An intricate knot was used by a man named Gordius to secure his oxcart. This man was a peasant who came to Phrygia in an oxcart. An oracle had told the Phyrgians that their next king would arrive in a wagon. The oxcart was good enough for them, and they made Gordius king. He responded by offering his oxcart to Zeus and tying the cart up with a difficult knot. Gordius was succeeded by Midas, who didn't leave an heir. The same oracle who had spoken before now told the people that whoever untied the knot would have the rule of all Asia.
It was quite the puzzle, this knot. Many men had tried to untie it; none had succeeded. So Alexander, no stranger to puzzles (having studied under the great Aristotle) and wanting to make a name for himself in this part of the world, announced that he would solve this puzzle.
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For solve the puzzle he did. He untied the knot by cutting it with his sword! Faced with a problem whose solution had eluded a great many men, Alexander changed the rules and found his own way forward a strategy that epitomized his entire career and very way of thinking. He reached the ends but by means other than what was expected.
What was it about this knot that had so vexed the brave and clever before Alexander? It was certainly a puzzle, this knot that looked like it had no ends. How could one possibly untie a knot that had nowhere to start untying? Surely many men had left, shaking their heads, after trying in vain to get the knot undone.
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Alexander saw through the way the problem was presented, beyond the "rules" that said one had to use one's hands and wits and seize the knot by the ends in order to untie it. Rather than try what others had, Alexander forged a new path, succeeding where everyone else had failed.
Was this a technicality? Probably. Technically, Alexander did untie the knot. After he cut it with his sword, the knot was easily enough untied.
Did he fulfill the prophecy foretold by the oracle? He most certainly did. Alexander and his loyal men conquered more territory than anyone before him (and many since) and stretched the boundaries of what Greek minds would know as "the known world" far beyond the imaginations of the time. His boldness, courage, and vision got him there the same skills that enabled him to see through the trap of trying to untie the knot in the conventional way and find a way to achieve the end by different means.
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If Alexander didn't cut the Gordian Knot, he should have.
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