The Zero power!!!!

Well.. this is going to be a short post...

Ummm..
what is zero raised to the power zero?
Yes, it's not defined..
Lets begin with simplest of all things..
what is the value we get when any real number (except 0 itself) is raised to the power 0?

The simple answer is.... 1!!!!

but how do we get this value?
and why can't this be true for zero raised to power zero/

We will see it in some time. first, lets clear up some basics...

Let n be a natural number....

then..

n^2 (said as n raised to the power n) = n*n
n^3 = n*n*n
.
.
.
.
n^m (where m is any other natural number) = n*n*n*n*n*n............ (m times)

all of this we all know...
When I came along these in school, there was a line written (or the teacher told us - i don't remember) that -
Anything (a real number except zero) raised to the power zero is 'taken' as 1.

I always thought that there must be something which gave us this value but no one ever explained it to me. The fact, that people did not tell me made me think. What i hate is though, it took me a hell lot of time just to think such a simple thing...

Lets see...

consider the expression ..

n^5/n^4

it can also be written as -
n^(5-4) = n^1

now i think you got my point..

n^0 = n^(m-m) = n^m/n^m = 1.....
for example -
let, n = 5  (any real number can be taken)
and m = 3 (any real number can be taken)
then,
5^0 = 5^(3-3) = 5^3/5^3 = 125/125 = 1...

Now, we can also see that why 0^0 is not defined..

put n = 0
let m be any real number..
then, we know that -
0^m = 0
now, doing as above-
0^0 = 0^(m-m) = 0^m/0^m = 0/0 
Which is not defined (anything divided by zero (even zero itself) is not defined)

So, now we have the answer to both the above questions!!!

Hilbert's paradox

Hilbert's paradox of the Grand Hotel is a really amusing one. The extensions are also amazing. But first, let us look up what Hilbert's paradox actually is...

One can see Hilbert's paradox as an attempt to define infinity or to make someone realize how infinity can be thought of. You see, infinity is termed as  'not defined' and hence, defining it can be taken as a paradox in itself.

Consider a Hotel with infinite number of rooms. Then, infinite number of guests can be accommodated   Now, since there is no definition of infinity, we can't see how we will accommodate infinite guests in infinite rooms. So think of it like this. There are right now 'n' rooms occupied. A new guest comes and asks for accommodation. Now, what the room manager does is shift the guest in room number 1 to room number 2, shift the guest in room number 2 to room number 3 ans so on such that at last, guest in room number n  occupies room number (n+1). The room number 1 is now empty and the new guest can occupy that room.
If r   number of news guests arrive, we can move each guest into (n+r) room where n is the room number presently occupied by them.

Sounds easy, doesn't it? There always exist a room with number (n+1) for every room with number n. So, whats the problem? What is the paradox?
The paradox is (as i understand it) that the Hotel should be able to accommodate infinite number of guests. So, suppose infinite number of guests arrive at the hotel. We have infinite rooms as described above. But how do we describe infinite number of guests? The infinite number of rooms were described by using a situation where finite number of guests arrived. So, we were able to see how there can be infinite number of rooms. But there is no way we can see how can there be infinite number of guests. Since we are not able to see how can there be infinite number of guests, how will the hotel give them rooms? So, the hotel is not able to accommodate infinite number of guests despite having infinite number of rooms.

Now it doesn't sound that easy.. right?
One way to describe infinite number of guests And this, can be taken as an extension to the paradox.
This is the famous Grand Hotel cigar mystery... (it is used for something in induction but i think it can be used here too)
suppose, no one is allowed to smoke a cigar in the Hotel (same hotel as above). Now, suppose, guest in room number 1 wants to smoke a cigar and goes to guest in room number 2 to ask for one. Now, since the guest in room 2 will also not have any cigar, he goes to guest in room number 3 to ask for two cigars, one for himself and the other for the guest in room 1. This can go one as far as we encounter a guest in say room number n  having n cigars. This guest gives n-1 cigars to the guest in room n-1  and smokes one himself. But, this situation never occurs since no one has the cigars. So, we see that infinite guests can be thought of there a guest in room n goes to guest in room n+1 to ask for n cigars, smokes one and pass the rest to the guest in room n-1.
So, we have infinite rooms and infinite guests. But, what about the cigars? They are not described as to be in infinite numbers. How do we do that for a cigar? We may do it with something like we did it for the rooms and the guests. But, in the end, we will be left with an object for which we have not defined infinite quantity.

