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Hand-waving - Wikipedia
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class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Term for attempting to be seen as effective</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the idiomatic term. For the everyday human gesture, see <a href="/wiki/Wave_(gesture)" class="mw-redirect" title="Wave (gesture)">Wave (gesture)</a>.</div> <p><b>Hand-waving</b> (with various spellings) is a <a href="/wiki/Pejorative" title="Pejorative">pejorative</a> label for attempting to be seen as effective – in word, reasoning, or deed – while actually doing nothing effective or substantial.<sup id="cite_ref-Dictionary.com_1-0" class="reference"><a href="#cite_note-Dictionary.com-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It is often applied to <a href="/wiki/Debating" class="mw-redirect" title="Debating">debating</a> techniques that involve <a href="/wiki/Fallacies" class="mw-redirect" title="Fallacies">fallacies</a>, misdirection and the glossing over of details.<sup id="cite_ref-NHD-JF_2-0" class="reference"><a href="#cite_note-NHD-JF-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> It is also used academically to indicate unproven claims and skipped steps in proofs (sometimes intentionally, as in lectures and instructional materials), with some specific meanings in particular fields, including literary criticism, speculative fiction, mathematics, logic, science and engineering. </p><p>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 <a href="/wiki/Debate_competition" class="mw-redirect" title="Debate competition">debate competition</a>, certain cases of this form of hand-waving may be explicitly permitted. </p><p><i>Hand-waving</i> is an <a href="/wiki/Idiom" title="Idiom">idiomatic</a> <a href="/wiki/Metaphor" title="Metaphor">metaphor</a>, derived in part from the use of excessive <a href="/wiki/Gesticulation" class="mw-redirect" title="Gesticulation">gesticulation</a>, perceived as unproductive, distracting or nervous, in communication or other effort.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2016)">citation needed</span></a></i>]</sup> The term also evokes the <a href="/wiki/Sleight-of-hand" class="mw-redirect" title="Sleight-of-hand">sleight-of-hand</a> distraction techniques of <a href="/wiki/Stage_magic" class="mw-redirect" title="Stage magic">stage magic</a>,<sup id="cite_ref-NHD-JF_2-1" class="reference"><a href="#cite_note-NHD-JF-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-NHD-JF_2-2" class="reference"><a href="#cite_note-NHD-JF-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> This implication of misleading intent has been reinforced by the pop-culture influence of the <i><a href="/wiki/Star_Wars" title="Star Wars">Star Wars</a></i> franchise, in which mystically powerful hand-waving is fictionally used for <a href="/wiki/Brainwashing" title="Brainwashing">mind control</a>, and some uses of the term in public discourse are explicit <i>Star Wars</i> references.<sup id="cite_ref-CBS_Bronco_3-0" class="reference"><a href="#cite_note-CBS_Bronco-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Actual hand-waving motions may be used either by a speaker to indicate a desire to avoid going into details,<sup id="cite_ref-Dictionary.com_1-1" class="reference"><a href="#cite_note-Dictionary.com-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> or by critics to indicate that they believe the proponent of an argument is engaging in a verbal hand-wave inappropriately.<sup id="cite_ref-NHD-JF_2-3" class="reference"><a href="#cite_note-NHD-JF-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Spelling_and_history">Spelling and history</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hand-waving&action=edit&section=1" title="Edit section: Spelling and history"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The spelling of the <a href="/wiki/Compound_(linguistics)" title="Compound (linguistics)">compound</a> varies (both with regard to this idiom and the everyday human communication gesture of <a href="/wiki/Wave_(gesture)" class="mw-redirect" title="Wave (gesture)">waving</a>). While <i>hand-waving</i> is the most common spelling of the unitary <a href="/wiki/Present_participle" class="mw-redirect" title="Present participle">present participle</a> and <a href="/wiki/Gerund" title="Gerund">gerund</a> in this usage, and <i>hand-wave</i> of the <a href="/wiki/Simple_present" title="Simple present">simple present</a> verb, <i>hand wave</i> dominates as the <a href="/wiki/Noun_phrase" title="Noun phrase">noun-phrase</a> form. <i>Handwaving</i> and <i>handwave</i> may be preferred in some circles, and are well attested.