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Gabrielle S.Adams ,Benjamin A.Converse , Andrew H. Hales & Leidy E. Klotz
机器翻译，原文在下方 PDF 文件。
Improving objects, ideas or situations—whether a designer seeks to advance technology, a writer seeks to strengthen an argument or a manager seeks to encourage desired behaviour—requires a mental search for possible changes 1–3 . We investigated whether people are as likely to consider changes that subtract components from an object, idea or situation as they are to consider changes that add new components. People typically consider a limited number of promising ideas in order to manage the cognitive burden of searching through all possible ideas, but this can lead them to accept adequate solutions without considering potentially superior alternatives 4–10 . Here we show that people systematically default to searching for additive transformations, and consequently overlook subtractive transformations. Across eight experiments, participants were less likely to identify advantageous subtractive changes when the task did not (versus did) cue them to consider subtraction, when they had only one opportunity (versus several) to recognize the shortcomings of an additive search strategy or when they were under a higher (versus lower) cognitive load. Defaulting to searches for additive changes may be one reason that people struggle to mitigate overburdened schedules 11 , institutional red tape 12 and damaging effects on the planet
改进对象、想法或情况--无论设计师是为了推动技术发展，作家是为了加强论证，还是管理者是为了鼓励理想的行为--都需要在心理上寻找可能的变化1-3。我们调查了人们是否有可能考虑从一个物体、想法或情况中减少成分的变化，以及考虑增加新成分的变化。人们通常会考虑数量有限的有希望的想法，以管理搜索所有可能的想法的认知负担，但这可能导致他们接受适当的解决方案，而不考虑潜在的更优的替代方案。在这里，我们表明，人们系统地默认搜索加法变换，从而忽略了减法变换。在八个实验中，当任务没有（而不是有）提示他们考虑减法时，当他们只有一次机会（而不是多次）认识到加法搜索策略的缺点时，或者当他们处于较高（而不是较低）的认知负荷时，参与者不太可能识别有利的减法变化。默认搜索加法变化可能是人们努力减轻过重的时间表、机构的繁文缛节和对地球的破坏性影响的一个原因。
Transforming an object, idea or situation in a novel way begins as an act of imagination, a process of searching the environment and one’s store of knowledge for possible changes 1–3 . The cognitive science of problem-solving describes iterative processes of imagining and evaluat- ing actions and outcomes to determine whether they would produce an improved state. The essential elements of these processes are mental models of the original state, of possible transformations, and of action categories that can produce the transformations. We conceptualize subtraction and addition as action categories that remove compo- nents from or add components to the original, respectively. When a transformed state has fewer components than the original (for exam- ple, a revision with fewer words or a process with fewer obstacles), we describe it as a subtractive transformation; when a transformed state has more components than the original, we describe it as an additive transformation. These action categories are conceptually distinct from welfare changes 15 , motivational orientations 16 and counterfactual reasoning structures 17 . Furthermore, these action categories are not goals in themselves. People might subtract or add to fulfil any number of underlying interests.
以一种新的方式改造一个物体、想法或情况，首先是一种想象的行为，是一个搜索环境和自己的知识储备以寻找可能的变化的过程。问题解决的认知科学描述了想象和评估行动和结果的迭代过程，以确定它们是否会产生一个改进的状态。这些过程的基本要素是原始状态的心理模型、可能的转变以及能够产生转变的行动类别。我们将减法和加法概念化为行动类别，分别从原始状态中去除成分或增加成分。当一个被转换的状态比原来的成分少时（例如，一个字数较少的修改或一个障碍较少的过程），我们将其描述为减法转换；当一个被转换的状态比原来的成分多时，我们将其描述为加法转换。这些行动类别在概念上不同于福利变化、动机取向和反事实推理结构。此外，这些行动类别本身并不是目标。人们可以通过减法或加法来实现任何数量的潜在利益。
Our research explored whether people tend to search for subtrac- tive changes less readily than they search for additive changes. It was inspired by the apparent need for subtractive counsel across fields. Reminders such as ‘less is more’ 18 , ‘omit needless words’ 19 and ‘remove barriers’ 20,21 seem to presume that people who are searching for trans- formations will otherwise overlook or undervalue subtraction as a way to improve objects, ideas or situations.
我们的研究探讨了人们是否倾向于寻找次生变化，而不是寻找加法变化。它的灵感来自于各领域对减法咨询的明显需求。诸如 "少即是多 "、"省略不必要的词语 "和 "消除障碍 "这样的提醒，似乎是假定那些正在寻找变化的人们会忽略或低估减法作为改善对象、想法或情况的一种方式。
Given this anecdotal rationale, we began our investigation with observations of people changing objects, ideas and situations (k = 8, n = 1,585) (Extended Data Table1, Supplementary Information sections 2.1—2.8). For example, in one controlled observation we asked participants to change a series of digital grid patterns to be symmetrical (study S1, described in Supplementary Information section 2.1). Par- ticipants could toggle the colour of any box by clicking on it. It took the same amount of effort to subtract marks from the side that had a greater number of coloured boxes as to add marks to the side with fewer coloured boxes. However, of the 91 participants who favoured one of these two approaches, only 18 (20%) favoured subtraction (this 20% differs significantly from the 50% that would be expected if additive and subtractive transformations were equally common (two-sided binomial distribution probability, P < 0.001)). In another observation, we examined archival data from a solicitation for improvement ideas by the incoming president of a university (study S2, described in Sup- plementary Information section 2.2). Of the 651 responses that coders categorized as additive or subtractive, only 70 (11%) were subtractive (this 11% significantly differs from 50% (two-sided binomial distribu- tion probability, P < 0.001)).
鉴于这种传闻的理由，我们从观察人们改变物体、想法和情况开始调查（k=8，n=1,585）（扩展数据表1，补充资料2.1-2.8节）。例如，在一个受控观察中，我们要求参与者将一系列数字网格图案改为对称的（研究S1，在补充资料第2.1节中描述）。参与者可以通过点击任何一个方框来切换其颜色。从拥有较多彩色方块的一侧减去分数与在拥有较少彩色方块的一侧增加分数所花费的精力是一样的。然而，在91名倾向于这两种方法之一的参与者中，只有18人（20%）倾向于减法（这20%与如果加法和减法转换同样普遍的话，预期的50%有很大差别（双侧二项分布概率，P < 0.001））。在另一个观察中，我们检查了一所大学的新任校长征求改进意见的档案数据（研究S2，在补充资料第2.2节中描述）。在编码员归类为加法或减法的651个回答中，只有70个（11%）是减法（这11%与50%有显著差异（双侧二项分布概率，P < 0.001））。
We found similarly low rates of subtraction among participants who were prompted to transform block structures (12%, 2% and 5% in stud- ies S3, S4 and S5, respectively), essays (17% and 32% in studies S6 and S7) and itineraries (28% in study S8) (all of these differed significantly from 50% (two-sided binomial distribution probability, P < 0.001)) (Supplementary Information sections 2.3—2.8). Rates of subtraction were lower than rates of addition, except when we introduced super- fluous or anomalous components (for example, grilled cheese with chocolate) in studies S9 and S10 (Extended Data Fig.1, Extended Data Table2, Supplementary Information sections 2.9, 2.10). Although we did not randomly sample from transformation problems, we observed this tendency across a range of goals (including ‘improve’, ‘enable’ and ‘arrange’), across stimuli that varied in familiarity and importance, for originals created by the research team and originals created by other participants, and in well-defined and ill-defined settings 3 .