I hope you got bored.... :-P
PS : All of this is how I understood the concept.. it may be wrong, please do tell me where i went wrong.. :-)

        

Exceptions in mathematics

Before you read -
There are some things which one may not understand in this post. Students can ask there mathematics teachers/parents/friends about what is written. The adults may consult anyone (or anything) they like...




"Exceptions are always there..."

If you study chemistry as a main subject in your 11th and 12th standard here in India, you are going to hear the above phrase more than any other student. Why? Because chemistry is full of exceptions (and this is the reason why I don't like it - in general). See, we have never seen an atom, have we? So, things are kind of 'assumed' on the basis of observations (the assumptions may be correct) and exceptions arise. 

Then you may look up physics. It you don't go to a higher level and talked about physics thought at 11th or 12th standard, you will see that major of it is all 'ideal physics'. 

There are situations which we can not realize in practice. But i am not saying its useless. This physics is the 'base level'. When you know how to deal with ideal conditions, then only you will be able to deal with 'real' conditions. 

Talking about exceptions, I don't know if physics have any exception here on 'earth'. All laws of physics are applicable on earth and objects near it. But what about the universe? I have heard that the laws of physics do not hold good at some parts of the universe. So, shall we say that even physics have exceptions? I don't know... We may consider them as exceptions, we may not.

Let us now com to the main point. Are there exceptions in mathematics?

Well, my answer is YES and NO.

confused?

See.. its how you treat those 'exceptions'. You may consider them exceptions, you may not. It's up to you...

Mathematics (in my view) have the most number of assumptions than any subject. As i see it, it is an universally accepted assumption that 2 comes after 1 and that 5 precedes 6. But that is 'the magic' of mathematics. If you want to multiply 39 with 11 , you don't need to add 39 eleven times but just simply multiply as follows - 

39 * 11 = (30 * 11) + (9 * 11) = 330 + 99 = 429..

There are many ways to do this of course...

What i want to say is, you don't need to break down the problem in really small bits, solve it and then compile them again. If you have an identity or formula, you simply substitute the values and you have the answer. Sign convention etc. are all takes care off automatically and you never need to bother about it. 

Take trigonometry for example - 

sin(pi) =  sin (pi + 0) or sin (pi - 0)

Now, some can get confused what to use. See.. sin(pi + x) = - sin x while sin (pi - x) = sin x.

i.e. above pi, sin is negative and below it sign is +ve. As we see, pi divides the two 'regions'. So, do we take +ve or -ve at pi itself? 

I does not matter. That is the thing. Either way, answer comes out to be 0. Which is neither -ve nor +ve. 

This is how everything just fits in. Or does it?

We just saw that everything is taken care of automatically. Since this is the case, there is no question to be raised about mathematics having exceptions.  But there are. 

FACT : many things that people think are exceptions in mathematics are actually not exceptions.

take 0! (0 factorial) for example. We 'take' it as 1. actually, its a calculated figure (read my post 'factorial of negative numbers' to know how).

So, this is not an exception. 

What I consider as exception are the assumptions we make. Like a straight line being a part of a circle which has a radius equal to infinity. A 'point' has no dimensions. A line has no breadth or height, its just a length.

Again, 'infinity' can not be defined but still comes in use at various places. Anything divided by 0 is taken as infinity ans anything divided by infinity is zero are some.
But then, why you will not call them exceptions because they don't really contradict any 'thing' or any 'trend'. 

These are just extra tools used in mathematics. 'Assumed Tools'.

This is the fun in mathematics, everything just works in a 'harmony'. If you have the power to analyze and control this 'harmony', there is nothing more fun than mathematics.... 

(ps: I dont have any such power but I don't know why I still enjoy it)             

  

Why do we need to save the environment?

Everybody is concerned about the environment nowadays. In schools, environment is major topic to test writing skills of students. People give stats like rate of depletion of forests going over the charts etc.
They say save resources. They say things like we have to think about the generation that are to come. But why? In my opinion these things are just going to ruin things even more. How? Well here's how -


The major power source are fossil fuels. Yes, there are hydro-power projects, solar energy, wind farms etc, but fossil fuels remain the main source of power. And these take a million years to form. So, no matter how much consumption rate we reduce, there 'stock' will finish someday.

Now let us think of a world where we actually have minimal consumption. There will be lack of comfort for us and for the coming generations too. You see, if we are compromising our comfort for the next generation, the next generation will do that to for the next. Yes, the survival time of our species will increase but there will be no comfort. High prices, lack of resources are some problems which will still be there. It just results in more people to be affected.
Suppose, we do use up all the resources now, the world will end right now. Lesser people are affected. (since only the present of the next two at maximum are effected while in other case, more generations will be affected). In this case, only we are affected and the coming generations do not suffer.
Isn't it better that only we suffer. The lesser the people suffer, the better it is, isn't it?

