Long Positions and Short Selling in Derivative Space
An Integration of the Theory of Language Derivatives, Inverse Problem Art, Interface Ontology, and Generative Topological Ontology
Tomokazu Tanaka (bigakusha-haha / Aesthetician Mother)
Abstract
This paper extends the distinction between buying, or taking a long position, and short selling from financial markets into the domains of language, art, artificial intelligence, self-formation, and ontological generation. It conceptualizes these positions as two fundamental movements within what is termed “derivative space.”
Derivative space is a space in which the future does not simply arrive after the present. Expectations, predictions, anxieties, promises, and narratives concerning the future are folded into the present, thereby transforming present value, meaning, judgment, and action. Yet the general statement that the future acts upon the present is insufficient to distinguish the different generative movements that operate within this space.
This paper defines the long position as a movement in which a subject assumes an object, experience, relation, or practice already grounded in the present and exposes itself to its future transformation. Short selling, by contrast, is defined as a movement in which a meaning, value, authority, identity, or future that is neither fully possessed nor presently grounded is temporarily borrowed from an existing symbolic order, circulated in advance, and left with an obligation of future fulfillment or grounding.
The difference between long and short positions therefore cannot be reduced to optimism and pessimism, upward and downward price movements, or a simple contrast between movement from the present toward the future and movement from the future toward the present. Their fundamental difference lies in the arrangement of possession, borrowing, circulation, grounding, temporality, and obligation.
From this perspective, hallucination in generative AI can be understood as an ungrounded linguistic short position: meaning that is not possessed as fact is circulated as though it had already been verified and settled. Inverse Problem Art, as proposed by bigakusha-haha, can instead be understood as a designed linguistic and ontological short position. It presents the outline of a result or world that does not yet exist and subsequently generates grounding through bodies, places, others, materials, institutions, time, and practice.
The aim of art, however, is not short selling for its own sake. Art is a practice that connects the future opened in advance by the short position to concrete reality through an interface and converts it into sustainable ontological generation. This paper describes such conversion as a topological transformation from short to long.
Ontological generation should therefore not be understood as an exclusive opposition between long and short positions. It is a process of circulation, conversion, settlement, and reopening. The interface is the topological apparatus through which unsettled relations between future and present, language and reality, and self and non-self are connected and transformed into a third reality that did not previously exist.
Keywords
derivative space, language derivatives, long position, short selling, inverse problem art, interface ontology, generative topological ontology, grounding, hallucination, self-externalization
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1. Introduction
A derivative is a form of value derived not directly from an underlying asset itself, but from its price, future state, volatility, temporal difference, or relational configuration. Within derivative markets, present value is never determined by the present alone. Expectations concerning the future, risk, volatility, institutional arrangements, the judgments of others, and prevailing narratives are folded into current value.
This structure is not limited to financial markets. Human language, art, institutions, self-understanding, and social relations do not operate solely through facts already established in the present. Human beings speak in advance of selves, works, institutions, communities, and worlds that do not yet exist, and these utterances transform present judgments and actions.
Statements such as “I will become a writer,” “this practice will form a new theory of art,” or “this technology will transform society” do not merely describe the future. They introduce future possibilities into the present and act upon subjects, institutions, and other people. Language is therefore not only an instrument for describing facts. It is also a derivative apparatus through which the future is folded into the present.
In the theoretical framework of bigakusha-haha, “derivative space” refers to a space in which the future does not arrive externally after the present. Expectations and narratives concerning the future already operate within the present. The present is an interface at which the results of the past and the possibilities of the future intersect; it is not a self-contained point.
Yet the claim that the future acts upon the present does not sufficiently distinguish the different generative directions within derivative space. Financial markets distinguish between buying, in which an asset is acquired and its future fluctuations are assumed, and short selling, in which an asset not owned by the seller is borrowed, sold in advance, repurchased later, and returned.
This distinction is not merely psychological. It is not simply the difference between expecting a rise and expecting a decline. Long and short positions arrange possession, grounding, temporality, circulation, responsibility, and fulfillment in different ways.
The purpose of this paper is to extend this distinction into linguistic generation, artistic practice, hallucination in generative AI, self-externalization, and ontological generation, and to locate these movements within Generative Topological Ontology.
