killion

My nephew, first grader Tyler Kennedy of the Alameda Kennedys, is a walking talking thinking machine. A few days ago 

[he] invented a new numerical unit. You know how they have million, billion, and trillion; thanks to Tyler we now have killion. "This number is so large that by the time you count to it, you're dead."

clankennedy: Tyler's First Grade Report Card

So of course I started wondering just about how big a killion actually was. Assuming that you could spend your whole life counting out loud, starting from say age 2 and diligently spending 16 hours a day counting until the numerical sequence terminates in a long dark tunnel with a white light at the end, how far would you get?

In about one second, I can count to six. But you couldn't just extrapolate from there of course, as it takes a lot less time to say 'five' than 'fourteen million six hundred fifty-two thousand seven hundred and forty-two'.

I remembered that one of the weekly Ruby Quiz challenges was to take an integer value and have a program spit out the English version of it. A quick search turned up the quiz and it's answers. I selected the first solution, by Eliah Hecht, since I love the way Ruby makes bare numbers Integer objects and that you can add methods at will to the standard classes. I modified his code so that instead of returning English words, it would return the number of syllables in the English version of the values.

My program initially calculated how many syllables you'd have time to utter, using 6 per second and assuming a lifespan of 72 years, starting at age 2 and counting 16 hours per day. It then set about iterating through an i+=1 loop until it reached that limit. Here's the output:

You have 1471680000 seconds (or 25550 days) to spend counting before you reach a killion.
That's enough time to utter eight billion, eight hundred thirty million, eighty thousand syllables.
Calculating killion now...
Up to one hundred thousand so far(5 seconds, 1052900 syllables}
[...]
up to four hundred thirty-one million, two hundred thousand so far (42180 seconds}...

"killion = four hundred thirty-one million, two hundred seventy-six thousand, three hundred and one"

So there you go, a killion is a bit shy of half a billion. Of course, an actual killion would seem to be a matter of personal constitution, but it's interesting to know the rough order of magnitude. It's going to be less than a billion (unless it's Ray Kurzweil counting).

That is, assuming my code wasn't buggy. You can check it if you're curious: killion.rb.

It took about 12 hours to run on my pentium 4 linux laptop. It looked like it was going to take 3 times that long on my G4 powerbook!

technorati tags: ruby

Comments

[Ian Kennedy]

It might actually be less. Tyler, now 6, has only just grasped the concept that when you get to 999, you jump a place and turn over to 1,000 (he calls it the "wheelie thing" in reference to the odometer which I used to explain the concept). Julia, who is just shy of 4 is still blissfully oblivious of such problems of the universe.

Instead of starting the 16 hour/day counting clock at age two, you probably should reset it to six.

[mikepop]

I'd venture to say it would be more. If you are spending 16 hours a day doing nothing but counting, while presumably eating sparse but nutrient-dense meals, then getting a solid 7 or 8 hours of sleep per night, your mind is going to enter an adnvanced zen-like meditative state that will probably keep your body stress-free and healthy enough to beat the average lifespan.