Letters (and Systematicity)

The second manipulation is (to our knowledge) a novel one for the Swaps task. The traditional implementation of the Swaps task includes a fixed three letter arrangement (e.g., T Q X) with varying number of swap steps (Stankov, 2000). However, as described earlier, this manipulation relates primarily to attentional control, since the actual binding demands of the task remain the same regardless of the step that the respondent is up to: there are always three letters to work with. By increasing the number of letters, we increase the number of

constituent elements (letters) involved in each step – the binding capacity required is

increased. Although each independent step still only requires the exchange of two letters (two letters are being unbound, exchanged, and bound to new positions), the ‘capacity’ demands of the task are increased because the full set of letters constitute additional bindings in the direct access region: more letters (contents) and more positions (contexts) need to be worked with throughout the problem. It should be cautioned now that the distance of these swaps and the resulting systematicity does impact on these capacity demands – this section will return to this point shortly. For now, it is simply important to outline that the current experiment includes three levels of letters, including the default level (3-letter/3L) and two additional levels (4L and 5L); reflecting (all else being equal) increases in binding capacity. We expect to see decreases in performance as the number of letters increases, as with other binding increases (e.g., Chapters III-V). Unlike steps (attentional control), we do expect to see covariation of this linear performance effect of Letters with Gf, because the additional bindings increase the capacity demands on the direct access region (Oberauer et al., 2007), which we have observed in earlier chapters. The additional bindings demanded in the access-

the LST in 4D items compared to 2D items (though this was not a linear complexity effect because 3D items failed to consistently differentiate from 2D items).

There are two provisos to consider for the Letters manipulation. The first is that the number of letters could be considered raw storage capacity, rather than binding capacity. As detailed throughout the thesis, the current perspective is that the direct access region is limited through limits on binding capacity, rather than the more ambiguous ‘storage capacity’. Through earlier studies in this thesis, we concluded that ‘storage’ capacity could refer to both active and passive elements (i.e., bound within direct access, and passively activated but outside direct access), but passive elements did not seem to relate to Gf (Bateman, 2015; Chapter IV). Binding capacity more specifically refers only to active

relations in the direct access region. The next concern then, is whether it is possible that some letters within a letter set of a Swaps problem could be considered ‘passive’. This is related to the second proviso.

The second proviso is more complex, to the point it requires an additional experimental manipulation. As we have identified in earlier chapters, problems of high complexity can be systematically chunked down, depending on how systematic the elements are. This is particularly important to a manipulation of Letters. In the basic Swaps task, there are only three letters. All three letters must be used in problems containing two or more steps, because if only two letters are used, then consecutive steps would simply be repeating (or reversing) the prior step, cancelling both steps out. For instance, in the item [T Q X | Swap 1 with 2 | Swap 2 with 1], the answer is simply [T Q X] because the two swaps used the same two letters. Thus, all three letters must be used within two consecutive steps to ensure this does not occur. This same restraint does not apply to items with more than three letters, because the three-letter logic that ensures steps are not repeated can be applied to four letters, effectively leaving the fourth letter out of all the steps. This also applies to five letters, except

that now two of the five letters can be excluded from the instructions. This has important implications for our interpretation of the Letters manipulation as being differentially demanding of binding capacity because, as we know from the ACT (Chapter IV), the systematic reduction of capacity demands can lead a three-binding problem to be completed as a one-binding problem. In this case, a five-letter problem can be solved as a three-letter problem with the simple application of systematicity. For instance, consider the item [T Q X B L | Swap 1 with 2 | Swap 3 with 2 | Swap 1 with 3]. In this item, the two adjacent letters of [B L] can be kept systematically fixed throughout the problem. The item can be solved as a 3- letter item with [T Q X] becoming [X T Q], then the [B L] can simply be addended to the response after the steps have been resolved as [X T Q B L]. Although the 4L and 5L conditions are novel, prior evidence from the Swaps task demonstrates the importance of considering the position of Letters. Unpublished data collected by Birney (n.d.-a) indicates that the distance of the swap determines the likelihood of the error: a distant swap (Swap 1

with 3) leads to higher error rates than a close swap (Swap 1 with 2). Our findings from the

ACT study in Chapter IV indicate this could be another example of the impact of

systematicity (Halford et al., 1998) where the isolated digit in the close swap (e.g., the ‘3’ in

Swap 1 with 2) reduces the binding demand because it can be held systematically fixed

during the unbinding/rebinding process (like our access-fixed condition). Although the current study does not specifically consider the positioning, this Birney (n.d.-a) data nonetheless demonstrates the important of considering how the increase in the number of letters influences more than just the overall binding capacity demands.

Although we can record the steps of each item, the nature of increasing letters means that items of higher letters and fewer steps have a higher chance of incidental systematicity. Because the Swaps problems would be randomly generated, this may result in inadvertent bias in items of higher letters on aggregation of the conditions just due to the increased

number of permutations that exclude one or two letters. Thus, instead of letting systematicity occur naturally, we experimentally manipulated the presence of systematicity as a third manipulation (Steps, Letters, Systematicity). Systematic items were generated using 3L generation logic only, effectively reducing the binding demands of all systematic items to 3L. Specifically, 4L systematic items would have one letter fixed in position (not used in any swap steps) while 5L systematic items would have two adjacent letters (a bigram) fixed in position (not used in any of the swap steps). Non-systematic items were generated with code that ensured all letters were used where possible. Because 3L items must use all letters in the swaps (otherwise they simply reverse the same swap repeatedly), 3L items would not be included in analyses of systematicity (i.e., 3L items are generated identically in the systematicity ‘on’ and systematicity ‘off’ conditions). Although we do not have any theoretical reason to suspect that 4L and 5L should differ (since both rely on 3L logic), the fixedness of one letter as opposed to a bigram may still cause some differences. Thus, we first consider 4L and 5L items independently for the purpose of verifying their equivalence in the further investigation of systematicity. We expect trials with systematicity on to be easier than those with it off. The increase in accuracy for having systematicity on for 4L and 5L items should end up with performance similar to that seen in 3L items, minus any deficit related to the additional storage of a single letter (4L) or bigram (5L), which we do not anticipate being substantial. There may however, be an interaction with Steps, as the benefit of systematicity is amplified for items with higher steps, because the fixed letters are held in place for longer. Given the results of the ACT, we would expect participants higher in Gf to be more capable of dealing with non-systematic items, where the binding capacity demands are highest.