## Tuesday, February 10, 2009

### Paul Krugman vis a vis Vis Viva

drawing by marguerita

Ancient philosophers as far back as Thales of Miletus had inklings of the conservation of some underlying substance of which everything is made.

However, there is no particular reason to identify this with what we know today as "mass-energy" (for example, Thales thought it was water). In 1638, Galileo published his analysis of several situations—including the celebrated "interrupted pendulum"—which can be described (in modern language) as conservatively converting potential energy to kinetic energy and back again. However, Galileo did not state the process in modern terms and again cannot be credited with the crucial insight. It was Gottfried Wilhelm Leibniz during 1676–1689 who first attempted a mathematical formulation of the kind of energy which is connected with motion (kinetic energy). Leibniz noticed that in many mechanical systems (of several masses, mi each with velocity vi ),

$\sum_{i} m_i v_i^2$

was conserved so long as the masses did not interact. He called this quantity the vis viva or living force of the system. The principle represents an accurate statement of the approximate conservation of kinetic energy in situations where there is no friction. Many physicists at that time held that the conservation of momentum, which holds even in systems with friction, as defined by the momentum:

He doubts that citizens will get much protection from moguls--or from most economists, for that matter--unless we trouble to grasp how the whole intricate game works, so that our legislators will form a consensus about how to regulate it. Mill supposed that we needed to see "the Dynamics of political economy," not just "the Statics." Krugman knows we need Liquidity Traps for Dummies. Crash Landings: Paul Krugman's Depression Economics