Shanai & Pseudosphere:
Cultural Artefacts
Worldviews &
Transformative Intercultural
Education
Bal Chandra Luitel
University of Kathmandu
Peter Taylor
Curtin University of Technology
Cultural Artefacts
Shanai
pseudosphere
intercultural educational alliance?
Research
• culturally ‘decontextualised’ maths education
in Nepal!
• Nepali cultural capital?
• autoethnographic inquiry (Luitel, 2003)
• stories (20) & critical reflective scholarly
commentary
• research:
prof development + cultural excavation
Nepali (Hybrid) Worldview
• Hindu-Buddhist Cosmology
• Modern Scientific Universalism
(Cartesian-Newtonian W-V, S&K, 98)
• Modern Mathematical Certainty
(Cartesian-Euclidean W-V, Kline, 85)
Nepali Worldview
“To me, Nepali cosmology believes in multiple
realities embracing an organic and dynamic view
of the universe. Indicatively, Nepali science does
not seem to be mechanical, technical and monoperspectival; rather it gives a view of science as
the process of conceptualizing multiple worlds
and their eternal dialogue.” (Bal, 04)
Modernist Mathematical
Certainty
Euclidean Geometry (300BC) + Descartes’
privileging of human reason (C 17th)
X
A
A
B
C
Y
B
Descriptive of properties of physical space
non-Euclidean Geometries
(C 19th)
• geometers: Gauss, Lobachevsky, Bolyai,
Riemann
• spherical & hyperbolic geometries for curved
surfaces
• countered Euclid’s ‘sacred’ postulates
Pseudosphere &
Hyperbolic Geometry
• better explains influence of large gravitational
masses on movement of planets, starlight
• force of gravity becomes a fiction!
Relativistic (Science) Worldview
• alternative properties of physical space-time
(Einstein)
• empirical & interpretive nature of all (Euclid’s)
geometries
• loss of mathematical certainty
• multiple scientific realities
Intercultural Educational Alliance?
Shanai
pseudosphere
problems…
Trivialisation of HG
“At the end of the topic, many of us asked our teacher
about the nature of a pseudosphere and its availability.
My short-term perception of hyperbolic geometry, as a
superficial and disconnected body of knowledge, was
challenged slightly when our teacher replied, “My
teacher said to me that a pseudosphere resembles the
Nepali Shanai”. Although he tried to familiarize us (was
that ‘contextualisation’?) with the complex body of
knowledge by that example, it was not sufficient for me
to understand hyperbolic geometry in my context.
Furthermore, only reciting that the Shanai is similar to
the pseudosphere did not establish a connection
between hyperbolic geometry and our culture; instead, it
only seemed to trivialize the practical aspects of
hyperbolic geometry.” (Bal, 04)
Trivialisation of IK
Neo-colonialism
• subjugation of indigenous knowledge
– decontextualisation
– “ethno” science/maths status
• essentialising of indigenous culture
(S&K, 98)
Worldviews in Dialogue
“Given the nature of Nepali cosmology, my
notion of the Nepali Shanai does not only
produce a literal view of non-Euclidean
geometries but also constructs a perspective
that our cultural artifacts reflect multiple
worldviews. Furthermore, using the Shanai as a
geometric object can indicate a way to promote
dialogue between local and non-local knowledge
traditions.” (Bal, 04)
?
Transformative Intercultural
Education in Nepal?
Contextualisation?
• whose interests are being served?
• cultural practices of “truth production”?
• what values and beliefs are linked?
• metaphors of ‘knowing’?
to be continued…