The following paradox is not my own creation. I forget where I stole it from. Nevertheless here's the deal.
What is a line?
A line is a geometric concept consisting of an arrangement of an infinite number of points. There. Infinity!
But wait. If I was to get in a car and travel in a straight line from any point A to any other point B, it would mean that I must be traveling through an infinite number of points. Or, in other words, I would be changing my location through infinite positions. Infinity, by its very nature, must ensure that I do not reach point B. Ever. I can get closer and closer to point B, but never really reach it. Rather strangely, in real life, I eventually do! So, doesn't that mean that the definition of a straight line needs alteration? A straight line is made up of only a finite number of points? No. That's clearly wrong. Because, as you zoom into the line, you will ultimately see that the finite number of points become discontinuous and hence technically do not form a line. In order to make a line that is continuous at all levels of zoom, so to speak, you do need an infinite set of points. So where does that leave us now?
I swear to God I am not on LSD.
And as a side note, when the dee and myself were a-fightin last week like them old times, she started agreeing to everything i said, just to wear down my defenses. Eventually she did and i snapped at her. I told her "Look, stop agreeing to everything I say from this moment on!"
What should she do now?
A. If she says "Ok, i shall stop agreeing", she is still agreeing, and hence actually disobeying my demand.
B. If she says "I shall never do that", it means she is going to disobey my request and continue agreeing with whatever i say, but in a way I won cos she disobeyed me by saying she would never stop agreeing with me.
Both of us took a time-out from the fight to figure out our options. And we are yet to get back to it. I love paradoxes.
What is a line?
A line is a geometric concept consisting of an arrangement of an infinite number of points. There. Infinity!
But wait. If I was to get in a car and travel in a straight line from any point A to any other point B, it would mean that I must be traveling through an infinite number of points. Or, in other words, I would be changing my location through infinite positions. Infinity, by its very nature, must ensure that I do not reach point B. Ever. I can get closer and closer to point B, but never really reach it. Rather strangely, in real life, I eventually do! So, doesn't that mean that the definition of a straight line needs alteration? A straight line is made up of only a finite number of points? No. That's clearly wrong. Because, as you zoom into the line, you will ultimately see that the finite number of points become discontinuous and hence technically do not form a line. In order to make a line that is continuous at all levels of zoom, so to speak, you do need an infinite set of points. So where does that leave us now?
I swear to God I am not on LSD.
And as a side note, when the dee and myself were a-fightin last week like them old times, she started agreeing to everything i said, just to wear down my defenses. Eventually she did and i snapped at her. I told her "Look, stop agreeing to everything I say from this moment on!"
What should she do now?
A. If she says "Ok, i shall stop agreeing", she is still agreeing, and hence actually disobeying my demand.
B. If she says "I shall never do that", it means she is going to disobey my request and continue agreeing with whatever i say, but in a way I won cos she disobeyed me by saying she would never stop agreeing with me.
Both of us took a time-out from the fight to figure out our options. And we are yet to get back to it. I love paradoxes.
1 comment:
IMHO, infinity is a myth..Try substituting indeterminate, and it becomes pretty simple..
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