progress+curve

=Progress Curve=

toc Read here about the progress curve, a quantitative pattern that is found in many phenomena and is a critical concept to comprehending scale.

=Overview=

Progress curve is a graphical representation of a chemical or enzyme-catalyzed reaction in which the product concentration or the substrate concentration or the ES binary complex are plotted against time.

An example progress curve for an enzyme assay is shown below. The enzyme produces product at an initial rate that is approximately linear for a short period after the start of the reaction. As the reaction proceeds and substrate is consumed, the rate continuously slowsMost enzyme kinetics studies concentrate on this initial, approximately linear part of enzyme reactions. However, it is also possible to measure the complete reaction curve and fit this data to a non-linear rate equation. This way of measuring enzyme reactions is called progress-curve analysis. >>> Insert image Generic enzyme progress curve. © Poccil 2010, used with permission.

Human global population rise is a special case of a progress curve.

See also sigmoid curve.

=War casualties=

Lewis Fry Richardson, a British scientist, analyzed war statistics from three hundred wars. He published in 1948 an analysis of the statistics of war called 'The Statistics of Deadly Quarrels'. Richardson found that wars with low death tolls far outnumber high-fatality conflicts, but the link between the severity and frequency of conflicts follows a smooth curve, known as a power law. Basically, the more people killed in a war, the less likely it will occur, and the longer before you will witness it, just as violent storms occur less frequently than cloudbursts. Neil Johnson, researcher of complex systems at the University of Miami Physics department, seeks to apply the results. He reports that the progress curve (T(n) = T(1)*n^-b where T1 is the number of days between the first and second attacks of an insurgency. The value of b varies widely from place to place. Progress curves are a consequence of people adapting to circumstances and learning to do things better. But in warfare, two antagonistic groups of people are doing the adapting. In biology, the Red Queen hypothesis is that predators and prey (or, more often, parasites and hosts) are in a constant competition that leads to stasis, as each adaptation by one is countered by an adaptation by the other. In the case Dr Johnson is examining the co-evolution is between the insurgents and the occupiers, each constantly adjusting to each other’s tactics. The data come from 23 different provinces, each of which is, in effect, a separate theatre of war. In each case, the gap between fatal attacks shrinks, more or less according to Dr Johnson’s model. Eventually, an equilibrium is reached, and the intervals become fairly regular.



See also war in human population.