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The Sphynx’s new riddle: How to relate the
canonical formula of myth to quantum
interaction
1 , PETER WITTEK1 , and Kirsty Kitto2
´
´
Daranyi
Sandor
1 University
2 Queensland
˚
of Boras
University of Technology
July 25, 2013
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Outline
1
Motivation
2
Mythology
3
The Canonical Formula
4
Quantum Interaction
5
Conclusions
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Conclusions
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Argumentation
Advanced access to DL begs to focus on text genres other
than scientific articles, with complexities of meaning being
an obstacle to process semantic content
One reason to include belief-based narratives in DL is to
add documents of and about the collective unconscious,
relevant for cognitive studies
With folk narratives, a major implication is that their
processing encourages methodology outside of linguistics,
such as biology and physics
We look at cases where bag-of-words methods do not help
and probabilistic approaches have not been tested this far.
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Outline
Work in progress with basic examples of a new research
idea linking the structural study of myth with group theory
and Bloch vectors
Briefly discussing:
Narrative processing
Folklore, mythology and text variation
Formulaity (with examples)
The structural study of myth
Insights combined with QI
Experiment and results
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Outline
1
Motivation
2
Mythology
3
The Canonical Formula
4
Quantum Interaction
5
Conclusions
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Conclusions
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Narrative processing
Emerging field of interest in text analytics, with focus on
storyline analysis and generation
Typical genres to be analyzed are folktales and myths
These present special challenges to computer analysis:
Formalization, formulaic structure
Building block identification
Genre identification based on available metadata
Broad field: digital humanities, own forum: CMN
Whence the need:
Special problems but related to S & T document indexing,
classification, retrieval and visualization
E.g. sentence-based indexing by tensor product,
Holographic Reduced Representations (Plate 1994), circular
convolution, etc.
Information filtering according to predefined semantic
criteria for semantic markup
Recurrent semantic pattern identification
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Basic concepts
Folklore:
Term first used by English antiquarian William Thoms in a
letter published in the London journal The Athenaeum in
1846
Consists of legends, [music], oral history, proverbs, jokes,
popular beliefs, fairy tales, stories, tall tales, and customs
that are the traditions of a culture, subculture, or group
The above genres are also called folk narratives
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Basic concepts
Mythology:
A body of myths, as that of a particular people or that
relating to a particular person, e.g. Greek mythology.
Myths collectively
The science or study of myths
A set of stories, traditions, or beliefs associated with a
particular group or the history of an event, arising naturally
or deliberately fostered, e.g. the Fascist mythology of the
interwar years
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Basic concepts
In folklore text analytics, a myth is a sacred narrative
usually explaining how the world or humankind came to be
in its present form, although, in a very broad sense, the
word can refer to any traditional story of e.g. origins
Text variation: in folklore/anthropology/ethnology, artifacts
such as texts, songs, objects etc. exist in variants rather
than canonical (archetypical) single examples, leading to
classification (conceptualization) problems (i.e. which one
is “the” original?)
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Two more categories
The fertility myth:
Fertility-related deities are a global phenomenon
Once widespread in the Mediterranean and the Ancient
Near East, this myth is a symbolic prescription of how to
regulate individual and community welfare
Briefly, proper moral conduct being the key, disaster strikes
due to ill behavior or violation of social norms, whereas the
role of the regulator (a deity or a human, a male or a female
such as a sacred king or queen) is to remedy the insult to
the supernatural, and thereby bring back fertility, an
indicator to signal if things are on the right track
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´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Two more categories
The dying god:
Now debated, a type proposed by Frazer (The golden
bough, 1890)
In comparative mythology, the motif refers to a deity who
departs and returns, e.g. is resurrected or reborn, in either
a literal or symbolic sense
Often related to the vegetation cycle, examples include:
Ancient Mesopotamia: during the journey of Inanna or Ishtar to the underworld, the earth
becomes sterile, and neither humans nor animals are able to procreate. After confronting
her sister Ereshkigal, the ruler of the underworld, Inanna is killed, but an emissary from the
gods administers potions to restore her to life. She is allowed to return to the upper world
only if someone else will take her place. Her husband, the vegetation god Dumuzi, agrees
to spend half the year in the underworld, during which time vegetation dies off. His return
brings regrowth.
