The success of cinematograph hides an ontological basis still in its fundamental principle for representation of motion by a linear (and thus well-ordered) series of static frames That representation of motion by static frames is absolute for it rests on the ontological equivalence of discreteness and smoothness The equivalence of discrete and smooth (continuous) motion underlies quantum mechanics as the principle of wave-particle duality offered by Louis de Broglie (1924) Henry Bergson (1907) suggested the “cinematographic method of thought” for distinguishing “durée” (time by itself) from the transcendental limitation for it to be represented in human knowledge and cognition

1. The “cinematographic method
of thought” in Bergson
Continuity by discreteness in cinematograph,
thought and mechanical motion

2. Vasil Penchev
• Bulgarian Academy of Sciences: Institute for the Study of Societies
and Knowledge: Department of Logical Systems and Models,
vasildinev@gmail.com
o“The Real of Reality”,
An International Conference in Philosophy and Film
oKarlsruhe, Germany, 2-6 November 2016
oZentrum für Kunst und Medientechnologie
o(ZKM, Kube, 3 Nov, 11:20-12:50)

3. A short abstract

4. A short abstract
• Henri Bergson (1907) utilized a metaphor borrowed from
cinematograph to represent the usual way of human thought
about motion and evolution in comparison with his original
approach to them grounded on his concept of time as “durée”
(duration)
o The analogy consists in restoring the motion from a series of
immovable pictures (frames) only as a subjective illusion
• On the contrary, “durée” is that understanding of time, in which
motion and evolution are primarily given rather than secondarily
and as an auxiliary or even illusion by a series of static states

5. A short abstract
• In the latter case, static underlies kinematic reducing it only to many
static states therefore cancelling the creative essence of motion and
evolution according to Bergson
o Bergson’s views influenced essentially Luis de Broglie (1925), who
offered in his thesis (1924) the wave interpretation of any particle and
its motion in quantum mechanics
• His work received the Nobel Prize in Physics (1929) “for his discovery
of the wave nature of electrons”.
o The wave-particle duality continues to be one of the most
fundamental principles in quantum mechanics nowadays

6. A short abstract
• The cinematograph embodied and thus made visible and
obvious the fundamental way of human thought of motion
o It is reflected and generalized in both philosophy of Bergson
and quantum mechanics
• Thus cinematograph rests on a fundamental ontological and
philosophical equivalence: that of continuity (smoothness)
and discreteness
o Just that equivalency allows for it to represent motion by a
series of static shots

7. The basic references:
Bergson, H. (1907) L'Évolution créatrice. Paris: PUF, 298-307.
Broglie, Louis de (1925) “Recherches sur la théorie des
quanta,” Thesis (Paris), 1924. Annales de Physique (Paris, 10-
ème série) 3, 22-128.
Kochen, S., Specker, E. (1968) The Problem of Hidden Variables
in Quantum Mechanics. Journal of Mathematics and
Mechanics 17(1): 59‐87 .
Neumann, J. von (1932) Mathematische Grundlagen der
Quantenmechanik. Berlin: Springer, pp. 167-173.

8. A few key terms
• Bergson, Henry
o Broglie, Louis de
• cinematographic method of thought
o continuity
• discreteness
o equivalence of discrete and continuous motion
• motion
o ontological ground of cinematograph
• smoothness
o wave-corpuscular duality

9. The thesis

10. The thesis
• The success of cinematograph hides an ontological basis still in its
fundamental principle for representation of motion by a linear
(and thus well-ordered) series of static frames
o That representation of motion by static frames is absolute for it
rests on the ontological equivalence of discreteness and
smoothness
• The equivalence of discrete and smooth (continuous) motion
underlies quantum mechanics as the principle of wave-particle
duality offered by Louis de Broglie (1924)
o Henry Bergson (1907) suggested the “cinematographic method of
thought” for distinguishing “durée” (time by itself) from the
transcendental limitation for it to be represented in human
knowledge and cognition

11. The principle of cinematograph
Continuous
motion
Time Cinematographic
frames
Only
Illusion?
Ontological
equivalence
OR

12. A short comment to the thesis
• There is a psychic mechanism for merging successive frames
changing fast enough
o Then, the principle underlying cinema seems as if be only a
psychological illusion due to the imperfection of human
perception
• Cinema is even called “the great illusion” transforming the
underlying merge of static frames into a metaphor to its
ability to replace the real world with an imaginary one
o On the contrary, my thesis reveals a deeper fundamental
equivalence of discreteness and continuity, underlying
ontologically the cinematograph, rather than a mere illusion

