Football in the fourth dimension

Sphere perceived in 2-D

In the 19th century, mathematician Georg Bernhard Riemann postulated the existence of a fourth spatial dimension. Whilst it is possible to represent this higher dimension mathematically, it is impossible for humans to visualise this extra dimension as our brains are constrained by a three-dimensional world. To demonstrate how this is possible we can conceive how a two-dimensional being might experience a third spatial dimension. If a two-dimensional person was pulled into a three-dimensional world they would only be able to understand this higher dimension via 2-D snapshots. The diagram shows how this person would encounter a sphere: they would only be able to perceive circular cross-sections.

Riemann also argued that if a 2-D world was ridged or curved, like a crumpled piece of paper, then this would manifest itself as forces felt by the inhabitants of this world although the direct cause of these forces could not be visualised. Riemann also considered that the fourth spatial dimension could have such an impact upon our 3-D world: we experience the warping of a fourth dimension as forces such as gravity and electromagnetism. Riemann hence showed how the laws of nature became simpler and more elegant when expressed in higher dimensions.

In football it can be argued that a team adopting an extra spatial dimension will have a significant advantage over its opponents. England’s favourite masochistic example of our technical inferiority to continental opponents is the 6-3 defeat to Hungary back in 1953. England believed they were unbeatable at home, but Hungary demolished this belief by presenting England with an unrecognisable mode of football that introduced a hitherto unseen dimension to the game.

England played a W-M formation in this fixture which was established as orthodoxy: at the time it could not be conceived that there was a superior alternative. Hungary arrived on these shores and played a more flexible game under a formation which resembled 4-2-4. England were used to playing sides that also played W-M, so games had a certain symmetry with both teams playing in the same dimension. Against a different formation the players did not understand how to address their opponents. For example, the Hungarian Hidegkuti played a position akin to a withdrawn forward: England’s defence had no idea how to mark him, as he did not fit into the regular spatial parameters of the game. It was as if the England players were 2-D beings in a 3-D world: they would only have understood snapshots of the Hungarian game through the lens of their narrower perspective. They inhabited an arena being shaped by a higher footballing dimension which they were unable to fully comprehend. A two-dimensional figure can be imprisoned simply by drawing a circle around it. In a sense Hungary had England immured, as they ran rings around them from their higher dimensional plane. Football also became simpler and more elegant when expressed by the Hungarians in a higher dimension.

Perhaps a team introducing an extra-spatial dimension to football may win World Cup 2010. Arguably the only time England have introduced an extra-dimension to football (Ramsay’s wingless wonders in 1966) they were crowned world champions. If Fabio Capello finds an extra dimension, maybe England could triumph for a second time!