How many?

If you look at any piece of the night sky through a 1mm diameter hole in a piece of paper held out at arms length, how many galaxies should be visible through that hole?

Our five children all  know my answer to this “fun”! question that I’ve raised at many parties over the years (you can tell I only go to the best parties!!!).

But I’ve been trotting the answer out for at least a couple of decades and I’m pretty sure the research it’s based on was at least 10 years older than that. When I saw an article about the James Webb Telescope, I thought I might spend a short while updating my answer. 

I have to say the answer surprised me and it’s yet another example of the massive difficulty we poor humans have comprehending how large very large numbers are. The scale just gets lost on us 

If the card is held at 1m from my eye and the hole is 1mm diameter, how many galaxies could I see through that hole?

Firstly, what is a good strategy for getting to the answer?

  • Find the number of the galaxies in the universe
  • Find the total surface  area of a sphere with a radius of 1000mm that is centred on my eyeball
  • Calculate the area of the 1mm diameter hole 
  • Calculate the fraction of the total 1000mm sphere surface area that is represented by the 1mm hole
  • Calculate that fraction of the total number of galaxies 

I calculated those numbers in a spreadsheet that you can see here:

And here is an image of it to save you clicking the link:

If I take a moment to think about that number, I am blown away!!

Every star (almost! – Thanks Lukasz!) we can see in the sky is from our own galaxy

And there’s a lot of them! (between 100 billion and 400 billion stars in our galaxy)

Through that 1 mm diameter hole held at arm’s length, there are 12,500 galaxies that are invisible to the naked eye. No matter where I put the piece of card and which bit of sky I look at through it. 

The number of stars in all the galaxies in the universe is beyond my comprehension

And then I started to think about intelligent life and the likelihood of it developing. 

In the last few years, we have been finding many more stars in our galaxy with planets that look like they could  support life (right distance away from the sun, right size, right age etc). 

This article from Forbes in June 2020 reported on scientists work indicating it’s likely that there are “at least” 36 planets with intelligent life on them in our own galaxy

If we multiply that by the number of galaxies we can see through our 1mm diameter hole, then we can infer there are something like 450,000 planets with intelligent life on them

And those 450,000 planets are just the ones visible through that 1mm diameter hole held at arms length. 

No matter where we point it, it’s likely that there are hundreds of thousands of planets with intelligent life. To me, the numbers are astonishing


You might not believe the numbers   and that is all good because scepticism is a healthy thing. 

But I think we can say that either: 

  • This fag packet analysis has some approximation to the truth 
  • Or it doesn’t 

To paraphrase Arthur C Clarke, either:

  • We are alone in the universe 
  • Or we are not. 

Either way, it’s utterly amazing!