Episodes

  • Did Copernicus steal ideas from Islamic astronomers?

    Did Copernicus steal ideas from Islamic astronomers?
    Nov 29 2023
    Copernicus’s planetary models contain elements also found in the works of late medieval Islamic astronomers associated with the Maragha School, including the Tusi couple and Ibn al-Shatir’s models for the Moon and Mercury. On this basis many historians have concluded that Copernicus must have gotten his hands on these Maragha ideas somehow or other, even … Continue reading Did Copernicus steal ideas from Islamic astronomers?
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    1 hr and 27 mins
  • Operational Einstein: constructivist principles of special relativity

    Operational Einstein: constructivist principles of special relativity
    Jul 23 2023
    Einstein’s theory of special relativity defines time and space operationally, that is to say, in terms of the actions performed to measure them. This is analogous to the constructivist spirit of classical geometry. Transcript Oh no, we are chained to a wall! Aaah! This is going to mess up our geometry big time. Remember what … Continue reading Operational Einstein: constructivist principles of special relativity
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    1 hr and 17 mins
  • Review of Netz’s New History of Greek Mathematics

    Review of Netz’s New History of Greek Mathematics
    Oct 11 2022
    Reviel Netz’s New History of Greek Mathematics contains a number of factual errors, both mathematical and historical. Netz is dismissive of traditional scholarship in the field, but in some ways represents a step backwards with respect to that tradition. I argue against Netz’s dismissal of many anecdotal historical testimonies as fabrications, and his “ludic proof” … Continue reading Review of Netz’s New History of Greek Mathematics
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    52 mins
  • The “universal grammar” of space: what geometry is innate?

    The “universal grammar” of space: what geometry is innate?
    May 20 2022
    Geometry might be innate in the same way as language. There are many languages, each of which is an equally coherent and viable paradigm of thought, and the same can be said for Euclidean and non-Euclidean geometries. As our native language is shaped by experience, so might our “native geometry” be. Yet substantive innate conceptions … Continue reading The “universal grammar” of space: what geometry is innate?
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    32 mins
  • “Repugnant to the nature of a straight line”: Non-Euclidean geometry

    “Repugnant to the nature of a straight line”: Non-Euclidean geometry
    Feb 20 2022
    The discovery of non-Euclidean geometry in the 19th century radically undermined traditional conceptions of the relation between mathematics and the world. Instead of assuming that physical space was the subject matter of geometry, mathematicians elaborated numerous alternative geometries abstractly and formally, distancing themselves from reality and intuition. Transcript The mathematician has only one nightmare: to … Continue reading “Repugnant to the nature of a straight line”: Non-Euclidean geometry
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    31 mins
  • Rationalism 2.0: Kant’s philosophy of geometry

    Rationalism 2.0: Kant’s philosophy of geometry
    Nov 17 2021
    Kant developed a philosophy of geometry that explained how geometry can be both knowable in pure thought and applicable to physical reality. Namely, because geometry is built into not only our minds but also the way in which we perceive the world. In this way, Kant solved the applicability problem of classical rationalism, albeit at … Continue reading Rationalism 2.0: Kant’s philosophy of geometry
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    30 mins
  • Rationalism versus empiricism

    Rationalism versus empiricism
    Sep 18 2021
    Rationalism says mathematical knowledge comes from within, from pure thought; empiricism that it comes from without, from experience and observation. Rationalism led Kepler to look for divine design in the universe, and Descartes to reduce all mechanical phenomena to contact mechanics and all curves in geometry to instrumental generation. Empiricism led Newton to ignore the … Continue reading Rationalism versus empiricism
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    44 mins
  • Cultural reception of geometry in early modern Europe

    Cultural reception of geometry in early modern Europe
    Jul 10 2021
    Euclid inspired Gothic architecture and taught Renaissance painters how to create depth and perspective. More generally, the success of mathematics went to its head, according to some, and created dogmatic individuals dismissive of other branches of learning. Some thought the uncompromising rigour of Euclid went hand in hand with totalitarianism in political and spiritual domains, … Continue reading Cultural reception of geometry in early modern Europe
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    34 mins