<sup id="cite_ref-note_4-0" class="reference"><a href="#cite_note-note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> "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.<sup id="cite_ref-Dictionary.com_1-2" class="reference"><a href="#cite_note-Dictionary.com-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A more arch, mock-antiquarian construction is <i>waving of [the] hands</i>. <a href="/wiki/Superlative" class="mw-redirect" title="Superlative">Superlative</a> 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 <i>hand-waver</i> has been applied to those engaging in hand-waving, but is not common. The opposite of hand-waving is sometimes called <b>nose-following</b> in mathematics (<style data-mw-deduplicate="TemplateStyles:r1033199720">.mw-parser-output div.crossreference{padding-left:0}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><span role="note" class="hatnote navigation-not-searchable crossreference selfref">see <a href="#In_mathematics">§ In mathematics</a>, below</span>). </p><p>However it is spelled, the expression is also used in 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 ..." (— <a href="/wiki/Sinclair_Lewis" title="Sinclair Lewis">Sinclair Lewis</a>),<sup id="cite_ref-Dictionary.com_1-3" class="reference"><a href="#cite_note-Dictionary.com-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> which dates to the mid-17th century as a hyphenated verb<sup id="cite_ref-OxfordDictionaries.com_UK_5-0" class="reference"><a href="#cite_note-OxfordDictionaries.com_UK-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and the early 19th century United States as a fully compounded verb.<sup id="cite_ref-OxfordDictionaries.com_US_1_6-0" class="reference"><a href="#cite_note-OxfordDictionaries.com_US_1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> It is unclear when the figurative usage arose. The <i><a href="/wiki/Oxford_Dictionary_of_English" title="Oxford Dictionary of English">Oxford Dictionary of English</a></i> lists it as "extended use",<sup id="cite_ref-OxfordDictionaries.com_UK_5-1" class="reference"><a href="#cite_note-OxfordDictionaries.com_UK-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and it appears primarily in modern American dictionaries, some of which label it as "informal".<sup id="cite_ref-Dictionary.com_1-4" class="reference"><a href="#cite_note-Dictionary.com-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_debate,_generally"><span id="In_debate.2C_generally"></span>In debate, generally</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hand-waving&action=edit&section=2" title="Edit section: In debate, generally"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Debate"></span><span class="anchor" id="In_debate"></span>Handwaving is frequently used in low-quality <a href="/wiki/Debate" title="Debate">debate</a>, including <a href="/wiki/Political_campaign" title="Political campaign">political campaigning</a> and <a href="/wiki/Political_criticism" title="Political criticism">commentary</a>, issue-based <a href="/wiki/Advocacy" title="Advocacy">advocacy</a>, <a href="/wiki/Advertising" title="Advertising">advertising</a> and <a href="/wiki/Public_relations" title="Public relations">public relations</a>, <a href="/wiki/Tabloid_journalism" title="Tabloid journalism">tabloid journalism</a>, <a href="/wiki/Op-ed" title="Op-ed">opinion pieces</a>, <a href="/wiki/Internet_meme" title="Internet meme">Internet memes</a>, and informal discussion and writing. If the opponent in a debate or a commentator on an argument alleges hand-waving, it suggests that the proponent of the argument, position or message has engaged in one or more <a href="/wiki/Fallacy" title="Fallacy">fallacies of logic</a>,<sup id="cite_ref-NHD-JF_2-4" class="reference"><a href="#cite_note-NHD-JF-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> usually <a href="/wiki/Informal_fallacy" title="Informal fallacy">informal</a>, and/or glossed over non-trivial details,<sup id="cite_ref-NHD-JF_2-5" class="reference"><a href="#cite_note-NHD-JF-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and is attempting to <em>wave away</em> challenges and deflect questions, as if swatting at flies. The <i>distraction</i> inherent in the sense of the term has become a key part of the meaning.