Hand-waving

The term handwaving is used in mathematics and physics to describe arguments that are not mathematically rigorous.

Category of arguments

Handwaving 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 z 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" or "furious 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 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.

Literary criticism

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 or will suspend disbelief. The fictional material handwavium (similar to unobtainium) is sometimes referred to in situations where the solution requires access to a substance that is probably possible to create, but only by means which would require a great deal of research, development, time, effort, and/or money, none of which the speaker intends to explain at the moment. (Note: handwavium is a rarely used term, with only 402 occurrences (excludes Wikipedia) found using Google (4/2007). By contrast, the terms unobtainium (and British variant 'unobtanium') have 159,500 unique occurrences. However, handwavium is mentioned in World Wide Words: Unobtanium.)

By extension, the term has come to be used in role-playing games to describe actions and conversations that are quickly glossed over, rather than acted out in full according to the rules; This may be done to keep from bogging down the play of the game with time-consuming but minor technical details.

Debate

Handwaving is also occasionally used in informal debate or discussion. If the opponent in a debate uses the term, it is meant as a shorthand way to accuse the proponent in the debate of having committed a logical fallacy.

The proponents in a debate might also use the term "handwaving" against themselves, in the same sense as a speculative fiction author, as noted above. When the proponents uses this term, they are exposing to the opponent that they know the portion of their argument to which the term is being applied is weak. "Vigorous handwaving" or "furious handwaving" may also be used to indicate a very weak argument. In an unplanned or informal discussion or debate, the proponent may have little or no preparation. The proponents in the debate can use the word "handwaving" as a way to indicate that while they believe a statement is true, they cannot prove the argument at this time. Even in an informal debate, the phrase is only used to an intermediate step or ancillary issue, never the primary subject matter or end conclusion. Use of the term indicates that the proponent wishes to exclude from the debate discussion of the weak point in order to discuss a more central or important issue.

Hand gestures

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, in the Jargon File