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It seems that researchers agree that physical exercise increases cognitive abilities. This seems to work universally for all ages: children, adults and old people.

It is suggested that everyone should exercise for half an hour at least 3 times a week. I'm wondering if there are any studies which try to find dependencies between the amount of training and the effect of it on cognitive abilities?

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so to clarify, you're not asking about what is optimal for physical health and fitness, you are asking about optimal for cognitive functioning? – Jeromy Anglim Nov 20 '13 at 6:14
    
@Jeromy Anglim That's correct. – Max Nov 20 '13 at 7:01
    
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It's unclear whether the question is about physical exercise or cognitive exercise. If the latter, it's a duplicate of cogsci.stackexchange.com/questions/4175/… – user7759 Nov 12 '15 at 5:14
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I've clarified the question – Max Nov 12 '15 at 12:17

Yes, there are several studies which found links between the amount of training and the effect of it on cognitive abilities. See the below for references and summaries of some of these:

Jaeggi, Susanne M., et al. "Improving fluid intelligence with training on working memory." Proceedings of the National Academy of Sciences 105.19 (2008): 6829-6833.

Jaeggi et al. found that dual n-back could improve fluid intelligence. This approach has been developed into a game, and this game which can be freely played online.

However, more recent research has failed to support its effectiveness for normal individuals, although I have read anecdotal evidence for effectiveness in increasing mental ability in older adults or individuals with ADHD.

Overall, it appears that the literature suggests that brain training does not work, that "the scientific literature does not support claims that the use of software-based “brain games” alters neural functioning in ways that improve general cognitive performance in everyday life, or prevent cognitive slowing and brain disease."

http://www.scientificamerican.com/article/brain-training-doesn-t-make-you-smarter/

However, working your brain hard through education has been linked to increases in IQ so maybe that is the best approach.

Winship, Christopher, and Sanders Korenman. "Does staying in school make you smarter? The effect of education on IQ in The Bell Curve." Intelligence, Genes, and Success. Springer New York, 1997. 215-234.

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Please let me know if you want more detail, or clarification on any of these points. – Peter Slattery Nov 14 '15 at 0:22

Yes, there is an interaction between physical fitness and the effect of physical exercise on cognitive improvement.

"The few available studies (Gutin, 1966; Weingarten, 1973; Zervas, Danis and Klissouras, 1991) suggest, on the whole, that an interaction between acute and chronic exercise effects exists. The interaction seems to consist of larger benefits of acute exercise on cognitive performance for highly fit individuals than for their less fit counterparts."

"Zervas, Danis and Klissouras (1991) examined the effects of acute physical exertion on performance on a visual discrimination task in pre-adolescent twins, who were randomly assigned to a six months training or nontraining period. At the end of this period, they performed the cognitive task twice, before and after an acute bout of 25 min treadmill running. A third group of age-matched controls performed the cognitive task twice, but resting between the two test sessions. Acute exercise led to better performances in the case of both trained and untrained groups and, more interestingly, the average improvement was largest for the trained group, suggesting the existence of interactive effects of acute and chronic exercise."

Source: Caterina Pesce: An integrated approach to the effect of acute and chronic exercise on cognition: the linked role of individual and task constraints http://onlinelibrary.wiley.com/doi/10.1002/9780470740668.ch11/summary

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