Sunday, April 05, 2009

What is the Grand Canyon Good for?

Some days ago, a friend of mine, posted this link. Apparently some folks over at NASA have calculated the square root of 2 to 10 million digits. My immediate reaction of seeing this was:

Things like this make me ask -- Why do it? Just so you can?

To this, another friend responded:

@Vinod: Sorry, just can't resist quoting this joke:

A math professor, a native Texan, was asked by one of his students: "What is mathematics good for?"
He replied: "This question makes me sick! If you show someone the Grand Canyon for the first time, and he asks you `What's it good for?' What would you do? Well, you kick that guy off the cliff!"

I still can't figure out what is the maths equivalent of kicking someone into the Grand Canyon, though ...

Frankly, I'm not satisfied with this response. Now, do not get me wrong. I do understand aesthetic beauty. I find encounters with naturescapes like the Grand Canyon to be very emotionally moving experiences. I also (sometimes) find encounters with scientific beauty to be emotionally moving. I myself have spend may idle hours trying to calculate prime numbers or the fibonacci series on my computer. And yet, I cannot help but wonder -- why calculate sqrt(2) to 10 million digits? Or, why visit the Grand Canyon?

The simplest answer is -- to feel the way it makes me feel. And I would have no problems with that answer either. However, it would make me wonder even further. Why do these things make me feel how I feel?

What really is special about the Grand Canyon? What do I mean when I say it is beautiful? I don't think a single answer exists but let me make a few guesses.

People find the Grand Canyon beautiful because it is big. Being big is one definition of being beautiful. The oceans are beautiful because they're big. The mountains are beautiful because they're big. Space is beautiful because it is bigger than anything we've ever known.

Being big is related to two inter-related concepts -- control and knowledge. If something is big, chances are that we have little control over it. Bridging the Grand Canyon? Perhaps impossible. Crossing the ocean? Rather difficult. Surviving in space? Requires billions of dollars.

If something is big, chances are that it contains something that we don't yet know about. Something that we can use to our advantage. Exploring the oceans let some people to discover other people and lands. We are yet speculating about the benefits that space exploration might bring us.

As a culture we've learned that anything that is big is most likely unexplored and uncontrolled. If we can learn more about it and learn to control it, we might end up with more resources to make our life better.

I think that is the charm big, unexplored terrains hold for us. I think that's why we find them fascinating and intriguing. That's what the Grand Canyon is good for.

Of course, this does not mean that every time I look at the Grand Canyon this is what I'm thinking about. I have internalized the concept to a degree that I can forget all about the benefits of encountering an unexplored terrain and concentrate just on the 'beauty' of it. Which is absolutely fine with me. But I do like to think further and find out what that beauty means.

Which is why I do not like it when specialists in pure sciences brush off questions like -- why do you do it? I think it is important to understand why we do pure science and pursue knowledge for knowledge's sake and derive pleasure in certain things. All sorts of beauty and aesthetic appreciation has underlying meaning which I think is important to unearth.


  1. Were they calculating square root just for the heck of it or were they testing some new algorithm and then decided to punch in some high value just for fun? You know a news reporter would like to report 10 million digits rather than new algo given the same peace of info since it's more sensational.

  2. @ Ankit - The link has following text -

    "These digits were computed
    by Robert Nemiroff (George Mason University and NASA Goddard Space Flight
    Center) and checked by Jerry Bonnell (University Space Research Association and
    NASA Goddard Space Flight Center). They were computed during spare time on a
    VAX alpha class machine over the course of several weeks."

    Looks like they were doing it largely for fun. :)

  3. Hi Vinod,
    When people were calculating prime numbers and trying to find a pattern in it a few years ago, it was very similar to finding the square root of 2 to a million places. Totally academic and purely for fun. It is now an integral part of many data encryption algorithms.

    Similarly when ages ago, people were watching at the stars with their telescopes, they only wanted to appreciate the beauty of the universe, but it became the foundation of astronomy.

    Similarly the endeavor to explore the unexplored, the thrill of doing something that no human has done before is the fundamental requirement for us, as human beings, to invent and discover.

    We might not find it very useful right now, perhaps it is not useful at all. But once in a while, one such experiment done purely for fun, brings about a revolution :)

    Just my 2cents for a Monday morning.

  4. Beautifully said... well written

  5. @ Rinchen -- thanks for dropping by and reading the blog.