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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)
Revision as of 19:58, 11 July 2008
, 19:58, 11 July 2008→Differential Propositions : The Qualitative Analogues of Differential Equations: HTML → TeX
: <math>\mathbb{D} = \{(\operatorname{d}a_i), \operatorname{d}a_i\} = \{\mbox{same}, \mbox{different}\} = \{\mbox{stay}, \mbox{change}\} = \{\mbox{stop}, \mbox{step}\}.</math>
: <math>\mathbb{D} = \{(\operatorname{d}a_i), \operatorname{d}a_i\} = \{\mbox{same}, \mbox{different}\} = \{\mbox{stay}, \mbox{change}\} = \{\mbox{stop}, \mbox{step}\}.</math>
Viewed within a coordinate representation, spaces of type '''B'''<sup>''n''</sup> and '''D'''<sup>''n''</sup> may appear to be identical sets of binary vectors, but taking a view at this level of abstraction would be like ignoring the qualitative units and the diverse dimensions that distinguish position and momentum, or the different roles of quantity and impulse.
Viewed within a coordinate representation, spaces of type <math>\mathbb{B}^n</math> and <math>\mathbb{D}^n</math> may appear to be identical sets of binary vectors, but taking a view at this level of abstraction would be like ignoring the qualitative units and the diverse dimensions that distinguish position and momentum, or the different roles of quantity and impulse.
===An Interlude on the Path===
===An Interlude on the Path===