Some Unanswered Questions!!

I have started thinking of the basic mathematical operations again. The thought process began when my father asked me - "why does negative number multiplied with a negative number produce a positive number?".

The basic reasoning on which we are taught multiplication does not seem to work here or if it does I just do not understand how? As per how we are taught multiplication if some one says 'a x b' then it would mean what is the value of adding 'a' 'b' number of times or what is the result of adding 'b' 'a' number of times. This scheme works perfectly when both a and b are positive. This is how we are first taught multiplication and once we understand this concept we start overlooking many things.

It works well even for if one of then is positive and the other is negative. For example 'a x -b' would imply -b added a number of times. As adding a, -b number of times seems absurd (the commutative law of multiplication seems questionable).

What if we have both the numbers negative. We all know because our teachers told that negative number multiplied with a negative number will give us a positive result. But, if I reason the way I have done before I can do no further how do I add something negative number of times. After all you can do a thing once, twice, etc.... or not do at all but how do you do it -1 time?

I am still stuck with this question. Answers and suggestions are welcome.

And the sun rises!!!

I have a question to ask. Are sunrise and sunset symmetrical? What I mean is that given the fact that one never visited the place in the photograph will he/she be able to tell if the picture is that of sunset or sunrise?
There may be few factors like fog in the morning that helps determine this but if there is no fog will it still be possible?

Mathematical Induction

I feel like demonstrating "Mathematical Induction", i.e. (n+1)th cycle will fall provided (n)th has fallen and I have kicked the first one. ;-)

73939133

73939133: I came across this fact. This is really cool. The specialty of this number is not just that it is a prime number but, every number that is produced by removing the last digit one by one is also a prime number. So, the following numbers are all prime.

7393913

739391

73939

7393

739

73

7

This is the largest such number known (as of today).

Every natural number is interesting

There is an interesting theorem in Mathematics. It states that every number is an interesting number. The proof is as follows and is based on the principle of mathematical induction:

One is interesting because it is the first natural number. Two is interesting because it is the first even number. Three is interesting because it is the first odd prime number. Let us now assume that the first ‘n’ numbers are interesting so that ‘n+1’ can possibly be uninteresting. But, this number will also be interesting as it is the first uninteresting number. Hence, by the principle of mathematical induction the all natural numbers are interesting.

India and China connect the world!!!

There is a theory called the "Six degrees of separation". According to this any person in the whole world is separated by any other person in the world by an average of six people.

For e.g : I know my friend Ashish with zero degree of separation. He knows his mother. So, the degree of separation between me and his mother is one. As I know Ashish who knows his mother. Similaretly if you are reading this and you know Ashish and do not know me the degree of separation between you and me is again one.

Let's get back to statistics (a very powerful tool but should be used carefully). We know that every 5th person in the world is a Chinese and every 6th person is an Indian. So, according to the theory "INDIAN AND CHINA CONNECT THE WORLD".

For more details on the theory, please refer to http://smallworld.columbia.edu project

How God used fuzzy logic!!!

In this post I will be pointing out how Lord Vishnu has used basic ideas from the fuzzy logic theory (that if a point lies on the fuzzy boundary then is not a member of any of the sets that share the boundary) for solving his problem. The article is based on a Hindu mythological story.


The Story:
There was a king named Hiranyakashap. He undergoes many years of austerity and penance. Bramha appears in front of Hiranyakashap and offers him a boon. Hiranyakashap asks for immortality. Bramha says that he will not be able to grant such a wish as everyone has to die one day. Then Hiranyakashap ask that- he should not be killed by any creature created by Bramha. He should not die within the residence or outside it, neither during the day nor during the night; neither on the ground nor on the sky; neither by a human nor by an animal; neither by any demigod nor by a demon nor by a weapon.
Hiranyakashap now considered himself to be god as it was virtually impossible to kill him. He wanted everyone to worship him. To his dismay his own son, Prahalada, was a devotee of God Vishnu which he did not like. He tried to kill Prahalada a number of times but was always unsuccessful. One day the he got very angry and asked his son if the god was there in the pillar he was pointing to. To which Prahalada answered that god Vishnu was there. Suddenly, the pillar split apart and Narsimha (the 4th incarnation of Lord Vishnu) appeared. He was part lion and part man i.e. according to fuzzy logic neither human nor animal. This happened in the evening i.e. neither in day nor at night. Hiranyakashap was taken to the entrance of his residence so that a part of his body would be inside the residence and the other outside the residence i.e. neither inside nor outside the residence. Lord put him on his knees i.e. neither on ground nor in the sky. Then he used his nails (not a weapon) to tear away Hiranyakashap’s body and killed him.

Hence, we see how God used the fuzzy logic to kill Hiranyakashap.