13. A short comment to the thesis
• The psychic and psychological mechanism for merging fast
changing static frames is not to be refuted
o It exists, but it misleads to the misunderstanding and
misinterpretation of the ontological basis of cinema as
an “illusion”
• In fact, the success and power of cinema should be
discovered in the fundamental equivalence of both smooth
motion (as it is seen by the filmviewers as observers) and
discrete motion (as it is technically prepared in the footage)

14. The historical and philosophical background
• That can include:
o The opposition of the discrete and continuous (motion) still
since Ancient Greece during the whole history of philosophy and
physics until the problem nowadays
• Kant’s concept of transcendental subject
o Bergson’s reinterpretation of Kant’s concept
as to time and evolution and its transcendental limitation
just as the “cinematographic method of thought”
• Louis de Broglie’s concept of wave-particle duality
o The interpretation of quantum mechanics as quantum
information unifying the discrete and smooth motion

15. A wider horizon about that background
• The equivalency of the discrete and smooth motion refers
furthermore to:
o The conception of infinity in mathematics,
philosophy, and theology
• The foundation of mathematics and thus to its consistency
and completeness
o The reformulation of all physics
in terms of information theory
• Merging and unifying physics and mathematics by means of
the theory of (quantum) information

16. The interpretation of the cinematographic art
and technics on that background
• Cinema as both art and technics is an embodiment of those
background and horizon
o Any human being refers to them by cinema though
indirectly and implicitly
• However, the so-called magic of cinema rests just on its
fundamental ontological background and horizon
o Any one without being a philosopher or a scientist can
touch the secret of the being by means of cinema
• Touching the being is the magic of cinema

17. A few possible objections commented

18. A few possible objections
• The thesis seems to be too speculative, “philosophical” in
the bad sense
o It addresses mystic feeling such as the “magic of cinema”
not allowing of any rational approach
• The replacement of the psychic or psychological illusion
underlying the perception of cinema with that equivalence is
not relevant for the equivalence refers to the Planck scale:
both cinematograph and spectator are much, much bigger
than that scale

19. Objection 1: “The thesis seems to be too speculative,
“philosophical” in the bad sense”
Comment:
• The thesis is intendedly speculative and philosophical
o Many ideas admit only philosophical formulations
• The etymology of “cinematograph” addresses a ‘record of
motion’ therefore implicitly questioning about the relation
between ‘record’ and ‘motion’, or between the ‘record of
motion and the motion itself
o Henry Bergson, an exceptionally famous philosopher, has
generated the tradition of the philosophical and speculative
discussion of cinema a long time ago

20. Objection 2: “It addresses mystic feeling such as the “magic of cinema”
not allowing of any rational approach”
Comment:
o The “magic of cinema” is used as a metaphor meaning the
generation of a specific kind of imaginary, but convincing ontology
different from the analogical imaginary ontologies in other arts
• That ontology is grounded just on the record of motion, right
“cinematograph” hinting the record of motion as the source of any
ontology
o Thus the “magic of cinema” means the cinematographic ontology as
both specific ontology of cinema and generation of any ontology as a
way for recording motion

21. Objection 3: “The replacement of the psychic or psychological illusion
underlying the perception of cinema with that equivalence is not
relevant for the equivalence refers to the Planck scale
Both cinematograph and spectator are much, much bigger than that
scale”
Comment:
o That is the one way of interpretation of the Planck scale. Indeed,
that equivalence would be irrelevant after such an interpretation
• However, the Planck scale may be also interpreted relatively, in terms
of kinematics, or “cinematically”. Then, that equivalence will be valid
macroscopically, in the scale of both cinematograph apparat and
spectator
o Both mechanism of cinematographic illusion and equivalence of the
discrete and smooth are valid simultaneously referring to one and
the same, but not linked to each other in any way known to science

22. Still a few possible objections
• The equivalence of the discrete and smooth (motion) is not
ultimately confirmed and scientifically established even in
the domain of quantum mechanics and information
o The corresponding phenomena of entanglement referring
to the experimental corroboration of quantum information
can be explained alternatively, without quantum
information, though rather unnaturally, by means of the so-
called loopholes, or “backdoors”
• The cinematographic art and technics belong to human
practice, and their alleged background and horizon to
science. Thus they cannot be ascribed to one and the same
circle