<sup id="cite_ref-NHD-JF_2-6" class="reference"><a href="#cite_note-NHD-JF-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The fallacies in question vary, but often include one of the many variants of <a href="/wiki/Argument_to_emotion" class="mw-redirect" title="Argument to emotion">argument to emotion</a>, 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.<sup id="cite_ref-NHD-JF_2-7" class="reference"><a href="#cite_note-NHD-JF-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> A tertiary meaning refers to use of poorly-reasoned arguments specifically to impress<sup id="cite_ref-OxfordDictionaries.com_US_2_7-0" class="reference"><a href="#cite_note-OxfordDictionaries.com_US_2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> or to persuade.<sup id="cite_ref-Dictionary.com_1-5" class="reference"><a href="#cite_note-Dictionary.com-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-OxfordDictionaries.com_US_2_7-1" class="reference"><a href="#cite_note-OxfordDictionaries.com_US_2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p><i>The New Hacker's Dictionary</i> (a.k.a. <i><a href="/wiki/Jargon_File" title="Jargon File">The Jargon File</a></i>) observes: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>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.<sup id="cite_ref-NHD-JF_2-8" class="reference"><a href="#cite_note-NHD-JF-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>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 <a href="/wiki/Magic_(illusion)" title="Magic (illusion)">illusionists</a> to distract audiences and <a href="/wiki/Misdirection_(magic)" title="Misdirection (magic)">misdirect</a> their attention from the mechanisms of the <a href="/wiki/Sleight-of-hand" class="mw-redirect" title="Sleight-of-hand">sleight-of-hand</a>, <a href="/wiki/Glossary_of_magic_(illusion)#G" title="Glossary of magic (illusion)">gimmicked</a> props or other trick being used in the performance. This meaning has become reinforced in recent decades by the influence of <i><a href="/wiki/Star_Wars:_A_New_Hope" class="mw-redirect" title="Star Wars: A New Hope">Star Wars</a></i> (1977) and its sequels, in which the fictional <a href="/wiki/Jedi_mind_trick" class="mw-redirect" title="Jedi mind trick">Jedi mind trick</a> 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;<sup id="cite_ref-CBS_Bronco_3-1" class="reference"><a href="#cite_note-CBS_Bronco-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> US Congressman <a href="/wiki/Luke_Messer" title="Luke Messer">Luke Messer</a>'s use of it in reference to <a href="/wiki/President_Barack_Obama" class="mw-redirect" title="President Barack Obama">President Barack Obama</a>'s 2016 <a href="/wiki/State_of_the_Union_address" class="mw-redirect" title="State of the Union address">State of the Union address</a> generated headlines.<sup id="cite_ref-Jedi_2_8-0" class="reference"><a href="#cite_note-Jedi_2-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>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 (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033199720"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><span role="note" class="hatnote navigation-not-searchable crossreference selfref">see <a href="#In_literary_criticism">§ In literary criticism</a></span>). 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 are not 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". </p><p>In formal <a href="/wiki/Debate_competition" class="mw-redirect" title="Debate competition">debate competition</a>, certain forms of hand-waving may sometimes be explicitly permitted. In <a href="/wiki/Policy_debate" title="Policy debate">policy debate</a>, the concept of <i><a href="/wiki/Fiat_(policy_debate)" class="mw-redirect" title="Fiat (policy debate)">fiat</a></i> 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. </p> <div class="mw-heading mw-heading2"><h2 id="In_literary_criticism">In literary criticism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hand-waving&action=edit&section=3" title="Edit section: In literary criticism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Literary_criticism"></span> By extension, handwaving is used in <a href="/wiki/Literary_criticism" title="Literary criticism">literary, film and other media criticism</a> of <a href="/wiki/Speculative_fiction" title="Speculative fiction">speculative fiction</a> to refer to a <a href="/wiki/Plot_device" title="Plot device">plot device</a> (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 <a href="/wiki/Suspension_of_disbelief" title="Suspension of disbelief">suspend disbelief</a> regarding such a <a href="/wiki/Macguffin" class="mw-redirect" title="Macguffin">macguffin</a>, <i><a href="/wiki/Deus_ex_machina" title="Deus ex machina">deus ex machina</a></i>, <a href="/wiki/Continuity_error" class="mw-redirect" title="Continuity error">continuity error</a> or <a href="/wiki/Plot_hole" title="Plot hole">plot hole</a>. </p><p>The fictional material "<a href="/wiki/Handwavium" class="mw-redirect" title="Handwavium">handwavium</a>" (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 <a href="/wiki/Melange_(fictional_drug)" title="Melange (fictional drug)">spice melange</a>, a fictional drug with supernatural properties, in <a href="/wiki/Frank_Herbert" title="Frank Herbert">Frank Herbert</a>'s far-future <a href="/wiki/Science-fantasy" class="mw-redirect" title="Science-fantasy">science-fantasy</a> epic, <i><a href="/wiki/Dune_(franchise)" title="Dune (franchise)">Dune</a></i>. </p><p><i>Hand-waving</i> has come to be used in <a href="/wiki/Role-playing_games" class="mw-redirect" title="Role-playing games">role-playing games</a> 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. </p> <div class="mw-heading mw-heading2"><h2 id="In_mathematics">In mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hand-waving&action=edit&section=4" title="Edit section: In mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Mathematics"></span><span class="anchor" id="In_mathematics"></span> In mathematics, and disciplines in which mathematics plays a major role, <i>hand-waving</i> refers to either absence of formal proof or methods that do not meet <a href="/wiki/Mathematical_rigor" class="mw-redirect" title="Mathematical rigor">mathematical rigor</a>. In practice, it often involves the use of unrepresentative examples, unjustified assumptions, key omissions and faulty logic, and while these may be useful in expository papers and seminar presentations, they ultimately fall short of the standard of proof needed to establish a result. <a href="/wiki/Proof_by_intimidation" title="Proof by intimidation">Proof by intimidation</a> is one form of hand-waving. </p><p>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.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2015)">citation needed</span></a></i>]</sup> The opposite of hand-waving in mathematics (and related fields) is sometimes called <b>nose-following</b>, which refers to the unimaginative development of a narrow line of reasoning that—while correct—can also end up making the subject dry and uninteresting.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>The rationale for this culture of hyper-critical scrutiny is suggested by a quote of <a href="/wiki/G._H._Hardy" title="G. H. Hardy">G. H. Hardy</a>: "[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."<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_applied_science_and_engineering">In applied science and engineering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hand-waving&action=edit&section=5" title="Edit section: In applied science and engineering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Science_and_engineering"></span><span class="anchor" id="In_science_and_engineering"></span> Hand-waving arguments in <a href="/wiki/Engineering" title="Engineering">engineering</a> and other <a href="/wiki/Applied_sciences" class="mw-redirect" title="Applied sciences">applied sciences</a> often include <a href="/wiki/Orders_of_magnitude" class="mw-redirect" title="Orders of magnitude">order-of-magnitude</a> estimates and <a href="/wiki/Dimensional_analysis" title="Dimensional analysis">dimensional analysis</a>,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> especially in the use of <a href="/wiki/Fermi_problem" title="Fermi problem">Fermi problems</a> 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 <var style="padding-right: 1px;">z</var> is an even number", as an intermediary step in reaching a conclusion. </p><p>Another example of hand-waving can be found in the oversimplifications of the geologic representations commonly used in <a href="/wiki/Groundwater_model" title="Groundwater model">groundwater models</a> created in support of land-development applications, especially those involving metal mining and aggregate extraction. </p><p><a href="/wiki/Back-of-the-envelope_calculation" title="Back-of-the-envelope calculation">Back-of-the-envelope calculations</a> are approximate ways to get an answer by