Swift Victory: Alexander’s Conquest and Strategic Optimization

Attack Where Undefended

The supreme art of war is to subdue the enemy without fighting. Yet observe Alexander: ten years conquering an empire that endured centuries. What gradient descent reveals about following steepest paths downward, what decisive battles at Granicus, Issus, and Gaugamela demonstrate about eliminating armies at strategic nodes—these are not different wisdoms but the same truth wearing different masks.

Memnon of Rhodes understood this paradox. His attrition strategy—burn crops, starve Alexander’s army, bribe Greek cities to rebel—guaranteed Persian victory through patience. Like gradient descent promising convergence through steady downward steps, the plan was mathematically sound. Slow but certain. Yet the Persian satraps rejected it, unwilling to destroy their own property for long-term gain. Alexander thus won before fighting, exploiting not military weakness but the gap between strategic wisdom and political will.

Greek equilibrium warfare reveals the trap of local minima. Athens and Sparta fought the Peloponnesian War without seeking total victory. Athens could have liberated Sparta’s helots, multiplying their enemy’s army tenfold—but this would destroy the very social order both oligarchies sought to preserve. They chose predictable equilibrium over decisive transformation. Like evolutionary algorithms trapped in local search, making small mutations around current positions, they feared the leap that might discover global optima.

Speed as Strategic Momentum

Alexander avoided this trap. His initialization—elite Macedonian phalanx, cavalry hammer, the asymmetric tactics Philip forged—gave him favorable starting position in the loss landscape of conquest. But observe: gradient descent also benefits from good initialization. Neural networks with poorly positioned starting parameters generate gradients that vanish, leaving them stuck despite architectural capacity for better solutions.

Alexander’s speed compounded his initial advantage. Strike at decisive points where Persian field armies concentrated, eliminate them before the empire mobilized its full strength. This is not gradual descent following local slopes but recognizing that certain nodes in a network carry disproportionate weight. Attack these critical points and the entire structure transforms.

Yet here wisdom demands deeper notice: Alexander died young, his empire fragmenting immediately. Was this global optimum found quickly but proving unstable? Memnon’s rejected attrition would have been slower but perhaps found more durable equilibrium. The Persian elite who invited Alexander, expecting to co-opt him with bribes as they had previous threats, discovered too late that his initialization was different—he considered himself son of god, immune to their standard optimization strategies.

The Formlessness of Water

All warfare is based on deception. Gradient descent reveals only local information, knowing steepest descent but not distant valleys. Evolutionary search explores through random mutation, vulnerable to dimensionality’s curse. Alexander’s genius—if genius it was—lay in refusing predictable algorithms. The Gordian Knot: cut rather than untie. The siege of Tyre: build causeway across sea when conventional wisdom said wait.

Is there an Alexander-like algorithm that combines gradient descent’s local precision with evolutionary search’s global exploration, that recognizes decisive nodes rather than treating all parameters equally, that compounds initialization advantages through momentum? Perhaps. But observe also that momentum can carry you past the valley you seek, that speed without wisdom creates fragile victories, that the supreme excellence—subduing the enemy without fighting—may require the patience Memnon advocated.

Thus the strategist studies both Alexander’s swift conquest and gradient descent’s measured steps, knowing that victory lies not in choosing speed over thoroughness but in recognizing which landscape you traverse and which algorithm that terrain demands.