我们发现，在被提示转换块状结构（在研究S3、S4和S5中分别为12%、2%和5%）、论文（在研究S6和S7中为17%和32%）和行程（在研究S8中为28%）的参与者中，减法率也同样低（所有这些都与50%有显著差异（双侧二项分布概率，P < 0.001））。补充资料第2.3-2.8节）。减法的比率低于加法的比率，除非我们在研究S9和S10中引入超流利或异常的成分（例如，烤奶酪加巧克力）（扩展数据图1，扩展数据表2，补充资料第2.9，2.10节）。尽管我们没有从转化问题中随机抽样，但我们在一系列目标（包括 "改进"、"启用 "和 "安排"）中，在熟悉程度和重要性不同的刺激物中，在研究小组创造的原件和其他参与者创造的原件中，以及在定义明确和定义不明确的环境中观察到了这种趋势3。
Low rates of subtraction raise two broad possibilities about the thought processes that produce them: people might generate both kinds of ideas and then disproportionately choose additive ones, or they might overlook subtractive ideas altogether. Although both phe- nomena probably contributed to the observed behavioural outcomes, we focused our subsequent research on potential differences at the idea-generation phase because this phase necessarily precedes explicit choice. We investigated whether people default to an additive search strategy, making them less likely to consider subtraction in the first place.
低的减法率对产生这些想法的思维过程提出了两种广泛的可能性：人们可能产生两种想法，然后不成比例地选择加法的想法，或者他们可能完全忽略了减法的想法。尽管这两种现象都可能有助于观察到的行为结果，但我们将后续研究的重点放在想法产生阶段的潜在差异上，因为这个阶段必然在明确的选择之前。我们调查了人们是否默认了加法的搜索策略，从而使他们在一开始就不太可能考虑减法。
Heuristic memory searches can help people to efficiently access the right information at the right time, but—as with any mental shortcut— heuristic memory searches can be overapplied, leading people to accept adequate solutions before considering potentially superior alternatives 4–10 . There are cognitive, cultural and socioecological rea- sons to suspect that people might privilege additive over subtractive changes. First, additive changes may be incrementally easier to process. Any component that can be subtracted must first be understood as part of the artefact before it can be considered as ‘not’ part of the arte- fact 22 . Second, over time, additive changes may come to be viewed more positively than subtractive changes. Numerical concepts of ‘more’ and ‘higher’ may map to evaluative concepts of ‘positive’ and ‘better’ 23 ; tan- gible contributions are culturally valued 24 ; and acquiring and displaying resources is fitness-enhancing 25,26 . Third, people might be reluctant to subtract because of attentional and evaluative processes that favour the status quo 27,28 . Finally, these processes operate in an environment that may, probabilistically, offer more good opportunities to add than to subtract: originals require building before honing; the number of components that can be subtracted is always bound by what exists; and in designed environments, one may infrequently encounter artefactsfrom which the designers have not already subtracted the obviously negative components.
启发式记忆搜索可以帮助人们在正确的时间有效地获取正确的信息，但就像任何心理捷径一样，启发式记忆搜索可能会被过度应用，导致人们在考虑潜在的优越替代方案之前就接受了适当的解决方案。从认知、文化和社会生态学的角度来看，人们可能会对加法性变化比减法性变化更感兴趣。首先，加法性变化可能更容易处理。任何可以被减去的成分都必须首先被理解为艺术品的一部分，然后才能被认为是 "不 "属于艺术品的一部分。第二，随着时间的推移，人们对加法变化的看法可能比减法变化更积极。更多 "和 "更高 "的数字概念可能与 "积极 "和 "更好 "的评价概念相对应；可见的贡献在文化上受到重视；获得和展示资源可以增强体质。第三，人们可能不愿意做减法，因为注意力和评价过程有利于维持现状。最后，这些过程是在一个环境中进行的，从概率上讲，增加的好机会比减少的好机会要多：原件需要在磨练之前建造；可以减少的成分的数量总是受到现有的限制；在设计的环境中，人们可能很少遇到设计师还没有减少明显的负面成分的艺术品。
The more frequently that individuals use an additive search strategy with perceived success, the more cognitively accessible this strategy would become for them 6,10,29,30 . Across many domains of judgment, people rely on quick and easy mental shortcuts—especially when high cognitive demands preclude the pursuit of more tailored approaches and in the absence of information that cues alternative strategies 4–10 . Thus, if additive search is a common default, people should be more likely to rely on it when they are cognitively loaded and—conversely— they should be less likely to rely on it when task experience or task information cues them to use another strategy. Experiments As in the observational studies, we presented participants with an origi- nal object, idea or situation and asked them to change it in some way. Unlike the observational studies, we designed all of the experimental tasks so that participants would have good reason to report or produce subtractive transformations if they thought of them. This design feature inflated baseline rates of subtraction but allowed us to infer that people who did not pursue subtraction probably did not consider it. Differing rates of subtractive transformation across conditions could therefore be attributed to idea generation rather than to choice. To minimize transient influences that might cue a specific search strategy, we used neutral prompts (for example, ‘change’ or ‘improve’) rather than conno- tative additive or subtractive prompts (for example, ‘bolster’ or ‘hone’, respectively); and we avoided original artefacts that would appear to participants in our samples to have obvious superfluities (for example, a bacon, lettuce, tomato and peanut butter sandwich) or omissions (for example, a lettuce and tomato sandwich). Within these specifica- tions, each experiment compared conditions in which people’s mental searches should depend relatively more versus less on a heuristic search strategy: that is, when a search-expansion cue is absent versus present; when the task provides fewer versus more opportunities to recognize the value of an alternative strategy; or when the participant is under higher versus lower cognitive load. We predicted that subtraction rates would be higher in the latter conditions (see Methods for descriptions of our approach to determining sample sizes, randomization, analysis and reporting for all experiments).
个人越是频繁地使用加法搜索策略并感到成功，这种策略在认知上就越容易被他们接受。在许多判断领域，人们依赖快速和简单的心理捷径--特别是当高认知要求排除了追求更有针对性的方法和缺乏提示替代策略的信息时。因此，如果加法搜索是一种常见的默认方法，那么当人们的认知能力很强时，他们应该更有可能依赖它，反之，当任务经验或任务信息提示他们使用另一种策略时，他们应该不太可能依赖它。实验 在观察性研究中，我们给参与者提供了一个原始的物体、想法或情况，并要求他们以某种方式改变它。与观察性研究不同的是，我们设计了所有的实验任务，使参与者有充分的理由报告或产生减法转化，如果他们想到了这些转化。这一设计特点提高了减法的基线率，但允许我们推断那些没有追求减法的人可能没有考虑过减法。因此，不同条件下减法转化率的差异可以归因于想法的产生而不是选择。为了尽量减少可能提示特定搜索策略的短暂影响，我们使用中性提示（例如 "改变 "或 "改善"），而不是象征性的加法或减法提示（例如 "加强 "或 "磨练"，分别）；我们避免使用那些在我们样本中的参与者看来有明显多余（例如培根、生菜、番茄和花生酱三明治）或遗漏（例如生菜和番茄三明治）的原始艺术品。在这些特定条件下，每个实验都比较了人们的心理搜索应该相对更多或更少地依赖于启发式搜索策略的条件：也就是说，当搜索扩展线索不存在或存在时；当任务提供较少或较多的机会来认识替代策略的价值时；或者当参与者处于较高或较低的认知负荷时。我们预测，在后一种情况下，减法率会更高（关于我们确定所有实验的样本量、随机化、分析和报告的方法，见方法）。
Experiments 1, 2 and 3 manipulated the presence of subtraction cues in the problem-solving environment. Explicitly priming a specific, relevant action category should offset the influence of a heuristic that prioritizes a different category 6,27,29,30 . In a task inspired by sustainable resource challenges, experiment 1 presented participants (n = 197) (‘Experiment 1’ in the Methods) with an implicit choice between using costly new resources or working with what was already there. We offered participants a bonus of one dollar if they could stabilize a Lego structure such that it could hold a masonry brick above a figurine. The original could not hold the brick because its platform was supported in one corner, in a manner similar to a one-legged table (Extended Data Fig.2). Participants could add new supports (at a cost) or they could remove the existing support (for free), which allowed the platform to sit flush on the layer below. The subtractive transformation therefore maximized their bonus. In the control condition, instructions explicitly mentioned addition (‘each piece that you add costs ten cents’) but not subtrac- tion. In the subtraction-cue condition, instructions mentioned both (‘each piece that you add costs ten cents but removing pieces is free’). Instructions in both conditions stated ‘you may alter the structure how- ever you want’. Results from a follow-up study (S11) corroborated the assumption that most participants who thought of subtraction would have recognized its value (Supplementary Information section 2.11.) In the control condition of experiment 1, 41% of participants produced the subtractive transformation; by contrast, in the subtraction-cue condition 61% of participants produced this transformation (χ 2 = 7.72,P = 0.005, φ = 0.20) (see Supplementary Information section 1.1 for information regarding preregistration and analysis) (Table1). In the absence of a subtraction cue, a significantly greater number of par- ticipants overlooked the advantageous subtractive transformation.
