Fighting mathematicians through the ages

[magid]

In 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.

Comments

[gingicat]

I think you have a book idea there.

[magid.livejournal.com]

It felt more like a short fiction snippet than something as long as a book. Maybe part of a larger group of "non-fiction" essays about fictional things, a la The Thackery T. Lambshead Pocket Guide to Eccentric & Discredited Diseases.

[cnoocy]

Don't forget sunya, the Orb of Annihilation that gave India such an advantage in the 5th-7th centuries

[cnoocy]

And you should totally read Celestial Matters.

[magid.livejournal.com]

Thanks :-)

I knew I'd miss all the non-Western stuff; my history knowledge is spottier off the European track. Though I should have mentioned how the newly-Muslim hordes conquering Spain enjoyed amazing military successes partly because their opponents had never seen a zero before, much less experienced its effects. Of course, it did encourage the Europeans to shift to a place value weapons scheme, setting the groundwork for later generations' advances.

[hrafn.livejournal.com]

I imagine a fractal defense would be awfully hard to get past! Not to mention strange attractors and chaotic systems.

[magid.livejournal.com]

Entire armies get lost in fractal defenses!