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Dual n-Back is a kind of cognitive training intended to expand your working memory (WM), and hopefully your intelligence (IQ1).
The theory originally went that novel2 cognitive processes tend to overlap and seem to go through one central bottleneck. As it happens, WM predicts and correlates with IQ3 and may use the same neural networks4, suggesting that WM might be IQ5. WM is known to be trainable, and so improving WM would hopefully improve IQ. And N-back is a family of tasks which stress attention and WM.
Later research found that performance and improvement on N-back seems to correlate better with IQ rather than classic measures of WM like reciting lists of numbers, raising the question of whether N-back works via increasing WM or by improving self-control or improving manipulation of WM contents (rather than WM’s size) or somehow training IQ directly.6 Performance on DNB has complicated correlations with performance on other tests of working memory or IQ, so it’s not clear what it is tapping into. (And the link between WM and performance on IQ tests has been disputed; high WM as measured by OSPAN does not correlate well with performance on hard Raven’s questions7 and the validity of single tests of WM training has been questioned8.)
Brain Workshop offers many modes, some far more elaborate than simple Dual N-back; no research has been done on them, so little can be said about what they are good for or what they train or what improvements they may offer; Jaeggi 2010 seemed to find Single N-back better than Dual N-back. Some of the more elaborate modes seem to focus heavily on shifting the correct response among various modalities - not just sound, but left/right, eg. - and so stress context switches; there are results that task switching can be trained and that it transfers9, but how useful this is and how well the BW modes train this are unknown.