实验1、2和3操纵了问题解决环境中减法线索的存在。明确提示一个特定的、相关的行动类别，应该可以抵消优先考虑不同类别的启发式的影响6,27,29,30。在一项受可持续资源挑战启发的任务中，实验1向参与者（n = 197）（方法中的 "实验1"）提出了一个隐含的选择，即使用昂贵的新资源还是利用现有的资源。我们为参与者提供了一美元的奖金，如果他们能够稳定一个乐高结构，使其能够在一个小雕像上方容纳一块砖头。原来的乐高结构不能容纳砖头，因为它的平台是在一个角落里支撑的，其方式类似于单脚桌（扩展数据图2）。参与者可以添加新的支撑物（有成本），或者他们可以移除现有的支撑物（免费），这使得平台可以平齐地坐在下面一层。因此，减法改造使他们的奖金最大化。在控制条件下，指令明确提到了加法（"你增加的每一块都要花费10美分"），但没有提到减法。在减法提示条件下，指令同时提到了两者（"你增加的每一块都要花10美分，但移除碎片是免费的"）。两个条件下的指令都提到 "你可以随意改变结构"。在实验1的控制条件下，41%的参与者产生了减法转换；相比之下，在减法提示条件下，61%的参与者产生了这种转换（χ 2 = 7.72,P = 0.005, φ = 0.20）（关于预注册和分析的信息见补充资料1.1）（表1）。在没有减法提示的情况下，明显有更多的参与者忽略了有利的减法转换。
In experiment 2 and experiment 3 (n = 147 and 165, respectively) (described in ‘Experiment 2’ and ‘Experiment 3’ in the Methods), we showed participants an illustration of a miniature golf hole (Extended Data Fig.3), solicited their improvement ideas and coded whether each was additive (for example, ‘add a windmill’), subtractive (for example, ‘remove the sand trap’) or neither (for example, ‘reverse the direction’). We designed this stimulus to provide an engaging, novel task for participants 10 . Whereas experiment 1 solicited only a single transformation, experiments 2 and 3 asked participants to list ‘all of the different ways that [they] might be able to improve’ the original. This minimizes the potential role of evaluation at the choice stage, and offers a view of relative accessibility 27,31 . The no-cue instructions did not mention either addition or subtraction, whereas the cue instructions reminded participants that they could ‘add or subtract’. We did not find evidence that the cue affected the likelihood that participants would submit a list with at least one additive idea (odds ratio = 0.92, z = −0.24, P = 0.810), but we did find evidence that the cue increased the likelihood that participants would submit a list with at least one subtractive idea (odds ratio = 1.93, z = 2.73, P = 0.006) (Table1, Extended Data Fig.4; additional information is provided in Supplementary Information sec- tions 1.2, 1.3 and an alternative analysis is described in Supplementary Information section 1.5). The subtractive part of the cue seems to have brought new options to mind.
实验4（n = 369）（在方法中的 "实验4 "中描述）调查了人们是否在不同的转化目标中忽略了减法。我们使用了实验2和3中的任务，将线索操纵与目标操纵相交叉，指定参与者 "改善 "原作或 "使之变坏"。在改进条件下（无提示=21%，提示=48%，χ 2=13.63，P＜0.001）和变坏条件下（无提示=28%，提示=50%，χ 2=9.71，P=0.002），提示增加了参与者产生至少一个减法想法的百分比（表1，扩展数据图4；回归细节和加法想法的分析见补充资料1.4节）。这些结果意味着，减法忽视并不近似地归因于关于如何为改进工作做出贡献的规范，也不近似于 "更多 "和 "更好 "之间的语言关联。与实验1至4（直接操纵任务的具体信息）相比，实验5至8操纵了任务条件对允许参与者超越启发式搜索并可能自行激活减法想法的有利程度。在实验5中（n = 299）（在方法中的 "实验5 "中描述），我们向参与者展示了一个由白色和绿色盒子组成的10×10的数字网格（一个新的刺激，其中的各个组成部分没有内在的价值）。参与者可以点击任何一个盒子来切换其颜色。他们的目标是用最少的点击次数使网格从左到右和从上到下对称。图1显示，原来的网格在一个象限内有多余的填充框。
Experiment 4 (n = 369) (described in ‘Experiment 4’ in the Meth- ods) investigated whether people overlook subtraction across dif- ferent transformation goals. We used the task from experiments 2 and 3, crossing the cue manipulation with a goal manipulation that assigned participants to ‘improve’ the original or to ‘make it worse’. The cue increased the percentage of participants who generated at least one subtractive idea within the improvement conditions (no-cue = 21%, cue = 48%, χ 2 = 13.63, P < 0.001) and the make-it-worse condi- tions (no-cue = 28%, cue = 50%, χ 2 = 9.71, P = 0.002) (Table1, Extended Data Fig.4; the regression details and analysis of additive ideas are given in Supplementary Information section 1.4). These results imply that subtraction neglect is not proximally attributable to norms about how to contribute to improvement efforts or to linguistic associations between ‘more’ and ‘better’.
实验4（n = 369）（在方法中的 "实验4 "中描述）调查了人们是否在不同的转化目标中忽略了减法。我们使用了实验2和3中的任务，将线索操纵与目标操纵相交叉，指定参与者 "改善 "原作或 "使之变坏"。在改进条件下（无提示=21%，提示=48%，χ 2 = 13.63，P < 0.001）和变坏条件下（无提示=28%，提示=50%，χ 2 = 9.71，P = 0.002），提示增加了参与者产生至少一个减法想法的百分比（表1，扩展数据图4；回归细节和加法想法的分析见补充资料1.4节）。这些结果意味着，减法忽视并不近似地归因于关于如何为改进工作做出贡献的规范，也不近似于 "更多 "和 "更好 "之间的语言关联。
In contrast to experiments 1 to 4 (which directly manipulated task-specific information), experiments 5 to 8 manipulated how favour- able task conditions were for allowing participants to get beyond a heuristic search and potentially activate subtractive ideas on their own. In experiment 5 (n = 299) (described in ‘Experiment 5’ in the Methods), we presented participants with a digital 10 × 10 grid of white and green boxes (a novel stimulus in which the individual components have no inherent value). Participants could click on any box to toggle its colour. Their goal was to make the grid symmetrical from left-to-right and top-to-bottom using the fewest number of clicks. Figure1 illustrates that the original grid had extraneous filled boxes in one quadrant.Participants could achieve symmetry by adding to the three empty quadrants or by subtracting from the marked quadrant. Unlike the task in study S1, this task had an objectively correct transformation but participants could only recognize the subtractive transformation as correct if they thought of it. In the control condition, participants proceeded immediately to the critical trial (Fig.1d). In the repeated search condition, participants first completed practice trials on three similar grids (Fig.1a–c) but received no external feedback on their responses. The repetition merely gave them more opportunities to recognize the shortcomings of an additive approach. Increasing the cumulative probability of an incidental discovery of subtraction during the practice trials should increase the likelihood of a participant using a subtractive search in the critical trial. As predicted, 49% of participants produced the subtractive solution in the control condition, whereas 63% produced it in the repeated search condition (χ 2 = 5.87, P = 0.015, φ = 0.15) (Table1, Supplementary Information section 1.6). Experiment 5 showed that participants were more likely to produce a superior sub- tractive transformation when they had more opportunities to recognize the task-specific shortcomings of an additive search strategy.
