Archive for the ‘Mathematician’ Category

Reading the great book of nature

January 9, 2008

The fact that the physical world conforms to mathematical laws led Galileo to make a famous remark.  “The great book of nature,” he wrote, “can be read only by those who know the language in which it was written.  And this language is mathematics.”  The same point was made more bluntly three centuries later by the English astronomer James Jeans: The universe appears to have been designed by a pure mathematician.”

Cosmic Jackpot by Paul Davies

What symbolism does ET use?

September 20, 2007

The simplest and universally known symbols are the integral numbers, represented in the Arabic notation by 0, 1, 2, …, 9, 10, 11, …, 98, 99, 100, 101, …

We are so used to these symbols that we think that they always existed.  However, it wasn’t until the 11th century when an Indian mathematician, Bhaskara, created them.

We see these symbols as obvious and natural.  And now we can’t imagine any other way of expressing numbers.

It’s interesting to ponder how a civilization on another planet symbolizes integral numbers.  It’s highly unlikely that they use the same symbols.  Perhaps they’ve created a symbology which makes things easier.  Perhaps it has enabled them to progress their mathematics and technology at a faster rate.  I wonder if their symbology uses base 10?  I wonder if we humans will discover an even better symbology than the notation we currently use?

“The symbols for integers illustrate the enormous importance of a good notation.  By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.” [Whitehead]

“Before the Arabic notation was introduced multiplication was difficult, and the division even of integers called into play the highest mathematical facilities.” [Whitehead]

I wonder if we are creating today any symbolism that will “increase the mental power of the race”, and will endure for centuries or millenium?

Great Book = Interesting Information + Arguments

July 29, 2007

What is the longest argument you’ve ever made? What is the longest argument you’ve ever read?

By an “argument” I mean: collect together some information nuggets, show how they are related, and then draw a logical conclusion from them.

Most of the (engineering) books I read are oriented toward providing information and techniques, not toward forming arguments.

Recently, however, I have been reading two outstanding books:

— Wealth of Nations by Adam Smith

— Introduction to Mathematics by Alfred Whitehead

And through careful reading I have become aware of the arguments being made in these books.  I say “careful reading” because their arguments aren’t immediately obvious, at least not to me.

After reading a page I pause and reflect on the ideas presented.  Slowly I am seeing how the arguments are being constructed.

In Smith’s book the arguments are well contained; at the end of each chapter he ties together the various parts of the argument.  Whitehead’s arguments are more complex and subtle; they can span multiple chapters.

Whitehead’s book is on mathematics.  It occurred to me, “Why are there arguments in a book on mathematics?  Shouldn’t it just contain information and techniques, like my engineering books?”  I’ve been puzzling over why I like Whitehead’s book so very much, particularly since I am not especially interested in mathematics. Now I think I know why: because it contains both information and arguments.

The realization that I have come to is that I like books which contain both interesting information as well as arguments.

Whitehead was both a mathematician and a philosopher.  Smith was both an economist and a philosopher.

A philosopher is a master of arguments.

I think great books are those that contain interesting information and are also philosophical (i.e. contain arguments).

In our sound bite society we don’t see many long, elaborate, elegant arguments.  That’s a shame.