This is an attempt to explain a concept from one of Swami Vivekananda's lectures. It was first raised on the SV community on Orkut.
There is no motion in a straight line. Everything moves in a circle; a straight line, infinitely produced, becomes a circle....
-Swami Vivekananda, Complete Works, Vol 5.
The essential thing to keep in mind is that there can only one thing which is infinite. A straight line when extended in either direction reaches infinity. However, it cannot reach two different infinities in two opposite directions, since having 2 infinities would be absurd. Hence, it reaches the same infinity in both directions, i.e. the two ends of a line when infinitely extended meet at infinity, or in other words, the line becomes a circle.
Apart from the geometry, what is the significance of saying 'line becomes a circle'? The point Swamiji was try to drive is that nothing in life is completely bad nor is it completely good. A person cannot have a life in which everything is bad, nor can one have a life in which everything is good. When things start taking a turn towards the downward side, they cannot keep doing so infinitely, for at some point, they have to take a turn towards good.
A belief in this inevitable cycle is 'hope'. Hope is what drives the world and makes a person do things amazingly. Hope is what provides energy to get up in the morning and do the same chores daily. Take out hope from a person and there is no difference in him and a robot. Keeping up one's hopes, inspite of the circumstances, is real test of life. What Swamiji says in the lecture is that there is no need to loose this precious hope, since it is nature's law that things will inevitably turn better.
Let our lives be always filled with the hope to do good things, and let the hope give us determination and courage to perform them.
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14 comments:
"The point Swamiji was try to drive is that nothing in life is completely bad nor is it completely good."
me agrees!
thanks vaibhav
fwennie, me tinks u so smart!
okay seriously now, this post, like all the rest of your posts, is awesome. i liked it because i have often thought that it is indeed hope that drives people to wake up everyday and do the same thing....like you said. I like the way you interpreted it. Your writing has a nice, calming effect. not harsh at all fwennie. u so cool! oi oi!
btw...me is happy to see u posting again!
fwennie, me tinks u is smartest guy on blogspot! poigi tinkey so too!
okay seriously now, this post, like all the rest of your posts, is awesome. i liked it because i have often thought that it is indeed hope that drives people to wake up everyday and do the same thing....like you said. I like the way you interpreted it. Your writing has a nice, calming effect. not harsh at all fwennie. u so cool! oi oi!
fwennie, me tinks u is smartest guy on blogspot! poigi tinkey so too!
okay seriously now, this post, like all the rest of your posts, is awesome. i liked it because i have often thought that it is indeed hope that drives people to wake up everyday and do the same thing....like you said. I like the way you interpreted it. Your writing has a nice, calming effect. not harsh at all fwennie. u so cool! oi oi!
fwennie, me tinks u is smartest guy on blogspot! poigi tinkey so too!
okay seriously now, this post, like all the rest of your posts, is awesome. i liked it because i have often thought that it is indeed hope that drives people to wake up everyday and do the same thing....like you said. I like the way you interpreted it. Your writing has a nice, calming effect. not harsh at all fwennie. u so cool! oi oi!
btw...me is happy to see u posting again!
Is it synonymous to the karmic cycle of life? or saying that u go back to what u came from...
Vami,
Thanks for your comments. Why's you posting it 4 times though?:)
Sirisha,
You can say karmic cycle is a part of this eternal cycle. The essential thing is that nothing that is manifest is permanent.
These posts are not meant to defeat anyone. They are just to carry on with the analysis. I am of the opinion that a profound topic has been trivialized and hence resume the discussion
From Real Analysis we know the following
The concept of number line is used only in two contexts :
1) Given any two numbers there exist a number in between them. Thus between any two numbers there are infinitely many numbers.
2) No number is too large or too small. If a number x can be defined the number x+1 and x-1 can be defined. Thus there exists no end or no beginning to the number line.
Laws of universe w.r.t to the concepts of number theory.
1) Let me first say that the concepts of number-theory cannot be used for real-time analysis. There is a fundamental reason for this.
Numbers are not quantized. In other words, numbers have no minimum limits. That is the smallest number greater than zero cannot be defined.
But in real-time, the world is quantized.
Given energy E= 0 we can define mass dE such that no energy level can exist between 0 and dE
Conversely, once we define M=0, we can define a dM such that no mass can exist between 0 and dM.
