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As cartoonist and journalist Joe Sacco once said, “It’s a visual world, and people respond to visuals”. Visual representations, which can be defined as holistic visual depictions or demonstrations of a notion, are essential to the communication of knowledge. By bringing ideas into a presence before us, visuals can aid the communication of concepts that are intangible or difficult to comprehend without the use of various mediums. As the transmission of information is significantly faster with such tools compared to written or spoken words, visual representations, more often than not, enrich communication considerably. In the human sciences, visuals are necessary to observe the correlation between concepts and illustrate occurrences that can only be comprehended when viewed from a broader perspective. Likewise, visuals are generally used in mathematics to provide access to abstract mathematical ideas. It is important to note that this essay has been explored with the assumption that such representations are only considered ‘helpful’ if they successfully communicate the knowledge intended for the knower to understand. Moreover, the term ‘always’ suggests that visual representations assist the transfer of knowledge from one party to another on all occasions; hence, the analysis will primarily focus on the extent to which this is true.

The human sciences require visual representations to understand and communicate complex phenomena, yet the misinterpretation of visual representations may tarnish the communication of knowledge. In an attempt to raise awareness of the Australian bushfires in January 2020, individuals took to social media to spread visuals of the fires. One infographic widely circulated online was Anthony Hearse’s 3D visualisation depicting the areas in Australia affected by the fires based on data from Nasa (Figure 1). However, social media users misinterpreted this image as a satellite photograph revealing the bushfires that had been burning across the country at that moment and captioned it, “This is a Nasa photograph”, thus resulting in the image getting flagged.

From this example, one may argue that when the context in which the visual is presented is either insufficient or inappropriate, the usefulness of the visual representation is disparaged as it no longer serves its intended purpose. Instead, it will become open to interpretation, where viewers will make assumptions and judgements based on their cultural background, experiences, and biases. Due to the presence of normative claims in the human sciences, elements of bias inherent in one’s interpretation of a visual are likely to be prevalent in this field. As the nature of such claims include the expression of values about observations and interpretations that are likely to differ from person to person, their lack of objectiveness may result in them being flawed. Hence, individuals must analyse visual representations from various perspectives to minimise the influence of their unconscious bias on how they perceive the visual. Thereupon, on account of the interpretability and bias that comes with visual representations, they may not always be helpful.

Furthermore, the adequacy of visual representations in disseminating information relating to the human sciences relies on how they are presented. For example, a pie chart created by the local station “Fox Chicago” for the American television programme Fox News (Figure 2) intended to illustrate the general public's preferences regarding Sarah Palin, Mitt Romney, and Mike Huckabee running for the 2012 Republican presidential nomination. As more than one vote was permitted, the results added up to 193% rather than 100%, as a correct pie chart should. Hence, the pie chart as a graphical representation of the spread of nomination results is inappropriate compared to a bar chart that would have accurately presented the absolute values for each category.

Furthermore, the graph is flawed because the segments rendering 63% and 60% appear to be significantly larger in size than the segment representing 70%, despite being smaller in value. Especially since it was aired on television, this poor display of data collection is problematic because it is unlikely that viewers had the opportunity to analyse the chart closely enough to notice its flaws. As a result, their voting strategy may have been influenced by the assumptions they are naturally drawn to after briefly viewing this visual. Ergo, this example demonstrates the dangers of misrepresenting data and highlights how it is critical for individuals to scrutinise the visuals presented to them to avoid poor decision-making. Conclusively, it may be said that if a visual representation presents data inappropriately, it is easy for the interpretation of the information communicated to be distorted, suggesting how they are not always helpful.

With respect to the field of mathematics, visual representations have the power to clearly and effectively communicate the abstractness of the subject. By way of illustration, elementary schools often utilise the Rainbow method (Figure 3) as a visual aid to teach younger students about factorisation. The factor rainbows in question aim to display factor pairs in order based on their sizes whilst revealing which factors multiply with one another to form the parent number by connecting them with the arcs of the rainbow.

Through observing and or constructing such diagrams, knowledge relating to the mathematical concepts of factors and multiples can be consolidated. Consequently, visual representations present individuals with a simplified approach to grasping an understanding of new topics. Moreover, they allow students to perceive this particular area of mathematics in a different light that is not limited to just words and numbers, leading to higher levels of engagement. Thus, there will also be an improvement in the communication of knowledge from teacher to student. As such, pictorial depictions have the potential to be beneficial to individuals in the communication of mathematical knowledge, regardless of their level of math proficiency, as they allow for the visualisation of mathematical concepts that may otherwise be difficult to comprehend. Having said this, the possibility that the oversimplification of visuals may hinder the student’s ability to apprehend more complex topics in the future still withstands. If an individual becomes overdependent on such visuals, they may struggle greatly in their absence. On the other hand, if the student is not a visual learner, the visual may confuse them. For these reasons, visual representations in mathematics help communicate knowledge in most cases, but there are exceptions depending on the receiver of the knowledge.

In many situations, visual representations in mathematics are also advantageous in the way that they can increase efficiency in the communication of mathematical concepts. To acknowledge this benefit, one may examine Pascal’s Triangle (Figure 4), a triangular pattern of numbers with applications significant in branches of mathematics ranging from algebra to combinatorics.

By illustrating patterns that may be difficult to memorise, Pascal’s Triangle can reduce the intricacy of complex calculations, thus allowing for greater efficiency in the communication of knowledge. For example, in the context of algebra, it provides the coefficients in the expansion of binomial expressions, including (x + y)^{n}, whereby ‘n’ corresponds to the numbered row in the triangle (Jerphagnon). Likewise, instead of continually finding the sum of two preceding numbers to generate the Fibonacci sequence or memorising the succession of integers, one could simply add the numbers on each parallel diagonal line of Pascal’s triangle. The work of Pascal has also greatly influenced the research of other mathematicians, such as Isaac Newton’s discovery of the general binomial theorem for fractional and negative powers (O’Connor and Robertson) and Jakob Bernoulli’s work regarding combinatorics and probability. Hence, it may be viewed as a foundation for developing newer mathematical axioms in certain fields. On the other hand, individuals who lack prior knowledge about Pascal’s Triangle will not be able to notice its properties, let alone use it to aid their learning and understanding of a mathematical concept. To them, this seemingly random array of numbers would be meaningless. Overall, although visual representations can assist one’s understanding of a concept and facilitate the development of new theories in mathematics, they are unhelpful when the viewer does not possess the ability to interpret the visual.

Ultimately, while visual representations can significantly assist the communication of knowledge in the human sciences and mathematics, they are not helpful under all circumstances. From the exploration of visual representations in geography and politics, it was showcased that the possibility of misinterpretation and the way in which the visual is presented may hinder its ability to communicate knowledge efficaciously. Contrariwise, the use of visual representations in mathematics reveals how the role of visuals in disseminating mathematical concepts and discovering new theories can be significant. However, they may not always be helpful depending on the individual’s learning style and the extent of the knowledge that they already possess. Having drawn this conclusion, it is not to say that visual representations should be avoided because, as previously mentioned, such judgements were made with the assumption that the visuals are only deemed helpful if they serve their intended purpose. Without this postulation, it can also be argued that the visual representation’s mere provision of a concept’s general idea may still be considered helpful. In a similar manner, what may not be helpful to one person may be of substantiated usefulness to another. In short, visual representations can aid the transfer of knowledge most of the time, but they are not always helpful.

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