have remarked on the importance of the "Infantry Revolution" taking place in the early 14th century, and David Eltis has pointed out that the real change to gunpowder weapons and the elaboration of a military doctrine according to that change took place in the early 16th century, not, as Roberts defended, in the late 16th century. Others have defended a later period for the military change. Jeremy Black thinks that the key time period was that of 1660–1710, which saw an exponential growth in the size of European armies, while Clifford J. Rogers has developed the idea of successive military revolutions at different periods, first an "infantry revolution" in the 14th century, secondly an "artillery revolution" in the 15th century, thirdly a "fortifications revolution" in the 16th, fourth a "fire weapons" revolution between 1580 and 1630, and finally a fifth revolution, the increase in size of European armies, between 1650 and 1715. Similarly, Geoffrey Parker has extended the period of the military revolution from 1450 to 1800, the period in which Europeans achieved supremacy over the rest of the world. Some scholars have questioned the revolutionary character of an evolution through four centuries. Clifford Rogers has suggested that the military revolution can best be compared with the concept of "punctuated equilibrium evolution" (a theory originating in biology), meaning short bursts of rapid military innovation followed by longer periods of relative stagnation. The military revolution failed in the Ottoman Empire. According to a 2013 study, there are two factors that explain this failure: "civil-military relations and historical timing. In the Ottoman Empire, the emergence of an institutionally strong and internally cohesive army during the early stages of state formation—in the late fourteenth century—equipped the military with substantial bargaining powers. In contrast, the great powers of Europe drew heavily on private providers of military power during the military revolution and developed similar armies only by the second half of the seventeenth century, limiting the bargaining leverage of European militaries over their rulers. In essence, the Ottoman standing army was able to block reform efforts that it believed challenged its parochial interests." Tactics Linear tactics Shallow formations are ideally suited for defensive deployments, but they are clumsy in offensive missions: the longer the frontage, the more difficult to maintain order and cohesion, or to perform any maneuver, especially wheeling. Gustavus Adolphus understood well that far from being slow and ponderous, the assault columns