It was a usual practise for me to ask my young and energetic audience, my students, about what they thought about a particular topic before I share my thoughts. Once the fact is revealed, both sides of the stage remain in satisfaction equillibrium which, seemed to me, set up the required chemistry for a successful knowledge transfer.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
As an interesting inquisition, I wanted to know what they thought on why is 1+1 = 2 and not some other number. For a moment, there was a long silent. People looked at me as if I had gone nuts and probably I had a morning tug of war with my ever patient wife! When I offered a plus one in their assessment credits, at least some of the participants realized there is nothing insane about the question! I knew they would require some clues and my key word was Number System.
Number systems evolved as a necessity and the whole world was, by and large, an automatic slave of decimal number system then. People first created new symbols for numbers and then sequenced it for counting. Perhaps when they reached 9 (the largest single “digit” decimal number), the next number selection was a logical selection? Could it have been that the choice was to have two “digits”? Perhaps they must have decided to choose the second single digit number and sequence it with the first approved 9 symbols and so on and so forth until they reached “99”?
As this dimension to the story stands, people traded with decimal operations and operators and they knew everything appeared had a decimal meaning! 1+1 became 2 in a decimal system. But why is it not 3? The computer age introduced several systems of numbers. This caused a split in the automatic choice group and people, all of a sudden, needed to use new operators and operations which caused unforseen results! 1+1 was no more 2.
So, how do we conclude with a universal definition?
When you add any number in the number system with the first number in the list (evergreen 0 is always an exception!) you have to move on to the next number in the number system. Similarly, when you add the second number in the number system you must move ahead two numbers (Snake and Ladders, but you can have more than 6 added!)This gives 1+1 as "10" in binary system and "2" in decimal, octal, hexadecimal systems. Does that mean that other than binary system, 1+1 will always remain 2?
Not when they have dimensions. As expected, there was an extended buzz around when I said 1+1 need not always be 2.
Leaving my dearest students perplexed, I had to leave the class as I had an important meeting!