Fallacies of Science (and Maths)

There are many fallacies that abound the Mathematical and scientific realm! Of course, as keen observers many of us would have wondered about these fallacies.

I was introduced to these kind of fallacies by my Maths Guru in school, Dr Shanmughamani. He was not a doctor at that time. But his thoughts and deeds were pretty clear. He was certainly destined for great things.

One of the fallacies he recounted before starting the xxxxxx (I am not saying the subject lest I leak the answer to you), was the famous fallacy from Socrates, the Achilles and the Tortoise!

Let me recount the story as it was told to me in my school days. Long forgotten, therefore, you might find it altered to suit my taste and style.

The story goes this way. Socrates once told his group of students this story. He said:

Gentleman, I will relate a story. Please tell me what is my mistake. 

Once a tortoise approached Achilles for a running race! As you all know, Achilles was the fastest runner in the world at that time. 

Imagine a tortoise racing him! Tortoise went up to Achilles, the fastest runner and told him, “Achilles, will you race with me? I will prove to the world that I can beat you”.

Achilles laughed and said,” If you so please. I don’t see how in the world you can beat me”. For which the tortoise replied, ”O Great Achilles! The world knows that you are the greatest runner of all time. Please give me, the slowest animal on the land, a head start of one hundred metres. As a fast runner you should be able to overtake me quickly. But then, being what I am, I will prove that you will never ever beat me. All that I need is a head start of 100 metres”.

On hearing this, Achilles laughed once again and said, “So be it!”.

So the race began. Tortoise was placed one hundred metres ahead of Achilles. Now, Achilles runs ten times as fast as the Tortoise. That is, if Toroise runs one metre, Achilles could run 10 metres at the same time! Ten times faster!

When the race started, Tortoise was 100 meters ahead of Achilles. Achilles ran very fast. Ten times as fast as the Tortoise. So when Achilles covered the gap of 100 meters, Tortoise had run 10 meters and was ahead of Achilles.

Achilles continued to run and when he reached the 10 meters by which the Tortoise was leading, Tortoise was one meter ahead. Again, when Achilles reached the 1 meter, Tortoise was ahead by 0.1 meter. When he reached the 0.1 meter, tortoise was ahead by 0.01 meter.

And so on and on and on.

As Achilles nears the tortoise further and further, tortoise was always ahead by a small distance. The distance would never be built up. Instead, the tortoise will always be very few inches or millimeters ahead of Achilles.

And therefore, Achilles will never ever overtake the Tortoise!

So said Socrates and then he asked his students.

But then, gentlemen, that is not what is happening in the normal course of life Give me an explanation. How and when will Achilles overtake Tortoise?

Type your answers in the comments section!