ABSTRACT

Background: Based on the studies which have investigated conscious and unconscious processes, simple arithmetic operations such as addition and multiplication can be automatically processed in the brain and affect subsequent responses. However, most studies have focused on addition and multiplication of one-digit numbers. In this research we used subliminal priming paradigm to assess automatic retrieval of subtraction operation for the first time.  

Objectives: The aim of this study was to use a subliminal priming paradigm in a naming task and investigate the automatic and unconscious processing of the subtraction operation. Research of this kind can help us determine different levels of unconscious and conscious processing in the brain.

Materials and Methods: Forty-five graduate student in psychology at the Faculty of Education and Psychology, University of Tabriz (between 18 and 25 years; mean 20.7, SD=2.7) participated in the experiment. For presenting the stimuli, an open-source software (DMDX) was used and presented on a 15-inch monitor. In the experiment, in the congruent condition, the prime was congruent with the target in terms of subtraction calculation result and in the incongruent condition there was no logical connection between the two stimuli. The vocal reaction time (RT) of participants was recorded and paired t-test analysis was conducted for comparison of the two conditions.

Results: The data showed that naming the target by the participants is carried out faster when the two stimuli are congruent with each other in terms of the result of the operation.

Conclusion: These findings may have implications on the levels of mathematical operations. In conclusion it seems that the calculation of one-digit numbers can happen at the level of simple neuronal circuits and may be carried out without conscious-awareness. The findings confirm the fact that calculating subtraction for one-digit numbers does not require conscious effort and can be processed automatically.

Keywords: Unconscious (Psychology); Task Performance and Analysis; Mathematical Computing

Introduction

Evaluation of conscious and unconscious processes in the brain is an important effort in understanding the human mind and its operation. Which levels of cognitive functions are unconscious and which need to be carried out through conscious awareness? This question is now one of the most important issues and interdisciplinary research in various fields of cognitive science and philosophy is investigating it [1]. The aim of this line of research is to investigate unconscious and conscious processing and determine to what extent and at what levels, unconscious processes are executed in the brain. According to the current neuroscience research, consciousness is linked to most capacities of the mind which are unique to humans and the unconscious mind is incapable of solving them. However, findings have shown that many cognitive functions including meaning extraction [1,2], cognitive control [3], emotion [4], agency [5], action selection [6], and political behavior [7] can also be processed unconsciously.

In addition, mathematical operations are also a part of the unconscious processing and it seems that simple neuronal circuits are responsible for their implementation [8]. Over the past two decades, neuroscientists proposed different mechanisms for unconscious mathematical operations and it has become one of the most important issues in the study of consciousness [9]. In general, most researchers agree that solving mathematical problems unconsciously occurs in adults due to retrieval of prior knowledge representations. However, the exact mechanisms of these processes are not yet fully understood. Some have  suggested that mathematical operators lead to the final solution issues by activating the related neural pathways unconsciously [10,4]. According to this view, mathematical facts are stored in a network of neural links in the brain; these networks include operators and nodes that represent a simple mathematical operation [11]. As a result, the operation for a mathematical problem like (2 + 3) leads to the activation of the node within the numbers (i.e., 2 and 3) and this activation is extended to deeper links, including the mathematical operation (addition) itself. As a result, representation of mathematical operations is carried out through some kind of spreading activation in nodes of networks and needs minimal cognitive resources. Regardless of which neuronal circuits are involved in mathematical operations, the general consensus is that these processes can be performed automatically and therefore do not need conscious awareness. This issue is the main subject matter of the present study.

So far studies showed that arithmetic operations of one-digit numbers can be carried out unconsciously. In these studies in order to prime a simple mathematical operation (such as 3×2) the operation is presented briefly (between 30 to 50 ms), with pre and post masks. Although, this process prevents entering the operation into conscious awareness, it can be processed in subliminal levels and facilitate recognition of the stimulus target. The same paradigm was used in this study by subliminal priming for the subtraction operation and repeats the results that subliminal priming of the subtraction operation can facilitate recognition and naming of the target number. In particular the current study suggests that participants can practice subtraction for one-digit numbers without conscious and deliberate efforts.

