Sub-atomic Philosophy

by Beth Metcalf

“If philosophy has a fundamental need for the science that is contemporary with it, this is because science constantly intersects with the possibilities of [philosophical] concepts and because concepts necessarily involve allusions to science….”  (What is Philosophy, 162)

Therefore, we should expect that the philosophy of Deleuze and Guattari must arrive at philosophical concepts that “intersect” with functions of modern quantum physics that do not resemble them.  The philosophical concept and the scientific function intersect, each according to its own line. 

(WiP 161) “The [philosophical] concept does not reflect on the [scientific] function any more than the function is applied to the concept.  Concept and function must intersect, each according to its line.”

This is the intersection of two types of multiplicities --- the intensive and the extensive.  The concept is inseparability of variations.  The scientific function is independence of variables.  D&G tell us (WiP 155-6) that the scientific line of functions goes from a chaotic virtual to the state of affairs that actualizes it.  The philosophical line goes in the opposite direction, from the state of affairs to another kind of virtual that is a consistent event eluding actualization.    

(WiP 126) “Philosophy continually extracts a consistent event from the state of affairs….science continually actualizes the event in a state of affairs….”    

(WiP 118-20) Philosophy wants to retain the infinite (the birth and disappearance of chaotic speeds) while gaining consistency of concepts on a plane of immanence.  Science approaches chaos by a slowing down of the infinite to gain reference.  By relinquishing the infinite, science gains reference with functions that actualize a virtual.  Therefore, science is the slowing down that sets limits to the infinite speeds of chaos.  Limits are conditions of this slowing down.  But a limit must not be a negative mediation.  There must be an immediate embrace of a limit with the infinite.  (See my article ‘Two Types of Multiplicities’.) That is, it is not a limited thing or set of things (on a plane of reference) that mediates a limit of the infinite.  Rather, it is the immediacy of the limit (on a plane of immanence-consistency) that makes functions possible.  So the limit is not mediated on an already presupposed reference frame extrinsic to an observer.  Rather, the limit must immediately embrace the infinite on the philosophical plane of immanence from which things will be actualized within a coordinate system.  Singular difference may be actualized as a singular plane of reference, each time.  There is no generalizing consistency.  There is no totalizing reference. 

“Is there just one or several planes of reference?  The answer will not be the same as the one given for the philosophical plane of immanence with its strata or superimposed layers.  This is because reference, implying a renunciation of the infinite, can only connect up chains of functives that necessarily break at some point….” (WiP 124)

Observations of quantum effects have made it more important than ever for contemporary physicists to ask some philosophical questions.  But the scientist, according to D&G, can only do this according to the scientific line of the function.  This leads D&G to ask (WiP 162) whether there are, as well as philosophical concepts of functions, also scientific functions of concepts.  This is to ask whether science is also in need of philosophy.  D&G acknowledge that only scientists can answer that question.  However, D&G believe science is also in need of philosophy since, whenever the physicist makes an observation of quantum effects, the conceptual interpretation must still be discovered.

(WiP 117) “…when an object….is scientifically constructed by functions, its philosophical concept….must still be discovered.”

This seems to imply that the philosophical concepts of D&G must involve allusions to contemporary science --- allusions that are not to be taken as examples, applications, or reflections belonging to the line of the scientific function.  Philosophy can only allude to scientific functions according to its own line of concepts.  Philosophy can only speak about concepts of functions.

Therefore, we should expect that the philosophical concepts of D&G involve allusions to contemporary sub-atomic, quantum physics.  And, there is abundant textual evidence that Delueze (with and without Guattari) lays out a plane of consistency involving concepts that are sub-atomic (or as Deleuze sometimes calls them, ‘sub-representative’).  And, of course, these “sub-atomic” concepts can only allude to the probability functions of sub-atomic effects.  These sub-atomic concepts on a philosophical plane of immanence are not at all similar to any scientific functions of reference.  There is no analogy or metaphor between them.  

