Wednesday, May 21, 2008

The why behind `1+1=2

Author: Khalil A. Cassimally

What does 1+1 equal to? Too easy of a question, you might think. Well yes the answer is 2. There were not any traps whatsoever. But why is it that 1+1 equals to 2? What's the logic behind? This is an amazingly complex question actually.

At first I was asking this question to literally everybody I met, just for fun. But then I realised that the why behind 1+1=2 may not be that simple; it was in other words of no joking matter.

People always say truth comes from a child. That was my chance to consequently test this saying. I asked my kid brother aged 6 why he thought 1+1 gave 2. Here is his answer: "If you take a sweet from the market and put it with the one sweet in your pocket, with how many sweets will you end up? TWO!"

Well he is half correct. He preferred to do an analogy with sweets instead of dealing with the figures. In this particular case, it may have been a better idea. However there was something missing in this answer. I came to find out that it would be missing in my answer as well.

To get a really clear and concise answer however, I decided to email some persons who work with mathematics everyday. I mean astronomers. Although I only received one reply – which came from Dr. Brad Carter of the University of Southern Queensland, thanks to thee – I knew that the answer that I was provided with matched (and even overlapped – see below) my original idea upon this complex question of why 1 and 1 makes 2.

My original thoughts were roughly as stated below: "Somebody wanted to give the number '1' the name 'one.' He also wanted to give the number '2' the name 'two'. So two '1's, which is equivalent to 1+1, will gives two."

As my brother, I'm only half correct and we both made the same mistake. We had not mention that two is defined as two ones. If we had done so, we would have consequently come to the answer of why 1+1 equals to 2! Confused? Well Dr. Carter's answer might be of some help. This exactly what he said: "The answer is simple: it is simply a matter of definition. '2' is the name we give to result of the process '1+1'"

The why to the complex question suddenly became crystal clear. But I wasn't finished with the question as yet. I decided to use one of the search engine Google, latest innovation to get a bit more info about the why behind 1+1=2. I therefore connected to Google Answers! Google Answers is a sort of forum where individuals ask questions and tag an amount of money on the former. A specialist then answers your question and pockets the money. The best part of it though is if a question had already been asked and answered, anybody could view both the question and answer free of charge.

I entered '1+1=2' is the search form and lucky me… somebody else had already asked why 1+1=2 and a mathematician had indeed given an answer.

I was satisfied and thought that that question was now filed. After having joked about it, questioned my kid brother, emailed astronomers and googled it, I think I now finally have a rather good and simple answer to the why behind 1+1=2.

"In number base systems higher than '2', 1+1=2 because it is defined as such. Based on the definitions of the number '2,' the number '4' and the mathematical operation of addition, the answer is always the same."

Such a simple question, which is at the base of so many complex equations, isn't that simple after all, is it? There is actually an entire book, Principia Mathematica by Whitehead and Russell (not the one by Sir Isaac Newton) which devotes several hundred pages to deriving and explanation of just why 1+1=2.

About the author: Khalil A.Cassimally is the editor in chief of Astronomy Journal and Astronomy Journal Ezine. He is also the co-founder of the RCPL Astronomy Club. He is currently Senior Columnist at BackWash.com and Columnist for bbc.co.uk h2g2 The Post where he writes 'Not Scientific Science' column.

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