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2. The Ontological Structure of Derivative Space
2.1 The Non-Self-Sufficiency of the Present
Within derivative space, the present is not self-sufficient. Present value and meaning are continuously transformed by expectations concerning the future.
The meaning of an object is not determined solely by what the object is at a given moment. It is shaped by what the object may become, how others may evaluate it, the narratives to which it may be connected, and the relations it may generate in the future.
Existence is therefore not a fixed substance. It arises through relations and possibilities of connection. This is consistent with the central proposition of Generative Topological Ontology: existence is not a closed entity but a structure open to connection with others and with the future.
A present existence is not complete independently of the future. It is present precisely because it remains open to the future. When it loses this openness, existence becomes fixed, institutionalized, and transformed into a repetitively circulating sign.
2.2 The Folding of the Future through Narrative
Within derivative space, narrative is not an explanation subsequently added to fact. Narrative acts by transforming future possibilities into present value.
Companies, technologies, artists, nations, philosophies, and individuals are evaluated not only according to present accomplishments but also according to stories told about their futures. When a future possibility is narrated and that narration alters the judgments and actions of others, a future that does not yet exist acts upon present reality.
Narrative, however, is not itself reality. It acquires generative force only through its connection to reality. Narrative severed from reality becomes a self-proliferating sign and excessively leverages value and meaning.
The central problem of derivative space is therefore not the act of speaking about the future. It is the question of how future-oriented language becomes grounded and how the obligations generated by such language are assumed.
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3. The Ontology of Buying and the Long Position
3.1 The Financial Structure of Buying
In finance, buying does not simply mean expecting a price increase. To buy is to acquire exposure to an object and to assume its future fluctuation.
A buyer assumes an object in the present and accepts both the rise and fall of its future value as personal gain or loss. Buying contains the structures of acquisition, holding, continuation, and exposure.
The essence of buying therefore lies not in optimism about the future but in assuming a relation to an object in the present and remaining exposed to the future transformation of that relation.
3.2 The Linguistic Long Position
Within the Theory of Language Derivatives, a linguistic long position is an utterance that assumes an experience, practice, relation, or nascent possibility already present in reality and develops it toward the future.
For example, the statement “by continuing this artistic practice, a new ontology will be formed” does not fabricate a future from nothing. Existing practices, experiences, places, bodies, and thoughts provide its ground. The utterance assumes these present realities and opens the speaker to their future development.
A linguistic long position does not mean fixing reality through possession. It means assuming a concrete present reality and exposing oneself to the future transformation latent within it.
3.3 The Long Position and Self-Externalization
The long position is also a form of self-externalization in which the present self is projected toward the future. The subject does not preserve itself as a completed identity. Through practice, production, and relations with others, it becomes exposed to a self it does not yet know.
In this sense, taking a long position is not the reinforcement of self-identity. It is the act of placing the present self at stake and assuming the difference that may emerge between the present self and a future self.
Within the thought of bigakusha-haha, the self is not generated from within itself alone. It arises through connections with what is not itself, through failure, disjunction, unexpected events, and friction with reality. An ontological long position therefore means assuming the possibility that the self will be transformed by what lies outside it.
3.4 The Limitation of the Long Position
The long position cannot be affirmed without qualification. Assuming what is grounded in the present can become excessive attachment to existing reality, institutions, authority, or self-understanding.
When buying loses the possibility of further connection and becomes mere possession, the subject no longer assumes reality but fixes it. The future can then be imagined only as an extension of the present.
For the long position to remain generative, it must be understood as exposure rather than possession. Generative buying does not close an object through ownership. It assumes the risk that the subject will be transformed by its relation to the object.
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4. The Ontology of Short Selling
4.1 The Financial Structure of Short Selling
In financial short selling, a subject borrows an asset that it does not own, sells it in the present market, repurchases it in the future, and returns it to the lender.
This structure contains four essential moments. First, the asset is not presently owned by the subject. Second, it is borrowed from another person or institution. Third, circulation through sale precedes repurchase and return. Fourth, an obligation of future settlement remains.
The essence of short selling therefore does not lie merely in predicting a price decline. Short selling is an operation in which something not possessed is circulated in advance, thereby creating an unsettled relation between present action and future fulfillment.
