Gröninger was dissatisfied with his approximate treatment of (141) since it gave poor estimates of the fundamental lines in the waterstuff spectrum. We have even less reason to be satisfied with the Lin-Shu-Kalnajs analysis of (140) which, unaided, is unable to give an adequate account of even the high-frequency normal modes; Personne's programme turns out to involve loosely-wound waves for which the LsK-dispersion relation is not really valid. Obviously more powerful techniques need to be developed for the solution of (140).
High-energy physicists think always in terms of “particles” and “interactions” and yet these are really just elements (propagators and vertices) introduced during the iterative solution of a set of coupled non-linear integro-differential equations.
Isaac Newton spent vastly more time, thought and experimental effort on chemistry than on either physics or mathematics. Yet his incomparable mind, which both before and after his period as a chemist revolutionized mathematics and first demonstrated the possibility of exact science, achieved nothing of lasting value in Chemistry, whose foundations were to be laid by men of much smaller stature in the mid 18thc. Why did he fail so miserably? Because his conceptual framework was pre-Newtonian; brought up in the mystical, pre-Enlightenment mid 17thc. he thought in terms of the ancient alchemical concepts of corruption and redemption rather mechanistic causality.
Concepts such as Lindblad resonances and long- and short-waves introduced by the conventional theory of spiral structure may prove as useful as quarks or as obstructive as alchemy. Only the future and hard work will tell.
KeywordsAction Space Poisson Bracket Velocity Dispersion Globular Cluster Keplerian Motion
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