In order for a result to publishable it must be within the probabilistic censor known as ‘p-value’. P-values, in short, measure how likely it is that these observations would happen by accident. Allowing higher p-values causes the information economy to inflate, like lowering the reserve ratio. Our world of uncertainty abandoned the truth standard long before the gold standard ever came into being.
Our tolerance of noise and uncertainty leaves open the question of whether we believe in a definite signal. I once misheard a favorite song of mine, “The Coloring of Pigeons,” which is about the theory of evolution, to have the lyric “More than forms exist in their own right”. It turned out to be “Northern forms existed in their own homes.” The “turned out to be” is what is important here; I maintained a faith that there is a particular lyric that I will hear or mishear, that is, that there is a meaningful distinction between signal and noise. It is a Platonic position, positing a perfect form presented to us imperfectly, through a glass darkly.
But what if more than forms exist in their own right? Evolutionary ontology posits only noise. The “signal” is only a particularly compelling or enduring variety of noise. Research relying on p-values is not cutting through the murk, as much creatively shepherding chaos into form, itself only a variety of chaos.
I call the former faith in the one signal underlying the noise, the idea that things are one particular way, “monotheism.” It has always been the secret basis of science, as is witnessed in the difficulties still lingering over the comprehension of the uncertainty principle.
The mathematical theory of the limit is a unique means of collapsing the distance between these two approaches. The limit is an elegant abstraction of the scientific process itself. Scientific method allows for the uncertainty introduced by the imperfection of its instruments. In high school, this concept is called “significant figures,” and it states that the results of the experiment can have a precision no greater than that with which the inputs were measured. This is the last remnant of what might be called “subjectivity” in science, an imprecision born of the defects of the observing instrument. The limit captures this tension by asking for a guarantee that improving the precision of the input will improve the precision of the output, which is to say that the supposed signal will always remain as more and more noise is removed.
The scientific laboratory is the locus, then, of a sort of redemptive process. Matter is more and more reduced to its eternal platonic form, and the patterns that rule it are likewise seen to emerge with increasing clarity. We can see clearly here the roots of science in alchemy, which explicitly aimed to bring out the eternal within the material as a means of redeeming the metaphysically besmirched (i.e. noisy) nature of the latter. The philosophers’ stone is merely the limit point of the material realm.
The limit does not posit the existence of the signal that it hones in on, merely what that signal would be if it existed. It therefore avoids being monotheistic, although it does gesture in that direction. There are after all plenty of processes with no limit, or with several oscillating points of accumulation. The definition of the limit is the most compelling analytic depiction of becoming, in contrast to being, that western science has produced. It does not say anything about particular existences, but rather the potential for ever-changing becomings. Indeed, one of the greatest critiques of calculus came from Bishop Berkeley, a monotheist, who accused early calculus (prior to its casting in terms of limits) of relying on “ghosts of departed quantities.” These ghosts where later corralled by means of the notion of a limit. The monotheist’s discomfort with calculus is that it is in league with the insubstantial and impermanent. Berkeley’s tract “The Analyst” is an exquisitely abstract witch trial.
Ambiguity is the ultimate monotheistic heresy. Witchcraft functions within the ambiguous and insubstantial wherein signal and noise are undifferentiated, and the question of whether the process is more like weeding your garden or watering it is not asked. Winnicott calls this “transitional space,” and considers its existence to be necessary for psychological health. As the infant begins to differentiate itself from merged symbiosis, it has need of objects that are neither fully internal nor external. Space that is neither subjective nor objective retains its importance throughout life. For example, the mechanism of projection requires it. We relate to another as if he is part of ourselves, yet in that instant he is not fully either a part of ourselves or a part of external reality, and nor would we be able to interact with him at all if he were.
Transitional space is the necessary home of that dance between inner and outer known as artistic creation. Its role in art is attested by Winnicott, but given an even more pleasing exposition by Merleau-Ponty in his essay “The Chiasmus,” or “crossing.” Merleau-ponty, in a maneuver that recalls Schopenhauer’s exposition of “Will,” points to the necessity of that which touches being itself touchable.
Again alchemy becomes relevant. As understood by Jung, alchemy is any process in which inner and outer objects are “worked” simultaneously, in which metaphor allows for erotic distance from ourselves. Every synchronicity or divination is a chiasmus; all meaning must weave internal and external (what Lacan calls the “Button tie”). Jung’s claim that synchronicities would begin to happen during productive phases of therapy can be understood in terms of an expanded transitional space. I don’t wish to fall into developmental reductivism that attributes all “mystical” experience to “regression.” I will say, though, that in the same way young children need to make sense of their world for the first time, those in therapy who are symbolically birthing new part of themselves are having experiences that are parallel to developmental milestones. Synchronicity reflects an ability to weave meaning into our lives by being open to events that belong to both internal and external reality. An over-emphasis on objectivity or subjectivity both lead to a sort of psychotic narcissism.
The arts and humanities are the praxis of this weaving. Science and art are the modern differentiation of alchemy into telos and technique respectively. Fritz Perls defines the ego as that which manages boundaries, between figure and ground and self and other. This includes creating them where appropriate as well as allowing them to blur on occasion. The sciences and the humanities play these roles in the collective psyche. Science allows for differentiation of self and other by lessening and collapsing the transitional space wherein meaning, ambiguity, and creativity can function. Scientific thinkers’ accusations of “illogical,” “un-falsifiable,” and “meaningless” are the witch-trials of our time, or put another way, the healthy functioning of the collective ego. Logic is the differentiation of true and false, which stems from the differentiation between me and not-me. Magic always happens in the liminal space, where ambiguity can be put to practical use. The arts and humanities, on the other hand, have the complementary purpose of enlarging transitional space and bringing us to together inside of it, which is to say integrating boundaries.