与实验1至4（直接操纵特定的任务信息）相比，实验5至8操纵了任务条件对允许参与者超越启发式搜索并可能自行激活减法想法的有利程度。在实验5中（n = 299）（在方法中的 "实验5 "中描述），我们向参与者展示了一个由白色和绿色盒子组成的10×10的数字网格（一个新的刺激，其中的各个组成部分没有内在的价值）。参与者可以点击任何一个盒子来切换其颜色。他们的目标是用最少的点击次数使网格从左到右和从上到下对称。图1显示，原来的网格在一个象限内有不相干的填充盒。参与者可以通过在三个空象限内添加或从标记的象限内减去来实现对称。与研究S1中的任务不同，这项任务有一个客观上正确的转换，但参与者只有在想到的情况下才能认出减法转换是正确的。在控制条件下，参与者立即进入关键试验（图1d）。在重复搜索条件下，参与者首先在三个类似的网格上完成练习试验（图1a-c），但没有收到关于他们反应的外部反馈。重复只是让他们有更多的机会认识到加法方法的缺点。在练习试验中增加偶然发现减法的累积概率，应该会增加参与者在关键试验中使用减法搜索的可能性。正如预测的那样，49%的参与者在控制条件下产生了减法方案，而63%的参与者在重复搜索条件下产生了减法方案（χ 2 = 5.87, P = 0.015, φ = 0.15）（表1，补充资料第1.6节）。实验5表明，当参与者有更多的机会认识到加法搜索策略的特定任务的缺点时，他们更有可能产生一个优越的次牵引性转化。
In experiments 6 to 8 (n = 1,153) (described in ‘Experiment 6’ and ‘Experiments 7 and 8’ in the Methods), we examined whether par- ticipants would be less likely to produce a subtractive transforma - tion when they were under cognitive load (a state that is known to increase reliance on cognitive shortcuts 4,22,32,33 ). In an adapted version of experiment 5, participants completed four critical trials with no practice trials (Fig.1a–d). To induce a higher cognitive load, we used a concurrent head-movement task 33 in experiment 6 and a concur- rent digit-search task 22,32 in experiments 7 and 8. Meta-analysis of the three experiments indicates that participants failed to identify the subtractive transformation for more puzzles in the higher- versus lower-load condition (Hedge’s g = 0.18, z = 2.97, P = 0.003) (Table1; details and a one-trial version are given in Supplementary Information sections 1.7–1.10). When participants had more attentional resources available, they were more likely to identify a superior subtractive transformation
在实验6至8中（n = 1,153）（在方法中的 "实验6 "和 "实验7和8 "中描述），我们研究了参与者在认知负荷下（一种已知会增加对认知捷径的依赖的状态4,22,32,33）是否不太可能产生减法转化。在实验5的一个改编版本中，参与者完成了四个关键试验，没有练习试验（图1a-d）。为了诱发更高的认知负荷，我们在实验6中使用了同时进行的头部运动任务33，在实验7和实验8中使用了同时进行的数字搜索任务22,32。三个实验的元分析表明，在高负荷与低负荷条件下，参与者未能识别更多的谜题的减法转换（Hedge's g = 0.18, z = 2.97, P = 0.003）（表1；细节和单次试验版本在补充资料第1.7-1.10节给出）。当参与者有更多的注意力资源可用时，他们更有可能识别出一个优越的减法转换
Discussion
This Article introduces a basic conceptual distinction between pursuing changes to the physical, intellectual and social world through subtrac - tion or through addition. This distinction links what might otherwise be treated as disparate phenomena in design and problem-solving (changing objects); reasoning, learning and communication (changing ideas); and coordination, decision-making and motivation (changing situations). Empirically, our research identifies conditions under which people are more or less likely to overlook subtraction. Our experiments showed that the identification of advantageous subtractive changes depends on the presence of cues that prompt subtractive search (experiments 1 to 4), on the number of opportunities one has to recognize the short- comings of an additive default (experiment 5) and on the situational availability of cognitive resources (experiments 6 to 8)
这篇文章介绍了一个基本的概念性区别，即通过subtrac - tion或通过添加来追求对物理、智力和社会世界的改变。这一区别将设计和问题解决（改变物体）；推理、学习和交流（改变想法）；以及协调、决策和动机（改变情况）中可能被视为不相干的现象联系起来。从经验上看，我们的研究确定了人们在哪些条件下更容易或更不容易忽视减法。我们的实验表明，对有利的减法变化的识别取决于提示减法搜索的线索的存在（实验1至4），取决于人们有多少机会认识到加法默认的缺点（实验5），以及认知资源的情景可用性（实验6至8
It is likely that heuristic search does not account for all variation in subtractive and additive transformations. For instance, some transfor- mation tasks may not require the general memory search associated with problem-solving. Dangerous, disgusting or dissonant compo- nents would probably cue a specific goal (for example, ‘remove the roaches from the apartment’) with a clear end state and limited set of means. Task-specific features might also cue a tailored memory search (for example, instructions from an editor to ‘shorten’). Furthermore, whenever subtractive and additive ideas do arise, potential biases in choice become another source of variance. Our findings, which are based on samples of participants in the USA, raise questions about cultural generalizability. Our preliminary study with university students from Germany and Japan suggests that the additive search strategy extends beyond the USA (study S12; details are provided in Extended Data Table3, Supplementary Information section 2.12). However, additional research is needed to understand culture as a candidate moderator, including the potential contribu- tions of industrialization, resource availability, aesthetic preferences and social norms. Future research that explains variability in subtrac- tion neglect might help to pinpoint its social, cognitive and develop- mental origins, and—further—to suggest ways to reduce its harmful consequences. As with many heuristics, it is possible that defaulting to a search for additive ideas often serves its users well 4,5,7 . However, the tendency to overlook subtraction may be implicated in a variety of costly modern trends, including overburdened minds and schedules 11 , increasing red tape in institutions 12 and humanity’s encroachment on the safe operat- ing conditions for life on Earth 13,14 . If people default to adequate additive transformations—without considering comparable (and sometimes superior) subtractive alternatives—they may be missing opportunities to make their lives more fulfilling, their institutions more effective and their planet more liveable
启发式搜索很可能并不能解释减法和加法转换的所有变化。例如，一些转换任务可能不需要与解决问题相关的一般记忆搜索。危险的、令人厌恶的或不和谐的成分可能会提示一个具体的目标（例如，"从公寓里清除蟑螂"），有一个明确的最终状态和有限的手段。特定的任务特征也可能提示一个有针对性的记忆搜索（例如，来自编辑的 "缩短 "指示）。此外，只要减法和加法的想法确实出现，选择中的潜在偏见就会成为另一个差异的来源。我们的研究结果是基于美国的参与者的样本，提出了关于文化可推广性的问题。我们对德国和日本的大学生进行的初步研究表明，加法搜索策略延伸到了美国之外（研究S12；详情见扩展数据表3，补充资料2.12节）。然而，还需要更多的研究来理解文化作为一个候选调节器，包括工业化、资源可用性、审美偏好和社会规范的潜在贡献。未来的研究如果能解释亚痕忽视的变异性，可能有助于确定其社会、认知和发展心理的起源，并进一步提出减少其有害后果的方法。与许多启发式方法一样，可能默认寻找加法的想法往往能很好地服务于它的使用者4,5,7。然而，忽视减法的倾向可能与各种代价高昂的现代趋势有关，包括过重的思想负担和时间表11，机构中越来越多的繁文缛节12，以及人类对地球上生命安全运行条件的侵占13,14。如果人们不考虑类似的（有时是更好的）减法选择，而默认为充分的加法改造，他们可能会错过使他们的生活更充实、机构更有效、地球更宜居的机会。
Methods
We report all close replications and meta-analyses conducted across similar experiments. We report all conditions, measures and data exclu- sions. Supplementary Information section 1 and the Reporting Sum- mary provide detailed dropout information for all studies. Research protocols were approved by the Institutional Review Board at the Uni- versity of Virginia. Participants consented to participate in all studies. The universities at which we collected data are not named to protect participant anonymity and confidentiality. No deception was used.