Materials and Methods

Participants

 Forty-five graduate student in psychology at the Faculty of Education and Psychology, University of Tabriz (between 18 and 25 years; mean 20.7, SD=2.7), were selected and participated as volunteers in the experiment with the available sampling method. These students did not have any visual problems and were completely ignorant of the purpose of the research. The results for two of the participants were excluded from the final analysis because they had an error rate greater than 25% (i.e., naming numbers after more than 1,000 ms) in the presented task. Two other students were excluded because they could see the priming stimuli in the majority of trials. Finally, among the forty-five participants, the data for forty-one participants remained for the final analysis (31 females, 10 males).

Hardware and software

The stimuli used in the experiment were presented on a 15-inch monitor with a refresh rate of 60 Hz, via a laptop model Lenovo G510, in a Windows 10 operating system. A simple microphone was used to record the reaction time of the participants in naming the numbers presented on the screen. After each response, the experimenter noted right or wrong answers in a paper.

For presenting the task, an open-source software (DMDX) (developed by researchers at the University of Arizona) was used. DMDX is a Windows-based software which is particularly suitable for precise timing (ms) in presenting different kinds of stimuli such as text, audio, graphics, and video and can record reaction time of participants with double precision compared with similar softwares [12]. The experiment is controlled via a text file (.rtf) which includes different trials and timing of the stimuli presentation (the reader may refer to the URL http://www.u.arizona.edu/~kforster/ dmastr/ dmastr.htm for more information and download the software which is particularly useful for language and subliminal processing studies).

Stimuli and task

 In the past two decades, subliminal priming has been one of the paradigms used in laboratories for investigating unconscious processing. In this method a word, image or specific number is presented for a fraction of a second (prime stimulus) and, subsequently, other stimuli (target stimulus) are presented to the participants. The priming stimuli are presented in such a way that the participants will not be able to see them in most of the trials; then participants are asked to recognize the target stimulus. In the subliminal priming paradigm, a priming stimulus facilitates classification and recognition of a target stimulus. In many neuropsychological tests the experimenter requires audio reaction times in response to the presented target stimuli. In these tasks called “naming tasks,” participants will be asked to name the stimulus presented on the screen verbally as soon as possible. In the present study the method of subliminal priming was combined with the naming task; therefore, as soon as the prime stimulus was presented to the participants and after the presentation of target stimulus, the participants were required to recognize it in the form of verbal expression (naming task).

Before conducting the experiment, the participants were asked to solve multiple mathematical operations on a paper. The task included random series of mathematical operations with  different functions (addition, subtraction, multiplication, and division). The aim of this task was to identify participants who are having difficulty in performing simple mathematical calculations.

Participants were seated at an approximate distance of 60 cm from the computer screen for conducting the subliminal task. Before the initiation of the task they were asked to name the target loudly as soon as the target stimulus was presented on the screen. Before presenting the target stimulus, two different kinds of prime stimuli were presented to the participants: 1) a one-digit subtraction operation with its answer congruent to the target stimulus and 2) a one-digit subtraction operation with the answer incongruent to the target stimulus. For example, in the congruent condition trial the prime stimulus was 9–1=and the target was 8, while in the incongruent trial the target was not consistent with the solution of the subtraction operation (e.g., the number 6 was presented as the target stimulus after the prime stimulus was 9–1=). Subtraction operators were presented with different Arabic numbers between 1 and 9. The prime stimulus (such as 9–1=) included the subtraction operator (−) and equals sign (=). For each participant, 40 trials were presented, of which 20 were congruent and 20 incongruent. All congruent and incongruent trials were presented randomly to participants. None of the participants were aware of the prime stimulus (the full list of prime and target stimuli is presented in table 1).