Krampf Experiment of the Week - #133
Nine Folds
http://www.krampf.com
A recent Thursday had the date
9/9/99. To celebrate this fun date, I wanted an experiment that had to
do with 9's. This week's experiment is actually more math than
science, but it is such a surprising demonstration that I decided to
use it. It is really very simple, once you think about it, and all
you need is:
* a sheet of
newspaper
This experiment is often done as
a challenge. Give someone a sheet of newspaper and challenge them to
fold it in half, and in half again, etc., for a total of 9 folds.
Simple, right? Try it before you continue reading.
No, I really mean it. Go try it
now.
As you found out, it is not
simple at all. In fact, unless you are using some powerful machinery,
you will not be able to do it, no matter how you try. Why not? Lets
do a little of the math. You start out with a single layer of paper.
After the first fold, it is two layers thick. Each time you fold
it, the number of sheets of paper doubles. The second fold gives
you four layers. The third gives eight. The fourth gives 16. Still
easy to bend and fold. The fifth gives 32. The sixth gives 64. The
seventh gives 128. The eighth gives 256 sheets of paper to fold. That
is not an easy task!
On top of that, with each fold,
the size of the paper to fold is cut in half. After 8 folds, the sheet
of newspaper is 1/256th of its original size and 256 times
thicker. There is no way you can make the 9th fold.
If you are familiar with
computers, you may notice that these numbers are familiar. 1, 2, 4, 8, 16, 32,
64, 126 and 256 are seen in
computer memory and other
computer applications. That is because these are the numbers of binary,
the language of computers. With an eight digit, binary number, each
of the eight digits can be either a 1 or a 0. The first 1 represents
1. The next 1 represents 2, and so on. The eighth 1 is 126. Then how
to we get to 256? If an eight numbers are 1's. Add them up.
1+2+4+8+16+32+64+128 = 255. Add one more to give you 256 and you
would have a 1 in the ninth place. This also represents the same as the
number of layers you get with nine folds. The next time you look at
a computer with 64 or 128 meg of RAM, etc., remember the folded
newspaper and how it relates to the language of your computer. Note
that some RAM allocations are not in this sequence, but are
combinations. 48 meg of ram is achieved by adding a 32 and a 16.