Imagine you have a four by eight chocolate bar sitting in front of you on a wooden desk. If you cut that chocolate bar in  “half’ diagonally, cut off four squares and then cut one piece of that chocolate off of the four piece chocolate section, rearranged them, and then back to how the pieces of chocolate originally started off , you have the same four by eight chocolate bar with a piece left over. Mind blown!

Now, this phenomenon is almost like a magic trick, it deceives you. What you don’t know is that, this bar is smaller than the original. That one left of piece of chocolate is the amount of chocolate missing from the bar sitting in front of you.

This “magic” trick that I just set up for you is called the Banach-Tarski paradox. This paradox proves that if you cut up any object into five different pieces, rearrange them, then you will have two exact items as the original. This paradox makes me question my life. This entire time my life has been a lie.This paradox questions all of the studies of mathematics,science experiments, and science theories that we’ve incorporated into our school teachings.

If this paradox is such a thing, then how come schools don’t talk about it. This paradox contradicts almost everything we’ve ever learned since elementary school.Perhaps schools don’t teach this paradox because another theory would come along with it. If the Banach- Tarski paradox is true, some still believe it to be false, then what’s the point of education. All we ever need to know in life is that you can end up with a duplicate of an item if you split it up into five different pieces.

Life as we know it right now wouldn’t be in place if we’ve known about the Banach-Tarski paradox before whole numbers, integers, real numbers, infinity and uncountable infinity then we wouldn’t be as civilized as we are today. In fact, we would technically be in the stages of the early 1900’s, this information was from a scientific journal. You wouldn’t be looking at this screen right now because laptops weren’t invented yet, you wouldn’t be reading this anywhere else because the internet wasn’t in play yet, you wouldn’t even be reading this because you would already know it.

Going off of that, if we’ve known about the Banach Tarski paradox before getting mathematically involved with anything else then our society would’ve gone two ways. We would’ve been even more advanced in society or in the early 1900’s.The Banach-Tarski paradox will forever be a questioning mathematical theory.