We must accept it that now nothing can be done. Our world is going to end, now or later. And it's better that lesser people suffer of it....

Factorial of negative numbers

In mathematics, Factorial of a positive number 'n' is defined as -

n! (pronounced as: n factorial) = n * (n-1) * (n-2) *............* 2 * 1....

where.. '*' is multiplication sign.

0! is taken as 1.
Actually, 0! is not 'taken' as 1. It is one as you will see shortly..

Factorial of positive numbers have great application in mathematics. Permutations and combinations is one (where we find the number of ways a group of objects can be arranged or selected in given group of objects). Expansion of terms like (a+b)^n (binomial theorem) are computed using factorials. 

If you search up this on Wikipedia, you will find a lot of data on it. 

Lets discuss about factorial of negative numbers.

a factorial can always be written as -

 n! = (n+1)! / (n+1)  .......... (since (n+1)! = (n+1) * n!)

(This is one way to calculate 0! ... just put n = 0 , and we get - 0! = 1 )

now, one can easily see the problem with factorial of a negative number : 

lets compute (-1)! this way... here, n =-1

hence, (-1)! = (-1+1)! / (-1+1)   ....................................... ( 0! = 1 )

                   = 1/0 

which is not defined.

If we go on this way. for every number 'n' , (-n)! =  not defined.

therefore, factorial of negative number is not possible.

But what if we define it some other way?

Why can't we take factorial of negative number as - 

(-n)! = -n * (-n + 1) * (-n+2) * ................ * -2 * -1

or 

(-n)! = (-1)^n * n!

The Idea is to deal with factorial differently when using for a positive number as compared to a negative number. Different identities and different formulas for negative numbers and positive numbers will exist.

I am no mathematician, but this can be used. May be it can not be used. It's just an idea. I can not say if it will have any applications, but it's not always about application. Its about developing the subject.

Lets just give it a thought. If it works, its great but if it does not, we can always leave it.... 

Why should I believe in GOD?

I may be wrong in what i am saying here... please do tell me if i am. Because i am still ready to learn more and change my view if i think there is a need to do so...
Just don't get furious...

It has been a really long debate. Some say that GOD exist, while some say he does not. I got confused. Should I believe in GOD or not?

My parents do, so I also believed in GOD as a child. I grew up praying to GOD. But now, I don't do that. Why? because I no longer believe in him... 

It is quite obvious that if one believes in GOD, one follows the religion in which he is born into and worships GODs associated with that religion. Also, there are some who believe that there is just one GOD, and every religion have named him differently. Been born into a Hindu family, i believed in 'Hindu' GODs. There are many of them too. One day, i happen to listen a story about lord Indra (The god of monsoon or weather, i dont remember). If I remember correctly (you see, I may be wrong), he was furious with some people in a certain village because they stopped praying to him. So, to punish them, he made it to rain endlessly so as too flood the village with water (the story continues and another GOD saved the people).

What got me to believe that this can't be true is that if I know correctly, a God never hurts anybody who has not committed a sin, and in the story, Lord Indra hurts all the people of the village just because they did't pray to him. That is not a trait of a good person. One should not make other's to pray to him.

Then there was another thing i noticed. Some people (very few) hate it when somebody praises some other GOD over the GOD the person believes in. They just hate all the other religions and GODs. Why are not people happy in just following their own religion and let the world be as it is. They should respect each other's religion, not condemn it. The good thing is though, this understanding is increases between the people. The bad news is, it is also decreasing. Majority of militants are made on the basis of religion. Terrorism is spreading on the basis of religion. 

All these never effected my choice to not to believe in GOD though. When i did believed in GOD, I found him responsible for everything. I know this is not what you should feel. But since i thought that GOD controls everything, everything which happened was because of him. I never bothered to think of my mistake. But now that i don't believe in any superior power, I can only blame myself for my problems and find a solution rather than visiting a temple to pray. That really has helped me a lot. I do better in academics now for example (this may be just a co-incidence though). 

