On thinking inversely
Some of us today are concerned essentially with the possibility and method of ‘escape.’ Escape from metaphysics, ‘data,’ psychologies, from the scattered omnipresence of politics, thinking, romanticism. Escape from materialism, from plastic and meat. Escape from the technologies of vulgar reductionism and positivism. Escape from recommendation algorithms—‘feeds’—quietly linearizing and then binning what we expect, anticipate, and hope for. “What do you do?” instead of “who are you?” What are we “doing to the Earth” instead of “how do we live?” Our profiles haunt us offline. Cheap conditioning, it’s easy: “oh that’s interesting.”
Withdrawal from these things, ‘dopamine fasting’ and asceticism, cannot ‘bring us’ there—they amount to no more than the trivial solution: multiply by zero.
Some of us today are beginning to become aware that we can no longer hope for a new principle or datum to bring us there, either. No maxim or scientific ‘paradigm shift’ will be enough to bring us to an understanding of what it is that conditions the awareness of these principles, that is, their horizons, the places we have already cut out for them in our thinking. We have already designated them as ‘new,’ and we have always already exhausted them. It can no longer be that escape resides elsewhere, that it lives ‘tomorrow’ but not ‘today.’ It cannot be that we will bring about an escape from somewhere ‘beyond what it currently means to be human’ while having a human heart, while retaining something of what it must mean to love one another now. If we recognize that we do not seek an escape ‘from,’ from a spatial domain (or belonging to the type of awareness of awareness which we implicitly make spatial with our words, the ‘mental arena’ or ‘public sphere,’ etc.) outside of which there is something else and it is this something from ‘outside’ that must find its way ‘inside’ so as to effect this escape, it must be that we have nothing to work with but what we have. In the strongest version of this claim, our faith in this kind of escape is material—it will not invoke a heaven. It will not pit an ‘everyday’ against a ‘extraordinary.’ We will not seek to bring into focus one more boundary to leap over or stitch into our great quilt of categories. In fact, we will categorically abandon the new, for even this we seek to escape.
The new, as far as we are concerned with it, is a kind of dying insofar as it is predicated by an ‘outside’ of our lives. Our escape will not involve dying nor resurrection. It can be nothing other than a reconfiguration, a massage and physical therapy. The possibility of this kind of escape is certain because what goes by the name of the ‘radical third option’ is an option at all—not outside in a qualitative way, but ontically leveled as an ‘option,’ just as option number one and option number two are options. This is the seed and bean of our faith. That it is possible to utter the phrase. That the radical third option resides, ‘somehow’ but not at all paradoxically, that is to say we can build a method for it, not outside of the Venn diagram but within the overlap. Meaning, and radically so, that it is already radical to pick synthesis. Why have we so far given up on synthesis, on saying “to the extent that,” “insofar as,” “with the caveat that,” on sub-optimality with respect to the absolute, on compromise? (Keep in mind that ‘using what we have’ is not cheaply looking ‘inwards,’ or ‘inside ourselves,’ because these phrases imply a vantage point on the self from which there is this ‘inside,’ a vantage point which is impossibly, and for us undesirably, externalizing.) To those who are essentially concerned with escape, and this is now an address, I will suggest one possibility regarding some subtle differences between confinement and ‘closure.’
Confinement: the boundary of the domain. The ‘edge of our thinking.’ The limits against which our circumstances circumscribe us. It is, in a naive kind of escape, these limits which we attempt to step beyond. Closure: the working principle of a synthesis which limits the kind and quality (category) of its product. We say that the integers, under an operation like addition, are ‘closed,’ because two integers added together will always produce another integer. The result is of the same kind as the ingredients. This is the first of a few mathematical analogies to come, the point of which, as usual, is to, in the analogical realm, make certain conclusions clear and inevitable and then retrieve these conclusions to make sense of them in our life. In actuality, this final retrieval operation cannot be done without an enormous leap of faith. It is already not without discretization, projection, and great extraction from the living world that we convert the foci of our attention into mathematical objects, and it is not without a faith in the methods and existence of ‘pure reason’ do we proceed with these objects; so it is a faith on top of a faith on top of a mistake with which we will pull our plan into focus. The reason for this faith is that, as usual, hopefully by abandoning the familiarity of our working materials (tools and people and otherwise the ‘entities’ of everydayness) we will be able to perform a ‘hat trick’ for ourselves, teach ourselves something about ourselves, pull, at the end, something we might not have ever reached in an infinite time into a finite future. We will be content to forfeit the contingency of our ordinary intuition for now to perform this trick, and we will also be content to reintroduce these contingencies ad hoc. We will have a faith in reason in the same way we will have a faith in a shared material reality. It is something common to us all, and, crucially, if not, then the faiths in these things are common to us all—as well as the very faiths in their commonality.
