folds

[userillusion]

I find the terms "twofold" and "threefold" (and all the other -folds) misleading.

Fold a piece of paper in half.  How many sides do you have?  2.  How many folds is that?  1.

Fold that same piece of paper in half again.  How many sides do you have now?  4.  How many folds is that?  2.

Again.  How many sides?  8.  How many folds?  3.

"X-fold" shouldn't

Comments

[pinterface]

But you don't necessarily get 2x for x folds. Two folds might get you three or four. Three folds could get you four, six, or eight. Nothing in -fold requires they be halving-folds, after all!

true, but...

[userillusion]

True enough, but you'll always get at least x-1 for x folds, so I think you and I can agree that the current use of x-folds doesn't make sense, right? So, ackowledging that the currently accepted definition doesn't work, we should either scrap the terminology altogether or redefine it so that it makes sense.

I propose 2^x because it fits when x=1 and is a potential fit for all other positive values of x. It is the upper limit for the number of parts that can be created by x number of folds, so while 3 folds could get you anywhere from 4 to 8 parts (you could get 5 if you don't require they be equal in size or shape and I'm sure you could get 7 as well), we know you will not end up with less than 4 or more than 8. For the sake of consistency, the term needs to have a definitive meaning. It seems silly to me to say "tenfold" to mean "eleven times", but I could easily see why someone might say "tenfold" instead of "one thousand twenty four times".

Re: true, but...

[pinterface]

Now that I think about it some more, I see you can get both five and seven sections from three folds.* Redefining it to mean one and only one of a broad range of possibilities seems to me as though it would create more confusion than it might clear up. For instance, how are you managing to fold something so many times? Even if you can make ten halving folds, after a while you lose the ability to leave a crease, so it isn't so much a fold as a bend, and then where's your accuracy? Nevermind the sheep!

* I wonder if that can be generalized for all x folds? That is, can all x folds result in [x+1, 2x] sections? (Good luck demonstrating that to even x=6!)

[valere]

Ahh, a reasonably interesting one. However, the thing is, a fold is also the two "sides" of the paper that result from folding a piece of paper. So, you fold once, you get two folds!

Look at the first two definitions in the 4th entry (it should default to the 4th).
http://www.merriam-webster.com/dictionary/fold%5B4%5D