Yet most of the problems we encounter have already been solved. For the sake of efficiency, speed, and mortal timesaving, research and reuse are usually the right choice for any problem considered alone. But what of problems generally? Invention is a habit; and there is no habit of invention without reinvention.

Otherwise an act of reinvention can have two values of its own: the public value of a new approach; and the private value of understanding. These values, though independent, may coexist.

The value of a new approach is plainest in mathematics, where the result is demonstrably the same. Transcendent numbers transcend the awkward operational definitions by which human beings named them—the ratio of diameter to circumference, the rate of interest perpetually compounded—they are rediscovered again and again, the world's true eternal conspiracy, everything traces back to them, they are behind all the fronts, inside all the shells and shadows. The sums of infinite series, the falling of coins on grids, the charted growth of flowers—there are an infinity of ways to reinvent them, and every way adds to our mastery of the world by revealing new shapes under which these our permanent companions can be found—culminating in the glorious absurdity and terrifying brevity of Euler's identity.

In the spectrum of intellect mathematics is usually marked at one extreme, poetry at the other; but here they touch. Most poetry is the reinvention of morality on new models and in new contexts: some new model perception (a flea, a red wheelbarrow), some new model interaction (the death of a lutenist god, the speech of a leech-gatherer), some new modeling context (splendor in the grass, dark Satanic mills, the worshipers who must tighten the bolts unwarned). They are not alone: much of technology has been reinvented: what was built on rumor before the plans arrived, like the cotton gin; what was reinvented blindly to avoid infringement of a patent, like the PC.

The private value of reinvention is to advance understanding. The simplest form is the imperative to recast another's thoughts in your own words. But this is not really students' business: by rephrasing they better remember another's understanding; but by reinvention one better understands. Indeed, where the strictures of licensing and regulation, and the friction of custom and community, outweigh the benefit in study and imitation, the rational course is to reinvent what you would know, rather than learn it. The hard parts are done already: you know that it is possible, what it is good for, why it is needful; the usual limits of human ability and conditions of human fallibility hold; the work is a matter of filling in blanks, which can usually be spliced with pieces of other disciplines.

All intellectual activities can be divided into those where reinvention is useful and those where reinvention is necessary. Those in which reinvention is useful but not necessary are the sciences and design; those in which reinvention is necessary are the arts, and the professions.

There are new things to be done in science, new discoveries to be made, new instruments leading to new worlds of exploration; and there are new things to be done in design, new needs to answer, new patterns to define. Here the effort of reinvention could always be applied otherwise.

But in the arts and the professions nothing is really new. To choose two, there is nothing new in literature or law. We cannot add new phenomena to those that Homer and Shakespeare knew; we cannot add new patterns to those that Aristotle and Machiavelli documented. If something in literature or law appears to be new, then it is gibberish, or it is deceit, or you do not understand it. Nothing can be done in either that is not an reinvention; yet we must do both, and for the same reasons: partly because life commands it, as it commands the yearly reinvention of flowers; but more because we who desperately need them cannot otherwise have them.

The criticism of literature and the philosophy of law do not create and do not decide law or literature; they cannot in themselves save or sustain anything. Shakespeare, however praised, without imitators would be forgotten; a constitution, however respected, without reinterpreters would obsolesce.

A generation passes away; what they loved and revered we cannot learn to love and revere from them. Their love is dust in the ground, their reverence collects dust in attics. We can love the life they loved and obey the law they obeyed only for our own sake; we must reinvent them, not even to maintain them, but just to learn to see them. We cannot see how the world was built for us until we have rebuilt it.