Over the years I’ve had the opportunity to collaborate with clock researchers on a few occasions. These folks now build clocks with a stability approaching one part in . This means that on average the clock “ticks” times before it misses a beat. The number is , a one followed by 18 zeros. It is a billion billions.
It’s not uncommon for physics research concepts to be difficult to explain to family and friends without a physics background. Numbers can be really large or really small. And this is one of those cases where the sheer size of a number makes it challenging to convey what the number means. Sometimes I like to play this game where I try to come up with every day life analogies that illustrate the size of a number and here is an example.
A large number that many people are at least aware of is the national debt. Last I checked the national debt was just shy of 20 trillion dollars. That’s a 2 followed by thirteen zeros. Let’s try and develop some intuition for this number. And then will see if we can use that intuition to get some understanding of .
Let’s assume that we are putting every single American from a one day old baby to a 100 year old senior to work to pay off the national debt. Somehow we find somebody (China?) to pay each one of us $30 per hour. How long would we have to work collectively to pay off the debt, assuming that we don’t need to pay for anything else during that time?
Well there’s about 320 Million Americans. With our assumed pay rate we’re making approximately $10 billion per hour. Not bad! With that income it would take us about 2000 hours to pay off all of the national debt. A year full time. That’s not horrible.
So we’ve got a good feel for (except that it’s kind of hard to visualize 320 Million people but let’s assume we could do that). Can we use that to understand ? If our national debt was the entire population of the United States would have to work for years to pay it off. Assuming we don’t need to spend any money on anything else. That is almost a thousand lifetimes of misery for the all of us. No thanks!
By the way I should mention that this whole exercise is a bit of a cheat because I’m comparing a dimensionless number with a dimensional number (dollars or time). But making this more correct would clutter up the whole story. Given the premise outlined above we’d have to ask something like “How many times two minutes would we have to work collectively to pay off the national debt?” Yeah, like I said, it gets clumsy.
So yes, still no good intuition for . It’s obscenely large.