What!? Stop looking at me like that! It's possible! I saw it on Mr. Wizard, so it has to be true!

The key to being able to do this is rethinking how you cut the hole. A hole is ultimately determined by the ring of material which defines it. If you are cutting a hole out of paper, the hole is defined by what's left of the paper. This means that a hole can never be larger than the size of the paper it is cut from. If you are using letter size paper, the largest the hole can be is just under 8.5" x 11", leaving some room for the ring of paper around the edge.

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| _ _ _ _ |
||       ||
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So if the size of a hole is a function of how much material there is in the ring (i.e., its length), we can begin to see the problem with making a hole like the one pictured above. When we cut away the middle part, most of the paper is being thrown away! That's valuable paper that could be used to form a larger ring and hence a larger hole. If the ring can be that large using only that skinny sliver of paper left over, how much larger could it be if we used more paper? But that seems like a paradox -- how can you use the paper we cut away to form the ring? Aren't we forming the ring by removing it in the first place?

Now here comes the zen. The key to cutting a hole in a postcard large enough to walk through is realizing that we must use all the material to form the ring, and waste none of it by throwing it away. We shall cut a hole that will use all of the paper. Repeat:

There is no hole.
There is only hole.

After you have performed a few breathing exercises, the first thing to do is take the postcard and fold in in half. You can fold it either the long way or the short way, it really doesn't matter, but you may find it easier to cut if you fold it the short way (the crease is parallel to the short edge). Now, starting on the side that is folded, make a cut near one of the edges that is perpendicular to the fold. The cut should extend almost all of the way to the other side, but it must not cut through. If you cut all the way through, you'll snip off the top and you'll be left with a paper V. Exciting, but not a hole.

Now just beneath that cut, make another cut that begins on the side where the last cut ended, and goes almost all the way to the fold, but does not cut through. Repeat these alternating cuts until the entire postcard is sliced. The thiner you make the slices, the larger the final hole will be.

  _ _ _ _ _ 
.|________ |
 | ________|
 |________ |  (folded side is on the left)
 | ________|
 |________ |
.|_ _ _ _ _|
The last step in the process is to snip all along the fold, seperating all of the siamese twin paper zizzags except for the top and bottom ones. These will hold the ring together and are marked by periods in the drawing above. Once the fold has been cut, it will look something like this from the side (zoomed in):

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|_______  |
 _______| | 
|  _______|
| |_______
|_______  |
 _______| |
|_________|
Now unfold the two halves and you'll find a rough circle made out of the zigzagging paper slices. If you gently pull it apart, you should be able to stretch it a bit and form it more into a circle shape. My best friend in high school and I did this neat little trick while we were in France, whiling away the boring bus trip from Lyon to Grenoble. If you take your time and make the slices thin enough, you too will be able to pull the edges wide (you may wish to pin them to a doorway) and actually walk through it! Can't say it beats knitting, but it sure is pretty darn nifty!