Ancient Egypt: the cultural achievements of Osiris among the peoples of the earth
provokes the envy of his brother Set, who kills and dismembers him. Osiris’s wife Isis
journeys to gather his fourteen scattered body parts. In some versions, she buries each
part where she finds it, causing the desert to put forth vegetation. In other versions, she
reassembles his body and resurrects him, and he then becomes the ruler of the afterlife.
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Formulatity, formulaic
The theory of oral-formulaic composition originated in the
scholarly study of epic poetry, being developed in the 2nd
quarter of the 20th century. It seeks to explain two related
issues:
The mechanism whereby some oral poets are able to
improvise poetry, and
Why orally improvised poetry has the characteristics it has
The key idea of the theory is that poets have a store of
formulae and that by linking these in conventionalized
ways, they can rapidly compose verse
A formula being “an expression which is regularly used,
under the same metrical conditions, to express a particular
essential idea”
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Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Formulatity, formulaic
Milman Parry (1902-1935), Albert Lord (1912-1991): their
approach transformed the study of ancient and medieval
poetry, and oral poetry in general, with an impact on
narratology
Major finding: standard sequences of content elements
(formulae) pertain to documents and document parts
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Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
The structure of Greek flower myths
Example: structural
similarities of Greek
myths about the
origins of plants
(flowers and trees)
The structure
demonstrates erosion
of content
Typical narrative
elements at typical
locations in the plot
are in canonical
relations with one
another
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Examples of formulaity (= structure) in narrative
research
Propp (1929): Russian fairy tales
have 7 actors (dramatis personae),
31 functions (types of actions) and
150 narrative elements
Thompson (1932-37): Folktales can
be indexed by their structure. Motif
index system to catalog individual
motifs.
´
Levi-Strauss
(1954): both narrative
segments in myths (called
mythemes), and myth variants,
manifest canonical content
transformations
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Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Conclusions
Motivation
Mythology
The Canonical Formula
Quantum Interaction
´
Levi-Strauss’
reading of the Oidipus (1955)
Paradigmatic
reading
Syntagmatic reading
Cadmos seeks his
sister Europa,
ravished by Zeus
Cadmos kills the
dragon
The Spartoi kill
one another
Oedipus kills his
father, Laios
Oedipus kills the
Sphinx
Labdacos (Laois'
father) = lame (?)
Laios (Oedipus
father) = lef-sided (?)
Oedipus =
swollen-foot (?)
Oedipus marries
his mother,
Jocasta
Eteocles kills his
brother, Polynices
Antigone buries her
brother, Polynices,
despite prohibition
Overestimating
blood relations
Underestimating
blood relations
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´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
Denial of
matriarchal order
("born from one")
Affirmation of
matriarchal order
("born from one")
The Sphynx’s new riddle
Conclusions
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Outline
1
Motivation
2
Mythology
3
The Canonical Formula
4
Quantum Interaction
5
Conclusions
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Conclusions
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
The canonical formula of myth: formulaic expression
of the above (by Andre´ Weil)
“Weak” form vs. “strong”,
canonical form:
The four components
stand for two oppositions
of four paradigms
From two “weak” formulae, two
“strong” (= canonical) versions
by symmetry breaking as
interaction between two Klein
groups:
They manifest the orbit of a
Klein group
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Research problem
The fundamental difficulty with myths is conceptual
contamination, also called eclecticism or syncretism, i.e.
different concepts belonging to the same category (e.g. the
dying deity) can appear in the same plot so that nobody
can tell them apart
The other is the fundamental insecurity of not knowing
what factor may be important and how much of its
manifestations can be out there. So a probabilistic tool,
should one exist or could one be designed, would be a
significant step forward
E.g. what is the probability that a text fragment is in state
fx (a), or a whole text as a mix of fx (a) : fy (b) :: fx (b) : fa−1 (y )
has a given outcome for fa−1 (y)?
