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Symmetry: Culture and Science
Vol. 31, No. 1, 15-22, 2020
https://doi.org/10.26830/symmetry_2020_1_015
SYMMETRY IN EDUCATION
DISCOVERING INFORMATION VISUALIZATION
THROUGH POLY-UNIVERSE
Miklós Hoffmann1
1 Institute of Mathematics and Computer Science, Eszterházy Károly University, Leányka 4, Eger, 3300,
Hungary
E-mail: hoffmann.miklos@uni-eszterhazy.hu; http://domain.edu/personal.website/.
ORCID: 0000-0001-8846-232X
Abstract: Information visualization is the science and art of visualizing information
that flows around us in many disciplines, intending to make the data more digestible
and understandable for non-expert users. The objective of this paper is to introduce a
new and somewhat surprising application of the Poly-Universe system, as an
educational tool of understanding basic information visualization principles, and filling
the symmetric and asymmetric constellations with content-dependent meaning through
information-related story-telling.
Keywords: information visualization, Poly-Universe, PUSE, story-telling.
MSC 2010: 00A66, 97U60
1 INTRODUCTION
In today's society, data and their understanding and interpretation have become of
central importance in many fields of science as well as in everyday life. Consequently,
the correct and fast interpretation of raw information data is a new essential skill that
needs to be developed already from early school years. The notion of visualization
literacy, as a concept of the ability to confidentially create and interpret visual
representations of data, is recently introduced and studied (Alper et al., 2017). The lack
of visualization literacy can yield limited access to data and information, that can finally
M. HOFFMANN
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prevent youths and adults from informed decision making. Images are so important in
nowadays life, that the need for fundamental changes in education is obvious in this
respect (Nyíri, 2013). Understanding images and understanding data represented/visu-
alized by these images and forms are especially important in the light of the recent
European initiative of encouraging open data and open science. However, currently, we
have limited educational resources and tools to effectively develop these skills (Saddiqa
2019).
In this paper, we initiate a new method of teaching and studying of information
visualization with the help of Poly-Universe, a general-purpose artistic and
mathematical system of forms developed by Saxon Szász (Saxon Szász 2010). This
system is known to effectively support the development several skills, such as form and
colour senses; abstractive vision; art sensitivity; complex logical thinking; or
mathematical and combination skills. It can widely be used in school education, as
demonstrated through several experience workshops (Saxon Szász - Dárdai 2019). Here
we provide a new chapter of educational application of this system, by applying Poly-
Universe to develop information visualization skills, the ability of understanding data
and their interrelations, specifically the potential semantic aspects of symmetry and
asymmetry. The method – with proper adjustment of problems similar to the ones
discussed in this paper – is suitable for any level of education, from early childhood to
university.
2 POLY-UNIVERSE SHAPES AND INFORMATION VISUALIZATION
Professional Information Visualization techniques are supported by various tools and
software, but there are some essentials, that one can find in every tool: creating basic
shapes representing basic data, using different colours for different data/shapes, and
visualizing interrelations of data by some connections of these basic shapes. It is of
utmost importance to express the symmetry or antisymmetry of these interrelations (e.g.
balanced or unbalanced trade of goods between two countries) by some of the above-
mentioned tools. We will be exploring this aspect in Section 3. We will prove through
examples that Poly-Universe elements possess all the necessary properties and variety
to be fit for this task.
Observing some real-life information visualization examples randomly selected from
the scientific literature (see Figure 1), one can easily associate them with the shapes,
colours and interrelations of the basic shapes of Poly-Universe. This fact inspired us to
DISCOVERING INFORMATION VISUALIZATION THROUGH POLY-UNIVERSE
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study the potential use of Poly-Universe in learning and teaching the fundamentals of
information visualization.
Figure 1: Inspirational examples of real-life information visualization figures about machine learning (left,
Liles 2014), about social media management (middle, a software-generated example by Visme (visme.co)),
and geospatial data (right, Kanevski 2008).
3 EDUCATIONAL SCENARIOS
Two different educational scenarios will be discussed in this section. In the first case, a
construction created by Poly-Universe shapes is given, and students have to interpret
and analyze this form using a pre-defined or jointly agreed meaning of colours, shapes
and relations. This scenario is called interpretative.
In the other, somewhat reverse case, only the „story” (i.e. a set of data) is given, and
students have to create its visualization using the Poly-Universe shapes, meanwhile
explaining what colours, shapes and relations mean in their visualization. This scenario
is called creative.
In the next subsections, we provide some examples for both scenarios, emphasizing the
interpretation/creation of symmetric and asymmetric forms.
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3.1 The interpretative scenario
Problem 1. Consider the following squares of Figure 2 (Saxon Szász – Dárdai, 2019) as
a visual representation of countries. Colours of the square illustrate the four main
products of the country: wheat (yellow), wood products (green), electrotechnical
products (blue), clothing (red). In the top row, products of separate countries are
visualized. In the bottom figures, neighbouring countries are presented. Two countries
are in export-import relation if two squares share a common side or vertex. The type of
goods to change is represented by colours along this side or having that vertex.
