Handwaving
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The term handwaving is used in mathematics and physics to describe arguments that are not mathematically rigorous.
Such arguments often include order-of-magnitude estimates and appeals to symmetry or dimensional consistency. Competent, well-intentioned researchers and professors rely on handwaving when, given a limited time, a large result must be shown and minor technical details cannot be given much attention—e.g. "It can be shown that x is even."
The term derives from the use of gestures to add emphasis when stating arguments, and the tendency to continue or increase the gesturing as a substitute for mathematics, when an argument is hard to put across or the proponent is tired of deploying words and/or symbols.
The expression "vigorous handwaving" is meant to suggest that the proponent should be aware of failing to convince; in addition it may suggest that the proponent lacks confidence in the validity of his or her own argument.
Back-of-the-envelope calculations are approximate ways to get an answer by over-simplification and are compatible with handwaving. Handwaving contrasts with use of abstract nonsense, that is, appeal to some intellectual superstructure of generalities.
By extension, handwaving is used in speculative fiction criticism to refer to a plot device (e.g. a scientific discovery, a political development, or rules governing the behavior of a fictional creature) that is left unexplained or sloppily explained because it is convenient to the story, with the implication that the writer is aware of the logical weakness but hopes the reader will not notice. The fictional material handwavium (similar to unobtainium) is sometimes referred to in situations where the solution requires access to an obviously impossible substance.
The gestures of handwaving (from the Jargon File): 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.
References
- handwave (http://www.catb.org/~esr/jargon/html/H/handwave.html), in the Jargon File