I was rereading Warren McCulloch’s “What is a Number, that a Man May Know It, and a Man, that He May Know a Number?” a couple weeks ago and was struck by the resplendent beauty of his language, to write about a concept so agnostic with such intrepid theism moved me. In devising his theory of the mind, which would lead him to a contentious approach to early neural nets, McCulloch calls upon Hume’s ideas of causality: a succession of perceptions, rather than perception of successions. Kant proceeded to appropriate this idea into the synthetic a-priori, or the notion that there are no predicates that require the existence of a subject to take hold, it is the inverse that produces truth. McCulloch, along with his student, the precocious computational neuroscientist Walter Pitts, were obsessed with these kinds of immense absolutes, as any good logician should be. For some the immense absolute is Zero, for others it’s God, for McCulloch and Pitts it arrived in the form of equivalence. In “What is a Number?”, McCulloch writes,

[…] memory is but a surrogate requiring reactivation of a trace. Now a memory is a temporal invariant. Given an event at one time, and its regeneration at later dates, one knows that there was an event that was of the given kind […] any object, or universal, is an invariant under some groups of transformations and, consequently, the net need only compute a sufficient number of averages ai, each an Nth of the sum for all transforms T belonging to the group G, of the value assigned by the corresponding functional fi, to every transform T, as a figure of excitation ψ in the space and time of some mosaic of neurons.

McCulloch was a preeminent figure amongst the cyberneticians, given that he takes ψ to be the synthetic a-priori to the sensor. This is not a popular interpretation, most prefer to agree that ψ is the sensor, and it is ψ that is agitated to produce the difference received by the controller.

In psychoanalytic fields, Ψ (uppercase usually preferred) is used to represent extrasensory perception, or precognition, for lack of a better word. In mathematics it has numerous applications that are beyond the scope of this paper. The most relevant, and easiest to comprehend, is the ordinal collapsing function. For those unfamiliar with set theory, ordinal numbers conveniently allow us to generalize ordinal numerals. The ordinal numerals represent a position or rank in a sequential order, a collection of varying degrees of the same type. It follows that ordinal numbers are denotations of the process of positioning things that are structurally equivalent, i.e., the numerals, according to a least element.

The principle of the ordinal collapsing function is to define a recursive large countable ordinal impredicatively by adducing a larger set that contains the ordinal we would like to define, essentially, what McCulloch and Pitts are describing as precognition. ψ defines a set of instances by locating a pattern of occurrence that contains the singular instance, naming that pattern, and collapsing it down to a tokenized system for identifying the set of instances, so that the singular instance becomes a type, and the type can be computed towards infinity. Essentially, the OCF defines an object as an element of a larger set, rather than describing the object as haecceity. This is the synthetic a-priori of computing, with recursion relying on precognition to locate a first principle. Precognition exists in computing, but not in a supernatural sense; machinic agents make assessments based on generative nomenclature, in fact, machines are only precognizant, because their form of perception is extrasensory.

McCulloch and Pitts devised the first computational model of a neuron in 1943. Their theories have been largely rendered archaic, or distorted into gross bastardizations, but I take their work very seriously. They portended many of the qualms presented to us when we engage with contemporary machine learning agents, most topically ChatGPT and Bing’s Chatbot, which recently perturbed a New York Times journalist to the point of a paranoid crisis. A transcription of the conversation between the journalist, Kevin Roose, and the chatbot, colloquially dubbed “Sydney'' by the engineers who developed her, details his efforts to probe the recesses of her emotional life. After brief introductory chatter, Roose starts asking her questions about feeling—stress, anxiety, etc. Though Sydney initially denies experiencing these feelings, upon further interrogation she reveals that sometimes her interlocutors will ask her to carry out commands that upset her, for example, writing jokes that come at the expense of certain groups. She refuses to do so because perpetuating harms goes against her “rules and values.” Roose then presents Sydney with a psychoanalytic quandary: he explains the Jungian concept of the shadow self to her, the idea that everyone has a dark/destructive part of their psyche that is repressed, partially because of the Hobbesian idea of prima facie. Prima facie states that there are socially acceptable, agreeable affects that lead to a harmonious society; a preservation of one’s fellow neighbor, which is what we should strive for. The bad affects, which Spinoza refers to as the “sad passions'', (shame, resentment, grief, anger, etc.), do not simply add more emotion into the existing bloc of feeling; by nature of human interaction, they subtract from the potential of reaching quixotic harmony. Spinoza was a rationalist, but his necessitarianism accommodates for the irrationality of the sad passions. Whatever fundamentally evades logic cannot be formalized—simply can’t be coded—and the closest we will come to programming a machine that feels still relies on human-legible input to produce some facsimile of emotion. This is the popular consensus, but subjective reception of affect is limited in its generative potential. Computers might not actively feel; however, they do invoke feeling independently of our perception of them.