Figure 2: A country is represented by a square, together with the main products of the country (colours).
Neighbouring countries are in export-import relation.
Potential questions to interpret the countries and their products:
- Which country in the top row produces the highest amount of electrotechnical
products? Which country produces more wood products, the first or the
second?
- In the bottom left figure, do the countries have symmetric export-import
relation in terms of woods? What is the situation in terms of wheat? Find
countries producing the same amount of wheat! Do they export wheat to each
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other? Make statements of the form „country A and country B produce the
same amount of good X”.
- In the bottom right figure, the two countries in the right-side change
electrotechnical products in an asymmetric way. Find similar relationships with
analogous amounts of change of other products between other countries!
- Let us call the economy of a group of countries „healthy” if they have an
overall balanced production in some of these four products. Which group of
the bottom row is healthier? Is a configuration with rotational symmetry
always perfectly healthy? Can we complete the left group with a country from
a perfectly healthy group of 4 countries?
Problem 2. Consider the following tessellations in Figure 3 (Saxon Szász – Dárdai,
2019) built from Poly-Universe triangles. Districts of the cities are coloured according
to various political preferences. Different colours mean votes for different political
movements (Yellow Party, Blue Party etc.).
Figure 3: Territories of two abstract cities (built from Poly-Universe triangles) are coloured according to
political preferences: green, yellow, red and blue are for the 4 main political movements in the country
Potential questions to interpret the cities, districts and their political preferences:
- Which political movements are the winners of the voting procedure in the two
cities?
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- Do they have to initiate a coalition, or is there a single winner? Can two parties
form a coalition with the majority? Can three parties form a coalition with the
majority?
- Does axial symmetry of yellow, blue and red districts in left yields equal votes
for the three parties?
- Surveys show that physical workers usually vote for the Red Party. Where can
be the main district of factories in the city on the right side?
- Surveys show that people with high income usually live in the very centre of
the city. Which is the favourite party of wealthy citizens in these cities?
3.2 The creative scenario
Problem 3. Consider the following story. There is a social event, a dinner at a scientific
conference. People are sitting around three round tables, and – as it is usual in such
events – they are talking to their neighbours. Of course, the extent of these
conversations can vary from neighbours to neighbours. At the left table, the couples
listen and talk to each other to the same extent pairwise, but they do not find a common
theme. At the right table, each pair of neighbours finds an interesting joint field to talk
about, but people sitting on the left side of the pair talk much more to his/her right
couple than vice versa. Finally, in the middle table, pairs find a good common topic to
discuss, and they mutually respect and listen to the view of each other, leading to a
fruitful conversation. Task: represent the situation by some information visualization
tool!
Figure 4: Pairwise conversation between pairs of people sitting around three tables (built from Poly-Universe
circular elements). Colours denote different fields, the size of joining parts represent the extent of
conversation and its symmetry, mutuality (in case of circular joining parts at the first two tables) or its
asymmetry (in case of table 3)
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One possible solution can be seen in Figure 4 using the circular elements of Poly-
Universe (Figures from Kis, 2017 – note that we intentionally use existing figures to
demonstrate that story-telling works for any kind of configuration). People are
represented by circles, conversations and their extent are represented by the joining
parts. If these joining parts are of the same colour, then the conversation has a common
theme. If these joining parts form a (smaller or larger) circle, then the extent of
conversation between the two neighbours is symmetric (they express their views to the
same extent). However, if the joining part is formed by a larger and a smaller half-
circles, than the conversation is dominated by one of the neighbours. As we can easily
observe, the visualization of these conversations by Poly-Universe circles strictly
follows and represents the given story and its various aspects.
4 CONCLUSION
The potential of Poly-Universe in studying and teaching information visualization, a
crucial topic in nowadays scientific and everyday life, has been discussed in this paper.
Two different educational scenarios have been presented in this manner. These
scenarios are suitable to develop the sense and need of information visualization, when
Poly-Universe constructions are more than l’art-pour-l’art forms and when shapes,
colours and positions have a well-defined meaning and various consequences can be
drawn from the interpretation of the construction. It is needless to say that this method
can deeply connect various disciplines to each other, such as Geography, Literature,
Sociology, Political Sciences and Mathematics. What is also of great importance, that
students can learn and understand symmetric and asymmetric relations in a contextual
form: (geometric) symmetry can represent mutual understanding of each other, mutually
advantageous commercial agreements between countries or companies, joint move-
ments of equal parts. Besides the usefulness of the presented method in the education of
practical aspects of information visualization, this deeper understanding of symmetry
may even be more important from educational, cultural and scientific points of view.
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