Back when curiosity wasn’t crushed through the ritual of “growing up” we used to ask questions like

- How many sand grains are there on earth?
- How many stars are there in the universe?
- What is the biggest number that I can think of?
- How many things is the brain made of?
- How many carbon atoms are in the human body?
- Are some infinites bigger than other infinites?

(Picture taken by my daughter outside of our house with her iPhone.)

Of course there are other questions like why is the sky blue? Why is water or the sky sometimes pink (no really)? Why do I cry when I hurt myself and grownups just swear? Does a stone know it is being thrown into a pond? Do plants know that they are plants? Did our Hamster go to Heaven? (Whoa who taught you that?)

But let’s focus on the number questions.

In fact there are roughly ten times more stars in the Universe than there are sand grains on earth. To be more precise there are 10 ** sextillion** stars in the Universe. I bet you never heard of that one being mentioned in front of kids. But in the decimal system it amounts to:

Number of stars = **10,000,000,000,000,000,000,000**

Number of sand grains on Earth = **1,000,000,000,000,000,000,000**

“Yeah right Pa! I can barely see what you call the big dipper or la Grande Ours or your fancy Ursa Major.” City kids…

Because of light pollution we only see a fraction of what is out there. Even in remote locations like the desert or the Alps where the atmosphere is more rarified. It is amazing what is out there away from artificial lights. Even then it is a tiny fraction of what is out there. It is like taking a handful of sand in your hand on the beach and conclude that there is a ** sextillion** sand grains on Earth.

What about some other big numbers? Infinity of course comes to our minds, the ultimate “big” number. But really it is not a number, rather a mathematical fiction that leads to a lot of fun stuff. Like the sum of all positive real numbers is equal to -1/12.

There is a number called ** Graham’s number** that is fantastically large but it is finite. It is related to graph theory. I cannot write it with ones and zeros. Donald Knuth had to invent a special notation to represent such big bad ass numbers.

You can say “yeah sure I can come up with arbitrarily large numbers!” Of course you can. But are they meaningful? Graham’s number is the largest number that results from a mathematical problem. Of course I can always add one to that number and claim it came from a mathematical problem plus one. That eventually leads you to the concept of “infinity.”

Here is some cool information about this bad ass number.

http://iteror.org/big/Source/Graham-Gardner/GrahamsNumber.html

Check it out and follow the links. This is somewhat related to hyper-cubes in Paris (see my previous blog).

But it is still not one of the many “infinities.” It is finite.

Let’s get back to earth.

Number of neurons: one hundred ** billion**:

Since every neuron has about **1,000** synapses connecting to other neurons. We have that.

Number of synapses: 1 ** quadrillion**:

To me it is amazing that the very small and the very large share a common trait: they involve huge numbers! But the large outperforms the small it seems.

What about Carbon that is the basis of life and make cells, DNA and other cool stuff possible?

How many Carbon atoms do we have in our bodies?

According to some estimates it is:

Number of Carbon atoms in a human: **1,000,000,000,000,000,000,000,000,000**.

Wow that is much bigger than the amount of stars in the Universe.

The current debt of the US is equal to about

**10,000,000,000,000**.

That is only ten ** trillion**. No worries.

Peanuts compared to Carbons in humans. There is a huge difference between these two numbers one has no units and the other has units of dollars. What are the units of Dollars anyway?

Large scale wins in the end because stars and galaxies are made up of small scale atoms. You multiply things and ta da! You get the biggest number of them all: the number of atoms in the Universe. Drum roll… Roughly

**100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000**.

And that is only the observable Universe. Did you read about or heard of "Dark" matter lately?

This puts a limit on what we can represent finitely in a computer.

For example we cannot model fluid flows with Reynolds numbers roughly higher than:

**10,000,000,000,000**

I hope I got the numbers right.

And even if they are wrong they are beyond our imagination anyway.

Large finite numbers defy our imagination but to the trained mind infinities do not.

But correct me if I missed some zeros.

“Dude there is this exponential notation.”

“I know man, but it was fun typing in zeros and besides it is more visual.”

To get small numbers just do one over the big ones.

Eventually you will get to the almighty Planck scale

**1/10,000,000,000,000,000,000,000,000,000,000,000**