Are visual representations always helpful in the communication of
knowledge? Discuss with reference to the Human Sciences and
Mathematics.
Word count: 1587
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The communication of knowledge1 is crucial in our world, be it in the past, in the present or the future.
Although there are multiple ways of communicating knowledge across, the visual representation was always
an effective one. However, is it always helpful to have a visual representation when communicating knowledge?
The keyword always2 shows that something is constant and never changing, meanwhile, helpful 3 indicates how
useful something is. Selecting the Mathematics and Human Science area of knowledge (AoK) creates a distinct
variation of the ways the two AoKs are visualised and what tools are used: diagrams, and mathematical
notation to give a few. This essay will argue both sides of the question for both Mathematics and Human
sciences, in which areas of Geography, Economics and Mathematics will be discussed. Visual representations,
are not always, but are more helpful in Human Sciences than in Mathematics, as Mathematics, discussed later,
relies heavily on prior knowledge of the knower to understand the knowledge a visual representation contains.
As the Human sciences encompass social, cultural, and biological parts of human existence, the AoK contains
dozens of helpful visual representations. For example, the visual
representations of geographical objects such as mountains, where
a part of the geographical map consists of contour lines4 to show
where the height and gradient vary (see Figure 1). This is a
significant example because it can display the physical attributes of
Figure 1 - National Geographic Society, “Make a
Contour Map,” National Geographic Society,
February 15, 2011,
https://www.nationalgeographic.org/activity/makecontour-map/.
our knowledge of a geographical object. Within Geography, there
are many examples of visualisation of information, because,
without it, it would be hard to compare and argue with the long sets of data from investigations. Typically,
TOK, “Knowledge and Language - TOK,” TOK, February 19, 2021, https://tok2022.com/knowledge-and-language/.
Cambridge Dictionary. “Always.” @CambridgeWords, January 25, 2023. https://dictionary.cambridge.org/dictionary/english/always.
3 Cambridge Dictionary, “Helpful,” @CambridgeWords, January 25, 2023, https://dictionary.cambridge.org/dictionary/english/helpful.
4 Ordnance Survey, “Learn All about Contour Lines,” OS GetOutside (Ordnance Survey, June 5, 2022),
https://getoutside.ordnancesurvey.co.uk/guides/understanding-map-contour-lines-for-beginners/.
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2
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maps, such as choropleth maps5, indicate areas in a
coloured manner within a certain criterion (see
Figure 2), such as poverty levels etc. This is
extremely helpful as it communicates information
far more effectively than numerical data; It is (at
least usually) more accessible to human cognitive
processes. Another example in the Human Sciences
is the Ishikawa diagram 6 , also known as the
Figure 2 - Georgianna Strode, “View of Operationalizing Trumbo’s
Principles of Bivariate Choropleth Map Design | Cartographic
Perspectives,” Cartographicperspectives.org, 2023,
https://cartographicperspectives.org/index.php/journal/article/view/15
38/1819.
fishbone diagram, frequently used in Economics.
The Ishikawa diagram helps to visualise and understand the cause and effect of a principle (see Figure 3).
When employing this tool, the ‘effect’ is tackled into multiple subsections of ‘causes’, which with the help of
our judgement allows us to efficiently communicate our knowledge to ourselves or others. Moreover,
Economic notations (see Figure 4) are an extremely useful tool as the visual representations of letters can
indicate common words in Economics such as ‘D’ for ‘demand’; it communicates knowledge with ease and
no fault. Both Human Sciences, have visualising tools that help envision big concepts which aid a better
understanding and communication of big sets of data.
Internet Geography, “Choropleth Maps in Geography,” Internet Geography, September 9, 2020,
https://www.internetgeography.net/choropleth-maps-in-geography/.
6 Hayes, Adam. “Ishikawa Diagram.” Investopedia, 2023. https://www.investopedia.com/terms/i/ishikawa
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diagram.asp#:~:text=Kirsten%20Rohrs%20Schmitt-,What%20Is%20an%20Ishikawa%20Diagram%3F,are%20required%20at%20specific%20t
mes..
