Reading Thoughts and Notes
Pure Immanence, Deleuze
On paper
Some kind of sensation that isn’t raw sense data, something like using preexisting knowledge to feel
Transcends object and subject and feels as a part of the same system

Summary
Deleuze writes extensively about the relationship between subjectivity, objectivity, immanence and transcendence. Though he is clear in what denatures the immanent plane (anything that can be said to represent the immanent plane, contain it, or do anything with it really), it then remains unclear what it is. The etymology of the word implies that something immanent is within, but with Deleuze’s immanence, this is not the case: “No more than the transcendental field is defined by consciousness can the plane of immanence be defined by a subject or an object that is able to contain it.” Which I’m afraid puts me in a position where I can summarize no further without the aid of mushrooms, as I cannot imagine something that is within something but also not contained by any object or subject, or what function this thing would serve if I could imagine it. Moreover, is the act of imagining it not a form of containment? Does not the authority of understanding with which Deleuze writes undermine the entire concept?

Deleuze’s transcendental field is perhaps more well defined: “it doesn’t refer to an object or belong to a subject… [it is] a pre-reflexive impersonal consciousness… without a self.” This reminds one of actualized, experienced phenomena like one’s unconsciousness, dreams without first person perspectives, or the feeling of the dissolution of self.

Compelling Points
Nietzche: The self is formed from habits that shape life, or in my own words, the self is a product of evolution, and probabilistically correlates to something Real since our belief in it keeps us alive
Hume, Deleuze our biggest challenge is believing in the world

Implications
While Locke thought the self as a function of sameness over time, it is necessary to refine this idea, as difference is guaranteed, and nothing is entirely the same. I am nearly unrecognizable from the person I was several years ago, and even in a minute sense, I am a different person after I, for example, call my mom and converse than I was before. Thus, it seems, someone like Deleuze may conclude, “the self is only a fiction or artifice in which, through habit, we come to believe”, or Hume may conclude it is, “a fiction required by our nature”. This is evidently true. When we speak of the self we tend to speak of a stable representation, as shown by policies of governance. If someone murders someone, they often receive life in prison. If we recognized the shift in representation of the self over time, we would not have conceived such a policy. There would, perhaps, be some sort of reevaluation after some period, to test if the person who committed the original violence has changed in our representations of their self. But that is not the case in our society. But then why do we systematically believe in this falsehood?

As alluded to, the falsehood is necessary. A stable representation of our selves is more definite and actionable than some acid-induced ego dissolution of a plane of immanence which is a life. Moreover, Locke was right, to some extent. The self is obviously constituted of some measure of sameness, but it naturally shifts. To understand what we mean by a self, then, we need to look at where the stable representation appears. We learn to recognize our selves as discrete objects based on the same time frame as the actions which necessitate the recognition.   

I would argue understanding of self precedes all conscious action. I would argue our understanding of self could be represented as a map of our degrees of control to every other point or grouping of points in space relative to our central locus of consciousness, the neural activity of the brain. This correlates to sameness, as that which can produce similar maps of degrees of control will have necessarily similar structure. But this self is not constituted or confused by the same paradoxes of changing sameness as Locke’s conception. It seems, however, that the idea of a central locus suffers from a privileging of particular stimuli and substrates. I would propose the following method to assign a central locus to avoid such problems: within the probable volume of a self, identified by a threshold of a high degree of control over surroundings or the empirical report of such, systematically remove points in space while maintaining the empirical phenomena of the self. When the “minimum spanning volume of self” has been found such that the phenomena exists in the smallest possible volume, this can be called the locus of the self. Though this at first appears intractable, I will point out that the dissolution of the self has been studied pharmacologically for some time [1, 2]. Next we can formulate the self mathematically in the following way:
Let phi = locus of self, at time t
Let epsilon = threshold of degree of control constituting the self, which would be generally empirically represented courtesy of our shared evolutionary history by the degree of control over body parts delineated by skin
Let theta(points1, points2) = the degree of control of points1 on points2
Let X be the width of the universe in an arbitrary, straight direction X, at this boundary there is no matter or energy
Let Y be the measure of the universe in an orthogonal direction Y to line X
Let Z be the measure of the universe in the direction orthogonal to Y and X
Points = {x for all reals in X, y for all reals in Y, z for all reals in Z}
P = the power set of Points
Self = pP ((, p))

I will note that the self is defined instantaneously, at a particular time and for a particular phi at that time. Also to note is that in practice, the points on which some form of this calculation might be performed is generally limited to the scope of our vision. Moreover, humans do not perform this entire, obviously intractable calculation. We cheat. We quickly scan our environment, knowing that chairs, pillows, trees, are well below this threshold of our degree of control compared to our hands, our heart, our body, so we eliminate large swaths of possible calculation. We may only seriously perform calculations such as these when we are very young, perhaps still forming a sense of self. Finally, it remains to be defined how one might calculate and define theta, but hopefully this mathematical formulation clarifies one conception of how to define the self. Perhaps this function can be related to measures such as integrated information as posited by Tononi’s Integrated Information Theory of Consciousness [3]. However, I am not certain this would account for scenarios where small exchanges of information can lead to exponential effects such as cancerous point mutations of genes for one example.

[1] https://www.frontiersin.org/articles/10.3389/fnhum.2017.00245/full
[2] https://www.frontiersin.org/articles/10.3389/fnhum.2016.00269/full
[3] https://blogs.scientificamerican.com/cross-check/can-integrated-information-theory-explain-consciousness/