‘Hand waving‘ in science has a bad reputation; referring to an argument as ‘hand waving’ suggests a lack of rigor. But is hand waving always a bad thing?
If by hand waving we simply mean omitting assumptions or steps in an argument for no good reason (or worse, for a bad reason, such as the desire to mislead the audience), then yes, hand waving is bad. But there are often good reasons for such lack of rigor. For instance, presentational reasons: the time constraints of a seminar often oblige the speaker to gloss over technical details. More interestingly, there can be substantive reasons for hand waving (and the line between presentational and substantive hand waving isn’t clear cut). Ecology is hard, and hand waving makes it easier. In order to make progress, we are often faced with a choice, not between a rigorous argument and a hand waving argument, but between a hand waving argument and no argument at all. Hand waving can include heuristic arguments, approximations, and rough ‘back of the envelope’ calculations. I’d also include rigorous models of simple situations which can, via hand waving arguments, be used to develop hypotheses about, or interpret data from, more complex situations. The hope is that the simple model somehow ‘captures the essence’ of the complex situation. (What it means to ‘capture the essence’, and how it’s different from, say, ‘getting the right answer for the wrong reasons’, is a subject for another post…)
Indeed, since all models (mathematical and otherwise) have simplifying (i.e. false) assumptions, all models are in a sense hand waving arguments about what the real world might be like. Simplifying assumptions are a feature, not a bug, a point well-articulated by philosopher Bill Wimsatt and in an ecological context by Hal Caswell. A model with no simplifying assumptions would be like a map as big as the world itself, and equally useless.
Hand waving arguments are perhaps especially common in community ecology, where our theoretical models typically are much simpler than the natural communities to which they’re applied (although not inevitably so, as I’ve discussed in a previous post). At least, that’s the perception of community ecology; I wouldn’t venture to guess at how true the perception is, though I’m not above joking about it. My former colleague Ed McCauley and I used to joke that community ecology consists of theory on one side, data on the other, and a bunch of community ecologists in the middle frantically waving their arms (arm waving being a more extreme form of hand waving). In contrast, the best population ecology involves tight, rigorous connections between theory and data; population ecologists hold their arms stiff at their sides like Irish step dancers. This was certainly true in the case of Ed, one of the world’s best and most rigorous population ecologists. If Ed were stranded on a desert island, I doubt he’d wave his arms to attract a passing ship (which brings us back to the point that sometimes arm waving is a good thing, such as when the alternative is to be stranded).
Ed and I are of course not the only ones to get a chuckle out of hand waving:
(cartoon by Sydney Harris)
Of course, there are no hard and fast rules about what’s a good (or good-enough) approximation, or what’s an essential vs. inessential detail. So hand waving arguments always involve some judgment calls. There’s an art as well as a science to hand waving. But just because hand waving involves judgment calls doesn’t mean there aren’t better and worse hand waving arguments (much like there are better and worse judges). I think that some ecologists definitely are better at hand waving than others. Mathew Leibold and Jon Chase are great hand wavers. They’re really good at using simple, equilibrial food web models with just 2-4 species to think about complex phenomena like turnover in species richness and composition along natural environmental gradients. No, I’m not going to tell you who I think the bad hand wavers are…
(UPDATE: Jon responds by saying ‘Thanks…I think’. In case there was any doubt, I really do mean it as a complement when I call Mathew and Jon great hand wavers, although I suspect they may not think of themselves in that way.)
Oikos recently published a nice piece of handwaving from Graham Bell. Natural populations are always fluctuating in size, and we’d like to infer from the pattern of fluctuations something about the underlying ecological mechanisms driving them. Graham develops simple alternative models to predict the relationship between successive minimum population sizes (i.e. population sizes lower than any that came before), and the expected time before the next minimum occurs, and tests those models with data from a long-term marine plankton monitoring program. The data support a model in which population fluctuations are driven by trophic interactions, so that minimum abundance decreases exponentially over time. There’s hand waving going on at multiple levels here, not just in the development of the models (all except for the food web model are extremely simple, ‘capture the essence’-type models). What justifies the hand waving is that the answer that comes out is extremely clear cut. The whole point of a hand waving argument is to skim over inessential details, and one indication that you’ve done so successfully is by getting a clear cut answer at the end.
Feel free to recommend any really good (or really bad!) examples of hand waving ecology in the comments.