over-simplification, and are comparable to hand-waving in this sense. </p> <div class="mw-heading mw-heading2"><h2 id="In_business">In business</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hand-waving&action=edit&section=6" title="Edit section: In business"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Hand-waving</i> has been used to describe work-related situations where productivity is seemingly displayed, but deliverables are not produced, especially in the context of intentional engagement in <a href="/wiki/Busy_work" title="Busy work">busy work</a> or pretend-work, vague claims of overwork or complications, impenetrably <a href="/wiki/Buzzword" title="Buzzword">buzzword</a>-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. </p><p>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. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hand-waving&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/List_of_logical_fallacies" class="mw-redirect" title="List of logical fallacies">List of logical fallacies</a></li> <li><a href="/wiki/Proof_by_example" title="Proof by example">Proof by example</a></li> <li><a href="/wiki/Proof_by_intimidation" title="Proof by intimidation">Proof by intimidation</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hand-waving&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Dictionary.com-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Dictionary.com_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Dictionary.com_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Dictionary.com_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Dictionary.com_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Dictionary.com_1-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Dictionary.com_1-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://dictionary.reference.com/browse/hand-waving">"hand wave"</a>. <i>Dictionary.com</i>. 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Dictionary.com&rft.atitle=hand+wave&rft.date=2016&rft_id=http%3A%2F%2Fdictionary.reference.com%2Fbrowse%2Fhand-waving&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span> Cites the <i><a href="/wiki/Random_House_Dictionary" class="mw-redirect" title="Random House Dictionary">Random House Dictionary</a></i> and <i>The Dictionary of American Slang</i> 4th ed.</span> </li> <li id="cite_note-NHD-JF-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-NHD-JF_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-NHD-JF_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-NHD-JF_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-NHD-JF_2-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-NHD-JF_2-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-NHD-JF_2-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-NHD-JF_2-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-NHD-JF_2-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-NHD-JF_2-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRaymondSteele1996" class="citation encyclopaedia cs1"><a href="/wiki/Eric_S._Raymond" title="Eric S. Raymond">Raymond, Eric S.</a>; <a href="/wiki/Guy_L._Steele,_Jr." class="mw-redirect" title="Guy L. Steele, Jr.">Steele, Guy L.</a>, eds. (1996). "handwave". <i>The New Hacker's Dictionary</i> (3rd ed.). MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-68092-0" title="Special:BookSources/0-262-68092-0"><bdi>0-262-68092-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=handwave&rft.btitle=The+New+Hacker%27s+Dictionary&rft.edition=3rd&rft.pub=MIT+Press&rft.date=1996&rft.isbn=0-262-68092-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span> Online edition: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.catb.org/~esr/jargon/html/H/handwave.html">"The Jargon File"</a>. 4.4.7.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Jargon+File&rft.series=4.4.7&rft_id=http%3A%2F%2Fwww.catb.org%2F~esr%2Fjargon%2Fhtml%2FH%2Fhandwave.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span> <a rel="nofollow" class="external text" href="http://www.catb.org/~esr/jargon/">Homepage</a> mentions a ver. 4.4.8, but the text of the work says <a rel="nofollow" class="external text" href="http://www.catb.org/~esr/jargon/html/index.html">4.4.7</a>.</span> </li> <li id="cite_note-CBS_Bronco-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-CBS_Bronco_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-CBS_Bronco_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">An example in the sports press of "Jedi mind trick": <a rel="nofollow" class="external text" href="http://www.cbssports.com/nfl/eye-on-football/25449738/one-bronco-thinks-roethlisbergers-injury-is-a-jedi-mind-trick">One Bronco thinks Roethlisberger's injury is a 'Jedi mind trick'</a> .