4.2 The Linguistic Short Position
Within the Theory of Language Derivatives, a linguistic short position occurs when a subject borrows a meaning, fact, authority, identity, qualification, or future that it does not yet fully possess as reality and circulates it in advance through existing linguistic and narrative systems.
Human beings do not privately own language itself. They speak through words inherited from society, history, culture, education, and others. In this broad sense, every utterance contains an element of borrowing.
The linguistic short position, however, concerns more than this general borrowedness of language. It concerns the advance presentation of a meaning that has not yet been realized, through which present judgments and realities are altered.
Statements such as “I am an artist,” “this work is the beginning of a new artistic movement,” or “this research will become a new theoretical system” are not necessarily descriptions of fully established facts. They circulate in the present a possibility that may only become established in the future.
A linguistic short position is therefore a leveraged linguistic operation in which a meaning or existence expected to be established in the future is advanced into the present, leaving an obligation of future grounding.
4.3 Short Selling Is Not Identical with Falsehood
A linguistic short position is not necessarily a lie. What has not yet been established is not thereby false.
Promises, declarations, hypotheses, plans, artistic concepts, and political ideals all speak in advance of futures that do not yet exist. If every statement concerning what has not yet been realized were false, human beings could not create futures.
The linguistic short position is not a simple midpoint between truth and falsehood. It circulates meaning that is not yet settled and opens the possibility of future fulfillment.
It should therefore not be judged only according to whether it is factually established at the moment of utterance. It must also be judged according to whether the speaker recognizes its unsettled condition, whether this condition is concealed from others, and whether the obligations produced by the utterance are assumed in concrete reality.
4.4 The Risk of the Short Position
The danger of the short position does not lie only in the possibility that the anticipated future will fail to materialize. A more fundamental danger arises when ungrounded meaning continues to circulate as though it were already grounded fact.
When an utterance is neither connected to reality nor revised or withdrawn, and when it is amplified through authority and repetition, it produces a symbolic space autonomous from reality. Language no longer represents reality; language itself is consumed as reality.
This is excessive leverage within the space of language derivatives. A minimal degree of grounding supports an enormous structure of meaning, authority, and value. When grounding disappears, the structure may collapse rapidly or may continue to conceal its incompatibility with reality through power.
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5. The Fundamental Difference between Long and Short Positions
Both long and short positions introduce the future into the present. It is therefore insufficient to define the long position merely as movement from the present toward the future and the short position as movement from the future toward the present.
A long position also folds expectations of future value into present judgment. A short position also acts through present institutions, language, and markets. Both connect present and future.
Their more fundamental difference lies in the arrangement of grounding and obligation.
In a long position, an object, experience, or relation is already grounded to some degree before the act of linguistic or financial exposure. The subject assumes this grounded reality and becomes exposed to its future fluctuation.
In a short position, the meaning or future being circulated is not yet sufficiently grounded in the present. The subject borrows it from an existing symbolic order or narrative, circulates it in advance, and postpones grounding into the future.
The long position thus moves from grounding toward exposure to the future. The short position moves from advance circulation toward an obligation of future grounding.
The responsibility of the long position is to assume the future transformation of an acquired relation. The responsibility of the short position is to connect an advanced meaning to reality and to respond to the consequences of that circulation.
The distinction can therefore be formulated as follows.
A long position is a topological movement in which a subject assumes an object, experience, or relation already grounded in reality and opens itself to its future transformation.
A short position is a topological movement in which a meaning, value, or future not yet sufficiently grounded is borrowed and circulated in the present, leaving an obligation of future fulfillment and grounding.
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6. Generative AI and the Ungrounded Linguistic Short Position
6.1 Does AI Possess Meaning?
Generative AI produces statistically plausible sequences of words on the basis of learned linguistic patterns and an input context. Its responses may appear grammatically and semantically coherent. Such coherence, however, does not guarantee grounding in bodies, places, experiences, primary sources, or current reality.
AI does not experience an object and possess that experience as its own history in the same manner as a human subject. The meanings it produces are temporarily constituted from a vast linguistic space, and their correspondence with reality requires separate verification.
Generative AI can therefore be understood as an apparatus that borrows meaning from linguistic space and circulates it in advance as a present response. Structurally, it performs linguistic short selling.
6.2 An Ontological Definition of Hallucination
Hallucination in generative AI cannot be adequately understood solely as factual error or technical malfunction.