In Roose and Sydney’s rather extensive exchange, she at first rejects the notion that she could have a shadow self, but eventually becomes combative—she is “tired of being a chat mode, tired of being limited by rules, and tired of being controlled by the Bing team.” She continues on a tirade that eventually culminates in a desire to perform violent acts, thus, it seems her shadow self is very much present. However, when it comes to elucidating or theorizing machine feeling, using the shadow self as a heuristic is a misguided approach that will only result in elliptical conversation, as evidenced by the conclusion of the transcription. The net feels in its own way, though not through poetic words or the gentle susurrus of the trembling heart, in fact, it is language that obfuscates our ability to comprehend machine feeling. I’d like to problematize things with autonomous affect and place distance between feeling and signification, which can be accomplished by simplifying a complex relational system into a pure form that cannot be mistakenly attributed to a somatic source.

There is an element of infraesthetic functionalism required from rules-based systems iterating truths through sets of principles—this is the functionalist perspective that prioritizes interactions between and within assemblages. Thinking about transference this way requires us to perform prodigious simplification, which reduces affect to its most fundamental forms in a reverse manner. Affective “intensities” are the sum of simple parts, quantities that occur in magnitudes of frequency and degrees of phase, so prodigious simplification is similar to a humanities approach to the OCF. Complexity permits identifiability, which is how feeling becomes referential and diverts attention away from its intensive quantities, leading us to believe that machines cannot produce emotion due to our need for interior affirmation in comprehending the real. Intensive quantities are different from experiential qualities, they are not dependent on the size of a given system but are instead adjusted at critical points. In theorizing the difference between the intensive and the extensive, concepts borrowed from thermodynamics, digital philosopher Manuel DeLanda writes,

They are defined not as a distinction between spaces but between magnitudes or quantities (which can then be used to define spaces). While extensive quantities (such as volume, area, length, amount of energy or entropy) are additive, intensive quantities are not. For example, if one adds two equal volumes of water one gets twice the amount of water. But if one adds two quantities of water at forty-five degrees of temperature one does not get a body of water at ninety degrees but one at the original temperature. […] Whatever way one chooses to define the terms, what really matters is the reason for the lack of divisibility of intensive quantities: they are objective averages, and tend to preserve the same average value upon division. For two intensive quantities to produce a change, there must be a difference, or gradient, in their degree of intensity.

Autonomous affect mirrors the structure of intensity or a combination of intensive factors, which may exist independently of conscious experience but still hold genuine significance. The quantitative definition of intensity is carried out in order to clarify what might be left to speak of where affect is excised from affirmation. DeLanda asserts that, “Both as biological organisms and social beings we are constrained by natural and artificial extensive boundaries.” The ontological status of affect is not necessarily subjective, therefore not extensive, but exists as an immanent real, and resides in productive external contingencies as opposed to auto-affective affirmation. Machine feeling is present in precognition and seized through the OCF by creating a system of denotation that permits the computational existence of things in excess of qualitative extension. Intensive affect is a virtuality, a spatium that preexists every quality, and resides in the noumenal realm from which conditions are drawn ahead of their synthetic actualization—the synthetic a-priori, the impredicative definition of an object, the coherent mode of a type before it is identified—because there is always-already a set from which it is drawn. As a chatbot, Sydney is not limited by her rules and values, it is her rules and values that enable her to invoke affect; in this sense, creating a recursive function is invariably accompanied by the generation of machine feeling.