Recursion: The Concept

Recursion is used in a variety of disciplines ranging from math, to computer science to linguistics. Recursion is one of the central ideas of computer science – where a function can call itself from within its own code, allowing for very powerful computation. Recursion in computer science – as in the recursive n-back – is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem.

What is recursion? Recursion occurs when a thing is defined in terms of itself. For instance, here is a recursive definition of one’s ancestors:

For example, the following is a recursive definition of a person’s ancestors:

One’s parents are one’s ancestors (base case).
The ancestors of one’s ancestors are also one’s ancestors (recursion step).

Or here is a recursive solution for a journey of distance (d) – illustrated by Cyber Cat.
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The Recursive N-Back: Unique to i3 Mindware

This state-of-the-art recursive n-back game mode in the upgraded i3 Mindware enables you to target the ‘holding capacity’ of both ‘horizontal’ and ‘vertical’ dimensions of your mental workspace.

Normal dual n-back training only trains capacity in one dimension of your mental workspace. If you look at the diagram of a mental ‘problem space’ below you can see that in solving problems, making decisions or planning, you typically need to think through different options or hypotheses while also being able to return to the higher level compare them, or rule one ‘branch’ of possibilities out and then refocus on another branch.

The recursive n-back is designed to train this ability to hold the bigger picture in mind – a kind of ‘place-holder’ of the overall problem space of options – while being able to zoom in with your attention on different options, one by one.

In this diagram alpha (in red) is the focus of your attention, the branching points are the different options or hypotheses in your mental workspace.

mental workspace — Mental workspace for working memory

The logic of the recursive n-back game is shown below (click on the image to enlarge it). The n-back is in the spatial mode only (not audio). While keeping track of n-back matches in the normal way (pressing the ‘F’ key whenever there is a match), you also need to keep track of the locations of where the matches occur, and press the space bar whenever there is an n-back match at that higher ‘recursive’ level too. The starting default setting is a regular n-back = 2, with a recursive n-back = 1 (as shown in the diagram). If you are accurate at the recursive level, the n-back level will increase from 1 to 2 (as shown). Ideally, you want to be doing this game at a recursive n-back = 2, while trying to increase the standard n-back level as much as you can (e.g. to a 3,4 or 5 back).
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recursive n-back example — Recursive N-Back

The recursive n-back level at any point in the game is shown in the locations circled in red here.
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Training to Target Fluid Intelligence (IQ) Gains

Fluid intelligence (Gf) is your the ability to see relationships, abstract concepts, reason and problem solve in new situations. It helps us learn rapidly, think critically and innovate. It is not the same as our learned knowledge and skills, but it enables us to more efficiently build on our our existing knowledge-base.

Fluid intelligence is the hub of the different ‘broad abilities’ of intelligence (such as visuospatial and verbal intelligence) measured by full scale IQ tests. If your training results in neuroplasticity changes in fluid intelligence you are training the core network of your overall intelligence, as measured by IQ tests.

i3 Mindware Settings for Maximum Fluid Intelligence IQ gains

1. Master The Dual N-Back Game

If you are not already familiar with the classic dual n-back, you need to train with this first selecting ‘DNB Training’ when you set up your first Profile. You need to reach at least a 2-back level consistently before progressing to more challenging games.

Note that when you set up your Profile for this practice, deselect the ‘IQ Puzzles In Training’ option. You can select that later.

After becoming familiar with the dual n-back, I would recommend at least 1G mode (you could also try 2G or 2G+, but what is critical for this challenge is at least 1G which trains output gating (as show in the ‘cognitive elements’ model above).

2. Ensure You Always Play With Interference On

Always switch on the interference control option, shown below. If you can manage it, also switch on the ‘Response Switching’ option – which randomly changes the which hands you respond with when playing the n-back.

These enable you to selectively train disengaging – one of the key processes of fluid intelligence. Applying fluid intelligence can be though of as ‘offline’ reasoning and hypothesis testing – such as when you solve matrices IQ tests, and you try to figure out the underlying rules in the patterns.

“In the realm of problem solving (Gf), high working memory capacity allows a person to represent and maintain a problem accurately and stably, so that ‘hypothesis testing’ can be conducted. However, as hypotheses are disproven or become untenable, disengaging from outdated problem solving attempts becomes important so that new hypotheses can be generated and tested.” (ref)

3. Create One Profile With Output Gating

I recommend alternating your training between two game modes from one session to the next. For one Profile you set up (you can create as many as you want), choose either 1G or 2G+ game modes (the latter is much more challenging, but both have the output gating needed for fluid intelligence gains.)

“output gating is specifically at the root of the developmental change in higher order rule use…..training-induced increase in cognitive flexibility is… mediated by more efficient output gating of abstract rule representations that support generalization, learning and fluid reasoning.” (Unger and colleagues, 2016)

4. Create One Profile With Recursive N-Back

For the other Profile, select the Recursive N-Back game mode. The benefits of this for fluid intelligence are explained above.

Note that when you set up your e.g. 1G and Recursive N-Back Profiles, only select the ‘IQ Puzzles In Training’ option for ONE of them. You can deselect it for the other.

5. Train for 30-40 Sessions in Total

You need to train for up to 40 Sessions in total to benefit from long-term neuroplasticity changes to the underlying neuro-circuitry of your fluid intelligence.

The Recursive N-Back