23. Objection 4: “The equivalence of the discrete and smooth (motion) is
not ultimately confirmed and scientifically established even in the
domain of quantum mechanics and information”
Comments:
o It is neither confirmed nor refuted experimentally. Yet even
any experiments for testing it are not offered
• Anyway as an abstract principle, it is consistent to quantum
mechanics and information as theories
o Even being experimentally wrong, it can be utilized as to the
philosophical interpretation of cinema
• Its application to cinematograph assists the elucidation of its
sense and how it might be tested experimentally

24. Objection 5: “The corresponding phenomena of entanglement
referring to the experimental corroboration of quantum information
can be explained alternatively, without quantum information, though
rather unnaturally, by means of the so-called loopholes or backdoors”
Comments:
• More and more new experiments close gradually one by one all
possible “loopholes” and “backdoors” of alternative
explanations
o The trend is to be closed practically all known ones
• Though the results in any separate experiment might be
alternatively explained, the only universal explanation of all of
them is by means of quantum information
o There is not any experiment refuting the phenomena of
entanglement directly

25. Objection 6: “The cinematographic art and technics belong to
human practice, and their alleged background and horizon to
science. Thus they cannot be ascribed to one and the same circle”
Comment:
o Indeed, the enumerated scientific theories cannot be
considered as theories referring to cinema, its technics, art,
or perception
• However, cinematograph and a series of scientific theories
might share one and the same ontology for all of them
including cinematograph are essentially related to motion
o Motion is able to unify so different areas of human activity
such as technics, art, science

26. Direct arguments “pro” the thesis

28. What the thesis states
• The essence of the thesis e: the cinematograph is an absolute
equivalent of continuous motion rather than only a
psychological or psychic illusion of motion
o In other words, cinematograph replaces the continuous
motion with discrete motion equivalently
• Meaning Bergson’s thesis about the cinematographic method
of thought as a kind of temporal transcendentalism, the thesis
can be so reformulated: motion represented transcendentally
is equivalent to the “motion by itself”
o Then, motion can be in turn defined as what is invariant to
the transformation of the transcendental and the
transcendent, and cinematograph rests just on that invariance

29. Ontological
equivalence
Motion by itself
Motion
cinematically
represented
Transcendent
motion
Transcendental
motion
Motion defined as what is
invariant after that
transformation

30. What kind of arguments would be direct?
They should refer to:
o The equivalence of continuous and discrete motion
• The equivalence of the motion represented transcendentally
and the motion by itself
o The definition of motion as what is equivalent to the
transformation of the transcendental and the transcendent
• The definition of time as an abstract fundamental and
common motion corresponding to Bergson’s “durée”, to
which the transcendental and the transcendent are
equivalent in definition

31. Argument 1: The equivalence of continuous
and discrete motion
• The main problem of quantum mechanics is how to be described
uniformly and thus invariantly the continuous (and even smooth)
motion in classical mechanics and discrete motion for the
fundamental Planck constant
o Quantum mechanics resolves that problem generalizing the
description of motion from the usual 3D Euclidean space of classic
mechanics to the infinitely dimensional, complex, and separable
Hilbert space of quantum mechanics
• Consequently, if description of cinematograph be generalized
from the former space to the latter one, the equivalence of the
real continuous motion and its representation frame by frame will
be proved

32. A few comments on the first argument
• Louis de Broglie’s conception about the wave-particle duality is
historically the first formulation of the equivalence of
the continuous and discrete motion as to the generalization
necessary for quantum mechanics
o It is directly influenced by the doctrine of Henry Bergson and
particularly by the conception of the “cinematographic
method of thought”
• In turn, the conception of the “cinematographic method of
thought” borrows the way for motion to be represented frame
by frame from the cinematograph thrived just in that age

33. Quantum mechanics
Cinematographic method
of thought
Quantum information
The separable complex
Hilbert space
Continuous
(smooth)
motion
Discrete
(quantum)
motion
Motion
by itself
Cinematic
Motion

34. Argument 2: The equivalence of the
transcendent and transcendental motion
• The essence of Bergson’s “cinematographic method of thought” can be
represented as a philosophical reflection on the cinematographic
principle. That reflection consists in both:
o Interpretation of the real motion, which is filmed in the movie, as
transcendent motion, i.e. motion by itself
• Interpretation of the movie taken frame by frame and observed by the
viewers as transcendental motion, i.e. motion for us, the spectators
o Utilizing Bergson’s way of interpretation and meaning the equivalence
of the continuous and discrete motion according to quantum
mechanics, one can deduces the equivalence of the transcendent and
transcendental motion hence

