Fighting mathematicians through the ages
May. 6th, 2008 02:46 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
magidIn warlike ancient Greece, battles were limited by the level of military technology. That is, troops were armed only with applied geometry, with the geometers preferring whole number situations. There were other numbers used (most notably, the use of π causing the tide of battle turning against the Spartans in the Battle of Radix), but the rules of engagement kept most irrational numbers off the battlefield.
The elegance of these geometrical platoons was lost through much of the medieval period, which depended more on rote arithmetickal handwavers than understanding the underlying forms.
In the early modern period, there was a shift towards the algebraic. Instead of the brute force of the medieval period, new quadratic weapons came into play, using parabolas for trajectories, circles and ellipses for defense, and hyperbolas for surprise attacks.
Since Leibnitz and Newton, there has been an enormous increase (one might even say an explosion) of weapons in the arsenal. First, of course, was the calculus, which has many applications, with both short- and long-range options for (dis)integration or derivation. After that, the pace of change increased, and there were more and more specialists in the field: advanced algebra shock troops ringing those in the fields, stealth topology spies sent across enemy lines, and so on.
The elegance of these geometrical platoons was lost through much of the medieval period, which depended more on rote arithmetickal handwavers than understanding the underlying forms.
In the early modern period, there was a shift towards the algebraic. Instead of the brute force of the medieval period, new quadratic weapons came into play, using parabolas for trajectories, circles and ellipses for defense, and hyperbolas for surprise attacks.
Since Leibnitz and Newton, there has been an enormous increase (one might even say an explosion) of weapons in the arsenal. First, of course, was the calculus, which has many applications, with both short- and long-range options for (dis)integration or derivation. After that, the pace of change increased, and there were more and more specialists in the field: advanced algebra shock troops ringing those in the fields, stealth topology spies sent across enemy lines, and so on.