Some of us confuse confinement and closure because we are subject to both of them. Meaning to say, we are both trapped and our methods cannot lead us out, where the trouble is that the latter masquerades as the former. The mask which is put on, so to speak, must be the facticity of thought, its propensity to exert itself as a state of being—a state with attributes, like a size or a place, and references to subjects who can ‘enter’ and ‘exit’ this state. Or become trapped. “I was lost in thought.” The kind of escape we seek, however, is not an onto-spatial one: we do not simply want to become unconfined, ‘move’ from one kind of being to another, however more ‘free,’ kind of being. We want instead to be free from the structures which have up until now predicated our thought as it masquerades as a state of being.
First case study. Digital people and their advertisements share, in a consummate dialogue, a fascination with ‘being mindful’ and ‘living in the moment.’ In the self-help genre, or in conversation with friends, this mindfulness certainly takes on a stateful character. To that end, it is a state among—and contingent on—other ontically leveled states. This mindfulness is supported and suspended by the anticipations and expectations, for it, of complementary ‘not mindful’ states of being. For example, it may be that we practice mindfulness during work so that we can escape the feeling of merely ‘going through the motions’ while being in our thoughts somewhere totally elsewhere. Or take for example the oft-billboarded twin concepts of vacationing hikers and their natural mindfulness, that they are ‘able to achieve’ mindful presentness as a result of their serenity. (The clever among us will claim that being mindful ‘does nothing’ and that its value lies in a way to ‘be here,’ that the purported psychological ‘state of mindfulness’ is only secondary and on top of its possibility as an ontic method. It now seems as if we have might freed mindfulness from contingency on other states, insofar as it does nothing to them, however, all we have done is driven its wires and pipelines down below states of mind into states of being: what we have now is a state of ‘being here’ which can just as easily be predicated by being elsewhere. A tool for growing into some being or other resembles thinking in this very sense—it will quickly, as soon as it can help it, don its stately mask.)
Being free from predicated thoughts and states, or most generally, any structure which made spatial makes room for adjacency, exteriority, etc., cannot, then, involve a sense of domain or boundary which we must step across—in some sense, we must free our conception of being from the kind of dividing lines which lend themselves to addition and subtraction. In fact, there is no such exterior perspective (oriented towards being) which we can take to ourselves become ‘apart’ from being and then combine its constituent parts, like we do with furniture in a room. This being said, we still have a faith in synthesis and reconfiguration—we still have a faith in the multiplicity and dynamism of human thought. That our ‘things’ are not useless. That, although being is complete, altogether coupled, and contented with itself, we can still refer to beings. As for our escape, it follows that we must step over the ‘closure’ of things. We turn to simple algebra in beginning the search for an open combinatorics, a method for categorical change.
The integers are closed under addition. So are unitful quantities, like pounds or gallons. If we add something with units of Newtons—the units for a force—to something with units of Newtons, their sum will also have units of Newtons. A force and a force added or subtracted—crucially, the operations of addition and subtraction can only take as their addends quantities with the same units, that is, we cannot add three gallons and six trees—make a force. Dialectics works this way through the use of the ‘not,’ or complement. It takes its ‘second choice’ from within what is not the first.