This article is about the idiomatic term. For the everyday human gesture, see Wave (gesture).
Hand-waving (with various spellings) is a pejorative label for attempting to be seen as effective – in word, reasoning, or deed – while actually doing nothing effective or substantial. It is most often applied to debate techniques that involve fallacies, misdirection and the glossing over of details. It is also used academically to indicate unproven claims and skipped steps in proofs (sometimes intentionally, especially in instructional materials), with some specific meanings in particular fields, including literary criticism and speculative fiction, mathematics and logic, and science and engineering. The term can additionally be used in work situations, when attempts are made to display productivity or assure accountability without actually resulting in them. The term can also be used as a self-admission of, and suggestion to defer discussion about, an allegedly unimportant weakness in one's own argument's evidence, to forestall an opponent dwelling on it. In debate competition, certain cases of this form of hand-waving may be explicitly permitted.
Hand-waving is an idiomaticmetaphor, derived in part from the use of excessive gesticulation, perceived as unproductive, distracting or nervous, in communication or other effort. The term also evokes the sleight-of-hand distraction techniques of stage magic, and suggests that the speaker or writer seems to believe that if they, figuratively speaking, simply wave their hands, no one will notice or speak up about the holes in the reasoning. This implication of misleading intent has been reinforced by the pop-culture influence of the Star Wars franchise, in which mystically powerful hand-waving is fictionally used for mind control, and some uses of the term in public discourse are explicit Star Wars references.
Actual hand-waving motions may be used either by a speaker to indicate a desire to avoid going into details, or by critics to indicate that they believe the proponent of an argument is engaging in a verbal hand-wave inappropriately.
Spelling and history
The spelling of the compound varies (both with regard to this idiom and the everyday human communication gesture of waving). While hand-waving is the most common spelling of the unitary present participle and gerund in this usage, and hand-wave of the simple present verb, hand wave dominates as the noun-phrase form. Handwaving and handwave may be preferred in some circles, and are well attested. "Hand waving" is mostly used otherwise, e.g. "she had one hand waving, the other on the rail", but is found in some dictionaries in this form. A more arch, mock-antiquarian construction is waving of [the] hands. Superlative constructions such as "vigorous hand-waving", "waved their hand[s] furiously", "lots of waving of hands", etc., are used to imply that the hand-waver lacks confidence in the information being conveyed, cannot convincingly express or defend the core of the argument being advanced. The descriptive epithet hand-waver has been applied to those engaging in hand-waving, but is not common. The opposite of hand-waving is sometimes called nose-following in mathematics (see below).
However it is spelled, the expression is also used the original literal meaning of gesturing in a greeting, departing, excited, or attention-seeking manner by waving the hands, as in "friendly were the hand-waving crowds ..." (— Sinclair Lewis), which dates to the mid-17th century as a hyphenated verb and the early 19th century United States as a fully compounded verb. It is unclear when the figurative usage arose. The Oxford Dictionary of English lists it as "extended use", and it appears primarily in modern American dictionaries, some of which label it "informal".
In debate, generally
Handwaving is frequently used in low-quality debate, including political campaigning and commentary, issue-based advocacy, advertising and public relations, tabloid journalism, opinion pieces, Internet memes, and informal discussion and writing. If the opponent in a debate or commentator on an argument alleges hand-waving, it suggests the proponent of the argument, position or message has engaged in one or more fallacies of logic, usually informal, and/or glossed over non-trivial details, and is attempting to wave away challenges and deflect questions, as if swatting at flies. The distraction inherent in the sense of the term has become a key part of the meaning. The fallacies in question vary, but often include one of the many variants of argument to emotion, and in political discourse frequently involve unjustified assignment or transference of blame. Hand-waving is not itself a fallacy; the proponent's argument may incidentally be correct despite their failure to properly support it. A tertiary meaning refers to use of poorly-reasoned arguments specifically to impress or persuade.
The New Hacker's Dictionary (a.k.a. The Jargon File) observes:
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 [i.e., incorrect]. Failing that, if a listener does object, you might try to dismiss the objection with a wave of your hand.
