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Very nice :tu
I knew that knapping didn't work, but this technique seems to work just fine. I stand corrected.

The problem is not that it is curved (which I like) but also that it would likely have a warp as well.
It would be similar to shaving with a sharpened spoon.

Also, you might get thin straight...

Some people consider glass a liquid because the crystalization process lasts lifetimes. I.e. plain glass is forever locked in a phase change. Or so I've heard.
You might as well call a tree 'liquid'.

I've had a piece of obsidian, and it is indeed impossible to knap it straight.
Of course if you are very skilled you could perhaps knap it to something that looks reasonably straight, but it would...