Archimedes the Liar

Archimedes is a famous guy. Even kids know how he ran through streets in, let’s say “special clothing”, shouting “Eureka Eureka”, after he understood the concept of buoyance. Without a doubt, Archimedes was a brilliant mind, and a great mathematician. Some of his inventions, such as Archimedes’ screw and claw of Archimedes have been deemed feasible, while some others like a Heat ray have been a topic of doubt. Nonetheless, it is undeniable that Archimedes’ was a genius way ahead of his time.

Archimedes lived in ancient Greece, and the king at that time, King Hiero II, is said to be a friend of his. Their relationship was a mutually beneficial one, with Archimedes solving many of the engineering problems faced by his home city, while king Hiero providing much needed material and manpower. Archimedes once famously said “Give me a place to stand on, and I will move the Earth” to king Hiero. This saying illustrates the power of Levers. But could he have actually lifted the earth?

First of all, Archimedes did not invent the lever. But he understood and utilized lever principal to fullest potential. Simply put, lever is a simple machine, used to get a much higher output force than input force. Imagine a seesaw. If two equally weighted people sat on either side, it would remain balanced. Now imagine an Elephant sitting on one end. Can a human balance the seesaw (provided that seesaw doesn’t break)? The answer is yes. An elephant weighs around 6000 Kg, and a man weighs around 60 Kg. That means, the elephant is 100 times heavier than the man! Now let us balance the forces.

Weight of Elephant * Length of seesaw arm = Weight of Human * Length of seesaw arm

6000 Kg * Length of Seesaw arm (Elephant’s side) = 60 Kg * Length of Seesaw arm (Human’s side)

100 * Length of Seesaw arm (Elephant’s side) = Length of Seesaw arm (Human’s side)

So, to balance the seesaw, the seesaw arm of man should be 100 times longer than the Elephant’s side! This is lever in action. So Archimedes thought, given that long enough lever, he could balance the force of the earth. But could this be done?

First of all, you need an EXTERNAL force to move something. Otherwise, you could have flied off just by lifting your own chair. This is the basis of first part of the quote, “Give me a place to stand on”. The rest is mathematics. Earth weighs around 60 * 1023 Kg. Assuming Archimedes was 60 Kg, let us do the math. If the length of the lever needed to move the earth is L, then

L * 60 Kg = Length on Earth’s side (Say 1m) * 60*1023

L = 1023 m

Now this seems all right, until you realize how large this number is. This is about 10 times the width of our Galaxy! Now assume Archimedes has a lever of this length. Then how long would it take to move the earth by 1 cm? Again, mathematics is our friend. It can be shown that the lever has to be moved 1021 m to move the earth by 1 cm. Even if Archimedes moved at the speed of light (highest theoretically possible speed), it would take him 1011 Years to move this distance! This is around 100 times the age of the Universe! So there, you have the numbers. Archimedes lied, or did he?

It is important to understand Archimede’s quote metaphorically, rather than literally. He might have only wanted to emphasis the power of levers. A brilliant mind like him would surely know the impossibility of such a task. Given his other achievements and contributions to mathematics and engineering, Archimedes should be worshipped a god, not berated by some wannabe mathematicians who dispute his claims. So what do you think? Did he lie, or was he simply trying to put an idea across, in a way our puny minds could understand?

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