All is Here

I've been working on a solid modeling software for some time. The software does not care about on which scale you are working. I can model a nanometer-scale cantilever and a kilometer-scale bridge with the same package. But problems arise when I give more detail to any model I create. As amount of detail builds up, it takes more computational effort to handle the model. I know it is too much of detail when the machine takes too long to respond to my commands. With my limited computational ability, I guess I have an upper limit to the amount of detail I can give.

There is a limit also to the amount of information a biological system can receive at a time. The amount of detail one can receive is the same when she looks at a single cell of E. coli or vastness of the Crab nebula. It is a fallacy then, that we need to look too close or too far to see exciting things.

But if you get bored here, you are free to go to these places. After all, we are all born to go places and see things, aren't we?

No. I have to complete my mini-project on refurbishment of compressors by this week. Bye.

On e

The base of natural logarithm, e, continues to interest people with some knowledge in maths. This is an irrational number, which means we can never pin-point its location on the line of real numbers with no error. (Pi, the ratio of circumference to diameter of any circle, is another such elusive number.) Logarithm with base e is called natural logarithm because of a reason. It is, to me, like this:

Remember compound interest schemes banks speak about? You deposit some money at first and after say, quarter of an year, an interest on your deposit is calculated for this period with some rate of interest. This amount of interest is compounded to your initial deposit and for the next quarter, you derive interest for this compounded amount. This addition continues till the deposit is with the bank.

If we reduce this period of calculation of interest to smaller intervals, to months, to days, to seconds, we approach an exponential rate of growth. From nowhere, irrespective of rate of interest, the factor e comes into picture, when the period is infinitesimally small. The ratio of amounts in your account at times 2t and t is equal to e raised to the rate of interest.

When the rate of growth of something is equal, not just proportional, to the amount of the thing, e appears. That is how a colony of bacteria grows, with very small periods and with characteristics very close to e. That is how temperature of a hot small metallic ball drops. That is how a radioactive element decays. A lot of naturally occurring growths and decays closely follow the e- based exponential curve. The title of 'natural' came this way, probably.

It is still a mystery how this number walks into these situations with complete authority and exuding confidence.

The Complete Model

It all started with an attempt to predict the outcome of coin-tossing. A complex model was developed. Give air conditions, mood and geometry of hand of tosser, the model could predict whether it would be a head or a tail. Accuracy was improved as years passed.
Now someone came up with this: why don't we enlarge this model to cover all of the world? A model was developed. A big computer contained algorithms of the model. It was a preliminary model. It needed a large amount of data to begin the process and accuracy was not very impressive. But both of the problems were getting solved as more resource flew into the project. The computer was getting bigger. Initial data requirement was coming down. Accuracy was improving. Computer getting bigger was a problem. So compact machines were developed, with greater complexity.
As time passed, beauty of the model set fire to men's hearts. At one point of time the model became indistinguishable from the world it was created to predict. And people never bothered to go back.