Skip to main content
SpringerLink
Log in

Formalization of Kublai Khan’s globalization using Kunii’s incrementally modular abstraction hierarchy

  • Original article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

Using the design method proposed by Kunii, this study mathematically explains the achievement of Kublai of merging two different societies to build a globalized nation after conquering China. The considered design method, called incrementally modular abstraction hierarchy, consists of seven levels, from the most abstract, homotopy, to the most concrete, computer graphics. Moreover, it allows a flexible design while moving up and down its hierarchy. Using this method, we attempt to restore the concepts of Kublai, aiming to build a globalized state by combining nomadic and agricultural cultures. Specifically, we examine the use of two capitals to resolve the problem of different lifestyles of the Mongolian Khan, who moved between the summer and winter camps of the nomads, and the Chinese Emperor, who lived in a fixed palace of the agricultural people. By incorporating the category theory into Kunii’s method, we discuss the adjunction of the Mongolian 1000-household social and military system based on decimal numbers with the Chinese bureaucratic system. The inclusion of the category theory in his original method allows visualization by programming, making the design more versatile and flexible.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. Definition of an attaching space. Let there be two topological spaces X and Y, and let Y be adjoined to X to obtain an attaching space \({Y}_{f}$$.\, {\text{Thus}},$${Y}_{f}=Y{\bigsqcup }_{f}X=Y\bigsqcup X/\sim \) is the space attaching Y to X with an attaching function f, where \(\bigsqcup \) denotes a disjoint union.

  2. The Central Secretariat was the policy-formulating agency. The Department of State Affairs managed the six ministries and was the highest executive institution. The Chancellery advised the Emperor and the Central Secretariat. Each department had a minister or secretary with two assisting vice-ministers or secretaries. The Ministry of Personnel was responsible for the appointments, promotions, and demotions of civil officials. The Ministry of Revenue was in control of collecting census data, collecting taxes, and handling state revenues. The Ministry of Rites commanded state ceremonies and rituals. The Ministry of War had the responsibility for the appointments, promotions, and demotions of military officials. The Ministry of Justice ruled judicial and penal processes. The Ministry of Works managed governance construction projects, hired artisans and laborers, and manufactured governance equipment.

References

  1. Kunii, T.L.: Cyberworlds—theory, design and potential. IEICE Trans. Inform. Syst. E88-D(5), 790–801 (2005)

  2. Kunii, T.L.: Cyberworld modeling—integrating cyberworlds, the real world and conceptual worlds. Int. Conf. Cyberworlds 2007, 3–11 (2006)

    Google Scholar 

  3. Kunii, T.L., Ohmori, K.: Cyberworlds: architecture and modeling by an incrementally modular abstraction hierarchy. Vis. Comput. 22(12), 949–964 (2006)

    Article  Google Scholar 

  4. Ohmori, K., Kunii, T.L.: Designing and modeling cyberworlds using the incrementally modular abstraction hierarchy based on homotopy theory. Vis. Comput. 26(5), 297–309 (2010)

    Article  Google Scholar 

  5. Sieradski, A.J.: An Introduction to Topology and Homotopy. PWS-Kent, Boston (1992)

    MATH  Google Scholar 

  6. Spanier, E.H.: Algebraic Topology. Springer, New York (1966)

    MATH  Google Scholar 

  7. Kunii, T.L., Ohmori, K.: Cyberworlds: a kaleidoscope as a cyberworld and its animation: linear architecture and modeling based on an incrementally modular abstraction hierarchy. Computer Animation and Virtual Worlds 17(3–4), 145–153 (2006)

    Article  Google Scholar 

  8. Ohmori, K., Kunii, T.L.: An incrementally modular abstraction hierarchy for linear software development methodology. Int. Conf. Cyberworlds 2006, 216–223 (2006)

    Google Scholar 

  9. Ohmori, K., Kunii, T.L.: Development of an accounting system. ICEIS2007, pp. 437–444 (2007)

  10. Ohmori, K., Kunii, T.L.: The mathematical structure of cyberworlds. Int. Conf. on Cyberworlds 2007, 100–107 (2007)

    Google Scholar 

  11. Ohmori, K., Kunii, T.L.: Mathematical modeling of ubiquitous systems. Int. Conf. Cyberworlds 2008, 69–74 (2008)

    Google Scholar 

  12. Ohmori, K., Kunii, T.L.: Pi-calculus modeling for cyberworlds systems using the fibration and cofibration duality. Int. Conf. Cyberworlds 2008, 363–370 (2008)

    Google Scholar 

  13. Ohmori, K., Kunii, T.L.: Mathematical foundation for designing and modeling cybeworlds. Int. Conf. Cyberworlds 2009, 80–87 (2009)

    Google Scholar 

  14. Ohmori, K., Kunii, T.L.: Visualized deformation of joinery to understand jointing process by homotopy theory and attaching maps. Int. Conf. Cyberworlds 2011, 203–211 (2011)

