1  2  3  Next

If you take a measurment of lets say, 20 cm over a piece of paper, and divide it by a half each time making half as much progress in each division would you make it to the end?

   

The paper is 20 cm long?

You are describing a diminishing return scenario. You will quickly get to a point where the forward advancement is simply too small to ever get anywhere.

   

When you get down to two atoms of paper then divide them and you will have one.

The left side of the atom will be one end and the right side will be the other end.

Now split that atom and when the dust settles nobody will give a rats-ass about your science question.

   

   

The answer is Blue!

   

   

If you divide it by a half each day, the paper would increase off towards infinity, eventually consuming all the matter in the universe.

However, if you divide it by 2 each day, you will get to the point where the molecular structure prohibits further division.

   

Whats i?

   

If you add n (aproaching infinity) to 1 then whats infinity+1?

So whats i?

   

no no it's turkey pie.

   

i is a variable. It gets infinitely large, eventually. Since it goes from 1 to n, 1/(2^i) is added to the sum of the previous results n times, which in this case, is an infinite number of times. Don't worry, nobody has been asked to count to infinity, though.

   

It's fairly standard math notation.

The sigma denotes a sum of the expression with i starting at 1 and continuing to n.

If n=4, for example, the sum would be

L/(2^1) + L/(2^2) + L/(2^3) + L/(2^4)

= L/2 + L/4 + L/8 + L/16 = L*(15/16)

Each term represents a measurement in this case, but if we continue ad infinitum, represented by letting n approach infinity, the sum would represent the total length.

So yeah, mathematically your measurement would find the total length, but it's not practically possible in a finite number of steps.

This is a variation of Zeno's Paradox. However the requirement of decreasing your measurement length every time is a little arbitrary in this case, and loses the effectiveness of the original - what would be the purpose of decreasing the length of your measurement every time? It's not a paradox because we all know an infinite number of measurements would require an infinite amount of time.

Zeno's Paradox is usually set up by your having to cross a room, from one wall to another. To do so you must first walk halfway across the room, and then continue to halve your distance from the wall. Since you must reduce your distance from the wall before reaching it, you supposedly should never reach the other side - it would require an infinite number of actions, yet we still reach the wall in a finite amount of time.

   

I'd say all you'll end up with is a paper cut.

   

You did not meet my wife.

   

PluggyRug and Lily sitting in a tree....

   

1  2  3  Next