2005-07-04

The power of numbers and mathematical models

There is some magic with numbers. I was always amazed why people needed such complex mathematical formulae to explain reality in the world whereas, i thought, just by simple counting or by multiplying or even by surmising we could explain the various phenomena in life. Hence, I was never able to appreciate mathematics, never attempted to learn a few concepts which could have made life simpler. A few examples made me realize how futile an exercise counting is and why it can never achieve the objective of explaining natural phenomena.

- if a salesman has to travel between three cities (1,2,3), assuming that he starts in city 1, there are only two ways in which he can travel. Easy to calculate and determine which is the shortest, thus cheapest, way to travel between cities. But when the number of cities between which he has to travel increases to, say, 17, the number of possible ways / routes in which he can travel will increase to, lo and behold, 21 trillion! How on earth can we calculate and determine which is the shortest possible route amongst these 21 trillion routes. This problem is famously known as Traveling Salesman Problem (TSP)

- the most obsolescent item in the world is perhaps a newspaper. A newspaper boy has to keep only those many newspapers as he can sell. If he keeps more, he will end up with papers no one will buy. If he keeps less, then he loses sales and thus his profits. How to know how many newspapers to carry.

For both the above problems, answers can be found using decision making models (linear-, integer-, nonlinear- programming) that we are learning in our Term II course.

Numbers & these models and their power to explain the natural phenomena have indeed started fascinating me. They have absolute utility in real life situations.

PS: Try this – keep folding an A4 sized paper for 20 times and see the results. If you are able to fold it so many times, you may have reached the height of a multi-stories building or even beyond……………folding the paper 20 times is equivalent of the thickness of 1032192 papers.

3 comments:

Anuj said...

Tried the last one :) (Was insane of me to try it , but still :) )

Not to mention :) Failed miserably !!!

Dhar said...

You *CAN* fold a paper 20 times.

It is folding it halfway everytime that is a problem.

Not sure if I made the difference between the two cases clear...

Cheers,
D.

Anonymous said...

Each attemp to fold will double the number of pages .. so after 20 folds, the number of pages will 2 to the power of 20 = 1048576

2005-07-04

The power of numbers and mathematical models

There is some magic with numbers. I was always amazed why people needed such complex mathematical formulae to explain reality in the world whereas, i thought, just by simple counting or by multiplying or even by surmising we could explain the various phenomena in life. Hence, I was never able to appreciate mathematics, never attempted to learn a few concepts which could have made life simpler. A few examples made me realize how futile an exercise counting is and why it can never achieve the objective of explaining natural phenomena.

- if a salesman has to travel between three cities (1,2,3), assuming that he starts in city 1, there are only two ways in which he can travel. Easy to calculate and determine which is the shortest, thus cheapest, way to travel between cities. But when the number of cities between which he has to travel increases to, say, 17, the number of possible ways / routes in which he can travel will increase to, lo and behold, 21 trillion! How on earth can we calculate and determine which is the shortest possible route amongst these 21 trillion routes. This problem is famously known as Traveling Salesman Problem (TSP)

- the most obsolescent item in the world is perhaps a newspaper. A newspaper boy has to keep only those many newspapers as he can sell. If he keeps more, he will end up with papers no one will buy. If he keeps less, then he loses sales and thus his profits. How to know how many newspapers to carry.

For both the above problems, answers can be found using decision making models (linear-, integer-, nonlinear- programming) that we are learning in our Term II course.

Numbers & these models and their power to explain the natural phenomena have indeed started fascinating me. They have absolute utility in real life situations.

PS: Try this – keep folding an A4 sized paper for 20 times and see the results. If you are able to fold it so many times, you may have reached the height of a multi-stories building or even beyond……………folding the paper 20 times is equivalent of the thickness of 1032192 papers.

3 comments:

Anuj said...

Tried the last one :) (Was insane of me to try it , but still :) )

Not to mention :) Failed miserably !!!

Dhar said...

You *CAN* fold a paper 20 times.

It is folding it halfway everytime that is a problem.

Not sure if I made the difference between the two cases clear...

Cheers,
D.

Anonymous said...

Each attemp to fold will double the number of pages .. so after 20 folds, the number of pages will 2 to the power of 20 = 1048576