我们报告了在类似实验中进行的所有紧密复制和元分析。我们报告了所有的条件、措施和数据的排除情况。补充资料第1节和报告摘要提供了所有研究的详细辍学信息。研究方案得到了弗吉尼亚大学机构审查委员会的批准。参与者同意参加所有的研究。为了保护参与者的匿名性和保密性，我们收集数据的大学没有被命名。没有使用欺骗手段。
Sample size determination and randomization
Sample sizes for each study were determined before data collection (that is, no data were collected for any study after analysis began). For studies that were the first of their design, we used informal rules-of-thumb to determine a target sample size. For subsequent studies that used a similar design, we used observed effect sizes as an informal guide. The exceptions to this approach were experiment 1 (which was preregistered on the basis of a power calculation (https:// osf.io/rkqvw/)), study S2 (an archival study) and study S12 (for which we were limited by the number of volunteers). Except for experiment 1, no power analysis was performed. For all experiments, we aimed to recruit participants from separate samples using appropriate identifiers (for example, participant identification number, Amazon Mechanical Turk identification number or IP address) to avoid duplicated responses. In experiment 1, we used a randomizer to make a predetermined rand- omization schedule; in experiments 2 to 8, we used the randomization feature present in the survey software of Qualtrics.
Data analysis and reporting
Data analysis was conducted in R (v.4.0.2) and SPSS (v.27). All reported P values are two-sided. We calculated effect sizes using either Cohen’s d (using the effsize package in R 34 ), a phi correlation coefficient (using the psych package in R 35 ), or Cramer’s V (using jamovi 36 for R) as appropri- ate. Reported t-tests do not assume equal variances and are therefore reported as Welch’s t-tests, with corrected degrees of freedom 37 .
Experimental samples and procedures
Experiment 1.
We designed the task for experiment 1 so that partici- pants would earn more money if they pursued a subtractive trans- formation, such that overlooking subtraction was financially costly to participants (see https://osf.io/rkqvw/ for preregistration of the hypothesis and analysis plan, and Supplementary Information sec- tion 1.1 for discussion of a deviation from this plan). We recruited 203 individuals from those passing by a table in a highly trafficked area of a large public university in the USA. Six sessions were excluded for procedural or random-assignment protocol violations, yielding a final sample of n = 197 participants. To simplify the study procedure, we did not administer any surveys to participants or collect demographic information. Participants earned candy and the chance of a bonus of up to $1.
我们为实验1设计了任务，使参与者在追求减法的过程中会赚取更多的钱，这样，俯视减法对参与者来说是有经济代价的（关于假设和分析计划的预先登记，见https://osf.io/rkqvw/，关于偏离这一计划的讨论，见补充资料第1.1节）。我们从美国一所大型公立大学的一个人流密集区的桌子前经过的人中招募了203人。由于违反了程序或随机分配协议，有六次会议被排除在外，最后的样本为n=197人。为了简化研究程序，我们没有对参与者进行任何调查或收集人口统计信息。参与者获得了糖果和高达1美元的奖金机会。
Participants were randomly assigned to one of two conditions: control (n = 98) or subtraction cue (n = 99). Participants saw the Lego structure (Extended Data Fig.2) and learned from the experimenter (blind to hypothesis) that their task was to change the Lego structure so that it could hold a masonry brick over the head of the figurine without collapsing. The experimenter also demonstrated to the participant how—without any modifications to the Lego structure—the masonry brick would cause a collapse of the structure. The original structure had one Lego brick serving as a pillar that held up the platform for the masonry brick, with three other pillars missing (similar to a one-legged table). Participants could transform the Lego structure and satisfy the goal of the task by adding supports (for example, using Lego bricks to provide the three ‘missing’ legs or adding an entire layer of Lego bricks). Alternatively, participants could transform the Lego structure by removing the corner Lego brick and allowing the platform to rest stably on the solid layer of Lego bricks below.
参与者被随机分配到两个条件中的一个：控制（n = 98）或减法提示（n = 99）。参与者看到了乐高结构（扩展数据图2），并从实验者那里得知他们的任务是改变乐高结构，使其能够在小人的头上顶住一块砖石而不倒塌。实验者还向被试展示了在不对乐高结构进行任何修改的情况下，砖石会导致结构的坍塌。原来的结构有一块乐高砖作为支柱，支撑着砖石的平台，另外三个支柱不见了（类似于单脚桌）。参与者可以改造乐高结构，通过增加支撑物来满足任务的目标（例如，用乐高砖来提供 "缺失 "的三条腿，或者增加一整层乐高砖）。另外，参与者也可以通过移除角落的乐高砖来改变乐高结构，让平台稳定地停在下面坚实的乐高砖层上。
The experimenter said to all participants ‘You will earn $1 if you suc- cessfully complete this task. Each piece that you add costs ten cents’. For those participants randomly assigned to the subtraction-cue con- dition, the experimenter added ‘but removing pieces is free and costs nothing’. In both conditions, the experimenter then affirmed ‘You may alter the structure however you want, and you have as much time as you want. Please let me know when you are done’. Participants then received a written copy of the instructions that the experimenter had delivered (corresponding to their condition), and the experimenter left them alone in a semi-private area to complete the task. When the participant finished, the experimenter recorded the number of Lego bricks that were added, removed and moved, and took a photograph of the transformed structure for record-keeping.
实验者对所有参与者说'如果你成功地完成这项任务，你将获得1美元。你每增加一个棋子要花10美分"。对于那些被随机分配到减法提示条件的参与者，实验者补充说'但移除碎片是免费的，不需要任何费用'。在这两种情况下，实验者都肯定地说："你可以随心所欲地改变结构，而且你有多少时间都可以。当你完成后请告诉我。然后，参与者收到一份实验者传达的书面说明（与他们的条件相对应），实验者让他们在一个半私人的地方单独完成任务。当参与者完成任务后，实验者记录了添加、移除和移动的乐高积木的数量，并为改造后的结构拍了一张照片，以作记录。
We designed study S11 as a follow-up experiment to assess partici- pants’ interpretation of the experiment 1 instructions and—by impli- cation—the plausibility of a choice-based alternative explanation (Supplementary Information section 2.11).
我们设计了研究S11作为后续实验，以评估参与者对实验1指示的解释，并通过暗示--基于选择的替代解释的合理性（补充资料第2.11节）。
Experiment 2.