This is a weighted superposition
For a probabilistic tool, enter QI
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Recent insights
Lost in translation for 50 years: Weil used group theory to
formalize the CF
The CF encodes a plot
Morava (2005) demonstrated that the CF is a
(non-commutative) quaternion group of order eight
Quaternions correspond to Pauli matrices and can be
displayed by Bloch spheres, so that a set of story variants
influence the behavior of the state vector in the space of
the CF, i.e. the Bloch sphere
Not one but 32 CF, and possibly many more
In other words the CF as a narrative generation tool
performs the same transformations on the plot but under
rotation of its group, leading to new actors and actions in
new situations, i.e. plot variants
All CFs are pure state vectors in a Bloch sphere
The CF is candidate for information filtering
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Insight 1: Not 1 but at least 32 “weak” vs. “strong”
versions of the CF exist
“Weak” forms
Octet A (term +, function +)
NF 1 = x(a) : y(b) :: x(b) : y(a)
NF 2 = x− 1 (a) : y− 1 (b) :: x− 1 (b) : y− 1 (a)
NF 3 = x(a− 1 ) : y(b− 1 ) :: x(b− 1 ) : y(a− 1 )
NF 4 = x− 1 (a− 1 ) : y− 1 (b− 1 ) :: x− 1 (b− 1 ) : y− 1 (a− 1 )
NF 5 = a(x) : b(y) :: b(x) : a(y)
NF 6 = a(x− 1 ) : b(y− 1 ) :: b(x− 1 ) : a(y− 1 )
NF 7 = a− 1 (x) : b− 1 (y) :: b− 1 (x) : a− 1 (y)
NF 8 = a− 1 (x− 1 ) : b− 1 (y− 1 ) :: b− 1 (x− 1 ) : a− 1 (y− 1 )
Octet B (term -, function +)
NF 9 = x(−a) : y(−b) :: x(−b) : y(−a)
NF 10 = x− 1 (−a) : y− 1 (−b) :: x− 1 (−b) : y− 1 (−a)
NF 11 = x(−a− 1 ) : y(−b− 1 ) :: x(−b− 1 ) : y(−a− 1 )
NF 12 = x− 1 (−a− 1 ) : y− 1 (−b− 1 ) :: x− 1 (−b− 1 ) : y− 1 (−a− 1 )
NF 13 = −a(x) : −b(y) :: −b(x) : −a(y)
NF 14 = −a(x− 1 ) : −b(y− 1 ) :: −b(x− 1 ) : −a(y− 1 )
NF 15 = −a− 1 (x) : −b− 1 (y) :: −b− 1 (x) : −a− 1 (y)
NF 16 = −a− 1 (x− 1 ) : −b− 1 (y− 1 ) :: −b− 1 (x− 1 ) : −a− 1 (y− 1 )
Octet C (term +, function -)
NF 17 = −x(a) : −y(b) :: −x(b) : −y(a)
NF 18 = −x− 1 (a) : −y− 1 (b) :: −x− 1 (b) : (−y− 1 (a)
NF 19 = −x(a− 1 ) : −y(b− 1 ) :: −x(b− 1 ) : a(−y)
NF 20 = −x− 1 (a− 1 ) : −y− 1 (b− 1 ) :: −x− 1 (b− 1 ) : −y(a− 1
NF 21 = a(−x) : b(−y) :: b(−x) : a(−y)
NF 22 = a(−x− 1 ) : b(−y− 1 ) :: b(−x− 1 ) : a(−y− 1 )
NF 23 = a− 1 (−x) : b− 1 (−y) :: b− 1 (−x) : a− 1 (−y)
NF 24 = a− 1 (−x− 1 ) : b− 1 (−y− 1 ) :: b− 1 (−x− 1 ) : a− 1 (−y− 1 )
Octet D (term -, function -)