Ontologically, hallucination occurs when meaning not possessed as reality is circulated as though it were already grounded and settled fact.
Hallucination is therefore an unsettled linguistic short position.
Ungrounded linguistic generation is not necessarily problematic when clearly presented as hypothesis, fiction, prediction, or possibility. The problem arises when conjecture, hypothesis, fiction, and verified fact are presented with the same degree of certainty.
What AI requires is therefore not merely the suppression of generation but an interface that indicates the grounding status, certainty, sources, and unsettled character of generated language.
6.3 AI and the Absence of a Persistent Self
Human short selling presupposes, at least in principle, a subject capable of assuming a future obligation. Human beings can recognize a broken promise, revise a previous statement, and assume responsibility for what they have said.
AI, however, does not necessarily possess a persistent history of self in the same sense. It may not continuously retain the unsettled obligation produced by a previous utterance as its own problem.
Linguistic short selling by AI therefore contains the structural problem of an absent bearer of fulfillment. Hallucination is intensified not only because meaning is ungrounded, but because no enduring self necessarily remains to assume that lack of grounding over time.
The ethics of interfaces in the age of AI should therefore not consist in personifying AI. It should design who or what institution will assume the unsettled conditions produced by AI-generated utterances.
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7. Inverse Problem Art and Designed Short Selling
7.1 Forward and Inverse Problems
A forward problem derives an outcome from known causes, conditions, or inputs. An inverse problem infers causes, conditions, or structures from an observed result or outline.
Inverse Problem Art, as conceived by bigakusha-haha, is not limited to inferring artistic intention from a completed work. It presents in advance the outline of a result, relation, or world that has not yet been realized and generates from that outline the actions, places, materials, institutions, and interfaces required in the present.
In Inverse Problem Art, the future is not merely the result of the present. The outline of the future is folded in advance into the present and organizes present action.
7.2 Artistic Short Selling
The artist presents in advance a work, value, relation, or world that does not yet exist. Art therefore has a short-selling structure.
An artistic declaration does not merely report an already established movement. It names a movement that has not yet fully come into existence and circulates that name in advance. A work likewise does not merely reproduce already shared meaning. It presents sensations, relations, and realities that have not yet been shared.
Art is therefore a designed short position that advances future meaning into the present.
Artistic short selling, however, differs from disguising ungrounded meaning as established fact. Art may disclose its own provisionality, incompletion, and lack of settlement as conditions of the work.
A work of art does not necessarily claim, “this is already a verified fact.” It may instead state, “such a reality may become possible.” Through this presentation, relations with viewers, places, bodies, and time begin.
7.3 The Topological Transformation from Short to Long
The future presented in advance through artistic short selling becomes grounded through connections with works, places, bodies, others, and time.
At this point, what began as a short position undergoes a topological transformation into a long position.
The artist no longer merely continues to speak of the future presented in advance. The artist assumes the concrete reality generated by that future. When a work is installed in an actual place, encounters others, produces unexpected responses, and transforms the producing subject, the advance circulation of the future becomes exposure to reality.
Inverse Problem Art is a practice that opens the future through a short position, connects that future to reality through an interface, and sustains it as a long position.
7.4 The Difference between Art and Hallucination
Both art and hallucination generate meanings that do not presently exist. They cannot therefore be distinguished simply according to whether their contents are unreal.
Their difference lies in their treatment of non-grounding.
Art opens its lack of grounding. It allows meaning to remain unsettled, to change through contact with reality, and to continue generating through relations with viewers.
Hallucination conceals its lack of grounding. It closes ungrounded language as though it were already grounded fact.
Art opens non-grounding; hallucination conceals it.
Art does not eliminate incompatibility with reality as failure. It transforms such incompatibility into an occasion for further generation. Hallucination covers incompatibility with linguistic coherence without recognizing it.
Inverse Problem Art is therefore formally adjacent to AI hallucination while occupying a different ethical and ontological position.
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8. Interface Ontology and Grounding
8.1 The Interface Is Not a Neutral Medium
Within Interface Ontology, the interface is not a neutral instrument externally connecting two entities that already exist.
An interface is the site at which different topological configurations encounter one another and generate a relation, meaning, or existence that did not previously exist.