In other words, given two numbers there exists infinitely many numbers between them. But given two levels of anything corporeal, there exists [b]finitely[/b] many levels betweent them.
Why this disparity? Because, numbers are not real. They are just a scale created in such a way that, they cannot fail. In other words, numbers are created such that, one can always define a number between two numbers. So to say, the number system is just a concept.
2) I want to make a point here.
Consider statement S =[i]Hence, it reaches the same infinity in both directions, i.e. the two ends of a line when infinitely extended meet at infinity, or in other words, the line becomes a circle.[/i].
Let me prove it, by the method of inversion.
Consider the number-line
{..... -4,-3,-2,-1,0,1,2,3,4....}
There is a very simple logic to prove that S is not a perfect logical construct.
Let us consider all the numbers whose absolute value is greater than one.
So my set R' is R-(1,1)
Let us define a function f from R' to (1,1) such that y = f(x) = 1/x
Consider two values of x = x' and x"
Now let the corresponding values of Y be y' and y"
Now there are three cases
1) Both y' and y" are greater than zero.
2) Likewise both y' and y" are less than zero.
3) One is greater and the other is less than zero.
In the first two cases, by the property of inversion, the greater the numerical distance between y' and y" the greater the difference of numbers
In the third case, by the property of inversion, the lesser the numerical distance between y' and y" the greater the difference of numbers.
Thus, if you consider 1 and -1 the difference in y' and y" would be approximately 2, meaning that they are nearest to each other.
But as x' and x" tends to very large positive and very large negative values. The difference between y' and y" becomes closer to zero. Thus the closer y' and y" the farther x' and x". Since y' = y" in case of the +ve and -ve infinities, they distance becomes so huge that, they simply cannot meet.
More later
Krishna, the main purpose of the blog was not to discuss geometry, but to say that change is a way of life and that hope for the better drives most human actions.
But coming to the geometric point, yes, the projections of 1/x where x = {-1,1} go away from each other as x approaches zero from both directions. But the whole idea is that they reach the same point when you come to x=0. Since you can only define y when x tends to 0, but is not equal to it, this projection never happens when you are moving towards zero. In other words, you do not define separate entities such as +/- infinity, but say it is only one infinity.
See the definition of parallel lines in non-Euclidean geometry, which is '2 straight lines which intersect at infinity'. But if 2 lines do indeed meet at infinity, it should be possible to travel along one for an infinite time and reach the other one. Same is said when one says 'line becomes a circle', in that if you travel for an infinite time along from point A in one direction along a line, you reach the point A from other direction.
Call it a geomtric non-duality, if you will.:)
eh?
you do not define separate entities such as +/- infinity, but say it is only one infinity.
Instead of looking at infinity as an entity (or the entity), look at it as a concept.
Infinity s merely a concept. My real analysis prof would kill me for saying this, but I daresay that an indefinitely large number (+ve or -ve) is infinitely positive or negative.
As such there is nothing such as infinity. The number system is defined in an all-inclusive manner. And there exists no ceiling value. So to say, the ceiling is infinite.
well talking about real analysis, then circle and line are isomorphic.being more specific...ther are one and the same.which can be easily seen from stereographic projection in two dimentional plane!!
"See the definition of parallel lines in non-Euclidean geometry, which is '2 straight lines which intersect at infinity'."
This reminds me of our last discussion. But this happens only in "Elliptic non-euclidean surfaces" not in "hyperbolic non-euclidean surfaces. Though your point of "a cyclic concept of time" is noted still the analogy is not appropriate. Furtherthough 1/x as x tends to zero does tend to +/-infinity but 1/x itself at x=0 is not infinity,rather it is undefined!!!!
Meaning y can tend to one limit say z, when x approaches a number but the actual value of y, at x = (that number) may be totally different from the limit z.
OK, just to reiterate what I said long back, the aim of the post was not to discuss geometry but to show how hope indeed can guide our actions.
Harini, what we should be discussing is not a hypothetical geometrical concept of space, but one that fit the physical distribution of actual space. Is space really Euclidean or non-Euclidean in nature? I believe any physicist who believes Einstein today would say space indeed is curved, in fact the curvature is affected by mass and hence by gravity.
In such a space, are 2 parallel lines even possible to draw? There is not even a concept of plane defined, since if an object moves in a "straight" line, it is actually moving along a curved space. Needless to say, any line which 'curves' is no longer a line in the strict definition of the term!
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