The oblique order was invented by Epaminondas and tested by Philippe. However, it only proved its tactical extent when Alexander made use of it during the battle of Gaugameles in October 331 BC. The basic element of this offensive technique is a dense unit of 256 heavy infantrymen forming 16 ranks. Each infantryman of the first ranks holds a 4 to 7 meter long sarissa according to the battles. The others of the next ranks rested their respective sarissa on the shoulder of the previous one. At that time, no reply had been found against this structure that led to the Roman turtle later. But its force came from its dynamics. As a matter of fact, this structured, spiked and fluffed mass had an unrivalled penetration force. By the way, it had been one of the basic constituents during the battle of Chaeronea, not being the spearhead of the Macedonian attack for all. During the battle of Gaugameles, as the historian and strategist Fortin highlighted, Alexander deployed his battle line so that it stood up in all the directions. So, his men, once surrounded could fight on all sides. The attack of Darius on the left wing has been a surprise for the latter, for it was preceded by a cavalry charge and led in an oblique way. Though the attack on the left wing is predictable because it corresponds to the natural development of shield wearing at that time, it still remains an original element within a context usually centered and frontal. Its essence directly arising from material physics is a posteriori clear for it allows action converging and attack strengthening via its angle reducing, meaning that if resistance is the same, it can break through the front because it is increased by the heavy weapons of infantrymen, taking advantage of its own launched inertia.
Via all its characteristics, the oblique order represents the military representation of mental schemata of lateral thinking. Its initial point is the realization of an impossible direct access to knowledge. Thus, any direct method is doomed to failure. This step that can seem elementary to a person not initiated to research is in fact the most difficult one in the conceptual world. It comes from the fact that it is extremely difficult and so, exceptional to get the demonstration of the non-existence of a direct method. So, the researcher in this non-explicit sentence depends on his/her intuition and his/her experience. But as they are precisely limited within this context, in the end his/her intelligence only remains for judging. One way to make it evolve in this field is to deal with problems banishing direct methods. This technique that seems artificial is an excellent means to deeper understand the problem considered. The increase of the difficulty to find a solution enables a more acute analysis of dynamic mental structures. Moreover, lateral thinking, as heuristic also opens up to the weak points of the problem entity for they are not necessarily on the visible side of the problem. Thus, it is comprehension that makes them visible. This point highlights an idea about the theory of mental schemata, that is to say, we can only see what we can understand.

At last, lateral thinking like oblique order is an efficient means to solve a problem via the realization of its dimensional complexity. Therefore, they are tactical elements requiring preliminary strategic knowledge. In that way, they mingle in the space of non-uniform reasoning.