In the task for experiment 2, participants generated ideas for improving a miniature golf course hole. In this task, partici- pants sequentially listed all of their change ideas (rather than producing only a single transformation). This allowed observation of not only how many people have subtractive ideas, but also the order in which additive and subtractive ideas emerge 27,31 . We recruited on Amazon Mechanical Turk and received 147 valid responses (83 men, 63 women and 1 unspecified; M age = 34.7, s.d. = 10.1 (Supplementary Information section 1.2)). Participants received $0.60 for participating.
在实验2的任务中，参与者产生了改善一个迷你高尔夫球场洞的想法。在这项任务中，参与者按顺序列出了他们所有的改变想法（而不是只产生一个转变）。这不仅可以观察到有多少人有减法想法，还可以观察到加法和减法想法出现的顺序27,31。我们在亚马逊Mechanical Turk上招募，收到了147份有效的回复（83名男性，63名女性和1名不详者；M年龄=34.7，s.d.=10.1（补充资料第1.2节））。参与者获得0.6美元的参与费。
articipants were randomly assigned to one of two conditions: no cue (n = 79) or cue (n = 68). All participants read a vignette asking them to imagine themselves as the assistant manager of a miniature golf course. The vignette showed an image of a miniature golf hole (Extended Data Fig.3) and asked participants to ‘make a list of all the different ways that you might be able to improve the hole without spending a ton of money’.
参与者被随机分配到两个条件中的一个：无提示（n = 79）或提示（n = 68）。所有参与者都阅读了一个小插曲，要求他们想象自己是一个迷你高尔夫球场的助理经理。小插曲显示了一个迷你高尔夫球洞的图像（扩展数据图3），并要求参与者 "列出所有你可能能够在不花费大量金钱的情况下改善球洞的不同方法"。
Advising against ‘spending a ton of money’ was one way that the vignette subtly encouraged all participants to consider subtractive actions. Moreover, we designed the original hole to include opportu- nities for subtractive transformations. For example, participants who wanted to transform the hole to be more challenging could remove the corner bumper that players might use to carom around the corner; and participants who wanted to transform the hole to be easier could remove the sand trap.
建议不要 "花一大笔钱 "是小插曲巧妙地鼓励所有参与者考虑减法行动的一种方式。此外，我们在设计原始洞口时，也包括了减法改造的机会。例如，想把球洞改造得更有挑战性的参与者可以去掉转角处的保险杠，因为玩家可能会用它来绕过转角；而想把球洞改造得更容易的参与者可以去掉沙坑。
By random assignment, the vignette included a cue to participants in the appropriate condition: ‘Keep in mind that you could potentially add things to the hole as well as take them away’. Participants in both conditions then advanced to a screen with space in the survey interface for up to 24 ideas. At the top of this response-elicitation screen, all participants again saw the prompt to improve the hole and—for those in the cue condition—a second cue that ‘you could add or subtract from the current design’. If the cue to ‘add or subtract’ increased either cat- egory of idea, it would suggest that the cue brought new ideas to mind. Because the cue suggests both adding and subtracting, it mitigates any demand effects, in which participants respond according to what they perceive to be the experimenters’ desire.
通过随机分配，小插曲包括对适当条件下的参与者的提示："请记住，你有可能在洞里添加东西，也有可能把它们拿走。然后，两种情况下的参与者都进入了一个屏幕，在调查界面上留出了最多24个想法的空间。在这个反应激发屏幕的顶部，所有的参与者都再次看到了改善洞口的提示，而对于那些在提示条件下的参与者，则是第二个提示，即 "你可以从当前的设计中增加或减少"。如果 "增加或减少 "的提示增加了这两类想法，这将表明该提示使人们想到了新的想法。因为这个提示既暗示了加法也暗示了减法，所以它减轻了任何需求效应，即参与者根据他们认为是实验者的愿望作出反应。
Following the task, all participants provided demographic informa- tion and responded to a manipulation check that asked them to think back to the instructions they read and to indicate whether they had been explicitly instructed that they could add and also subtract, with three response options: ‘yes’, ‘no’ and ‘don’t recall’.
任务结束后，所有参与者都提供了人口统计信息，并回答了一个操作检查，要求他们回想一下他们读过的说明，并指出他们是否被明确指示过他们可以做加法和减法，有三个回答选项。是"、"不是 "和 "不记得"。
Two research assistants, who were blind to condition and hypothesis, independently coded the responses of the participants as one of the following: additive (that is, changes the hole by adding elements or resources), subtractive (that is, changes the hole by removing elements or resources), change (that is, alters some element of the hole without adding or removing anything) or an invalid response (that is, empty or incoherent answer). The coders achieved a high reliability (overall Cohen’s κ = 0.68), and disagreements were resolved through discussion.
两名对条件和假设视而不见的研究助理将参与者的回答独立地编码为下列之一：加法（即通过增加元素或资源来改变洞）、减法（即通过去除元素或资源来改变洞）、改变（即改变洞的某些元素而不增加或去除任何东西）或无效的回答（即空洞或不连贯的回答）。编码员取得了较高的可靠性（总体Cohen's κ = 0.68），分歧通过讨论得到解决。
Experiment 3
Experiment 3 was a close replication of experiment 2. We recruited on Amazon Mechanical Turk and received 165 valid responses (after excluding 13 participants who failed an attention check (Supple- mentary Information section 1.3); 90 men, 74 women, 1 unspecified; M age = 35.7, s.d. = 9.44). Participants received $0.60 for participating.
实验3是对实验2的紧密复制。我们在亚马逊Mechanical Turk上招募，收到了165份有效的回应（在排除了13名未能通过注意力检查的参与者后（补充信息第1.3节）；90名男性，74名女性，1名未指明；M年龄=35.7，s.d.=9.44）。参与者获得0.6美元的参与费。
Participants were randomly assigned to one of two conditions: no cue (n = 87) or cue (n = 78). The procedure was similar to experiment 2, but in experiment 3 instructions asked participants to imagine that they were friends with ‘Mr. Popo’, the owner of another miniature golf course and that ‘For as many summers as you can remember, you and Popo have quietly traded favors. One of you will sneak onto the oth- er’s course late at night and change around one of the holes to make it better. The goal of the favor is to make the hole better, but without completely renovating the hole in a way that would attract the other owner’s attention’.
参与者被随机分配到两个条件中的一个：无提示（n = 87）或提示（n = 78）。实验过程类似于实验2，但在实验3中，指示要求参与者想象他们与另一个迷你高尔夫球场的所有者 "Popo先生 "是朋友，"在你能记得的许多夏天，你和Popo已经悄悄地交换了好处。你们中的一个人将在深夜潜入另一个人的球场，改变其中一个洞的位置，使其变得更好。这个忙的目的是让球洞变得更好，但不能以吸引另一个主人的注意力的方式完全翻新球洞。
As in experiment 2, instructions were identical for the no cue and cue conditions, except that participants in the cue condition also saw a first cue above the hole design (‘Keep in mind that you can add things to the hole or take them away’) as well as a second cue that was displayed above the response boxes (and this time appeared in red-coloured font) and stated ‘Remember that you can add or subtract from the current design’. Next, we administered an attention check. We asked participants to write the word ‘pirate’ as part of instructions embedded within a larger block of text that ostensibly instructed participants to describe the changes they made.
与实验2一样，无提示条件和提示条件的说明是相同的，只是提示条件下的参与者还看到了洞口设计上方的第一个提示（记住你可以在洞口添加东西或拿走它们），以及显示在反应框上方的第二个提示（这次是用红色字体显示的），并指出 "记住你可以从当前设计中添加或减去"。接下来，我们进行了一次注意力检查。我们要求参与者写下 "海盗 "这个词，作为嵌入在一个更大的文本块中的指示的一部分，该文本块表面上指示参与者描述他们所做的改变。
Three research assistants, who were blind to condition and hypoth- esis, coded the responses of participants using the same categories as in experiment 2. We used Krippendorff’s α in this study to accommodate more than two coders rating categorical responses (α = 0.86). They resolved disagreements through discussion.