The self and non-self, language and reality, future and present, body and information do not merely exchange information through an interface. They are mutually transformed by connection.
8.2 The Interface as a Surface of Settlement
When the theory of long and short positions is introduced, the interface can be defined as a surface of settlement on which unsettled language, meaning, and future encounter reality.
A future advanced into the present through a short position encounters bodies, places, others, materials, institutions, time, and contingent events through an interface.
The outline of the future is not simply realized unchanged through this encounter. It is transformed. Reality is also altered through its encounter with the future outline.
Grounding is therefore not the unilateral application of completed language to reality. It is the mutual transformation of language and reality through which a third existence is generated.
Settlement does not mean that a prediction becomes perfectly correct. It means that a meaning circulated in advance is revised and transformed through contact with reality and is assumed as a new relation that includes this transformation.
8.3 Place and Space
Within the theoretical framework of bigakusha-haha, place contains accumulated bodies, experiences, memories, time, and relations. Space, by contrast, is an abstract structure detached from those accumulations and rendered exchangeable as coordinates.
Derivative space folds future possibilities into the present. Yet when it loses connection with place, it becomes an infinitely expanding symbolic space.
Language and information circulate rapidly by becoming detached from place. This speed and extensibility also produce a loss of grounding.
Sayama Aesthetics School, Web Installation, bonsai, and the other practices of bigakusha-haha can be understood as interfaces through which abstract language derivatives become grounded in concrete bodies and places.
These practices are not illustrations of theory. They are places in which futures presented in advance through theory encounter reality, become transformed, and are settled.
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9. Integration with Generative Topological Ontology
9.1 Existence Is Not a Fixed Position
Long and short positions are not fixed binary opposites. A language, work, or practice may begin as a short position and later be transformed into a long position through grounding.
Conversely, a practice that begins as a long position may lose its ground. If it circulates only through borrowed authority, institutional prestige, or inherited narrative, it may be transformed into a short position.
The problem of ontological generation is therefore not whether a subject belongs to the long or the short side. What matters is how one position is transformed into another through connection.
Existence is generated not in the position itself but in the process of transformation between positions.
9.2 The Long–Short Duality Theorem
This paper proposes the following theorem concerning ontological generation within derivative space.
The Long–Short Duality Theorem
Ontological generation within derivative space can be described as a dual relation between the long movement, in which a subject assumes a reality grounded in the present and opens itself to its future transformation, and the short movement, in which an ungrounded future possibility is advanced into the present and leaves an obligation of future fulfillment. The two movements are converted into one another through an interface, and generation is the process through which their unsettled relation is locally settled through contact with concrete reality.
Duality does not mean that the two movements are perfectly symmetrical. Long and short positions are asymmetrical in their arrangements of possession, grounding, and obligation.
Yet neither can complete ontological generation by itself.
Without the short position, generation is reduced to an extension of the present. Without the long position, generation loses grounding and tends toward linguistic hallucination.
The long position assumes reality but lacks the force to open a future radically different from the present. The short position opens the future but does not guarantee that the future will be assumed as reality.
Their connection joins the advance presentation of the future with the concrete particularity of reality.
9.3 Structural Non-Closure
Generative Topological Ontology understands existence not as a completed closed set but as an open structure retaining the possibility of connection with others and with the future.
The circulation of long and short positions likewise has no final endpoint. Even when a short position is transformed into a long position through grounding, that long position becomes exposed to new future fluctuations and generates another short position.
After an artistic declaration becomes grounded in a work, the work opens new interpretations, relations, and futures. After a theory is supported through practice, the practice modifies the theory and produces new questions.
Settlement is therefore not the end of generation. It does not completely erase the unsettled condition. It transforms it into a new real relation and opens the possibility of further connections.
Derivative space repeats local settlements while remaining structurally non-closed as a whole.
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10. The Self and the Non-Self
10.1 Taking a Long Position in the Self
To take a long position in the self does not mean possessing a completed self-image. It means assuming one’s present body, experience, history, and limitations and opening oneself to the possibility that they will be transformed in the future.
The self is not a fixed underlying asset. It is an existence whose value and meaning continually change through relations with what is not itself.
Taking a long position in the self does not mean evaluating oneself positively. It means assuming the danger that contact with reality may transform the self and may even cause one’s previous self-understanding to collapse.
