A small preface: If you only read two parts of this, read the bolded sentence and the final section. Graduated iteration is an important principle of reality, and, like many principles of reality, recognizing it will greatly help you to make sense of the world and your life. This is written to provide several different points and contexts in which to understand graduated iteration, some of which may be more or less helpful to you.
Coining and Definition
In his book Newton the Alchemist, William R. Newman coined (to my knowledge) the term “graduated iteration.” He derives it from an analysis of Eirenaeus Philalethes, or George Starkey, a North American alchemist who lived from 1628-1665. In Newman’s words, “[the linguistic technique of graduated iteration] involves repeated use of the same term at different stages in the progress toward the alchemical magnum opus.”1 Notably, the meaning of said term can vary quite wildly between stages. It can be as similar as different chemical referents for a specific term, or as different as one usage being a chemical and another being a process. My definition and analysis of graduated iteration owe much to Newman’s work, but the direction I take it is more of an analysis of it as a principle of reality instead of a method of textual analysis.
Graduated iteration is, shortly, a method of exoterically encoding a symbolically cyclical pattern. As Newman notes, it was also used to esoterically encode quite different incarnations of its symbol. Several things which are very different in incarnation such as, in the case of Philalethes, “copper, the ‘amorous’ mercurial component in stibnite…, and the venereal regimen”2 are all symbolic of Venus and are exoterically encoded as such, that is, under the name of Venus. Graduated iteration can also esoterically encode for the same process which is to be performed on a changing object. Think boiling a substance, condensing it, then boiling the result and condensing it, and so on.
In the Emerald Tablet
The Emerald Tablet, the foundational text of alchemy, provides a textual basis for this last interpretation of graduated iteration. It says, “it ascends from the earth to the heaven & again it descends to the earth & receives the force of things superior & inferior.”3 While it does not explicitly bring in the principle of iteration, it does bring in the principle of graduation. That is, the object, which is probably the nascent philosopher’s stone, completes a process of movement, its ascension and descension, and gains valence.
Looking more closely into this passage of the Tablet, one may find an esoteric principle of iteration in it. The first, most obvious, is that the object returns to its origin. It passes from earth to earth: it is a cyclical process. The fact that the idea of the cycle has been introduced indicates that there is the potential for the cycle to be done again. Having returned to the beginning, a journey can be made again. Equivalently, a graduated object can be iterated upon again.
Further, the earth and heaven are separated in verticality, by ascension and descension. That is, the initial symbol of their separation is spatial separation, so we may be justified in saying that we are initially seeing the physical Earth and the physical heavens. The physical earth and heavens are related also in revolution, either in the heavens revolving about the Earth or in the Earth and parts of the heavens revolving about the sun. In fact, besides verticality, this is the only other phenomenal way in which they are spatially related. Each of the stations of the object’s movement are symbolic of revolution when they are spoken of together, the lens of spatial relationship introduced.
The object, then, implicitly passes through three different revolutionary stages. Its initial revolution on or in Earth, its second revolution in Heaven, and its third revolution on Earth again. Its great revolution in ascension and descension becomes a macrocosmic symbol of these revolutions; it is an explication of them, of revolution and its purpose. It shows the actualization of the aforementioned potential of repeating the cycles. We get a picture of cycles of cycles, or, less esoterically, cycles of processes. In any case, the cycle implies iteration.
Of course, graduation is the simplest and best-known goal of alchemy: the creation of the philosopher’s stone, the apotheosis of the adept, chrysopoeia. It makes sense that its presence in the Tablet is exoteric, that the promise of power and force is explicitly made. The method of obtaining it, which requires iteration, is the work of the adept, and it is where esotericism is vital.4
In Life
In The Screwtape Letters,5 C.S. Lewis elaborates on a method of graduated iteration which might make the concept more concrete. He speaks of “that union of change and permanence which we call Rhythm. He gives them the seasons, each season different yet every year the same, so that spring is always felt as a novelty yet always as the recurrence of an immemorial theme.”6 Lewis’s primary concern in this passage is with cycles, not objects. Spring is something that seems to have the character of an eidos , or Platonic form, which is incarnated annually, that is, cyclically. He is most directly saying that there is material, cyclical, incarnation of an eternal idea, Spring. Substituting symbol for eidos, which are maybe identical thoughts, this passage speaks of cyclical incarnation of a symbol, or iteration.
The graduation can be very easily supplied by considering Spring’s real presence in the world. Every year, Spring is a little bit different. The rains are a little heavier or lighter, the temperature is a little warmer or cooler, and the flowers are a little denser or sparser. The incarnate process of Spring is a little different. Further, the objects of Spring, such as the people experiencing it, are different, having grown and changed in the previous year, that is, the objects of the process are different. This combination of the incarnate difference and the cyclically constant symbol is the essence of graduated iteration, or, as Lewis calls it, “Rhythm.”
I don’t want graduated iteration to be necessarily identified with a stuffy or obscure academic analysis. This is a literary device which is present in the narrative of your life. Graduated iteration is every day and every year, every commute and every dream. The fixed stars revolve about you daily, lavishing new perfections on the conscientiously transcending subject, the person humble enough to accept them.