Aerobic-Exercise and resistance-training interventions have been among the least effective ways to improve executive functions of any method tried thus far

We appreciate that our colleagues, Hillman et al. (2018), would like to conclude that aerobic exercise improves executive functions (EFs).We, too, would like to conclude that.However, the facts thus far indicate that aerobic exercise interventions (with greater or lesser cognitive and motor skill demands), resistance training, and yoga have produced the weakest results for improving EFs of any method tried.We refer to that evidence briefly below and discuss how physical activity (in ways that researchers have largely ignored) may indeed help to improve EFs.All of this is discussed in far greater depth in Diamond and Ling (in press), which systematically reviews 179 studies reported across 193 papers.We would like to mention three important caveats: First, "weakest" evidence does not mean "no" evidence; 44% of aerobic-exercise studies and 25% of resistance-training studies have found at least suggestive evidence of EF benefits.Thus, some studies have demonstrated EF benefits from these activities.Compare that, however, to 79% of Cogmed ® studies and 100% of studies of taekwondo, t'ai chi, Chinese mind-body practices, and Quadrato motor training (which can all be considered mindfulness practices involving movement) finding at least suggestive evidence of EF benefits (see Table 1 below).Second, our focus is exclusively on EF outcomes.We are not saying that physical activity has shown weak benefits across all domains; we are saying that physical activity interventions have thus far shown weak benefits specifically for EFs.Ours was never meant to be a review of the whole exercise-cognition literature nor a review of the physical fitness, health, or neural benefits of exercise.Third, we are not saying that physical activity does not benefit EFs.There are reasons to think it does.We are saying that interventions used to try to prove that have generally met with disappointing results.As scientists we need to set the record straight.We show below that almost all of the many criticisms leveled by Hillman et al. ( 2018) of the summary of our review presented in Diamond and Ling (2016) are wholly incorrect or at best misguided.It does not advance science to mischaracterize what we said.We acknowledge, however, that two of the criticisms leveled by Hillman et al. are well-taken; we apologize for those errors.Correcting those errors, though, does not change our conclusions. The overwhelming preponderance of evidence is that resistance training and aerobic exercise interventions have thus far generally not been successful in improving EFsDiamond and Ling (2016) was part of a special issue presenting invited addresses from the Flux International Society for Integrative Developmental Cognitive Neuroscience Meeting in 2014.Both that paper, and the invited address on which it was based, were explicitly a brief summary of the initial findings of the systematic review by Diamond and Ling (in press).Diamond and Ling (in press) is an especially comprehensive and extensive review of interventions, programs, and approaches that have tried to improve EFs: "Previous reviews have focused on the large literature on cognitive training approaches to improving EFs or the large literature on physical activity approaches to improving EFs, often concentrating only on studies in children or adults.This review looks at all the different methods that have been tried for improving EFs (including cognitive training and physical exercise, but also all the other approaches) and at all ages (not only children or only the elderly)" (Diamond and Ling, in press) To locate studies for review, "we searched PubMed and PsycNET for all publications that had any keyword, or word in the title or abstract, from both of the following sets (Set 1: evaluate, evaluation, intervention, program, randomized control trial, train, or training; Set 2: attention (apart from Attention Deficit Hyperactivity Disorder [ADHD]), cognitive control, cognitive flexibility, EF, inhibition, inhibitory control, fluid intelligence, mental flexibility, reasoning, self-control, self-regulation, set shifting, task switching, or WM)" (Diamond and Ling, in press).Initially that search was limited to papers published by 2014.(That search did not pick up some important papers, such as the seminal one by Kramer et al. (1999), since none of our search terms was in its title, "Ageing, fitness and neurocognitive function," and since it had no abstract or keyword list, where terms included in our search might have appeared.)Publication of Diamond and Ling (in press) had been expected in early 2016.When that was delayed we used the time to (a) systematically investigate the references cited in papers that had met our search criteria for still more studies meeting our 11 inclusion criteria (hence Kramer et al.