    Google Scholar 

  15. Ohmori, K., Kunii, T.L.: Visualization of Joinery using Homotopy Theory and Attaching Maps. Transaction on Compuer Science XVI, pp. 95–114. Springer, Berlin (2012)

  16. Ohmori, K., Kunii, T.L.: Mathematical foundations for designing a 3-dimensional sketch book. In: Transaction on Computer Science XVIII, pp. 41–60. Springer, Berlin (2013)

  17. Ohmori, K., Kunii, T.L.: Clay flower creation based on homotopy type theory. Int. Conf. on Cyberworlds 2014, 198–204 (2014)

    Google Scholar 

  18. Todd, E.: The Diversity Of The World: Family and Modernity (La Diversité du monde: Famille et modernité). Éditions Le Seuil, Paris (1999)

    Google Scholar 

  19. Todd, E.: The Origin of Family Systems, Volume One: Eurasia (L'origine des systèmes familiaux, Tome 1: L'Eurasie). Éditions Gallimard, Paris (2011)

  20. Lévi-Strauss, C.: The Savage Mind (La pensée sauvage). Plon, Paris (1962)

    Google Scholar 

  21. Foucault, M.: The Archaeology of Knowledge (L’Archéologie du savoir). Éditions Gallimard, Paris (1969)

    Google Scholar 

  22. Bourdieu, P.: Distinction: A Social Critique of the Judgment of Taste (La distinction: Critique sociale du jugement)

  23. Richter, B.: From Categories to Homotopy Theory. Cambridge University Press, Cambridge (2020)

    Book  Google Scholar 

  24. Spivak, D.: Category Theory for the Sciences. MIT Press, Boston (2014)

    MATH  Google Scholar 

  25. Milewski, B.: Category theory for programmers. Blurb. (2019)

  26. Okada, H.: The Rise and Fall of the Mongol Empire. [Translation from Japanese.] Chikuma Shobo, Tokyo (2001) (in Japanese)

  27. Sugiyama, M.: The World of Great Mongol: Huge Empire of Land and Sea. [Translation from Japanese.] Kadokawa, Tokyo (2014) (in Japanese)

  28. Sugiyama, M.: Mongol empire and long afterwards. [Translation from Japanese.] Kodansha, Tokyo (2016) (in Japanese)

  29. Sugiyama, M.: The Riding Steppe Conquerors: Liao, Western Xia, Jin, and Yuan Dynasties. [Translation from Japanese.] Kodansha, Tokyo (2021) (in Japanese)

  30. Sugiyama, M.: Kublai Khan's Challenge: The Big Turning Point in World History by Mongolia. [Translation from Japanese.] Kodansha, Tokyo (2021) (in Japanese)

  31. Furumatsu, T.: Conquest of the Steppe: to the Great Mongol. [Translation from Japanese.] Iwanami Shoten, Tokyo (2020) (in Japanese)

  32. Okamoto, T.: How to read Chinese History for Cultural Refinement, PHP Institute, Tokyo (2020) (in Japanese)

  33. Shiraishi, N.: Genghis Khan. [Translation from Japanese.] Chuokoron-Shinsha, Tokyo (2006) (in Japanese)

  34. Shimada, M.: Khitan Dynasty: Nomadic People of Khitai. [Translation from Japanese.] Toho Shoten, Tokyo (2014) (in Japanese)

  35. Wittfogel, K.A., Fong, C.S.: History of Chinese society: Liao. APS 36, 907–1125 (2012)

    Google Scholar 

  36. Kalemis D.: Trees as Monads. Dimitrois Kalemis Web. https://dkalemis.wordpress.com/2014/03/22/trees-as-monads/

  37. Ohmori, K., Kunii, T.L.: Visualizing logical thinking using homotopy—a new learning method to survive in dynamic changing. In: 2011 Int. Conf. of Frontiers in Education: Computer Science and Computer Engineering, pp. 181–186 (2011)

  38. Ohmori, K., Kunii, T.L.: A general design method based on algebraic topology—a divide and conquer method. Int. Conf. Cyberworlds 2013, 267–273 (2013)

    Google Scholar 

Download references

Acknowledgements

We would like to thank Editage (www.editage.com) for English language editing.

Author information

Authors and Affiliations

  1. Faculty of Computer and Information Sciences, Hosei University, 3-7-2 Kajino-cho, Koganei-shi, Tokyo, 184-8584, Japan

    Kenji Ohmori

Authors
  1. Kenji Ohmori
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kenji Ohmori.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ohmori, K. Formalization of Kublai Khan’s globalization using Kunii’s incrementally modular abstraction hierarchy. Vis Comput 37, 2989–2997 (2021). https://doi.org/10.1007/s00371-021-02234-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-021-02234-y

Keywords

Search

Navigation