Probability Notes - Probability Introduction Probability...

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Probability Introduction- Probability:  The Antithesis of Newton's Laws As we have seen, Newton's accomplishments had a tremendous effect on all  aspects of human intellectual thought.  Probably the two most revolutionary outcomes of  Newton's work were (1), that the basic structure of the universe can be best understood in  the interplay between observation, mathematics and speculation unrestrained by existing  orthodoxy. and (2), that the universe is fundamentally mechanistic and determined.  The  latter conclusion follows from Newton's laws.  Another way of stating it is that a  knowledge of all of the forces between all masses, together with their current positions  and velocities, will, in principle, allow one to calculate that future configurations of those  masses at any future time;  in other words, the present determines the future. The latter of these two outcomes has profound philosophical and theological  implications, but it was the first that attracted more opposition from theologians and  philosophers.  I should also remark, for completeness (despite the fact that they are  beyond the scope of this course), that two advances in physics during the twentieth  century, namely quantum mechanics and chaos, place limits on the degree to which the  present determines the future. Despite these philosophical implications of Newton's laws, in the real world, it is  rare that one ever knows the forces and initial positions and velocities of all the relevant  masses with enough precision to predict the future with high accuracy.  For instance, we  know a lot about the motion of a ball that has left a baseball bat (at least we could if we  photographed it with high precision time sequence photography), but we know very little  about the details of the internal motion of the molecules that make up the ball and the  positions and velocities of all the air molecules the ball will encounter on its way to the  outfield.  If the trajectory of the ball is very close to the foul line, even with very high  precision time sequence photography, we would be unlikely to bet our life's savings on  whether the ball will be called fair or foul.  But that is not to say that Newton's laws give  us no predictive ability.  If the ball were headed towards second base, a computer  programmed with Newton's laws could make the call far quicker than the umpire could.
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