Handwaving is a pejorative label applied to the action of displaying the appearance of doing something, when actually doing little, or nothing. For example, it is applied to debate techniques that involve fallacies. It is also used in working situations where productive work is expected, but no work is actually accomplished. Handwaving can be an idiomatic term, and it can also be a literal descriptive term for the use of excessive body language gestures that may be perceived as lacking productivity in communication or other effort.
The superlative expressions for the term, such as "vigorous handwaving" or "furious handwaving", are used to imply that the handwaver lacks confidence in the information being conveyed, and cannot actually convey the essence or core of his argument. The opposite of handwaving is sometimes called "nose-following".
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 an informal fallacy. In this sense, it is also as if a participant is waving their hands as to discourage an insect that is flying around their head, so are they waving away questions. 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 use 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.
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 is sometimes referred to in situations where the solution requires access to a substance that is physically impossible to create as it defies physics but is convenient to solving a problem in the story.
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.
In mathematics, handwaving refers to the following behavior, which is expected from students (and can be used to advance instruction), but which is considered intolerable and inexcusable among professionals. The important distinction from the benign and informal interpretation of "proof by handwaving" in science and engineering, is that the validity or fallacy of any proposals or hypotheses, though asserted and claimed to be true, are never called into question; instead, a diagnosis of mathematical handwaving is effectively a professional attack, intended to undermine the legitimacy of a speaker who has attempted to assert a proposition, without necessarily having the power to prove it. At least not without appealing to authority, or consulting his notes or references.
Note that this is not merely a pedagogical paradigm or rhetorical device. Rather, it represents a formal logical fallacy, wherein an uncontested conclusion is ascribed to follow from a demonstrably unreliable source of argumentation.
The opposite of handwaving is sometimes called nose-following, a behavior which, although usually counter-productive, is characteristic of logical veracity. The reason why behaviors such as handwaving and nose-following, and the particular ways that these are identified and responded to, tend to be more unique and profound in mathematics than in other disciplines, seems to be suggested by the following quote of G. H. Hardy. "[A mathematician's] subject is the most curious of all-- there is none in which truth plays such odd pranks. It has the most elaborate and the most fascinating technique, and gives unrivalled openings for the display of sheer professional skill."
In general, working mathematicians are implicitly more receptive to legitimate contributors than to any source of equivocation, and consequently consider themselves to be more rewarded by a constructive denunciation than by any competent and correct but illegitimate or indefensible instruction. Especially when expositing a newly discovered theorem, a mathematician must be able to validate any proposition that is explicitly attested in the course of his argumentation. In the practical event that any of his assertions are challenged (in good faith) by a member of the audience, his professional qualifications entail that he be fully prepared to achieve such validity up to any degree of absolute certainty, including rigorous demonstration by formal mathematical proof.
This is important because, should a speaker apparently or demonstrably fail to achieve this standard, anyone in his audience having a sufficiently superior expertise to provide the needed demonstration can often be expected to mercilessly upstage this person on the spot; and such an attack is likely to be deemed warranted in the eyes of an audience which, generally speaking, does not like to be handwaved at. Moreover, the objector is likely to receive, in such a case, most or all of the credit for proving the speaker's theorem.
Science and engineering
Handwaving arguments often include order-of-magnitude estimates and dimensional analysis. 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."
Back-of-the-envelope calculations are approximate ways to get an answer by over-simplification and are compatible with handwaving.
- handwave, in the Jargon File
- Proof by Handwaving at Everything2
- James Lavin Proving almost anything IEEE Potentials February/March 1996, pp. 6–7.