Tuesday, July 29, 2014
Saturday, July 5, 2014
In the mind of a young man, a thought like a burning bush flares and a dialog between God and boy that explores the universe begins:
young man: God, how big is infinity?
God: Young man, how many numbers are there to count with?
young man: An infinite number of counting numbers, God.
God: Good. Using those numbers, how many negative numbers can you count?
young man: There are just as many, Lord. I would use all my counting numbers to count the negative numbers.
God smiles and the boy’s mind lights with a rainbow glow. Such a smart boy, the Lord of Hosts thinks.
God: Young man, do you know what a fraction is?
young man: I do, God. We have had them in math already. I made a C+ in fractions. Sometimes they can be tricky.
God: I know, I made them that way, but there are no tricks here. How many fractions are between 0 and 1?
young man (concentrating a little harder now): An infinite amount I think. If I count backwards starting at 1/1 and keep working down, there is one counting number for every number on the bottom of the fraction.
God (impressed by the lad’s application of logic): Exactly! So if those fractions live between 0 and 1, and that is the first “gap” between our counting numbers, how many other gaps are there to be filled with fractions?
young man (sweat now breaking upon his brow trying to work this out): An infinite number of gaps?
God (more pleased than ever): Just so. There are infinite gaps between the counting numbers. How many fractions fit in each gap?
young man (smiling as he gets a handle on this): There are an infinite number of fractions in each of the infinite gaps between the infinite number of counting numbers!
God (grinning ear to infinite ear): And if you include negative fractions, and the gaps between the negative numbers?
young man (suddenly feeling more annoyed than excited): There are an infinite amount of gaps between the infinite number of negative numbers with an infinite number of negative fractions filling each of those gaps to add to the infinite number of counting number gaps each filled with an infinite number of fractions. But how does this tell me how large infinity is?!?
God (grinning): Sssshhhh, I am not finished yet.