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I think I just met my distant self
Nov. 24th, 2009 01:30 pmI was in the break room, heating my lentil stew and brewing some decaf. I wound up talking for about half an hour with a man that is semi-retired at 73 and planning to move back to the villa he built in Belize for good.
"I can still sail, but I can't do the trip across the Pacific I wanted now that I have a pacemaker. My wife and I still plan to sail to the Azores."
We offered pieces of each other's brains. He mentioned a relationship involving the net of the differences between each increment of all the fractions. I'll see if I can describe it here:
The number of fractions, like the quantity of all rational numbers, is infinite. Any point surrounding any fraction has a neighborhood of other fractions. However, all fractions are based solely on the counting numbers. You could build a spreadsheet with the numerators along the x-axis and the denominators along the y-axis... wait, now I'm losing it. There's something missing. You can create a string from the upper left corner of the sheet to each number... ugh, I gotta look some of it up.
Anyway, there will still be differences between each increment of fractions in the string, even though the sum of the series what I want to describe creates (sigma 1/2 ** n whereas n is each counting number). The sum is still one, but the sum of the differences is in the billionths.
Yeah, I was really enjoying this. It was like being back in college for a few minutes. Other than the pacemaker, I want to be him when I grow up.
"I can still sail, but I can't do the trip across the Pacific I wanted now that I have a pacemaker. My wife and I still plan to sail to the Azores."
We offered pieces of each other's brains. He mentioned a relationship involving the net of the differences between each increment of all the fractions. I'll see if I can describe it here:
The number of fractions, like the quantity of all rational numbers, is infinite. Any point surrounding any fraction has a neighborhood of other fractions. However, all fractions are based solely on the counting numbers. You could build a spreadsheet with the numerators along the x-axis and the denominators along the y-axis... wait, now I'm losing it. There's something missing. You can create a string from the upper left corner of the sheet to each number... ugh, I gotta look some of it up.
Anyway, there will still be differences between each increment of fractions in the string, even though the sum of the series what I want to describe creates (sigma 1/2 ** n whereas n is each counting number). The sum is still one, but the sum of the differences is in the billionths.
Yeah, I was really enjoying this. It was like being back in college for a few minutes. Other than the pacemaker, I want to be him when I grow up.
