Bal Chandra Luitel University of Kathmandu Peter Taylor Curtin University of Technology

1. Shanai & Pseudosphere:Cultural Artefacts Worldviews & Transformative Intercultural Education Bal Chandra Luitel University of Kathmandu Peter Taylor Curtin University of Technology

2. Cultural Artefacts Shanai pseudosphere intercultural educational alliance?

3. 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

4. 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)

5. 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 mono-perspectival; rather it gives a view of science as the process of conceptualizing multiple worlds and their eternal dialogue.” (Bal, 04)

6. Modernist Mathematical Certainty Descriptive of properties of physical space Euclidean Geometry (300BC) + Descartes’ privileging of human reason (C 17th) X A A B Y C B

7. non-Euclidean Geometries (C 19th) • geometers: Gauss, Lobachevsky, Bolyai, Riemann • spherical & hyperbolic geometries for curved surfaces • countered Euclid’s ‘sacred’ postulates

8. Pseudosphere & Hyperbolic Geometry • better explains influence of large gravitational masses on movement of planets, starlight • force of gravity becomes a fiction!

9. 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

10. Intercultural Educational Alliance? Shanai pseudosphere problems…

11. 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)

12. Trivialisation of IK Neo-colonialism • subjugation of indigenous knowledge • decontextualisation • “ethno” science/maths status • essentialising of indigenous culture (S&K, 98)

13. 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) ?

14. 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’?

15. to be continued…