Friday, June 29, 2007

Exponential growth mathematics


How many cell divisions (mitosis) will it take for a 1 gm tumor to become 1 Kg?......I was reading my pathology book, and then I came to know about this information...The answer is 10 !!.....Don’t believe this? Let me explain. Let’s take a 1 gm tumor. First division- 2 gm, Second- 4 gm, Third- 8 gm, Fourth- 16 gm, Fifth- 32 gm, Sixth- 64 gm, Seventh- 128 gm, Eighth- 225 gm( aprx), Ninth- 500gm and Tenth- 1 Kg!
This is called exponential growth mathematics, where things grow exponentially in successive divisions or time intervals. After reading this, my brain took a break, and started wandering in my philosophy land. I realized that this exponential growth mathematics is really a very important and core key to success. I saw some associations between this mathematical law, and real life incidents. Let me explain this-

1:- BEGINNING IS NOT ALWAYS DRAMATIC:- As you can see from the cell division example above, in the initial part of cell divisions, the results were not so dramatic. Even after Sixth or Seventh division, we had only around 100 gm……What happens if we add only 3 or 4 more divisions? Answer is “Mega changes”!
In the same way we keep working for success. We work hard, we work long,….still we don’t seem to see a dramatic result. Sometimes after working long enough, when we don’t see any dramatic changes, we think to give up, but hey, stop! Don’t quit!.....Could be we are only a few steps away from the “Mega change”.

2:- A LITTLE CHANGE IN THE BEGINNING, MAKES HUGE DIFFERENCE IN THE END:- What if we had taken 2 gm instead of 1 gm in the beginning?? In the beginning it doesn’t seem significant enough. One might think, what difference an extra gm can make? But if you see the end result, we would have 2 Kg, instead of 1 Kg. Isn’t it a huge difference? Can you realize what adding only 1 gm in the beginning does at the end of the result?
Now in the same way, sometimes we are reluctant to add some extra grams in the beginning of our life. We try to procrastinate things. While reading, we think that ok, this is only one chapter, what difference it would make if I read it now, or tomorrow?? Indeed it doesn’t seem to make any difference in the ‘beginning’ of career. But it is possible that reading that one extra chapter in the beginning might reward us 1 extra million at the end of our career??

Success does ‘grow’, whether or not strictly following the law of exponential growth, but I am for sure that it does grow. Even if in some extent, it does follow the law of exponential growth, and by understanding this law, and implementing changes at this point of our life, I am for sure that we can make huge differences in the end.

2 comments:

Anil Kumar said...

Excellent observation! They say an ocean is a collection of tiny drops. Each bit of hard work matters. Also take a look at this

koshish said...

It's a very interesting analogy: tumor- (malignant in this case) symbolizing the moribund to that of knowledge (weighed in terms of success)- symbolizing the growth at one's peak years.
The two are so dissimilar and similar in ways that makes me wonder if success, after a particular point acts as a bane. As long as the growth is controlled, everything's pleasant and as soon as it goes berserk,it doesn't take much time for the person to see and live with the consequences.