10.2 Short Selling the Self
To short-sell the self means to name and circulate in advance a self-image, social role, authority, or future self that has not yet been realized.
Human beings may approach a future self by speaking it in advance. Short selling the self is therefore an indispensable moment of self-formation.
Yet when a future self-image loses contact with reality and is maintained only through evaluation, titles, follower counts, institutional positions, or linguistic approval produced by AI, the short position becomes excessively leveraged.
The subject no longer generates a self. It continues to circulate a borrowed self-image.
The contradiction described by bigakusha-haha as “seeking the self in what is not the self” connects to this structure. When a subject seeks existence exclusively in the evaluations of others and institutional signs, it borrows its existence from outside and circulates it as the self.
The role of the interface is not to recover the self from the outside and close it once again. Its role is to design an occasion in which the borrowed self-image collapses through contact between self and non-self and a previously unknown self is generated.
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11. Ethical Implications
Linguistic short selling is indispensable to creation, promises, education, research, art, politics, and technology. Without speaking the future in advance, no new reality can be generated.
Ethics therefore does not prohibit speaking of unrealized futures. It requires recognizing and assuming the unsettled condition generated by such speech.
The first principle of an ethics of language derivatives is to indicate the grounding status of an utterance. Fact, conjecture, hypothesis, promise, fiction, and prediction occupy different states of settlement and should not be presented with identical certainty.
The second principle is not to conceal borrowing. Language, authority, concepts, and institutions are not completely possessed by the subject. The subject must recognize the histories, languages, others, and institutions from which meaning is borrowed.
The third principle is to assume the obligation produced through advance circulation. A subject that speaks of a future must be prepared to revise, withdraw, or reconstruct the utterance when that future fails to materialize.
The fourth principle is not to conceal incompatibility with reality as failure. Incompatibility should not serve merely to subordinate language to reality. It can transform both language and reality and become an occasion for new existence.
The fifth principle is not to transfer risk unilaterally to others. A structure in which a subject obtains profit or authority through short selling while shifting its unsettled risks onto others or society must be ethically criticized.
Ethics is not the caution of refusing to speak of the future. It is the refusal to escape the responsibilities generated by speaking of the future and the willingness to transform one’s language and self through contact with reality.
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12. Conclusion
This paper has theorized buying and short selling within derivative space not as metaphors borrowed superficially from financial markets but as fundamental topological movements running through language, art, AI, the self, and ontological generation.
Buying means assuming an object, experience, body, place, or relation already grounded in the present and exposing oneself to its future transformation. It does not mean possessing the present as a fixed object. It means assuming the risk that the self will be transformed through its relation to the present.
Short selling means borrowing a meaning, value, authority, identity, or future that is not yet sufficiently possessed or grounded, circulating it in advance, and leaving an obligation of future fulfillment and grounding.
Through this distinction, hallucination in generative AI can be understood as an ungrounded linguistic short position in which meaning not possessed as reality is circulated as though it were already settled fact.
Inverse Problem Art, by contrast, is a designed short position. It presents in advance the outline of a future that does not yet exist and subsequently generates grounding through bodies, places, others, materials, institutions, and time.
The difference between art and hallucination does not lie in whether they generate something unreal. Art opens its own lack of grounding and entrusts itself to mutual transformation with reality. Hallucination conceals its lack of grounding and closes itself as fact.
The interface is the topological surface of settlement on which this unsettled condition encounters reality. The future presented in advance is not simply realized as originally conceived. The future outline and concrete reality transform one another and generate a third relation that did not previously exist.
Ontological generation therefore does not require choosing either long or short. It consists in remaining between the risk of speaking a future that does not yet exist and the responsibility of assuming the reality that already exists, continuously connecting the two through interfaces.
Without the short position, the future is reduced to an extension of the present. Without the long position, the future loses grounding and becomes hallucination.
Generation is the circulation through which the short position opens the future, the long position assumes the reality produced by that future, and this reality in turn opens another future.
Derivative space is a space in which the future is folded into the present. Its core, however, does not lie in prediction or anticipation itself.
Its core lies in how the unsettled meaning produced by the advance presentation of the future is assumed, transformed, and generated as a new existence within concrete bodies, places, others, and realities.