Tuesday, August 29, 2006

On number theory - Perfect Numbers

This post is about perfect numbers which is a very interesting concept in number theory. 

According to bible God created everything including man in six days.

"And God saw every thing that he had made, and, behold, it was
very good. And the evening and the morning were the sixth day." (genesis 1:31 (KJV) )

But why he took six days for doing that??? He could have done all these in a fraction of a second right???

The reason is that six is the smallest perfect number.

By definition perfect numbers are those numbers that are equal to the sum of it's distinct proper factors.

for example 6= 1+2+3

the next perfect number is 28 =1+2+4+7+14

the third one is 496 and the fourth being 8128

All the known perfect numbers are even. But it is not yet proved that odd perfect numbers does not exist.

There is one theorem on even perfect numbers ie.

If (2^n -1 ) is prime, then (2^n -1 )* ( 2^ (n-1)) is a perfect number.

Friday, August 18, 2006

Universe and Electrical Control Systems

Assume an automatic control system

an automatic control system can rectify minor problems in it and hence work smoothily by using the feedback mechanism in the system. Minor problems means changes in certain parameters due to temparature variation etc
The system itself can correct all these without any external intervention.

But if some bigger problems arise (some component out of order)
the designer can replace it, but the system itself cannot do anything. And since the designer is external to the system, the system does not know that a designer exists. So when suddenly a component is replaced the system will think a miracle has happened, where according to the designer everything works as expected.

The problem with we human beings is that we are part of a big system (the universe) and we can understand only that, and nothing external to that. Surely there exists something external to the universe which has its own laws and rules. But we cant comprehend the laws and hence we can just hope that if some problem occurs the external agent will intervene and correct it.

The external agent being superior to man can think and act in better ways and we may call him God.

So God is not different from us except that he lives in a super universe.And there may be super super universes where super super Gods may be maintaining super universes and so ad infinitum.

Wednesday, August 09, 2006