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Mathematics in Nature

  • Ole Ravn
  • Ole Skovsmose
Chapter
Part of the History of Mathematics Education book series (HME)

Abstract

This chapter gives the Renaissance and rationalist philosophers of the 16th and 17th century have the word. The Renaissance is generally characterised by the belief that human reason can provide insight in the organisation of the world. The world was still considered God’s creation, but it became increasingly common to view it as machine, which functioning the deity has not interfered with since its creation.

The chapter starts out with an account of the so-called scientific revolution and the break with Aristotelian physics that it represents. The move from a geocentric to a heliocentric worldview becomes analysed in detail. The use of mathematics for describing nature is a central element in this move, and the chapter examines the tying together of explanations of nature and mathematics that took place during this tumultuous time. Infinitesimals challenged mathematical ontology. If mathematics is the “language of nature,” infinitesimals must somehow relate to entities in reality. But as such, they are rather unmanageable, for how can a world that has actual extension be built by units so small that they have no extent? How many infinitesimals have to be added up in order to turn into a natural object?

Keywords

Geocentric worldview Heliocentric worldview Infinitesimals Laws of nature Newton’s Principia Renaissance Scientific revolution Unnatural mathematics 

References

  1. Abbud, F. (1962). The planetary theory of Ibn al-Shatir: Reduction of the geometric models to numerical tables. Isis, 53(4), 492–499. Chicago, IL: The University of Chicago Press.Google Scholar
  2. Berkeley, G. (2002). The analyst. Retrieved from http://www.maths.tcd.ie/pub/HistMath/People/Berkeley/Analyst/Analyst.pdf
  3. Bodin, J. (1945). Method for the easy comprehension of history. New York, NY: Columbia University Press.Google Scholar
  4. Bury, J. B. (1955). The idea of progress: An inquiry into its origin and growth. New York, NY: Dover Publications.Google Scholar
  5. Copernicus, N. (1996). On the revolutions of heavenly spheres. New York, NY: Prometheus Books.Google Scholar
  6. Descartes, R. (1993). Meditations on first philosophy in focus. Edited and with an introduction by Stanley Tweyman. London, UK: Routledge.Google Scholar
  7. Descartes, R. (1998). The world and other writings. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  8. Dobbs, B. J. T. (1983). The foundations of Newton’s alchemy. Cambridge, UK: Cambridge University Press.Google Scholar
  9. Foscarini, P. A. (1991). Letter of opinion over the Pythagorean and Copernican opinion concerning the mobility of the earth and the stability of the sun. In R. J. Blackwell (Ed.), Galileo, Bellarmine, and the Bible (pp. 217–251). Notre Dame, IN: University of Notre Dame Press.Google Scholar
  10. Galilei, G. (1957). The assayer. In G. Galilei (Ed.), Discoveries and opinions of Galileo (pp. 229–281). New York, NY: Anchor Books.Google Scholar
  11. Galilei, G. (2001). Dialogue concerning the two chief world systems: Ptolemaic and Copernican. New York, NY: The Modern Library.Google Scholar
  12. Galileo Project. (1995a). Johannes Kepler. Retrieved from http://galileo.rice.edu/sci/kepler.html
  13. Galileo Project. (1995b). On motion. Retrieved from http://galileo.rice.edu/sci/theories/on_motion.html
  14. Kepler, J. (1596). Mysterium cosmographicum (The sacred mystery of the cosmos). Retrieved from http://www.e-rara.ch/doi/10.3931/e-rara-445
  15. Kepler, J. (2008). The harmony of the world. London, UK: Forgotten Books.Google Scholar
  16. Kepler, J. (2014). New world encyclopedia. Retrieved from http://www.newworldencyclopedia.org/entry/Johannes_Kepler
  17. Newton, I. (1999). The principia: Mathematical principles of natural philosophy. Berkeley, CA: University of California Press.Google Scholar
  18. Whiteside, D. T. (1961). Patterns of mathematical thought in the later Seventeenth Century. Arch Hist Exact Sci, 1(3), 179–388.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ole Ravn
    • 1
  • Ole Skovsmose
    • 1
    • 2
  1. 1.Department of Learning and PhilosophyAalborg UniversityAalborgDenmark
  2. 2.Department of Mathematics EducationState University of São Paulo, (Universidade Estadual Paulista, Unesp)São PauloBrazil

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