Mind boggling scale of large numbers

I have a seven year old kid with whom I engage in conversations about the Universe and the world around us frequently. We both enjoy talking about these topics. Our conversations leave me amazed at how intelligent kids are these days.

However, whenever we talk of large numbers such as the age of the Universe (~13.8 billion years), the age of the Earth (~ 4.5 billion years) or number of galaxies in the observable Universe (~ 2 trillion), I am left with the feeling that kids today don’t appreciate the mind boggling scale of those numbers as maybe kids of previous generations did.

I don’t know the reason for this. It maybe because billions and trillions are bandied about so casually these days in popular media. There are 19 countries with over trillion dollar GDP, 3000+ billionaires and 9 trillion dollar companies in the world. I wonder if all of this has caused lack of appreciation for how big these large numbers really are and made us numb to them.

One way that I have found to be effective to think about large numbers (billions and trillions) is to imagine having to count upto them. If I count from one to one million non stop and assume it takes a second to say each number’s name on average (this is of course a crude assumption as it takes several seconds to say larger numbers — try saying three hundred and ninety two thousand seven hundred and thirty four in a second), it would then take almost 12 days to finish counting. If you had to count from one to one billion, it would take 32 years to finish counting (assuming you don’t need to stop for eating, sleeping and attending to other nature calls). Counting till one trillion will take almost 32000 years. We would still not exhaust all of the numbers that are there. Of course, there are uncountably infinite numbers because there is always a next number to any number you can think of. Thinking this way and explaining to my kid this way helps both of us appreciate how unfathomable the scale of the Universe really is.

Of course, the motivation for all this to inject a sense of wonder in the minds of our children and kindle their curiosity to learn more about the world and the Universe which is our home.