Etymology of とんでもない

Question

Where did とんでもない (meaning "not at all" or "outrageous!") come from?

Could it be 飛んでもない ? ("will not even jump/fly" in a similar way how "When pigs fly" is considered a remark for something outrageous?)

Or is there a more complete sentence in which とんでもない was taken out of?

Answer 1

Rough extraction/translation from http://gogen-allguide.com/to/tondemonai.html:

Originally from 途でもない, 途 meaning "way", "road", "path". Combined with adjective 無い, this becomes 途でもない "off the path".

Answer 2

It has nothing to do with flying. Tondemonai derives from an older todemonai. Some speculate that the initial to is to be identified as 途 (to, "road"). While you may want to further break it into to demo nai, there is little evidence to support this so you should treat it as a single word. That being said, modern re-analysis of the final nai into a separate morpheme is quite common resulting in tondemo arimasen, a supposedly more polite form.