What i want to say is... Not believing in GOD works for me and i will continue to not to believe in him. Different things work for different people. If believing in GOD works for you.. fine, believe in him. I don't have any problem. And you should also not have any problem for i don't believe in GOD. I don't know why people get angry at this. I have friends who believe in GOD. They don't have any problem with me and i don't have any problem with them. We just follow what we believe in and don't try to force each other to accept our views. Remember: Religion is made for humans, humans are not made for religion (copied it from a movie, but its true). if religion does not work with you, leave it. If it do, leave those people alone for whom is does not.

Why do we need flying cars?

Everybody now days is saying that in a few years time we will have flying cars commercially available. And I just think why do we even need them? Why do we have small private jets for? Flying cars will just be an expensive smaller jet and nothing else. It will take a hell lot of lime to make them cheap enough for the common man to buy it.They still are not able to make the plane fare cheap enough, how are they going to make the machine cheap?
Then, what if you run out of fuel in mid air? There can be all hell of warnings and other things, but what if it did happened? And that there is no place you can 'land' you machine? then what? Oh, nothing.. just a few fools will have to leave this world. What's the loss.. right?

And then is the training. Not everyone can fly a plane. They have to undergo training. And that training is also quite expensive. Why would somebody first buy an expensive car and then spend more just to qualify to be able to drive it. That's insane.

What is the problem with the cars here on the ground? What if two cars collide with each other? You won't have a parachute on your back at all times do you? And even if you do have a parachute loaded up on your back, but what if you are unconscious. You still die. You won't be able to open the parachute will you?

Yes, people do die in car crashed down on the ground too. But just imagine, there are more ways to die up in the air (falling from the sky being one) than on the ground. So, it is obvious that flaying cars will bring more deaths.
Then is the problem of roads. I just can't imagine where the roads will come from up there? Why do we need roads up there you say?? Well, some idiot just fancied to drive (or rather, fly) drunk here and there are crashed his machine into a Boing 787. Doesn't sound good right?
 If there is no defined space, one is just going to point to his direction and start flying until the idiot collides with some other idiot.
Suppose you do have a space defined. One will have to be skilled enough to fly in that particular zone without crashing. And there are sky-scrappers being built everywhere. Flying one of the cars into these magnificent buildings is not a big thing. The target is really big you know...
I really don't see any merit in building cars that can fly. If they are still built, i think i will be the last one to buy them. Maybe some of the only ones sensible enough who won't even buy them.
Ill rather bye a bullock-cart or a 2 mile-per-gallon pollution machine that will do more than 250 miles an hour right here on the ground. Or, return plane tickets to Hawaii for a holiday. That will cover the 'feel of flying' bit too.          

Do we really have souls??

After reading this... don't think i have a heart made of stone.. because it's not...

First thing, I don't really understand exactly what a soul is. So, this must be the reason why I think there is nothing like a soul (There.. I said it..).
The reason?? No reason. I just don't feel like there just might nothing like a soul. Then how are we alive you say?? Well, I have some explanation for that..

We are living in a world where there are endless machines all around us. The computer or tablet you are using to read this, the air conditioning systems, the cars.. all of 'em are machines. So, why can't we think that we are just way to advance machines? When we die, we just stop functioning. That's it. End of story. Then you will say that if this is the case, them explain this - "We can always revive a machine, from almost any problem. then why can't we bring a dead person to life?"
To this, I have another simple explanation, all those machines which we can revive are those which we have made. About which we understand each bit. The problem with the human body is that its way to complex for us to completely understand it. Me may understand the whole of it someday, and that day, we will be able to revive dead people.
Also, the way i understand it-
for a machine to work properly, each part, each component should work together for the whole machine to work. In our machines, these components are not very small. But if we talk about the human body, there are billions of small components. There are components of components. The organs have tissues, the tissues have cells, the cell have it's own component etc. If, we are able to start all of these components of a dead person simultaneously, we may be able to revive the person. But, this is really difficult to achieve. Since, there are billions of small components.
Then you can say  one more thing, we have feelings and we can think.. this is sufficient to prove we have a soul. Well, we are working on artificial intelligence aren't we? Which will enable computers to think and show emotions. Will you say that we are putting in souls in them? I Don't think so.. It's just the Operating system. Or we can say that we have the most advance operating system in the world in yourself. And if that is what we call the soul?? Then it's okey, there is something like soul but, this soul can not leave the body after we die.. (OS from the computers don't)..
But if I know correctly, soul is supposed to leave the body and so, i think that not believing in souls is a much better idea.   
+Manisha Kashyap  told me that humans do have souls. And that has been proven scientifically, but i think until i hear how, ill stick to my opinion...
  

Why do we wish on birthdays???