</span> </li> <li id="cite_note-note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-note_4-0">^</a></b></span> <span class="reference-text">Usage patterns are easily observable with Google and other search engines, which also reveal the difficulty of excluding false positives from various particular search terms.</span> </li> <li id="cite_note-OxfordDictionaries.com_UK-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-OxfordDictionaries.com_UK_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-OxfordDictionaries.com_UK_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20151110025053/http://www.oxforddictionaries.com/us/definition/english/hand-wave">"hand-wave"</a>. <i>Oxford Dictionaries Online</i> (British and World English ed.). <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. 2015. Archived from <a rel="nofollow" class="external text" href="https://www.oxforddictionaries.com/us/definition/english/hand-wave">the original</a> on November 10, 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">January 26,</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Oxford+Dictionaries+Online&rft.atitle=hand-wave&rft.date=2015&rft_id=https%3A%2F%2Fwww.oxforddictionaries.com%2Fus%2Fdefinition%2Fenglish%2Fhand-wave&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span> This is an online edition of <i><a href="/wiki/Oxford_Dictionary_of_English" title="Oxford Dictionary of English">Oxford Dictionary of English</a></i> with additional material.</span> </li> <li id="cite_note-OxfordDictionaries.com_US_1-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-OxfordDictionaries.com_US_1_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160201142153/https://www.oxforddictionaries.com/us/definition/american_english/handwave">"handwave"</a>. <i>Oxford Dictionaries Online</i>. American English. Oxford University Press. 2015. Archived from <a rel="nofollow" class="external text" href="https://www.oxforddictionaries.com/us/definition/american_english/handwave">the original</a> on February 1, 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">January 26,</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Oxford+Dictionaries+Online&rft.atitle=handwave&rft.date=2015&rft_id=https%3A%2F%2Fwww.oxforddictionaries.com%2Fus%2Fdefinition%2Famerican_english%2Fhandwave&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span> This is an online edition of the <i><a href="/wiki/New_Oxford_American_Dictionary" title="New Oxford American Dictionary">New Oxford American Dictionary</a></i>.</span> </li> <li id="cite_note-OxfordDictionaries.com_US_2-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-OxfordDictionaries.com_US_2_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-OxfordDictionaries.com_US_2_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160201135034/https://www.oxforddictionaries.com/us/definition/american_english/hand-waving">"hand-waving"</a>. <i>Oxford Dictionaries Online</i>. American English. 2015. Archived from <a rel="nofollow" class="external text" href="https://www.oxforddictionaries.com/us/definition/american_english/hand-waving">the original</a> on February 1, 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">January 26,</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Oxford+Dictionaries+Online&rft.atitle=hand-waving&rft.date=2015&rft_id=https%3A%2F%2Fwww.oxforddictionaries.com%2Fus%2Fdefinition%2Famerican_english%2Fhand-waving&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span></span> </li> <li id="cite_note-Jedi_2-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Jedi_2_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.bbc.com/news/world-us-canada-35256156">"Obama's 'Jedi mind trick' and a revealing admission"</a>. <i>BBC News</i>. 13 January 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=BBC+News&rft.atitle=Obama%27s+%27Jedi+mind+trick%27+and+a+revealing+admission&rft.date=2016-01-13&rft_id=https%3A%2F%2Fwww.bbc.com%2Fnews%2Fworld-us-canada-35256156&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://fox59.com/2016/01/17/in-focus-rep-messer-calls-presidents-speech-jedi-mind-trick/">"IN Focus: Rep. Messer calls President's speech 'Jedi mind trick'<span class="cs1-kern-right"></span>"</a>. 17 January 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=IN+Focus%3A+Rep.