# Visual search: complexity of positive vs negative search tasks

Thinking about experiments where participants perform visual search tasks, I remember hearing in a Cog Psych lecture that if the instructions of the task were of the form "find the element that has property X", the participants would accomplish the task faster and with greater ease than when the instructions were of the form "find the element that does not have property Y".

It was then discussed that this exemplifies one of the themes in cognitive psych: The cognitive processes handle positive information better than negative information. Is this positivity effect?

I wonder if there is something about the second task that is algorithmically more complex than the first. Would a computer show the same slow-down for these tasks? Anyone know of any research exploring this?

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Building on @JohnPick's answer and my comment, but being a little bit more formal. The difference can be explained by the difference between parallel versus sequential processing, and the difficulty of the predicate being evaluated. Your specific question is answered by Treisman (1985) (which I summarize in the second section) but I try to provide a more general explanation.

### Basic idea

Whenever we say "does the element have property $X$", we usually pick a very simple property for $X$, which can be checked quickly. On the other hand a predicate like "does not have property $Y$" becomes something like "has propert $\neg Y$" and is usually a much more difficult property to evaluate. Thus, I expect the main problem is not in the negation, but the fact that $X$ is usually much faster to evaluate than $\neg Y$. In general, we would expect similar effects with other experiments that use a very easy property $X$ versus a very difficult but still positive property $Z$.

However, if this was the only factor, we would only see a constant-factor slow-down, which would we expect to be interpreted as quantitative but not qualitative slow down. This is where we throw in parallel processing. If we assume that the vision system is capable of highly parallel processing, but the difficulty of the property evaluation involved must be very low or we need to switch to sequential processing. In a computer, think GPU: the GPU can do many many simple calculations in parallel, but we have to use the slower CPU to do difficult computations one at a time.

### Relevant literature support

Classic work like Treisman (1985) suggests that my assumption of very bounded computations being done in parallel, while more complicated properties require attention and sequential processing is a reasonable one. In particular, Treisman completely answers your question:

It suggests that search for the presence of a visual primitive is automatic and parallel, whereas search for the absence of the same feature is serial and requires focused attention.

### Testing the theory with non-negative properties

To test my whole theory we can consider the following experiments. We present the participant with $N$ integers $r_1, ... r_N$ arranged randomly in the visual field, each integer is colored $c_1, ... , c_N$. We ask one of two possible questions:

1. Property $X$: Name a green number, or
2. Property $Z$: Name a number divisible by $3$.

As we increase $N$ from $1$ up to some reasonable limit, we get a function of reaction times $f_X(N)$ and $f_Z(N)$ for the two cases:

1. If both predicates ($X$ and $Z$) are processed in the same way (i.e. ever both parallel or both sequential), then we expect that $\forall N \; \frac{f_X(N)}{f_Z(N)} \approx \frac{f_X(1)}{f_Z(1)}$. In other words, we expect just a constant slow-down from the fact that checking in a single number is green is easier than checking if it is divisible by $3$.

2. If $X$ is processed in parallel, while $Z$ is not, then we expect $\forall N \; \frac{f_X(N)}{f_Z(N)} > \frac{f_X(N + 1)}{f_Z(N + 1)}$. In other words, as we add one more item to the visual field, the parallel processing is slowed down significantly less than the sequential processing.

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Treisman did not explain this phenomenon in terms of different task difficulties. Rather she suggests differences in the activation of feature maps. For the "Find X" task, she assumes that the feature map for X shows a well defined focused activation spot, whereas, for the "Find ~X" she assumes that activity spreads all over this feature map with only a small decrease at the position of the target. –  H.Muster May 24 '12 at 6:41
@H.Muster I am not saying she explained it in terms of task difficulties, I am suggesting that her work makes my assumption "a reasonable one". In that there are two types of processing observed: highly parallel pre-attentive and serial post-attentive. I think my answer is structured pretty poorly right now, and I will try to restructure by moving the Treisman answer to the top and my conjecturing and analogies below. –  Artem Kaznatcheev May 24 '12 at 16:32
But your theory explains the phenomenon in terms of differences in task difficulties (you argue that not-Y usually is more difficult to evaluate). However, the phenomenon is about the difference between evaluating X and not-X, that is, there is no difference in task difficulty. –  H.Muster May 24 '12 at 20:42
@H.Muster not-X is almost always a more difficult task than X. –  Artem Kaznatcheev May 24 '12 at 23:13
That's not what Treisman said. She just observed that people are faster "finding a red square" compared to "finding something that is not a red square". Actually, the fact that the difficulty of the tasks similar makes this observation interesting. If the tasks would differ in difficulty, this observation would be rather trivial, wouldn't it? –  H.Muster May 25 '12 at 5:57

I would doubt that the effect you described is an example for the positivity effect, which is a form of attributional bias, rather than connected to basic perceptual phenomena.

Instead I think that the experimental results you described can be explained by a priming effect. Priming describes the phenomenon that the exposure to one stimulus influences the processing of following stimuli. If the first stimulus shares perceptual, semantic, or conceptual similarities with the next stimulus, processing is enhanced (positive priming). If it provides conflicting information, processing can be depressed (negative priming).

Would a computer show the same behavior for these tasks?

Attempts to explain (positive) priming effects usually discuss an activation of associated memory contents, which, in turn, lead to enhancements in the following processing steps.

Since memory access is often indeed a limiting factor of computer performance, priming effects can possibly observed with computers, too. Computer have different types of storage systems which differ in access speed (e.g., hard disc, RAM, cache). For instance, information that is (pre-)loaded into cache memory (which is limited) can be accessed faster than information that is stored on the hard disc. Since it is context dependent which information is in cache memory at a point in time (i.e., it depends on the things you are doing at the moment), memory contents connected to the things you do right now are probably accessed faster (because they are in the cache) than other memory contents, hence, a priming effect.

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As others have already noted this doesn't seem like a positivity effect. However, what you are describing is an asymmetry in search. This means that it's easy to do things one way (looking for a specific feature) than the other (looking for the absence of a specific feature).

There's a great introduction and review of the literature relating to this available in a published paper which is also online here:

http://search.bwh.harvard.edu/pdf/IntrotoSearchAsym.pdf

Note also that the paper I've linked to comes from a special issue of a journal in which there are several other papers which deal with search asymmetries.

UPDATE: New paper just out, on exactly this topic: http://psycnet.apa.org/journals/xhp/38/3/580/

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This is off the top of my head. No references to the literature.

Assuming the elements are all in the subjects's present visual field, the brain interprets the two tasks as:

• Positive task: Property $X$ is somewhere in your present visual field and thus can be seen immediately. Tell me which element has that property. [2 steps]
• Negative task: Search the $n$ elements in your visual field until you find the one that doesn't have property $Y$. [$\frac{n}{2}$ steps, on average]

In contrast, an unintelligent computer program would use an exhaustive search algorithm for both tasks and thus require $\frac{n}{2}$ steps, on average, for either task.

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this is not a fair comparison between human and computer. You are allowing a human to do parallel processing in the first case by saying "thus can be seen immediately" while you force the computer to do only sequential processing. This would be a poor model. –  Artem Kaznatcheev May 24 '12 at 3:02