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Lets assume your claim that Newtonian notation was not "clearly inferior"* to an unbiased person of the time, it follows then that teaching both ideas in Englis

Lets assume your claim that Newtonian notation was not "clearly inferior"* to an unbiased person of the time, it follows then that teaching both ideas in English Universities might have helped to more quickly determine which notation is more useful. Consider the result for the English Mathematical community if the Analytical Society was never formed. If biases exist then a spectrum of ideas from cultures which hold a different of set bias can be a critical aid in the search for truth. *I disagree with this assumption but it is a hard case to make in either direction and I recognize the value of your perspective.

Chris2048 10y ago
Wouldn't it make more sense to either standardise the notation, or translate papers into both notations? I feel this is a poor analogy to cultural cross pollination: notation is not the same kind of 'idea' as those found in philosophical paper.
- yummyfajitas 10y ago
  The fundamental dispute was not over the notation, but over whether the notation was misleading. I.e., is df/dx = (df/dz)(dz/dx) a real description of what is happening, and a valid calculus, or just a coincidence that sometimes won't work? Newton had a variety of arguments in favor of why his calculus worked, only some based on infinitesimals. Liebniz just asserted without proof that infinitesimals were fine, used them, and got good results. Additionally, there were a variety of religious arguments mixed into this, most of which are lost in the sands of uninteresting history. I.e., disputes over whether god (the perfect watchmaker) periodically wound his watch or whether he build a perfect watch that never needed winding. For instance, Liebniz believed in noninteracting dualism, but got set up the world so perfectly that the mind and body agreed. (I'm a mathematician and only minimally familiar with these - they have been discarded by history.) These religious arguments did play a role in the debate over infinitesimals, and acceptance of divine coincidences like Liebniz notation - unjustified though it may be - working perfectly all the time.
  - shanacarp 10y ago
    Variations of those arguments exist to this day unresolved in the form of Platonic Realism vs Nominalism. Resolving that argument in some ways is really important to our understanding of physics and certain parts of biology, especially evolution.
  - Chris2048 10y ago
    Then, both factions were fighting over pet bogosities? I believe https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of... and similar methods are used to show equivalence today. The subject seems more insulated from this kind of philosophy.

Chris2048 10y ago

Wouldn't it make more sense to either standardise the notation, or translate papers into both notations? I feel this is a poor analogy to cultural cross pollination: notation is not the same kind of 'idea' as those found in philosophical paper.

yummyfajitas 10y ago
The fundamental dispute was not over the notation, but over whether the notation was misleading. I.e., is df/dx = (df/dz)(dz/dx) a real description of what is happening, and a valid calculus, or just a coincidence that sometimes won't work? Newton had a variety of arguments in favor of why his calculus worked, only some based on infinitesimals. Liebniz just asserted without proof that infinitesimals were fine, used them, and got good results. Additionally, there were a variety of religious arguments mixed into this, most of which are lost in the sands of uninteresting history. I.e., disputes over whether god (the perfect watchmaker) periodically wound his watch or whether he build a perfect watch that never needed winding. For instance, Liebniz believed in noninteracting dualism, but got set up the world so perfectly that the mind and body agreed. (I'm a mathematician and only minimally familiar with these - they have been discarded by history.) These religious arguments did play a role in the debate over infinitesimals, and acceptance of divine coincidences like Liebniz notation - unjustified though it may be - working perfectly all the time.
- shanacarp 10y ago
  Variations of those arguments exist to this day unresolved in the form of Platonic Realism vs Nominalism. Resolving that argument in some ways is really important to our understanding of physics and certain parts of biology, especially evolution.
- Chris2048 10y ago
  Then, both factions were fighting over pet bogosities? I believe https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of... and similar methods are used to show equivalence today. The subject seems more insulated from this kind of philosophy.