by Daisy Luther, The Organic Prepper:
Many enmeshed within the world of art are well aware of Pythagoras’ discovery of the Golden Ratio – a mysterious figure that is inherently beautiful. Just what is that ratio? 0.618, or around 3/5. Anytime you have a painting that utilizes this ratio, it will be recognized to have traits of beauty within it. Photographers will recognize the ‘rule of thirds’ present within the Golden Ratio, being a rough estimate of 0.618.
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Of course, the painter’s skill with a brush, the subject matter, and the time spent on the final piece are also vital components of determining how beautiful a piece will be, but the point remains: there is something inherently special about the Golden Ratio.
But are there other aspects of life where we can see the Golden Ratio at work? Can it be applied to fields other than art? What about the field of war? History appears to instruct us so. If we examine the life of war throughout history, we can find multiple examples of the Golden Ratio being applied successfully, resulting in victory for the man who uses its secrets, knowingly or not.
And while generals throughout history may not have realized this was what they were doing – using the Golden Ratio – the fact remains that it still seems to benefit the user. Perhaps mathematical beauty applied to war is an ingredient for constant success? Perhaps it can warn us as to when conflict is soon to turn sour?
If we take a closer look, I think you’ll be surprised at what we find out…
10.) The Battle of Arbela
War is part art, and few displayed this as well as the man who would have “The Great” tacked on to the end of his name: Alexander.
Alexander the Great would demonstrate his ability to paint a masterpiece with his sword at the Battle of Arbela, where he would finally vanquish his long-time foe, King Darius. The two men had fought each other for years, with Alexander even going so far as to capture Darius’ family.
The Battle of Arbela was identified by both men as to be the final decision as to who would reign throughout their section of the world. Both men were formidable enemies to behold, and knowing he was in for no easy fight, in preparation for Alexander’s attack, Darius set about fortifying his position as best he could. Obstacles and traps were placed throughout the battlefield, scythed chariots were pre-positioned so that they could best mow down enemy troops, and longer swords and spears were handed out to his men. By some estimates, Darius’ position was a million men strong.
He should’ve been unstoppable.
Yet Alexander was able to take the field and become King over all Asia with only 40,000 men.
How did he do such? Aside from ensuring his men were well-rested, learning of the positions of the traps from POWs, and keeping his men well-fed, Alexander also seemed to have a little golden help.
As the battle began, Alexander sent much of his right front towards Darius’ left flank. As the men approached one another, the Macedonians then turned to hit the “golden point” of Darius’ front line – hitting approximately 3:5 of the way down Darius’ line.
Darius’ troops were separated, Alexander took the field, and the rest is history.
9.) The Characteristics of the Mongolian Hordes
None could strike fear into the heart of Medieval men as could the Mongols. Traveling light and seemingly as fast as light itself, these mounted soldiers seemed to be an unbeatable foe. And at the head of these Mongol hordes was a man simply known as the “Universal Ruler” – Genghis Khan.
Throughout his lifespan, Genghis Khan would go on to conquer the largest landmass of any human being in history, taking over somewhere between 11-12 million square miles of land, roughly the size of Africa. This massive landmass would eventually result in being a large part of the reason the Mongolian empire crumbled – it was too much land for too few men – but the feat alone was an act of military brilliance.
Using horse-mounted dummies to trick his enemies into thinking his army was stronger than it truly was, being experts with archery on horseback, and the ability to move with minimal equipment were all some of the reasons that the Mongols were able to conquer as much landmass as they did, but could the Golden Ratio apply here as well?
It appears so.
The Mongols had a very different cavalry formation than did the rest of Europe. How so? The Mongols had an approximate 3:5 ratio of heavy to light cavalry. For every four heavy cavalry soldiers, the Mongols had six light cavalries. This combination seemed to be the perfect mix for dealing with European defenders as the heavy cavalry could sweep through the aftermath the light cavalry had picked off from a distance, once more showcasing the role of the Golden Ratio during war.
8.) King Gustavus of Sweden
Perhaps no other medieval warrior applied the Golden Ratio as effectively as did the man who could go on to be known as “The Lion of the North.” Taking the throne at the age of 17, King Gustavus had no easy transition period. At his coronation, Sweden was in the midst of a war with Russia, Poland, and Denmark, all whetting their swords for Swedish blood.
At the time, battle had largely grown into a logistical nightmare. European countries largely had similar weaponry, and generals had turned to using wars of attrition and outmaneuvering one’s opponent to bring about surrender.
The only problem with this was the cost of resources. To move an army is expensive, and to engage in attrition warfare even more so – in cost of ammunition, food, weaponry, and lives. Knowing that Sweden would never be able to survive such warfare economically intact if he used these methods, Gustavus instead focused on changing his tactics.
He took his brigades – composed of three 500-men squadrons – and made 2/3 of each of them musket men as the remaining third remained pikemen.
The resulting combination led to a devastating combination of weaponry, revolutionized the role of firearms in warfare, and helped to propel Sweden to being a powerful force to be reckoned with throughout Europe at the time.
All because a 17-year-old kid was willing to think outside of the box. Perhaps he had studied Pythagoras?
7.) The Battle of Trenton
The element of surprise certainly matters. And when it’s compared with the Golden Ratio? Well, then you may just have a recipe for the complete annihilation of your enemy. On Christmas night, 1776, George Washington rallies his men for a raid across the Delaware River.
Their target? The German mercenaries, known as Hessians, who reside ten miles away at the town of Trenton. Washington concocts a three-pronged attack, but bad weather forces two of the columns to have to turn back. A third of his men make it through, however, and Washington is able to catch the invaders completely unaware.
It appears that Washington’s three-tiered attack ended up being a three-layered insurance policy.
A total of 2400 men join Washington for the fight against a force of 1500 unexpecting Hessians. This means that out of the 3900 men engaged in the Battle for Trenton, Washinton held roughly 61% of them, a perfect match with the Golden Ratio.
And it most certainly didn’t fail him either. By the end of the battle, there would be 905 Hessian casualties and POWs, while only five casualties remained on the American side. This means that roughly 60% – another close match of the Golden Ratio – of the Hessians were defeated at Trenton.
Is this coincidence? Or perhaps, is it something more? We’ll leave that up to you to decide for yourself.
6.) The Battle of Yorktown
Even within the American War of Independence, we can find evidence of the Golden Ratio at work. George Washington was not only an architect of human freedom, but it appears he was something of an artist as well.
After hearing that a French fleet was going to be available to lay siege south of New Jersey, Washington and Rochambeau marched their 8000 Continentals to meet up with 12,000 militiamen, French, and Continental soldiers – a wonderful 2/3 ratio.
As the siege of Yorktown began, Washington’s men blasted away at the British fortress with their artillery. Over 15,000 artillery rounds would be fired by America into British defenses, and the abundance and accuracy of the fire were so pronounced it had a massive impact on the British desire to surrender.
But did the Golden Ratio play out even with the choice of artillery used?
It appears so.
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