NF 25 = −x(−a) : −y(−b) :: −x(−b) : −y(−a)
NF 26 = −x− 1 (−a) : −y− 1 (−b) :: −x− 1 (−b) : −y− 1 (−a)
NF 27 = −x(−a− 1 ) : −y(−b− 1 ) :: −x(−b− 1 ) : −y(−a− 1 )
NF 28 = −x− 1 (−a− 1 ) : −y− 1 (−b− 1 ) :: −x− 1 (−b− 1 ) : −y− 1 (−a− 1 )
NF 29 = −a(−x) : −b(−y) :: −b(−x) : −a(−y)
NF 30 = −a(−x− 1 ) : −b(−y− 1 ) :: −b(−x− 1 ) : −y(−a)
NF 31 = −a− 1 (−x) : −b− 1 (−y) :: −b− 1 (−x) : −a− 1 (−y)
NF 32 = −a− 1 (−x− 1 ) : −b− 1 (−y− 1 ) :: −b− 1 (−x− 1 ) : −b− 1 (−y− 1 )
“Strong” forms
Octet E (term +, function +)
CF 1 = x(a) : y(b) :: x(b) : a− 1 (y)
CF 2 = x− 1 (a) : y− 1 (b) :: x− 1 (b) : a− 1 (y− 1 )
CF 3 = x(a− 1 ) : y(b− 1 ) :: x(b− 1 ) : a(y)
CF 4 = x− 1 (a− 1 ) : y− 1 (b− 1 ) :: x− 1 (b− 1 ) : a(y− 1 )
CF 5 = a(x) : b(y) :: b(x) : y− 1 (a)
CF 6 = a(x− 1 ) : b(y− 1 ) :: b(x− 1 ) : y(a)
CF 7 = a− 1 (x) : b− 1 (y) :: b− 1 (x) : y− 1 (a− 1 )
CF 8 = a− 1 (x− 1 ) : b− 1 (y− 1 ) :: b− 1 (x− 1 ) : y(a− 1 )
Octet F (term -, function +)
CF 9 = x(−a) : y(−b) :: x(−b) : −a− 1 (y)
CF 10 = x− 1 (−a) : y− 1 (−b) :: x− 1 (−b) : −a− 1 (y− 1 )
CF 11 = x(−a− 1 ) : y(−b− 1 ) :: x(−b− 1 ) : −a(y)
CF 12 = x− 1 (−a− 1 ) : y− 1 (−b− 1 ) :: x− 1 (−b− 1 ) : −a(y− 1 )
CF 13 = −a(x) : −b(y) :: −b(x) : y− 1 (−a)
CF 14 = −a(x− 1 ) : −b(y− 1 ) :: −b(x− 1 ) : y(−a)
CF 15 = −a− 1 (x) : −b− 1 (y) :: −b− 1 (x) : y− 1 (−a− 1 )
CF 16 = −a− 1 (x− 1 ) : −b− 1 (y− 1 ) :: −b− 1 (x− 1 ) : y(−a− 1 )
Octet G (term +, function -)
CF 17 = −x(a) : −y(b) :: −x(b) : a− 1 (−y)
CF 18 = −x− 1 (a) : −y− 1 (b) :: −x− 1 (b) : a− 1 (−y− 1 )
CF 19 = −x(a− 1 ) : −y(b− 1 ) :: −x(b− 1 ) : a(−y)
CF 20 = −x− 1 (a− 1 ) : −y− 1 (b− 1 ) :: −x− 1 (b− 1 ) : a(−y− 1 )
CF 21 = a(−x) : b(−y) :: b(−x) : −y− 1 (a)
CF 22 = a(−x− 1 ) : b(−y− 1 ) :: b(−x− 1 ) : −y(a)
CF 23 = a− 1 (−x) : b− 1 (−y) :: b− 1 (−x) : −y− 1 (a− 1 )
CF 24 = a− 1 (−x− 1 ) : b− 1 (−y− 1 ) :: b− 1 (−x− 1 ) : −y(a− 1 )
Octet H (term -, function -)
CF 25 = −x(−a) : −y(−b) :: −x(−b) : −a− 1 (−y)
CF 26 = −x− 1 (−a) : −y− 1 (−b) :: −x− 1 (−b) : −a− 1 (−y− 1 )
CF 27 = −x(−a− 1 ) : −y(−b− 1 ) :: −x(−b− 1 ) : −a(−y)
CF 28 = −x− 1 (−a− 1 ) : −y− 1 (−b− 1 ) :: −x− 1 (−b− 1 ) : −a(−y− 1 )
CF 29 = −a(−x) : −b(−y) :: −b(−x) : −y− 1 (−a)
CF 30 = −a(−x− 1 ) : −b(−y− 1 ) :: −b(−x− 1 ) : −y(−a)
CF 31 = −a− 1 (−x) : −b− 1 (−y) :: −b− 1 (−x) : −y− 1 (−a− 1 )
CF 32 = −a− 1 (−x− 1 ) : −b− 1 (−y− 1 ) :: −b− 1 (−x− 1 ) : −y(−a− 1 )
By interaction between their respective fourth arguments, 32 CF can be generated from 32 NF.
