Joy in Small Packages recounts a recent conversation with a 3 year-old about the magnitude of numbers.
“I want to live there because it’s up high!”
I chuckle as understanding dawns, “Ohhh! You mean you want stairs?”
“Yah! Ten stairs! So I can go way up high and sleep. And 10 is a lot.”
As I thought about this, I realized my understanding of high magnitude numbers is just as fuzzy.
Author Arthur C. Clarke wrote, “Any sufficiently advanced technology is indistinguishable from magic.” Applying this concept to numbers, I think we’d have, “Any sufficiently huge number is indistinguishable from infinity.”
I’m not sure I really grasp the concept of 1 million—that is, 1 million objects. I do have a pretty good understanding of the effect of 1 million though. For instance, most new homes in my area cost $1 million or more (that’s the price of living in the bay area). I even understand that 2 billion bytes is about 1 hour of recorded digital video. But if you showed me a stack of dollar bills, I couldn’t tell you if it was close to 100,000 or 1 million or 10 million.
I once attended a conference where Captain (at the time, later to become Admiral) Grace Hopper was the keynote speaker. (She was notable for contributions to the early software industry.) In order to make a point about a nanosecond, which she claimed none of us could really understand (although we could understand it’s effect), she passed out lengths of wire about a foot long. That is roughly the distance an electrical signal will travel down that wire in 1 nanosecond.
Luckily I don’t have to understand the magnitude of numbers at that level of detail. It is enough to just specify that for my next computer I want 4 CPU cores running at 3+ GHz with 1.5 terabytes of disk storage. And that’s a lot.
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