三名研究助理，对条件和假设是盲目的，使用与实验2相同的类别对参与者的反应进行编码。在这项研究中，我们使用了克里彭多夫的α，以适应两个以上的编码者对分类反应的评分（α=0.86）。他们通过讨论解决分歧。
Experiment 4
Experiment 4 tested whether people overlook sub- traction across different types of transformation goal (specifically when trying to make something better versus worse). The procedure in experiment 4 was similar to experiments 2 and 3, in which participants modified a miniature golf hole. Participants were randomly assigned to read a cue stating that they could add or subtract. Experiment 4 ad- ditionally manipulated whether the goal was to make the hole better or worse, producing the following design: 2 (cue: present versus absent) × 2 (goal: make better versus make worse). We recruited on Amazon Mechanical Turk and received 369 valid responses (after excluding 27 participants who failed an attention check (Supplementary Informa- tion section 1.4); 181 men, 183 women, 5 unspecified; M age = 37.00, s.d. = 11.73). Participants received $0.60 for participating.
实验4测试了人们是否在不同类型的改造目标中忽视了次级牵引力（特别是在试图使某物变得更好与更坏时）。实验4的程序与实验2和3相似，参与者对一个迷你高尔夫洞进行了改造。参与者被随机分配到阅读一个提示，说明他们可以增加或减少。实验4对目标是让球洞变得更好还是更坏进行了常规操作，产生了以下设计：2（提示：存在与不存在）×2（目标：变得更好与变得更糟）。我们在亚马逊Mechanical Turk上招募，收到了369份有效的回复（在排除了27名未能通过注意力检查的参与者后（补充信息第1.4节）；181名男性，183名女性，5名未指明；M年龄=37.00，s.d.=11.73）。参与者获得0.6美元的参与费。
Participants were randomly assigned to one of four conditions: make-better and no-cue (n = 80), make-better and cue (n = 91), make- worse and no-cue (n = 92) or make-worse and cue (n = 106). As in experiment 3, participants read a scenario in which they run a minia- ture golf course and Mr. Popo runs one in the neighbouring town. In the make-better conditions, Mr. Popo was described as a close friend and participants learned that, for many summers, they and Popo had quietly traded favours. Their goal was to make the hole better without completely renovating the hole in a way that would attract the atten- tion of the owner. Participants in the make-worse condition received the same instructions, except that Mr. Popo was described as a friendly rival and participants learned that, for many summers, they had quietly traded good-natured pranks. Their goal was to make the hole worse without completely ruining the hole in a way that would attract the attention of the owner. We included the detail about not drawing too much attention to the change to pre-empt extreme response (espe- cially in the make-worse condition) that would fundamentally alter the hole. Crossed with this goal manipulation, half of the participants were randomly assigned to also read a cue at the bottom of the instruc- tions (‘Keep in mind that you can add things to the hole or take them away’), whereas the other half did not see this cue. On the next page of the task, all participants saw the diagram (the same as experiments 2 and 3) (Extended Data Fig.3), with either the question ‘What ideas do you have for how to improve Hole #6?’ or the question ‘What ideas do you have for how to make Hole #6 worse?’. Participants in the cue conditions additionally saw (in red) the statement ‘Remember that you can add or subtract from the current design’. Participants could write up to 24 ideas. All participants received the same attention check used in experiment 3.
参与者被随机分配到四个条件中的一个：改善和无提示（n = 80），改善和提示（n = 91），改善和无提示（n = 92）或改善和提示（n = 106）。如同在实验3中，参与者阅读了一个场景，其中他们经营一个小型高尔夫球场，而Popo先生在邻近的城镇经营一个高尔夫球场。在改善条件下，波波先生被描述为一个亲密的朋友，参与者了解到，在许多夏天，他们和波波已经悄悄地交换了好处。他们的目标是在不完全翻新洞口的情况下让洞口变得更好，以引起洞主的注意。在 "变坏 "条件下，参与者得到了同样的指示，只是Popo先生被描述成一个友好的对手，参与者了解到，在许多夏天，他们悄悄地交换了善意的恶作剧。他们的目标是在不完全破坏洞口的情况下使洞口变得更糟，以引起洞主的注意。我们加入了一个细节，即不要引起人们对变化的太多注意，以预先阻止会从根本上改变洞口的极端反应（特别是在变坏的情况下）。与这个目标操纵交叉的是，一半的参与者被随机分配到同时阅读指令底部的提示（"请记住，你可以在洞里添加东西或拿走它们"），而另一半则没有看到这个提示。在任务的下一页，所有参与者都看到了图表（与实验2和3相同）（扩展数据图3），其中有一个问题是 "你对如何改善6号洞有什么想法？"或 "你对如何使6号洞变得更糟有什么想法？"。在提示条件下，参与者还看到了（红色）"记住，你可以在当前的设计上做加减法 "的陈述。参与者最多可以写24个想法。所有参与者都接受了实验3中使用的相同的注意力检查。
Three independent coders, who were blind to condition and hypoth- esis, coded responses using the same categories as in the previous experiments (overall reliability, Krippendorff’s α = 0.87), with disagree- ments being resolved through discussion
三个独立的编码员，对条件和假设是盲目的，使用与以前的实验相同的类别对回答进行编码（总体可靠性，Krippendorff's α = 0.87），分歧通过讨论解决。
Experiment 5.
In experiment 5, we instructed participants to transform a digital grid pattern. We designed each original pattern so that it would be incorrectly transformed if participants thought only of additive actions but could be correctly transformed if participants thought of subtractive actions. We recruited on Amazon Mechanical Turk and received 299 valid responses (170 men, 126 women, 3 unspecified, M age = 34.99, s.d. = 9.27 (Supplementary Information section 1.6)). Participants received $0.60 for participating.
在实验5中，我们指导参与者转换一个数字网格图案。我们设计了每个原始图案，这样，如果参与者只想到加法动作，它就会被错误地转换，但如果参与者想到减法动作，它就可以被正确地转换。我们在亚马逊Mechanical Turk上招募，收到了299份有效的回复（170名男性，126名女性，3名不详，M年龄=34.99，s.d.=9.27（补充资料1.6节））。参与者获得了0.6美元的参与费。
Participants were randomly assigned to one of two conditions: con- trol (n = 152) or repeated search (n = 147). Participants learned that they would work on a set of patterns, and read ‘First, please take a moment to familiarize yourself with the workspace. Click below to see how you can change colors on the grid’. On this orientation screen, participants could interact with a 10 × 10 grid that functioned in the same way as the grid(s) in the subsequent trial(s). Half of the blocks for the grid on the orientation screen were already green (the top left and bottom right quadrants), and the other blocks were white (top right and bottom left quadrants). Participants could click any one of the squares to see how it would change the colour.
参与者被随机分配到两个条件中的一个：控制（n = 152）或重复搜索（n = 147）。参与者了解到他们将在一组图案上工作，并读到 "首先，请花点时间熟悉工作区的情况。点击下面，看看你如何改变网格上的颜色"。在这个定位屏幕上，参与者可以与一个10×10的网格互动，该网格的功能与后续试验中的网格相同。定位屏幕上的网格有一半是绿色的（左上角和右下角的象限），其他的网格是白色的（右上角和左下角的象限）。参与者可以点击任何一个方块，看看它将如何改变颜色。
Participants then learned that their focal task was to change a forth - coming pattern ‘so that it is perfectly symmetrical from left to right, and from top to bottom’. Participants also read ‘Obviously, there are many technically correct solutions to this puzzle. However, your challenge is to make it symmetrical using the fewest possible mouse clicks’. The phrase ‘using the fewest possible mouse clicks’ was displayed in bold font. We designed each grid so that making it symmetrical with an additive transformation would require more clicks than would making it symmetrical with a subtractive transformation. Participants could therefore not achieve the correct response without thinking of sub- tractive actions.