Take now ‘life paths’ as our units. We who, stuck in a ‘loveless relationship’ or a ‘soul-crushing job,' fitfully envision (and then seek out) another relationship or job, or no relationship, or no job, from within the complement of the first—from within its ‘not,’ “what aren’t I doing in my life that I would like to be.” Further, if we don’t simply seek to replace the former with the latter, we seek to combine them: “What is it in this other path I find so inspiring that I can incorporate into the path I walk now?” “What can I take from my previous relationship to inform this one?” There are manifestly three problems. Firstly, the second principle, force, or path is drawn from the not. This is precisely the domain which is already wholly reliant on the first to make sense. That is, for example, what we ‘aren’t doing’ comes down to an arbitrary choice of what—out of the full spectrum of our being—we ‘are doing,’ what ‘path’ (now with a fully developed suspicion for this category) we pursue, and it is therefore a first set of blinders to reify thoughts qua objects. The production of the statement “this is what I am doing,” and nothing else. Secondly, the resulting principle, the sum, will have no possibility for transcendence, qualitative escape, since the method of addition is closed over addends with already chosen units. The life path we devise making full use and fusion of our existing paths can only be just that—another path. In our attempts to include the negative space we simply enlarge the space; wielding the word ‘radical’ and sketching out the elusive ‘outside of the Venn diagram’ we end up oscillating, in a vulgar series of linearizations and projections, between the two halves of the diagram. (The metaphysical trouble is that by drawing from either side of the ‘not’ we seem to destroy the overlapping part of this diagram, for something and its negative add to zero. In this sense we are skipping over but here giving a glowing nod to the possibility of authentic compromise, which can only be built from love.) Thirdly, additive synthesis does not grow in an organic sense, but whirs. It is automatic, ‘zero-sum,’ taking parts from each and swapping them, replacing them, organ transplant, economic exchange, focus on ‘the best of both worlds,’ or if not, the best of one world and the best of the other. In a single domain the two principles are put into a competition of building blocks and particles. It is already a ‘land grab.’ The transcendence of the ‘result’ (now we can even begin to cast doubt on the dominance of this term over the others) is excluded because the domain into which the addends enter is the domain in which the sum already is. Whats more, this kind of ‘land grab’ is a kind of reliance on the concept of confinement: we need to invoke the ‘pulling in’ of new information, a hope for the ‘outside’ to save us, a truly outwards-facing ‘not,’ a faith in the complement, the so-far excluded environment which will contain the until-now hidden resource from which we will build our salvation. It is only by assimilation, then, will this all occur: we will build our salvation on our terms which will hereby include another’s. Every number has a successor.
What is thinking inversely? In actuality, it is a proposal inside of a metaphor. It is a suggestion to open up to a suggestion, a call to do analogical labor. If it is a task, it is to pull the concept of the inverse out of a word and into a life. Here is this task. The multiplicative inverse is a number which, multiplied with a number, yields unity. Four times one-fourth is one. One pound times one ‘inverse pound’ is one. This second kind of unitful statement is the crux of the analogical work and its living center. The ‘inverse pound,’ one over pounds, is not a measure of weight but of something else. It is the measure of something which is contingent on weight but is not weight, something ‘per weight:’ one of ‘these’ per each gram. It is something which is reliant on weight to make sense, but qualitatively not something captured by the reading on a scale. Sometimes a unitful inverse will be easy, intuitive: One cubic inch times ‘one per cubic inch’ is one, where the inverse now means a density. Sometimes it will be otherwise—what is ‘one over a force?’ What is ‘one over a life path?’ Only something counted ‘per,’ a kind of response.
Of special interest too is the product, unity, which has no units. Unity is not a quantity but a pure number; a number without units can only stand for pure relation, a ratio.
In essence, we are done. We have now sketched out the analogical end of this ‘multiplicative’ method, implying all along how the prudent use of inverted units develops a way to escape category and kind. However, we have not yet any hint of how the ‘inverse’ functions as a method of thinking, and we have not yet specified what would be necessary to bring this kind of thinking to life. If this bringing—or retrieval—were simple, we would have already been done with it. Its difficulty may be its preeminent hope, our proof that it is something we haven’t tried yet. In full view of the opacity of ‘inverting’ a real-life category, I can only offer some preliminary ideas. Clues as to where we will look.
