Correct me if I'm wrong — straightenin a one dimensional saw

This comes after some really good explanation Jason gave me and hope he agrees to publish  here. 

Today, I will be focusing on the firsts statements of Mark's instruction to straighten a blade:

1) work from both sides

2) work by halves - sneak up on straight little by little

3) don't focus on a couple square centimeters

Again, enters physicist mind. First, let's assume we have a one dimensional saw, not too useful in the real world but works for illustrative purposes. That's a line. Second, assume that the length of the saw is not affected by the straightening process. This seems sounded to me, but it just an assumption.

Figure 1 shows several lines that have the same length, doesn't look like but they are. Or I say they are and you just trust, ok? If you remember from calculus 1 the length of a curve is given by the integral of the square root of 1 plus the square of the derivative. Wiki it if you forgot it or never had calculus. If you don't like math to the kitchen and grab a rope, then do the experiment yourself. 

Fig. 1: Several same length curves.

Looking nice, isn't it? That's my theoretical saw for different amounts of hammering.  Let me take a look step by step.

First, you start with a bump in you saw:

Fig.2 Initial bump

You hammer it from the top, say at the right of the peak. With that, you reduce the bump but create waves:

After one hit

Now to fix this you need to hammer from both faces (up and down), and you need a few more hits, from both sides (left and right). Eventually you end up with something like this:

few hits later

Great, the bump is gone but now the waves are all over the place. So you see, you cannot focus on 2cm only, you need to look at the whole saw.

If you keep on hammering, side by side, and from the left and right of the original bump, eventually you end up with something much more similar to a straight saw.

final "straight" 1-d saw

Now, in 2D this will be the same but the waves will spread radially from the original bump and they will interact, so you need to consider that to attain a global straight saw.

The previous reasoning has to hold true if there is no substantial elongation of the saw when hammering it cold, and it's independent of how you do the hammering, this is only a geometrical characteristic of the material. To say it in another way, I have no idea how to do it, but I know that if I can make it, something along these lines needs to happen.

The next step would be to properly understand how and where to hit the blade in order to obtain the desired deformation and how the properties of the hammer and the anvil influence this. Once you understand that, you can make a plan.

That's it, does it make sense?