As D&G see it, scientific reference constantly intersects with the possibilities of philosophical consistency.  Therefore, because contemporary sub-atomic physics is so different from classical physics, shouldn’t we expect that the concepts of contemporary philosophy must be different from all traditional philosophy too?  Traditional philosophy has inadvertently turned the philosophical concept into a scientific function.  Traditional philosophies have often confused themselves with science.  If it is the case that philosophy needs the science contemporary with it, and that science constantly intersects with the possibilities of the philosophical concepts, then contemporary philosophy must find concepts of a sub-atomic realm that allude to modern quantum physics. 

In the recent history of philosophy, attempts have been made to escape the essential structure of traditional philosophies.  Can atomism reach beneath essential forms of generality?  Atoms are (A Thousand Plateaus 254) “finite elements still endowed with form.”  No matter how far we divide extensive elements into finer and finer granularity, we can finally only reach the atom which is still endowed with the same extensive form. 

(Difference & Repetition 237) “The divisibility of extensive quantities is defined in the following manner: by the relative determination of a unit (this unit itself never being indivisible but only marking that level at which division ceases); by the equivalence of the parts determined by the unit; by the consubstantiality of the parts with the whole which is divided.  Division can therefore take place and be continued without any change in the nature of what is being divided.” 

Nor do diverse relations among already formed elements help.  Changing relations among already formed substances can’t change the essential nature of the structure.  Whether philosophy is atomic or relational, forms do not become open.  With division or augmentation of extensive quantities, there is no change in the nature of the form.  Contemporary philosophy must reach a domain that opens the forms.  We must reach the source of singular (not general) forms.  We must reach an inessential domain beneath the atomic and the relational.  We must reach a sub-atomic domain (the domain that Deleuze sometimes calls the ‘sub-representative’) that escapes any essential structure of generalizing Representation. 

Therefore, what Deleuze calls the “sub-representative” domain underneath forms cannot be an atomism.  Nor can it be relations among formed matter already in an extensive frame of space-time reference.  We must reach a sub-representative field that is the transcendental condition of any form of space-time reference --- a field of immanent conditions that does not resemble an already conditioned frame of empirical reference.  Deleuze says (DR304), “…Opening [of forms] is an essential feature of univocity.”  Therefore, when Deleuze writes about the sub-representative domain of univocality, he cannot be referring to atomism or any relations among elements of formed matter.  By “sub-representative” forces, he means forces of ‘singularity’ or ‘intensity’ (terms whose philosophical sense must not be confused with their scientific signification).  These sub-representative forces must be sub-atomic.  With division or augmentation, they change in the nature of their form. Intensive forces are inseparable variations on conceptual planes of consistency.

Deleuze says (DR 237) “An intensive quantity may be divided, but not without changing its nature.  In a sense, it is therefore indivisible, but only because no part exists prior to the division and no part retains the same nature after division.”

Therefore (DR 238), Deleuze’s philosophy distinguishes two types of multiplicities.  There are extensive multiplicities which carry the invariable principle of their metric; and there are intensive multiplicities whose metric varies with division.  The forces of intensity are always singular difference that, with each augmentation or division, changes nature while always filling the whole of ontologically singular Substance.  Intensities are sub-atomic quanta that change quality of the ontologically same Substance.  Deleuze’s forces (on the conceptual plane of consistency) are sub-atomic quanta that reveal the qualitative content of quantity.  There is qualitative content of quantity because there is always heterogeneous doubling of content and expression.  Being is expressive.  Ontology is expressionism.  Multiplicity is univocal being.  

(DR 222) “Intensity is the form of difference in so far as this is the reason of the sensible.  Every intensity is differential, by itself a difference.  Every intensity is E – E’, where E itself refers to an e – e’, and e to e – e’ etc.: each intensity is already a coupling (in which each element of the couple refers in turn to couples of elements of another order), thereby revealing the properly qualitative content of quantity.” 

