new approach to maths?

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I have had this nagging thought floating around in my head for a couple years now that was just re-ignighted today.  Some of the books that I have ordered came in the mail today.

The Nothing That Is: A Natural History of Zero, by Robert Kaplan
e: the Story of a Number, by Eli Maor

It was as I skimmed through the preface of the latter book that the spark hit me.
It contained a short narative about Pi and how its exact value has been difficult to completely understand for many thousands of years.

When trying to solve a problem in computer science whe have several "tools" in the form of programming languages that come in handy when something is strange, difficult or abstract.  Often times if a concept is difficult to grasp in one language we will switch to another to handle that piece of the puzzle and translate it so that the other can get what it needs out of it.

Can we do this in math too?
What is math really?

If the way we approach math today makes it difficult to process certain concepts why don't we use a different math?

Does it work this way?
Is that what multi-dimensional physics and string theory are all about?

You can even see it in spoken languages.

I had the opportunity to see a private screening for "Sky Crawlers," based on a Japanese novel was based around these fighter pilots that flew WWII type planes into battle in a fantasy world.  After the screening we got a Q&A session with the director and some of the voice actors.  A question came up,
"why do the pilots speak english when flying, but never any other time?" 
The answer was something to the effect of,
"the english language is much better at getting the point across using as few words as possible. if the pilots were to speak Japanese, it might take them 10 more words just to say they are low on fuel.  In this aspect, english is more efficient."

This idea maps to programming languages in a similar fashion.
Some languages require 10-15 lines of code to accomplish the same thing that another language can do in 1 line of code.

I remember having an "ah hah" moment in one of my calculus classes where I noticed that the integral of y=2 from x=0 to x=3 is the same as saying 2 * 3.  Is this the same thing?

Is calculus just a different mathematical language or is it just a more verbose form of the same language?

I enjoy reading books like, The (Fabulous) Fibonacci Numbers, by Alfred S. Posamentier & Ingmar Lehmann, as well as the books mentioned earlier because they often speak about the how these parts of math came to be.  Smart people that observed things happening and had the right imagination to describe it with a type of language and extend it if necessary.  It is almost like early mathematicians were the programmers of today.  And it was all open source!  In order to get a change accepted it had to be published and scrutinized by many people in the community before it would be accepted into the everyday build.

Have we ever looked back at math and said... "I think we need to redo it."
The design is wrong.  Can we do this?  Has it been done?

I know that math has many forms to it, like, binary, hex and imaginary, complex number systems.  And it also has its different packages like calculus and non-linear algebra but has there ever been an effort to really dig in and build a new compiler for math?

Maybe this is what physics is all about?
Maybe string theory is doing this?

I think this is a really fun concept to think about.

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This page contains a single entry by published on May 25, 2009 3:37 PM.

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