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Figure 3 - BPI, “Fishbone Diagram,” Leansixsigmadefinition.com,
2023, https://www.leansixsigmadefinition.com/glossary/fishbonediagram/.
Figure 4 - State Government of Victoria, Australia, “Drawing Visual
Representations of Economic and Business Concepts,”
www.education.vic.gov.au, November 10, 2020,
https://www.education.vic.gov.au/school/teachers/teachingresources
/discipline/english/literacy/Pa
On the other hand, Human Sciences can be argued in creating a
misleading visual representation. Therefore, the knowledge
communicated is from a skewed perspective. The choropleth map’s
variation – the ‘rainbow map’7 can represent a harsher change due
to the variety of colours in use. As our eyes have the ability to
distinguish thousands of hues, using much too colourful maps
Figure 5 - Robert Kosara, “How the Rainbow
Color Map Misleads,” eagereyes, July 8, 2013,
https://eagereyes.org/basics/rainbow-color-map.
skews our perspective due to our primitive colour evaluation skills.
For example, Figure 5 can seem to show that there is a harsh divide
between the east and west of the US regarding precipitation loss. However, after paying closer attention to
the legend we can notice that the numbers change very smoothly, whilst the colour change noticed is very
abrupt. Therefore, by manipulating our perceptions of colour, data can be skewed for one’s benefit. Another
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Robert Kosara, “How the Rainbow Color Map Misleads,” eagereyes, July 8, 2013, https://eagereyes.org/basics/rainbow-color-map.
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example is in Economics, where line graphs can be subject to one’s perception. A famous phenomenon of
data skewing is ‘cherry picking data’, where a suitable data set is selected for one’s argument, which gives you
the impression that you are aware of all the variables, when in fact you are not. Misleading graphs lead to
partially true communication of knowledge, as seen in Figure 6, where ‘USA Today’ has skewed their y-axis
to make it seem that Federal welfare is increasing. This shows the occurrence of deceptive visual
representation in our media and everyday lives.
The Human Sciences show that communication through visual representations can be both helpful and not.
Firstly, maps and graphs are the centres of visual representation in
this AoK, which can efficiently transfer knowledge from a massive
numerical data set. Nonetheless, in the process of transferring and
receiving knowledge, the information can be changed to fit a
certain perspective as seen in Figure 6. It can also be argued that
this is relatively helpful when trying to prove one’s perspective,
but not necessarily keeping its data’s integrity. I believe integrity
might be the line of argument while the data collected stands true,
but how it is used and portrayed is essential in communicating
Figure 6 - Statistics How To, “Misleading Graphs:
Real Life Examples,” Statistics How To, January 12,
2022, https://www.statisticshowto.com/probabilityand-statistics/descriptive-statistics/misleadinggraphs/.
worthy knowledge.
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Another AoK that can be argued to have a visual communication of knowledge is Mathematics. Mathematics
has always employed a visual representation of its knowledge – numbers, shapes, mathematical notation8;
without it, it would be hard to understand and visualise
concepts of mathematical complexity. The discipline of
Mathematics has been around for thousands of years and
therefore fundamental concepts such as addition can be
denoted using +. This shows that by using mathematical
notation, you can already fully communicate mathematical
knowledge with ease. Moreover, prefixes such as milli(𝑚),
micro(𝜇 ), and nano(𝑛 ) can identify the magnitude of a
Figure 7 - OnlineMathLearning.com, “Complex Numbers - Argand
Diagram (Examples, Solutions, Worksheets, Videos, Activities),”
www.onlinemathlearning.com, 2022,
https://www.onlinemathlearning.com/complex-numbers-a5.html.
number, which can hide its full form- ie 0.000006 grams is
6𝜇𝑔. Another example is the use of diagrams, for example,
the Argand diagram9 which represents complex numbers. Although the diagram may seem straightforward
forward representing imaginary and real numbers in two dimensions (see Figure 7), it can have even more
complex applications as the complexity of Mathematics increases. Therefore, by representing an imaginary
and a real number through a diagram it can communicate multiple things silently. Finally, geometry is a branch
of Mathematics that strongly focuses on shapes which are present everywhere, be it in the sky or a classroom,
we can identify any object to have a shape and a name. This attribute can speak a lot about the object's
functions and possibilities. As a human race, we all agree upon the fact that a triangle is a shape with three
edges, three sides, and angles that add up to 180°. Knowing these fundamental facts in Mathematics can
therefore communicate faster and more than any words may ever.