Before commenting do read the whole post... am not responsible for any misunderstanding you may have after reading this..

"Her birthday is on Jan the 5th.. I have to wish her at midnight... "

One day, I was just sitting idle (as usual) and thought that why people want to wish each other on birthdays?? That too, at midnight (not all but friends).
Someone once asked me (he was joking) - "Why do we even celebrate birthdays? We should be sad as there is now one year less to live.." That made me think... why do we get happy on our birthdays?? Is it the presents that people gift us, or that you are the center of attraction between all people who know you and as you pass, they wish you "HAPPY BIRTH DAY".. I thought that can not be the reason. I thought of things.. many things.. and found an answer that is satisfactory..

The icing and the cherry...

We celebrate because we have enjoyed and are lucky to survive a year. Also, they say that if you start something new with happiness, it ends with happiness. So, i guess, since people get happy on their birthdays because they want to pass the next year happily. That been said, i turn to the topic, is wishing at midnight sane?

In my view, most of the wishes one get on his birthday are not genuine. People just complete the formality to wish each other. That being the icing of the cake, and doing it at midnight in quest to do it before any of the other friends is like the big cherry on the top of the cake. It sure makes is look beautiful, but only a handful of people are happy to eat it.  
Wishing at midnight may create inconvenience to the person you are wishing. Suppose, the person is not
accustomed to be awake at midnight. Now because every body gets "hurt" if you won't reply them, so... what you do is stay awake till midnight to reply to all the messages you get.
The next day, these people also show-off to each other that i wished the guy before you (not everybody do that though). They say that this is the 'proof' that i am a better friend of his than you.
ridiculous...
What you prove is that you have no feelings for the poor guy but are focused on getting yourself some reputation. I ask you, what is the problem is you wish the guy in the evening, or the afternoon??
If your feelings are genuine, what time you wish at does not matter. Not everybody was born at midnight were they. unless you are wishing Harry Potter (who was born at midnight), this makes no sense at all.
And those who do wish at midnight, demand that they should be wished at midnight too. You cant force someone. But the, the poor guy thinks that he wished me at midnight and if I don't, he sure will say that you are not a good friend.
I just want to say, wishing at midnight is not important, having genuine concern for your friend is what counts. And if you have that, and your friend feel the same for you, I don't even see the use of wishing at all..
I know many will disagree with me.. but this is just how I feel about wishing on birthdays...
(footnote: The poor guy above... thats me.. ;-) )

Dark matter: Key to parallel universe???

First thing first, I don't really know much about dark matter. I just think of what i know and develop on it. I am not a scientist, I am just a student so my concepts may be wrong. I invite you to correct me. One more thing, I would like to tell you that this is my imagination based on what I have heard about dark matter. Universe is something on which anyone can think (Read my post "Universe.. what is it?"). It may sound like friction, but you can never tell...

Most of us, in our everyday lives have at least once used the phrase, "May be, in parallel universe". I often wondered that can there be actually something like parallel universe? If yes, where is it and how much different is it from our universe? 

I first thought that if there are more than one universe , all of them having some ending boundary touching each other just like small beads in a bag, then, any universe other than other will qualify for a parallel universe. And this may be true. But then, why do we have to think of a universe like a bead in a bag? That stuff is boring. Why not something more amazing to hear? 

One day, i was watching discovery channel or nation geographic channel (i don't remember which), and there was a show on dark matter. The scientist explained that dark matter does not interact with any matter we can interact with. Millions of particles of dark matter or even none may be are passing through your head as you are reading this. The scientist also said that there may be just two or three particles in millions that interact with the matter wee see around us and that if we are able to detect these interaction, we may find dark matter. 

That fact that dark matter and the matter we see do not interact with each other made me think of a new idea for a parallel universe. See, if there is no interaction at all, the two can never collide. They will just pass right through each other!! Just like we say ghosts can go through walls. (Who knows, the ghosts may be made of those particles of dark matter which do interact with the matter occasionally.. ;-) ) 

So, in a given space, in a given dimension, the matter we see and dark matter can be there simultaneously. It's not easy to think for some, but it may be true. And if it is true, the very space where our own universe stands, there can be a 'parallel' universe made up of dark matter.

Now, after that i had thought of this, some more thoughts came to my mind. Here, we are considering a two particle system. The matter we see and dark matter. But what if there are more? suppose, there are four such different types of particles. Name then A, B,C and D, such that no two different types of particles interact with each other. Only the like one's do (eg. A only interacts with A). Now suppose, we are made up of particle A. So, we will only see and feel particle A. In this case, particles B,C and D will become dark matter for us (since we cant distinguish between them). So, this way, four universe can exist simultaneously in a given space!!! And that is what i will call 'parallel' universe!!!  