D&G see something new in Spinoza’s philosophy that traditional readings could never see.  (ATP 253-4) Spinoza critiques substantial or essential forms.  He does this by reaching sub-atomic forces (singular-intensive) that no longer have form or function.  Singular points coexist in all varieties and distributions.  All differentiations of singular points coexist in really distinct distributions of composition.  The Real is the coexistence of all differentiations of singular points, in every ramification.  Singular compositions are distinguished by speed and slowness, movement and rest.  Singular points are not atoms that would be finite elements still endowed with form.  They are infinitely small parts distributed on disparate planes of consistency.  Singularities come in disparate infinities of real distinction.  Yet when their forced movement changes their nature, they are still ontologically same singular Substance because they are not extended in form.  Therefore, smaller and larger infinities are not distinguished by their number, but by their ordinal composition.  They are not numerically distinct substances.  Each Individual plane is singular infinite multiplicity.  Any degree of this intensive difference belongs to a singular Individual which is part of another Individual, ontologically one.  Nature is individuated multiplicities of singularities said, in whatever degree of real difference, as ontologically the same Individual.  This plane of univocality is the intersection of all forms and the machine of all functions.  “Being expresses in a single meaning all that differs.  What we are talking about is not the unity of substance but the infinity of the modifications that are part of one another on this unique plane of life.”     

(DR38) The sub-representative is “underneath matters and forms……If individuation does not take place either by form or by matter, neither qualitatively nor extensionally, this is not only because it differs in kind but because it is already presupposed by the forms, matters, and extensive parts.” 

If the philosophical concept and the scientific function cannot be reduced to one another, how can they be said to intersect?  (WiP 159-162) It seems that D&G are saying that an event, being inseparable variation on the plane of consistency, is also inseparable from a state of affairs in which it is actualized on a plane of reference.  And conversely, a state of affairs is inseparable from the event that gives consistency to the concept.  We must go back up to the event that gives the concept its virtual consistency, and come down to the actual state of affairs that gives the function its reference.  The event releases from states of affairs “a vapor that does not resemble them….”  The event is actualized in states of affairs without resemblance.  It is counter-actualized when abstracted from states of affairs in order to reach the consistency of a concept.  The two types of multiplicities intersect, each on its own line.  They are inseparable yet independent.  The line of science takes from chaos states of affairs that actualize a virtual in a coordinate system.  Conversely, philosophical concepts have a virtuality that extracts consistency.  Philosophy alludes to science.  Science speaks of philosophy as a cloud.  But they do not constitute each other.

(WiP159) “The event is actualized or effectuated whenever it is inserted, willy-nilly, into a state of affairs; but it is counter-effectuated whenever it is abstracted from states of affairs so as to isolate its concept….Philosophy is always meanwhile.”

Werner Heisenberg (1), from the scientific line of the function says, “The elementary particles are certainly not eternal and indestructible units of matter, they can actually be transformed into each other….all particles are made of the same substance: energy.”  And, on the line of the concept, according to D&G, there is ontologically one single Substance whose sub-atomic (‘intensive’) transformations are the source of all real singular difference.  And since every degree of this intensive difference is singular, all are ontologically the same.  The scientific plane is not the same as the philosophical plane.  Yet, according to D&G, they intersect as an intensive mode, on the philosophical plane of consistency, actualized in an extensive mode, on a scientific plane of reference.  But (WiP 124-5) neither of these modes is any longer to be seen as a linear temporal succession.  The philosophical plane of immanence has superimposed strata.  Before and after are different strata that become a same superimposed stratum while changing in nature.  Science has serial, ramified time where before indicates ruptures to come in the future, and after indicates retroactive reconnections.  On the philosophical plane of immanence, there are inseparable variations that communicate in zones of indiscernibility.  On the scientific plane of reference, there are independent variables constituting the function.  Neither plane can any longer be thought as unifying.  They are two types of multiplicities.

