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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)
Revision as of 18:24, 28 February 2009
, 18:24, 28 February 2009→Example 1. A Square Rigging: del extra space after period so the stupid linker can link to it
Observe that the secular inference rules, used by themselves, involve a loss of information, since nothing in them can tell us whether the momenta <math>\{ (\operatorname{d}A), \operatorname{d}A \}</math> are changed or unchanged in the next instance. In order to know this, one would have to determine <math>\operatorname{d}^2 A,</math> and so on, pursuing an infinite regress. Ultimately, in order to rest with a finitely determinate system, it is necessary to make an infinite assumption, for example, that <math>\operatorname{d}^k A = 0</math> for all <math>k\!</math> greater than some fixed value <math>M.\!</math> Another way to escape the regress is through the provision of a dynamic law, in typical form making higher order differentials dependent on lower degrees and estates.
Observe that the secular inference rules, used by themselves, involve a loss of information, since nothing in them can tell us whether the momenta <math>\{ (\operatorname{d}A), \operatorname{d}A \}</math> are changed or unchanged in the next instance. In order to know this, one would have to determine <math>\operatorname{d}^2 A,</math> and so on, pursuing an infinite regress. Ultimately, in order to rest with a finitely determinate system, it is necessary to make an infinite assumption, for example, that <math>\operatorname{d}^k A = 0</math> for all <math>k\!</math> greater than some fixed value <math>M.\!</math> Another way to escape the regress is through the provision of a dynamic law, in typical form making higher order differentials dependent on lower degrees and estates.
===Example 1. A Square Rigging===
===Example 1. A Square Rigging===
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