35. A short comment on the second argument
• There exist two fundamental and equivalent ways of representing
motion corresponding exactly to the Hamilton and Lagrange
approach in classical and quantum mechanics
o The Hamilton approach separates disjunctively, as independent of
each other variables of motion, the dynamic variables such as
energy and momentum from the static ones such as space position
in time
• The Lagrange approach unifies them interpreting the former
variables as derivatives of the latter ones
o The equivalence of the continuous as transcendent motion and
the discrete as transcendental motion can be also deduced from the
equivalence of both approaches in mechanics

36. Bergson’s conception
of motion as evolution
Cinematographic method
of thought
Motion as being
Bergson’s conception of
time as “durée”
Transcen-
dent
motion
Transcen-
dental
motion
Motion
by itself
Cinematic
Motion

37. Argument 3: Motion as the equivalence of
the transcendental and the transcendent
• The argument is a philosophical generalization of the theorems
about the absence of hidden variables in quantum mechanics
(Neumann 1932; Kochen, Specker 1968) implied by a few
properties of the separable complex Hilbert space
o The theorems can be furthermore interpreted as
the fundamental identity of model and reality in quantum
mechanics: indeed, any mismatch of model and reality would
mean one or more “hidden variables” being out of the model
but within reality
• Then, the relation of model and reality corresponding to the
relation of the transcendental and the transcendent implies the
equivalence of the latter ones

38. A short comment to the third argument
• Anything describable as a quantum system, i.e. by a wave
function (an element of the separable complex Hilbert space),
should be considered as a motion
o Motion is also correspondingly understood as the equivalence
of the discrete and the continuous furthermore unifying them
• The argument generalizes the previous one (Argument 2)
complementing to that equivalence of the discrete and
the continuous and of the transcendental and the
transcendent
o It corresponds to Hegel’s dialectic conception of motion
understood philosophically as a generalization of Kant’s
transcendentalism

39. The theorem about the absence of
hidden variables in quantum mechanics
Model Reality
Transcendental Transcendent
Motion

40. Argument 4: Time as an abstract and
fundamental motion
• The representation in the separable complex Hilbert space may be
also interpreted in terms of Fourier transformation, straight and
reverse, and thus as the invariance to both time (𝑡𝑡) and frequency
(ω = 𝑡𝑡−1
)
o That invariance implies the uniform representation of the discrete
and continuous motion as well as the arrow of time interpreted as
the indistinguishability of the straight and reverse course of time
• Then, time as an abstract and fundamental motion can be
mathematically defined in turn by means of those invariances as
the identity of the separable complex Hilbert space and its dual
counterpart

41. A short comment to the fourth argument
• The cinematograph divides the film footage of frames (as many
discrete positions in equal intervals of time) from the velocity of
reproduction (i.e. the speed, with which the footage moves
trough the projecting ray)
o That velocity is constant and equal to the speed, by which
the footage is filmed
• That constant velocity corresponds also to the normal course of
time of what is filmed
o Than one can interpret the normal course of time as
the identical velocity of the fundamental motion of both
continuous and discrete, or of both transcendental and
transcendent

42. Multiplicative
group
1
𝑡𝑡−1
= 𝜔𝜔
𝑡𝑡
Additive
group
0
𝑡𝑡
−𝑡𝑡 = ln𝜔𝜔
Any doubled
well-ordering
is a group
1 1
2
Hilbert space
unifies both
symmetries and
well-ordering
2
3
n
𝑡𝑡𝜔𝜔
3
n
……….
……….

43. Conclusions
• The cinematograph rests on a fundamental ontological
principle about the equivalence of the discrete and
continuous motion rather than only a psychic or
psychological illusion
o That principle a much larger horizon of human practice and
cognition
• Bergson was the first who pay attention to that horizon
philosophically by its conception of “cinematographic
method of thought”
o Broglie’s wave particle duality won the Nobel Prize in physics
is maybe the most eminent theory in the same horizon

44. You may find the presentation or the paper
taping the title, The “cinematographic
method of thought” in Bergson in any search
engine such as Google, Bing, etc.
Thank you very much for
your kind attention!