When one has a series of measurements of something, a bunch of dots, there are two basic choices. You can look at them as an equation to be described, connecting them in the plane of the page. You can also look at them as physical processes to be found, not directly connecting the dots to each other, but indirectly connecting them through other things. That links the dots through loops perpendicular to the page.
Math is parallel to the page, processes perpendicular. Together they provide useful independent dimensions of understanding made possible by measurement. There's a very useful corollary of the conservation laws, following from their implication that rates of change and their derivatives can not be infinite. For things to begin or end there must be periods during which all rates of change are of the same sign, and fall between upper and lower bound exponential curves. That's a reasoning that could equally lead to the conclusion that there had to be an inflationary period in the big bang. I'm not certain the principles used are the same, but there's a similarity. What's new for the scientific method in this, though, is that you can see the same phenomenon in most any sort of beginning or ending too. It provides a very useful standard hypothesis for probing the clues of how events that begin and end occur. Math and process reasoning can be used together, or you can ignore one or the other. Each deals with the same world in a different way. For just one example, building an equation that has the same structure from beginning to end to represent any natural process of change, will not help much for picking out what actually happening. Carefully filtering data to reveal its independent shapes and their start and end points, on the other hand, can coax clues from the data about many new kinds of events. The main reason that's useful, of course, is there's lots there to see, frequently evolving systems. Phil Henshaw ¸¸¸¸.·´ ¯ `·.¸¸¸¸ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 680 Ft. Washington Ave NY NY 10040 tel: 212-795-4844 e-mail: [EMAIL PROTECTED] explorations: www.synapse9.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