Our first clue resides in the term of primary interest: it will no longer be the result, what was once the sum and is now the product, but the inverted term. The ‘one fourth.’ To think inversely is no longer to draw from a vast and categorically equivalent complementary space, but to draw out an inverse (which, if you must, could conceivably come from an ‘inverted space,’ or ‘dual space,’ but this is a space in which our intuition must fail us, because here our notions of distance have limited meaning, here we can no longer ‘bring near’ or grab ‘from yonder,’ and so our hasty spatialization is blocked) from what we have. This drawing out takes hold of and guides the method. Drawing out the inverse is not a locus onto which something new is ‘tacked on,’ but a reconfiguration of existing principles. To think inversely, we must cease considering the space of ‘options’ drawn from the idea of an exterior, cease to wonder what we can ‘bring into the fold’ from a smorgasbord which is already displayed in a kind of subservience to our question, and begin to wonder what it would mean to have an inverse for the category which was the horizon and basis of this question. It is first of all this new focus which could draw attention to how the categories of the working objects of our question, the psychologically sticky but otherwise artificial ‘units’ of thought, build up our confinement from its roots. “How does what I call this or that, my use of certain stock-phrases and ‘states,’ ground the content of my thinking about it? What would it mean to come into transformative contact with its ‘kind?’”
Without even having so far touched on the ‘equals sign,’ have we yet begun an advance on the notion of quality? In thinking inversely we first hope to lay bare the modes of contingency which our thoughts inevitably take on, and then probe some method of combination which denies these modes sufficient hold on our thought. It is nowhere written that we must cobble together our lives from options, possible identities, and states. Our second clue to retrieving our method from mere words would be its connection to building the categorically transcendent ‘radical third option.’ Excepting, again, that this transcendence would not just be a function of the product alone; the third option is no longer just the right hand side of the equals sign but a dual consideration of the inverse term and the product. That is to say, we have already noted that the inverse term is of new units and the product has no units: we have twice over escaped. In beginning to draw out a qualitatively distinct inverse, we have already decided on a nonqualitative product. Not emptied of content like the zero, but emptied of measuredness, the sense of being measured ‘in terms of.’ Again, since the right hand side is always simply one, the focus or burden of meaning is split on both sides of the equation—a true and authentic escape from ‘metaphysics’ and ‘data’ would requires of us a reconfiguration of question and answer, cause and effect, reason and method. (Do we find ourselves lost in ‘computations’ instead of thought? Do we identify our subconscious with ‘feeds?’ Images bubble up and lend themselves. Are we concerned with finding ourselves? or our ‘profiles?’) Again and again, the ‘one’ of the right hand side is not an absolute or central category of thinking, but almost a placeholder, a counterweight, a contrapunctal asteroid against which the center of mass can flutter and find itself.
Most importantly, the difficulty of finding a proper example of what an ‘inverted thought’ would be like points not to its impossibility, or the impossibility of the method as such, but towards the intrinsic rejection in this method of the primacy of ‘thoughts’ as entities. As in, to fixate on what an ‘inverted life path’ would look like would be a grievous mistake. It could very well be, and it would represent no great weakness of the method, that there is no way to make sense of an ‘inverted force’ or ‘one over Newtons’ in a living context, that the concept of a unit which intimately depends on but which may not be qualitatively nearby or deformable to another is an empty concept. So far as this could be the case, retrieving ‘inverse thinking’ from inside its analogical shell would involve quite a bit of luck. Luck, however, is not a category rooted in chance but in openness. We are willing to. The relationship between escape and inverted thinking is that we are willing to begin both of them. It is that, as a first step, we are willing to renew our relationship with entities, routes, ‘inputs and outputs,’ and spatialization. The ‘edges of thinking’ or the ‘arena of thought.’ So far as spatializations begin as analogies we are not afraid to begin our exploration of escaping them in analogy. The trick is, as the first step on the other foot, to then retrieve ourselves…
and it may be that, because we are taking a leap, these two steps need to happen at once.