Werner Heisenberg (2) says, “In classical physics science started from the belief --- or should one say from the illusion? --- that we could describe the world or at least parts of the world without any reference to ourselves.”  And the Copenhagen interpretation of quantum theory, as Heisenberg tells us, still complies with this objective criterion of the scientific method as far as possible.  And this is because the scientist can only ask philosophical questions according to the scientific line of the function.  Quantum theory does not include the mind of the physicist as part of the atomic event.  But it does arbitrarily divide the “object” from the rest of the world.  Quantum physicists, as a consequence of the scientific method, use classical concepts to describe the rest of the world.  And that is because (as D&G tell us) science can only present functions as propositions of a discursive system (WiP 117).  Theoretical interpretations based on functions (which we know cannot fit nature accurately) can have only a statistical probability.  So, just as philosophical concepts can only allude to the probability functions of quantum science, the functions of quantum physics cannot be applied to theoretical concepts about “what happens” in the sub-atomic domain.  

Traditional philosophies do not escape the “belief” or “illusion” that separates the objective world from our subjectivity.  They can’t help but divide an “object” from the rest of the world that includes our subjectivity.  But contemporary philosophy must try to overcome that separation of subject and object.  It must try to reach a metaphysical sub-atomic field that is the source of the actualizations that allude to experimental results of science.  Deleuze offers his “sub-representative” plane of univocality as that “sub-atomic” plane.  And, as the functions of science change, due to the intersection of the two types of multiplicities, the philosophical concepts must change too.  Concepts are multiplicities of singular difference (the transcendental source of consistency) alluding to the actualized empirical reference frames of science.  Metaphysical conceptual surfaces are expressed as a doubling of the speed of ‘What happened?’ with the slowness of ‘What is going to happen?’  But this coupling is not an act of a subject. It is the necessity of chance.  It is a sub-atomic dice game of univocal being.  Just as the laws of classical physics are not adequate for the interpretation of observed quantum effects, traditional philosophies are not adequate for interpretation of the paradoxes we encounter.  D&G write:

(WiP 38) Infinite movement is double, and there is only a fold from one to the other.  It is in this sense that thinking and being are said to be one and the same.  Or rather, movement is not the image of thought without being also the substance of being.”

This ideal dice game of univocity cannot be played without thought.  The content-expression doubling is the necessity of chance in the sub-atomic dice game that is univocal being.  

(LOS 60) “For only thought finds it possible to affirm all chance and to make chance into an object of affirmation.  If one tries to play this game [of univocal being] other than in thought, nothing happens….” 

It is only at the surface that something happens, because thought is the expression that actualizes something at the surface.  But this dice game is the unconscious of pure thought.  This expression of thought is not an act of a subject.  It is an unconscious game that can only be thought as nonsense.  Everything may be affirmed at the sub-atomic level without exception when we reach univocal being.  All singularly differentiated ramifications of intensive forces are real.  Univocal being reaches that sub-atomic domain where anything may be possible.  Everything is possible at the same time at the level of the sub-representational, sub-atomic time of Aion.  Singularities are distinguished by the slowness of waiting for ‘What is going to happen?’ in the future, and by the speed of ‘What happened?’ in the past.  But nothing “happens” in this present without thickness --- this time of Aion at the sub-representative, sub-atomic realm.  Nothing “is happening” in this present without thickness.  (158) The event is not in a time between two instants.  It is the time of Aion --- a “meanwhile” that “belongs to becoming”.  Nothing happens, but everything becomes or changes.  The function is of states of affairs, or the measurement of ‘What happens?’ in the present (Chronos) on the scientific plane of quantum effects.  However, on the philosophical plane of immanence of the event, the present does not exist.  The event is a “meanwhile” that belongs to becoming.  The event is the meanwhile where nothing happens but is an ‘already past’ and ‘yet to come’.  Nothing happens, but everything changes. 