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Insight 2: For the fertility myth, a linguistic rendering of
the CF translates group components into text variants
fx(a) : fy(b ):: fx(b) : fa-1(y)
„divine adult male creates [other]:
mortal adult male destroys [other] ::
mortal adult male creates [other] :
divine adolescent male destroys
[himself]”
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Outline
1
Motivation
2
Mythology
3
The Canonical Formula
4
Quantum Interaction
5
Conclusions
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Conclusions
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
The quaternion group of order eight
Q = {±1, ±i, ±j, ±k}
The noncommutative product operation defined as
ij = k = −ji, jk = i = −kj, ki = j = −ik, ii = jj = kk = −1,
and (−1)2 = 1.
The canonical formula: Fx (a) : Fy (b) 7→ Fx (b) : Fa−1 (y).
x 7→ 1, a 7→ i, y 7→ j, and b 7→ k
This automorphism reproduces the canonical formula.
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
The Pauli matrices
σx =
0 1
,
1 0
σy =
0 −i
,
i 0
σz =
1 0
.
0 −1
With the identity matrix I, they form a basis for the real
Hilbert space of 2 × 2 complex Hermitian matrices.
The real linear span of {I, iσx , iσy , iσz } is isomorphic to the
real algebra of quaternions H.
1 7→ I,
i 7→ −iσx ,
j 7→ −iσy ,
k 7→ −iσz .
A density matrix can be written as ρ = 12 (I + sσ)
s is called the Bloch vector
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Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Mapping to the Bloch sphere
(a) A pure state.
(b) A mixed state.
Figure : A pure state corresponds to a point on the surface of the
Bloch sphere, whereas a mixed state is inside the Bloch sphere.
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´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Conclusions
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Applying the probabilistic description
“Belief contamination”
Different concepts belonging to the same category (e.g. the
dying deity) can appear in the same plot
Insecurity of not knowing what factor may be important and
how much of its manifestations can be out there
What is the probability that a text fragment is in state Fx (a),
or a whole text as a mix of Fx (a) : Fy (b) 7→ Fx (b) : Fa−1 (y)
has a given outcome for Fa−1 (y )?
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Case study
Linguistic rendering of the CF exemplified on the myths of
Adonis and Attis (minor deities from Asia Minor in the
Hellenistic period, 323-31 BC)
Typical plot: a youth invites harm by being too beautiful,
losing his virility from which a specific plant springs up
Attis’ story (13 variants) relates the loss to direct
self-mutilation (8); to mutual castration with partner (indirect
self-mutilation, 1); to being born as an eunuch or killed by
spear through an unspecified wound (indirect not-self
mutilation, 2); or the goddess mutilating him as punishment
for his infidelity (direct not-self mutilation, 2)
Direct self (DS) : not-direct self (DNS) :: not-direct not-self
(NDNS) : direct not-self (DNS) constitute two oppositions of
four paradigms as per the CF
The axes Fy (b) = xˆ , Fx (b) = zˆ , and Fa−1 (y ) = yˆ , where
the latter can have four outcomes as above, the result is a
mixed state vector weighted by the outcome probabilities.
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Outline
1
Motivation
2
Mythology
3
The Canonical Formula
4
Quantum Interaction
5
Conclusions
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle
Conclusions
Motivation
Mythology
The Canonical Formula
Quantum Interaction
Conclusions
Summary
Bridging the gap
Analytical studies in need of processing methodology
Processing methodology development in need of raw
material
A concrete example how a topical set of myth variants
correspond via their syntagmatic transcripts to narrative
formulae
Families of narrative formulae, some with double inverted
values in their arguments, some without, all share the same
group structure with a certain quaternion group of order
eight.
A quantum probabilistic framework further generalises the
formulae.
´
´
Daranyi
Sandor,
Peter Wittek, and Kirsty Kitto
The Sphynx’s new riddle