whitefork
4th February 2003, 01:27 PM
33 hits and no one wishes to discuss poor Philbert Desenex. Que lastima.
1900 years before Newton Apollonius of Perga derived a large number of properties of the conic sections (circle, parabola, ellipse, hyperbola). That's a lot of the mathematics required for Newtonian physics, and all of it mathematically necessary.
It's possible that Apollonius drew on observations made while cutting up cones, but who's to say - in any event the mathematics as presented does not depend on physical measurement. It's not contingent on the material of the which the cone is made or the tools used to section it.
Now, the observation that bodies accelerate while falling is a contingent one - there's no reason to expect a priori that they would have this property. The fact that the path taken by an accelerated body is described by the same equations that describe a conic section is quite remarkable to me.
So, what if anything should we conclude from this coincidence, and is it a coincidence at all, or an indication of an underlying property of space, time, and matter?
1900 years before Newton Apollonius of Perga derived a large number of properties of the conic sections (circle, parabola, ellipse, hyperbola). That's a lot of the mathematics required for Newtonian physics, and all of it mathematically necessary.
It's possible that Apollonius drew on observations made while cutting up cones, but who's to say - in any event the mathematics as presented does not depend on physical measurement. It's not contingent on the material of the which the cone is made or the tools used to section it.
Now, the observation that bodies accelerate while falling is a contingent one - there's no reason to expect a priori that they would have this property. The fact that the path taken by an accelerated body is described by the same equations that describe a conic section is quite remarkable to me.
So, what if anything should we conclude from this coincidence, and is it a coincidence at all, or an indication of an underlying property of space, time, and matter?