This is all just silly fun but I think it helps illustrate just how amazingly huge we are compared to the building blocks from which we are made. Each of us is a massive collection of molecules working together to maintain a complex biological and chemical machine. There are so many pieces to this machine that it is impossible to wrap your head around it. But that doesn’t mean we can’t try.

Humans contain about 10 trillion (10^{13}) cells.That’s a lot of cells. Actually I think the precise mathematical term is lot^{lot}. For some reason I got to wondering how big a person would be if their cells were enlarged to the size of a LEGO block.

I did a little browsing and it seems that human cells range in size from about 1 to 100 µm. ( µm = micrometers or 1×10^{-6} meters. ) That sounds pretty small but just how small is it?

Assumption #1 – The average size of a cell is 10 µm

Lets do the math. If the average height of a man in the USA is 178.2 cm ( 5′ 10.2″ ) then how many cells tall are we?

Assumption #2 – Cells are not stacked one on top of the other like LEGO blocks. But for the sake of the math I’m going to assume they are.

That works out to 17,820,000,000 µm tall.

So if our cells were stacked one on top of the other – they aren’t – then we would be approximately 17.8 billion cells tall.

Now we’re going to enlarge those cells so that they are about the size of a LEGO block which is 9.6 mm tall – I’m going to round up to 1 cm just to make the math easier.

Instead of being 17.8 billion cells tall this LEGO-Man is going to be 17.8 billion centimeters tall. If we convert that to kilometers we’ll have 178,200 km. That’s a biggish number. By comparison the earth is 12,756.2 kilometers in diameter. If we divide our LEGO-Man by earth’s diameter we get 13.97. That means our LEGO-Man would be about 14 EARTHS tall.

Put another way if our LEGO-Man stood on the Earth and jumped up and reached as high as he could then he could come pretty close to touching the Moon which is about 30 Earth diameters away.

Don’t forget that a cell – at 10 µm – is still very large compared to the molecules that it is made of. For instance a water molecule is about 2.5 Angstroms wide. That means a cell is about 40,000 water molecules wide.

So lets get crazy and make a water molecule the size of a LEGO block. Now a cell would be 40,000 LEGOs in diameter which is 400 meters, or about a quarter of a mile in diameter – 1,320 feet. Even at this relatively modest size it is a struggle for me to get my head around just how big a cell would be. By comparison Dallas Cowboys stadium, which is a very large stadium, is only 900 feet long. I guess the best way to try and grasp the size of our LEGO-Cell is to think about the size of a large football stadium and then double it. Now picture that volume full of LEGO blocks and you have the scale of water molecules inside a cell. ( Is your head swimming yet? I know mine is. )

What did that do to our LEGO-Man? Now he’s about 40,000 times taller which is 7,128,000,000 kilometers tall. To make that distance more digestible that’s about 47.6 AU ( Astronomical Units ). Meaning if our SUPER LEGO-Man stood on the Sun then the Earth would be orbiting about where his ankles are and his head would be out near Pluto, if Pluto were at apogee – farthest distance from the sun in it’s orbit. To put that another way it would take 6.6 hours for light to travel from our SUPER LEGO-Man’s feet to the top of his head.

Please let me know if you notice any errors with my math.

Hey Polygeek, what happened with your blog?

Thanks for asking. I’ve just been doing other things. I’ll start blogging again soon but not about programming. I’m working on a novel now so I’ll be blogging about that and other things.

Hey Polygeek, you disappeared.

Yeah, I know. Thanks for noticing. Been busy doing other things. I’ll start posting more soon but it won’t all be programming anymore.