“All the meanwhiles are superimposed on one another, whereas times succeed each other……It is a concept that apprehends the event, its becoming, its inseparable variations; whereas a function grasps a state of affairs, a time and variables, with their relations depending on time….”  (WiP 158)

Aion is the pure empty form of time --- the source of all real difference of singular forms.  In the empty form of Aion, the pure instant endlessly subdivides a present without thickness.  The time of Aion eludes the present by flying in both past and future directions at once.  In this present without thickness, we can only ask “What is going to happen?” and “What happened?”  The philosophical concept can’t say “What is happening.”  Aion is that doubling of the event that gives consistency to a concept.

(LoS 164) “In accordance with Aion, only the past and future inhere or subsist in time.  Instead of a present which absorbs that past and future [Chronos], a future and past divide the present at every instant and subdivide it ad infinitum into past and future, in both directions at once…..”

What “happens” at the sub-atomic level of quantum physics?  The scientist has no concept.  Schrödinger’s cat is both dead and alive.  Only when the scientist makes an observation is the cat either dead or alive.  A quantum physicist can say “what happens” only when an observation or measurement is made and expressed in functions.  And what “happens” at the sub-atomic realm of philosophical univocality?  All ramifications of past conjoin with all ramifications of future at the sub-representative (sub-atomic) level.  The philosopher plays an intensive game of unconscious doubling or coupling that may actualize a conceptual consistency in expressive thought at the surface. (Might we say that this coupling of inseparable variations on the philosophical plane alludes to entanglement of particles on the scientific plane?)

Heisenberg (3) says, “Therefore, the transition from the “possible” to the “actual” takes place during the act of observation.  If we want to describe what happens in an atomic event, we have to realize that the word “happens” can apply only to the observation, not to the state of affairs between two observations”.  In other words, he understands that what happens in the “meanwhile”, between two observations, is not within the realm of the scientific function.  He continues by saying that the act of observation applies to the physical interaction of the object with the measuring device, not the subjective act of observation. 

I have compared Deleuze’s sub-representational domain of univocality with the sub-atomic realm of quantum physics.  Being is saying.  Ontology is expressionism.  The physicist can only express ‘what is’ when a measurement or observation has been made within a mediating frame of reference.  The philosopher can only think a conditioned “use” of a concept when there is first an immanent expression of conditions that may be actualized as limits that mediate a frame of reference.  But this ontology of univocal expressionism is never an act of a subject.  (WiP 128-133) On the plane of immanence, philosophy needs conceptual persona for the creation of concepts.  On the plane of reference, science needs partial observers in relation to functions.  Neither conceptual persona nor partial observer is a subject of enunciation.  Conceptual personae are non-subjective perceptions and affections of concepts.  Partial observers are non-subjective sensibilia (sense data distinct from sensation).  Subjective interpretations are inadequate. 

(WiP 129-30) “As a general rule, the [partial] observer is neither inadequate nor subjective: even in quantum physics, Heisenberg’s demon does not express the impossibility of measuring both the speed and the position of a particle on the grounds of a subjective interference of the measure with the measured, but it measures exactly an objective state of affairs that leaves the respective position of two of its particles outside of the field of its actualization, the number of independent variables being reduced and the values of the coordinates having the same probability.  Subjectivist interpretations of thermodynamics, relativity, and quantum physics manifest the same inadequacies.  Perspectivism, or scientific relativism, is never relative to a subject: it constitutes not a relativity of truth but, on the contrary, a truth of the relative….”

There is no analogy or metaphor between the concepts of philosophy and the functions of science.  There are only two types of multiplicities that intersect to defy any totalizing conceptual consistency or any actualized unification of reference.  There is no unifying frame of reference that can be actualized.  D&G say that science is not a unity of reference.  Its heterogeneity of systems and discontinuity of thresholds are the proliferation of axes.  Therefore, Deleuze and Guattari (WiP 119) feel entitled to “doubt the unitary vocation of science.”  Would this mean that D&G allude to a multi-verse interpretation of quantum physics?  Of course, only scientists can assess the relevance of an interpretation.


1) Physics and Philosophy:  The Revolution in Modern Science, by Werner Heisenberg, p. 71.  Harper & Row, 1962.

2) Ibid. p. 55-6.

3) Ibid. p. 54-5.

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