Friends, feel free to give your opinion on this. And do tell me where I went wrong... :) :)     

The Universe.. What is it?

The  universe.. everybody has his own understanding of it. I had one too. But, unlike some, and more like many, I am always ready to change my views. So, now I don't really have any understanding. The more you think you come to know about the universe, you get even more confused. The problem is, you have to imagine something, which you think can never happen. You have to get over your rebelling mind and actually picture stranger that fiction things.

Earlier, the people never had to do this. They just thought of something and stick to it like super glue. Just think of this, earlier people thought that out earth is supported on one of the bull's horn and that when the bull gets tired, he sifts the earth to the other horn due to which earthquake occurred. This explanation is not at all easy to digest. But people did believed in that. So, its just you who can picture your own universe. And who knows.. what happens in your imaginary universe, may actually be exactly what is happening right now in some different part of the universe.

Now, after all that chit-chat, lets come to the point. My picture of the universe is more of a question than an answer...

 What do we think makes the universe? Is there actually some kind of boundary? 

You never know what you will find up there!!!

suppose, we do develop the technology such that we can travel at high speeds and cover way to big distances. So, we set off from earth and just travel pointing at just one direction. The thing is, how will we know that we actually are going in the same direction at all times? See, if you are lost in a big desert, the sahara for example, you just cant simply keep walking and get to the end of it. You are bound to change the direction. even way to small changes in direction can result in a big change in direction over time..

You may even be going in a very big circle!! One solution is to calibrate your direction with the sun or a compass. But i wonder if we can even build something like a compass that will work in space.
Then there is the problem of recognition. How will we know that we have actually reached the end of our universe and are entering in a new one (if more than one do exist). So, what we need to do, is picture a boundary. With out an end, one can not define a universe. Like we can not define a system in thermodynamics. But then, what if the universe expands infinity and there is no other universe.
Now, if we say that we are just simulations of some computer program then an infinitely big universe is possible. If you are familiar with basic computer programming, you will know we can always put an infinite loop. For those who don't, think it like this. Is we start going in just one direction from a starting point and keep going straight, after covering a fairly big distance, we will see the point from where we started from. Just take it like we have copied the whole block and pasted it just ahead of it. So, this way, an infinitely big universe can be thought of.  
Similarly, one can think of millions of things. We can have millions of explanations, millions of ideas for how we can picture our universe. The most idiotic one to sound may be actually the right one. May be the most boring one may be true. I can't say. What matters is, never completely agree with someone else's model. Make your own, challenge it and see if it makes you smile with satisfaction. The universe is what you think it is.
The more ideas we have, the more we get to the reality. That is the very reason we our brains with us. To think, to dream and relate the two.

Think.. because its important

Hello friends. I am Aayush .I am passionate about cars. New ideas and new discoveries always get my attention. So, i think a lot for new ideas (they never work though ;-) ) and try to think - will it even work?? (which it never do). Hey.. do look up my other posts...
First thing, what i mean by a new idea is not to make the society better or just for something to use as a decoration, what new idea is thinking something which no one has ever thought of related to how we can picture things. For example, everybody have their own understanding of how the universe works. There are some who think that there is an all-mighty power, some think we are just simulations of a lost computer program etc. Thinking of something new, making an understanding of how things work or can work, is my idea of a new idea.
Henry Ford, for example,  had a new idea when he asked for an engine to made in which cylinders were arranged in a 'V' shape. And today, this 'V' shape is the most common engine we get to see in most of the super cars.
What i mean to say is, even some really small and insignificant changes brought through new ideas (The 'V' shape was not insignificant when it was thought of though) actually can greatly affect our lives, our way of living. The change in our life is big, but we don't even realize that what made that change to come because the think behind is really small!
Lets take another example, It you live in India, you will know that there is a car called Inova here. In the previous model of the car, the rear view mirror was where one would expect it to be, on the roof (not exactly). In the new model though, the rear view mirror is mounted on the wind screen of the car and an the roof (where it was in the first place), they have given a small storage compartment where you can keep some money for toll-booths or business cars etc.
The change is insignificant. But if you think about it, the affect may look small but is significant. You now don't have to go for your wallet every time you need your business card or cash. It adds to the comfort.

What i am trying to say, small ideas are significant, some are more and some are less, and to get new ideas is my hobby!!