Handwave [poss. From Gestures Characteristic Of Stage Magicians] 1.

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[poss. from gestures characteristic of stage
magicians] 1. v. To gloss over a complex point; to distract a
listener; to support a (possibly actually valid) point with
blatantly faulty logic. 2. n. The act of handwaving. "Boy, what
a handwave!"

If someone starts a sentence with "Clearly..." or
"Obviously..." or "It is self-evident that...", it is
a good bet he is about to handwave (alternatively, use of these
constructions in a sarcastic tone before a paraphrase of someone
else's argument suggests that it is a handwave). The theory behind
this term is that if you wave your hands at the right moment, the
listener may be sufficiently distracted to not notice that what you
have said is bogus. Failing that, if a listener does object,
you might try to dismiss the objection with a wave of your hand.

The use of this word is often accompanied by gestures: both hands
up, palms forward, swinging the hands in a vertical plane pivoting
at the elbows and/or shoulders (depending on the magnitude of the
handwave); alternatively, holding the forearms in one position
while rotating the hands at the wrist to make them flutter. In
context, the gestures alone can suffice as a remark; if a speaker
makes an outrageously unsupported assumption, you might simply wave
your hands in this way, as an accusation, far more eloquent than
words could express, that his logic is faulty.