8
Herke, Sarada. “Mathematical Notation - the Language of Mathematics.” YouTube Video. YouTube, December 10, 2014.
https://www.youtube.com/watch?v=Y-c_CgxxPF0.
OnlineMathLearning.com, “Complex Numbers - Argand Diagram (Examples, Solutions, Worksheets, Videos, Activities),”
www.onlinemathlearning.com, 2022, https://www.onlinemathlearning.com/complex-numbers-a5.html.
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Even so, Mathematics may not always be able to communicate clearly through only visual representations.
Mathematics requires a lot of prior knowledge before the knowledge can be communicated exclusively via
visual representations. This means that all the knowledge contained behind a mathematical notation can
only be understood if and only if the person knows what the notation means, and what an equation
represents. For example, the equation10:
𝑏
𝑉 = ∫ 𝜋𝑦 2 𝑑𝑥
𝑎
Without the knowledge of integrals and functions, the person won’t know that this is the equation for finding
the volume of revolution of a shape. This results in the equation not communicating its value and contents
meaningfully and efficiently. The complexity of the equation also plays a big role, as with more complexlooking equations, the likelihood of the knowledge that you can receive from it decreases. Furthermore,
sometimes Mathematics may portray something that you may seem to know but is something different. An
example of this is different base number systems. The world's agreed-upon number system is the denary
system, where we count in powers of 10. However, if something was presented to us in a base 2 (binary) or
base 8 (octal), we won’t be able to visualise the value of the number, as we are used to seeing everything in
denary. The denary number ‘14’ is represented as ‘1110’ in binary and ‘16’ in octal; at the first glance you may
have thought that is ‘1110’ and ‘16’ in denary, but they are both ‘14’. This shows that Mathematics can’t be
fully communicated and understood without the prior.
Mathematics, as discovered earlier, depends heavily on visual representations of formulas, shapes, and
notations. This means that without prior knowledge, a visual aid of the mathematical formula or notation
won’t be effective in communicating any knowledge to a person. This leads to the conclusion that both prior
10
Revision World Networks Ltd. “Volumes of Revolution - Mathematics A-Level Revision.” Revisionmaths.com, 2019.
https://revisionmaths.com/advanced-level-maths-revision/pure-maths/calculus/volumes-revolution.
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knowledge of Mathematics and visual representation go hand in hand and can’t communicate knowledge
efficiently without one another; a formula can’t be understood without an explanation of what it does and
how it does, and an explanation can’t be visualised without a formula.
Although both the AoKs represent the communication of knowledge through visual representation efficiently,
Mathematics debatably depends on it more often: constant use of equations, mathematical notation and
diagrams representing shapes. Nonetheless, these fundamentals of Mathematics are built upon thousands of
years of knowledge that is passed down from generation to generation. Without this knowledge, visual
representations are not always intuitive and therefore may not communicate through reasoning. Compared to
Mathematics, Human Sciences are relatively more intuitive which means that by the first look at a diagram,
one may understand its contents and what it is trying to portray, therefore, showing that visual representation
is always helpful for people without a prior understanding. Therefore, this leads me to conclude that visual
representation is debatably less helpful in Mathematics at a first glance, while in Human Sciences it's more
helpful to visualise and understand certain patterns and trends within data. However, one shouldn’t solely
focus on visual representations, as they may not hold the full picture of the data set or meaning of something,
as information can only be visualised to a certain extent.
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Bibliography
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4. ———. “Helpful.” @CambridgeWords, January 25, 2023.
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%3F,are%20required%20at%20specific%20times..
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https://www.internetgeography.net/choropleth-maps-in-geography/.
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https://eagereyes.org/basics/rainbow-color-map.
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