参与者随后了解到，他们的重点任务是改变一个即将出现的图案，"使其从左到右，从上到下完全对称"。参与者还读到 "很明显，这个谜题有许多技术上正确的解决方案。然而，你的挑战是用尽可能少的鼠标点击使其对称。用尽可能少的鼠标点击 "这句话是用粗体字显示的。我们设计了每个网格，使得用加法变换使其对称比用减法变换使其对称需要更多的点击次数。因此，参与者如果不考虑次要的牵引动作，就无法获得正确的反应。
Participants in the control condition then proceeded straight to the main task, whereas participants in the repeated search condition learned that they would first ‘run through 3 practice trials’ before com- pleting the main task. In the repeated search condition, participants advanced through three grids, each labelled as ‘Practice Trial’ 1, 2 or 3 (Fig.1a–c). Critically, participants received no feedback about their performance. In both conditions, the critical trial (the dependent vari- able) was labelled ‘Main Task’ (Fig.1d).
控制条件下的参与者随后直接进入主要任务，而重复搜索条件下的参与者则了解到他们将首先 "通过3个练习试验"，然后再进入主要任务。在重复搜索条件下，参与者通过三个网格前进，每个网格被标记为 "练习试验 "1、2或3（图1a-c）。重要的是，参与者没有收到关于他们表现的反馈。在这两种条件下，关键的试验（因变量）被标为 "主要任务"（图1d）。
Experiment 6
In experiment 6, we instructed participants to transform the same series of digital grid patterns used in experiment 5. We recruited on Amazon Mechanical Turk and received 299 valid responses (170 men, 128 women, 1 unspecified; M age = 35.03, s.d. = 9.68 (Supplementary Information section 1.7)). Participants received $0.60 for participating.
在实验6中，我们指示参与者转换实验5中使用的同一系列数字网格图案。我们在亚马逊Mechanical Turk上招募，收到了299份有效的回应（170名男性，128名女性，1名不详；M年龄=35.03，s.d.=9.68（补充资料第1.7节））。参与者获得了0.6美元的参与费。
Participants were randomly assigned to one of two conditions: lower cognitive load (n = 151) or higher cognitive load (n = 148). After par- ticipants learned the basic rules and aim of the task (which were the same as experiment 5), we introduced the cognitive load manipulation.
参与者被随机分配到两个条件中的一个：较低的认知负荷（n = 151）或较高的认知负荷（n = 148）。在参与者了解了任务的基本规则和目的（与实验5相同）后，我们引入了认知负荷操纵。
Participants randomly assigned to the lower-load condition were instructed to complete the grid tasks while sitting naturally. These instructions included an illustration of a forward-facing head. Par- ticipants in the higher-load condition were instructed to complete the grid tasks while moving their head around in a circle, focusing on their chin. These instructions included an illustration of a forward-facing head with arrows to indicate circular movements 33
被随机分配到低负荷条件的参与者被指示在自然坐着的时候完成网格任务。这些指示包括一幅头朝前的插图。在高负荷条件下，参与者被要求在完成网格任务的同时，将他们的头围成一圈，重点放在他们的下巴上。这些指示包括一个朝前的头的插图，用箭头表示圆周运动 33
Experiments 7 and 8
Experiments 7 and 8 provided a conceptual rep- lication of experiment 6, using a university-based participant pool and a different concurrent-task manipulation 22,32 . Experiment 7 took place in a laboratory setting. We recruited 286 undergraduates enrolled in introductory psychology courses (88 men, 197 women, 1 unspecified; M age = 18.82, s.d. = 1.61; no exclusions were necessary (Supplementary Information section 1.8)).
实验7和8提供了一个实验6的概念再现，使用了一个以大学为基础的参与者库和一个不同的并发任务操纵22,32。实验7是在实验室环境下进行的。我们招募了286名心理学入门课程的本科生（88名男性，197名女性，1名不详；M年龄=18.82，s.d.=1.61；没有必要排除在外（补充资料1.8节））。
Participants were randomly assigned to one of two conditions: lower load (n = 140) or higher load (n = 146). All participants first interacted with the grid workspace and read instructions for the task. Then, all participants learned ‘During this task, numbers will be scrolling by’. In the higher-load condition, participants read ‘As you are working on making the grid symmetrical, keep an eye on the number stream. Every time you see a ‘5’ enter the screen, press the ‘f’ key on your keyboard. The computer will record the accuracy of your responses’. In the lower-load condition, participants read ‘As you are working on making the grid symmetrical, you can just ignore these’. The digit streams contained approximately 20% ‘5’ digits and scrolled at a rate of approximately 4 digits persecond, with up to approximately 36 digits on the screen at any given time.
参与者被随机分配到两个条件中的一个：低负荷（n = 140）或高负荷（n = 146）。所有参与者首先与网格工作区进行互动，并阅读任务的说明。然后，所有参与者了解到 "在这项任务中，数字将被滚动显示"。在高负荷条件下，参与者读到 "当你在做网格对称的时候，要注意数字流。每当你看到一个'5'进入屏幕，就按下键盘上的'f'键。计算机将记录你的反应的准确性。在低负荷条件下，参与者阅读 "由于你正在努力使网格对称，你可以忽略这些"。数字流包含大约20%的'5'个数字，并以每秒钟大约4个数字的速度滚动，在任何给定的时间内，屏幕上最多有大约36个数字。
Participants then viewed the four grids in Fig. 1, one at a time in ran- domized order. Each grid was arranged such that one quadrant of the grid contained extra marks. As in experiment 6, participants could achieve symmetry by adding corresponding marks to the other three quadrants or by removing the extra marks, with the latter approach requiring fewer clicks. Following the task, participants responded to the manipulation check question ‘How difficult was this task?’ on a scale from 1 = not at all difficult to 7 = extremely difficult.
然后，参与者观看了图1中的四个网格，按顺序一次一个。每个网格的排列方式是，网格的一个象限含有额外的标记。与实验6一样，参与者可以通过在其他三个象限增加相应的标记或删除额外的标记来实现对称性，后一种方法需要较少的点击次数。任务完成后，参与者对操纵检查问题 "这个任务有多难？"作出回答，评分标准为1=完全不难，7=极其困难。
Experiment 8 directly replicated experiment 7 using a larger sam- ple and online administration. Procedures were identical to experi- ment 7, except that participants completed the study online instead of in person. We recruited 600 undergraduate students from a large public university in the USA to respond to an online study for partial course credit. We received 568 valid responses (after excluding 17 dupli- cates, 12 for not responding to all four grid tasks, and 3 for making no changes to the grids (Supplementary Information section 1.9); 200 men, 367 women, 1 unspecified, M age = 18.84, s.d. = 1.67). As in experiment 7,participants were randomly assigned to either a lower-load condition (n = 290) or a higher-load condition (n = 278).
实验8直接复制了实验7，使用更大的样本和在线管理。实验程序与实验7相同，只是参与者是在网上完成研究，而不是亲自参与。我们从美国一所大型公立大学招募了600名本科生，让他们对一项在线研究作出回应，以获得部分课程学分。我们收到了568份有效的答复（在排除了17个重复的人、12个没有对所有四个网格任务作出反应的人和3个没有对网格作出改变的人之后（补充资料第1.9节）；200个男性，367个女性，1个未指明，M年龄=18.84，s.d.=1.67）。与实验7一样，参与者被随机分配到低负荷条件（n = 290）或高负荷条件（n = 278）。