+Messer+calls+President%27s+speech+%27Jedi+mind+trick%27&rft.date=2016-01-17&rft_id=http%3A%2F%2Ffox59.com%2F2016%2F01%2F17%2Fin-focus-rep-messer-calls-presidents-speech-jedi-mind-trick%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGarner2006" class="citation journal cs1">Garner, Richard (2006). "Polycategories via pseudo-distributive laws". <i><a href="/wiki/Advances_in_Mathematics" title="Advances in Mathematics">Advances in Mathematics</a></i>. <b>218</b> (3): 781–827. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/math/0606735">math/0606735</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006math......6735G">2006math......6735G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.aim.2008.02.001">10.1016/j.aim.2008.02.001</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17057235">17057235</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Advances+in+Mathematics&rft.atitle=Polycategories+via+pseudo-distributive+laws&rft.volume=218&rft.issue=3&rft.pages=781-827&rft.date=2006&rft_id=info%3Aarxiv%2Fmath%2F0606735&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A17057235%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.aim.2008.02.001&rft_id=info%3Abibcode%2F2006math......6735G&rft.aulast=Garner&rft.aufirst=Richard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">G. H. Hardy (1940). "A Mathematician's Apology".</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChiang" class="citation web cs1">Chiang, Eugene. <a rel="nofollow" class="external text" href="http://w.astro.berkeley.edu/~echiang/dta_statement_chiang.pdf">"Order-of-Magnitude Physics: Hand-Waving as Performance Art"</a> <span class="cs1-format">(PDF)</span>. <i>University of California Berkeley — The Department of Astronomy</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=University+of+California+Berkeley+%E2%80%94+The+Department+of+Astronomy&rft.atitle=Order-of-Magnitude+Physics%3A+Hand-Waving+as+Performance+Art&rft.aulast=Chiang&rft.aufirst=Eugene&rft_id=http%3A%2F%2Fw.astro.berkeley.edu%2F~echiang%2Fdta_statement_chiang.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHand-waving" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hand-waving&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://everything2.com/title/Proof+by+handwaving">"Proof by Handwaving"</a>, article at <i><a href="/wiki/Everything2" title="Everything2">Everything2</a></i></li> <li><a rel="nofollow" class="external text" href="http://www.sciencecartoonsplus.com/pages/gallery.php">"And then a miracle occurs"</a>, cartoon by <a href="/wiki/Sidney_Harris_(cartoonist)" title="Sidney Harris (cartoonist)">Sidney Harris</a>, published in <a href="/wiki/American_Scientist" title="American Scientist"><i>American Scientist</i> magazine</a></li> <li><a rel="nofollow" class="external text" href="http://www.ece.ust.hk/~mchan/collections/humor/prove.pdf">"Proving almost anything"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110721094630/http://www.ece.ust.hk/~mchan/collections/humor/prove.pdf">Archived</a> 2011-07-21 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, humor essay by James Lavin, <i><a href="/wiki/IEEE" class="mw-redirect" title="IEEE">IEEE</a> Potentials</i> February/March 1996, pp. 6–7.</li></ul> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐5dc468848‐z5j67 Cached time: 20241122142715 Cache expiry: 2592000 Reduced expiry: false Complications: [vary‐revision‐sha1, show‐toc] CPU time usage: 0.263 seconds Real time usage: 0.365 seconds Preprocessor visited node count: 1559/1000000 Post‐expand include size: 25455/2097152 bytes Template argument size: 2943/2097152 bytes Highest expansion depth: 12/100 Expensive parser function count: 4/500 Unstrip recursion depth: 1/20 Unstrip post‐expand size: 42484/5000000 bytes Lua time usage: 0.139/10.000 seconds Lua memory usage: 5555689/52428800 bytes Number of Wikibase entities loaded: 0/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 329.563 1 -total 36.55% 120.457 1 Template:Reflist 26.79% 88.274 7 Template:Cite_web 22.67% 74.706 1 Template:Short_description 13.19% 43.461 2 Template:Citation_needed 12.32% 40.587 2 Template:Pagetype 11.30% 37.226 2 Template:Fix 8.16% 26.889 2 Template:See_below 7.43% 24.470 4 Template:Category_handler 7.40% 24.376 2 Template:Crossreference_printworthy --> <!-- Saved in parser cache with key enwiki:pcache:idhash:263233-0!canonical and timestamp 20241122142715 and revision id 1233539154. 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