The implication that hand-waving is done with the specific intent to mislead has long been attached to the term, due to the use of literal waving of a hand – either natural-looking or showy, but never desperate – by illusionists to distract audiences and misdirect their attention from the mechanisms of the sleight-of-hand, gimmicked props or other trick being used in the performance. This meaning has become reinforced in recent decades by the influence of Star Wars (1977) and its sequels, in which the fictional Jedi mind trick involves a subtle hand wave with mystical powers – that only work on the weak-minded – to disguise reality and compel compliance. Consequently, there is an implication in current usage that a hand-waver may be craftily intending to deceive, and has a low opinion of the intelligence of the opponent or (especially) an audience or the general public. The labels "Jedi hand wave" and "Jedi mind trick" themselves are sometimes applied, in a tongue-in-cheek way, to this manipulation technique in public discourse; US Congressman Luke Messer's use of it in reference to President Barack Obama's 2016 State of the Union address generated headlines.
In an unplanned debate or presentation, an off-the-cuff essay, or an informal discussion, the proponent may have little or no time for preparation. Participants in such exchanges may use the term in reference to their own arguments, in the same sense as an author admitting a minor plot flaw (see below). When the proponents use the term, they are conceding that they know an ancillary point of or intermediate step in their arguments is poorly supported; they are suggesting that such details aren't important and do not affect their key arguments or conclusions, and that the hand-waved details should be excluded from current consideration. Examples include when they believe a statement is true but cannot prove it at that time, and when the sources upon which they are relying conflict in minor ways: "I'm hand-waving over the exact statistics here, but they all show at least a 20% increase, so let's move on".
In formal debate competition, certain forms of hand-waving may sometimes be explicitly permitted. In policy debate, the concept of fiat allows a team to pursue a line a reasoning based on a scenario that is not presently true, if a judge is satisfied that the case has been that it could become true.
In literary criticism
By extension, handwaving is used in literary, film and other media criticism of speculative fiction 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 audience will not notice or will suspend disbelief regarding such a macguffin, deus ex machina, continuity error or plot hole.
The fictional material "handwavium" (a.k.a. "unobtainium", among other humorous names) is sometimes referred to in situations where the plot requires access to a substance of great value and properties that cannot be explained by real-world science, but is convenient to solving, or central to creating, a problem for the characters in the story. Perhaps the best known example is the spice melange, a fictional drug with supernatural properties, in Frank Herbert's far-future science-fantasy epic, Dune.
Hand-waving 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 details.
In mathematics (and formal logic, philosophy, theoretical science)
In mathematics, and theory-dominated disciplines in which mathematics plays a major role, hand-waving refers to a reliance on heuristic, as opposed to rigorous, arguments. These may be useful in expository papers and seminar presentations, but fall short of the standard of proof needed to establish a result.
An accusation of mathematical hand-waving can be a professional attack, intended to denigrate the reliability of a speaker who has attempted to assert a proposition without being able to prove it. The mathematical profession tends to be receptive to informed critiques from any listener, and a claimant to a new result is expected to be able to answer any such question with a logical argument, up to a full proof. Should a speaker apparently fail to give such an answer, anyone in the audience who can supply the needed demonstration may sometimes upstage the speaker. The objector in such a case might receive some measure credit for the theorem the hand-waver presented. The opposite of hand-waving in mathematics and related fields is sometimes called nose-following,[clarification needed] meaning the unimaginative development of a narrow line of reasoning.
The rationale for this culture of hyper-critical scrutiny is suggested by a 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 applied science and engineering
Hand-waving arguments in engineering and other applied sciences often include order-of-magnitude estimates and dimensional analysis, especially in the use of Fermi problems in physics and engineering education. However, competent, well-intentioned researchers and professors also rely on explicitly declared hand-waving 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 is an even number", as an intermediary step in reaching a conclusion.
Back-of-the-envelope calculations are approximate ways to get an answer by over-simplification, and are comparable to hand-waving in this sense.
Hand-waving has been used to describe work-related situations where productivity is seemingly displayed but deliverables are not produced, especially intentional engagement in busy work or pretend-work, vague claims of overwork or complications, impenetrably buzzword-laden rationalizations for delays or otherwise poor performance, and plausible-sounding but weak excuse-making and attention-deflecting tactics. In employment situations, as in political discourse, a hand-waving effort may seek to shift blame to other parties.
Another use is in reference to fiscal problems, such as an inability to adequately explain accounting discrepancies or an avoidance of accountability for missing funds.