Friday, July 17, 2009

Thinking Maps


    Dr. D. Hyerle grouped under Thinking Maps syntagm a set of eight metacognitive visual tools rooted in the eight cognitive skills: defining in context, describing attributes, comparing and contrasting, classification, part-whole spatial reasoning, sequencing, cause and effect reasoning, and reasoning by analogy [1]. He used the tools to create a easy to use language for learning and information representation, the eight graphic primitives can be used in an infinite of ways. There are several diagrams which summarize what the eight Maps are about:

Thinking Maps [8] Thinking Maps [9]

    Benefits associated with the use of Thinking Maps can be found in [3], [11] and [2] together with modes of employment.

Circle Maps

    Circle Maps are used to place concepts into a context with the help of two concentric circles, the smaller one containing the context, while in the outer circle are placed the associated concepts, acting like properties or association bag. Concepts are usually clustered without creating explicit relations between them, more complex Circle Maps being created using multiple concentric circles, a target diagram according to [12], or by partitioning the outer circle, creating thus different spheres of meaning.

    Given its geometrical properties (e.g. centricity, equidistance, regularity), the circle is a perfect tool for representations, though it doesn’t have to be used as a leitmotif; triangles, squares, rectangles or any other regular polygons can be used for the same purpose, especially when additional intrinsic characteristic are highlighted, for example trinity, square of opposition, n-tuplicity, etc.

    Circle Maps can be pretty simplistic, in simplicity residing their beauty and use; overall Circle Maps are a perfect tool to introduce concepts, especially in primary school. Their importance should not be underestimated, they can have strong representational power especially when used in combination with other representational patterns.

Bubble Maps

    Bubble Maps focus on direct associations between a concept and its descriptors, also called adjectives, qualities, attributes or characteristics [11]. Such representations are integrant part of many types of Maps that represent associations explicitly (e.g. Mind Maps, Concept Maps). Extensively, a Bubble Map could be used for the same representations as Circle Maps, allowing thus explicit associations between a concept and its attributes, same it can include other part of speech, concepts or fragments of text. For greater effect, Bubble Maps could be combined with Circle Maps, especially when needed to highlight different boundaries.

Double Bubble Maps

    Double Bubble Maps are used for comparing and contrasting the descriptors of two concepts. Another popular tools used for the same purpose are the Venn diagrams, which mixes some of the characteristics of Circle Maps and Double Bubble Maps, though they are sometimes more complex to use and, in plus, they allow the comparison of multiple concepts. Are few the situations in which more than two concepts need to be compared, how should such a Map be called?! Maybe Multi-Bubble Maps…

Flow Map

    Most probably many people are already familiar with flowcharts or flow diagrams, one of the process diagrams used to model the flow of processes (systems), and sometimes considered synonym to them. Hyerle’s Flow Map seems to be slightly different than the flow diagrams used to model processes, and even if both maps are based on sequencing and ordering principle, the later seems to be more complex and use more representational elements, containing symbols for decision, delays, predefined subprocesses or data input/output. Hyerle’s Flow Map resumes only at presenting information in sequencing and ordering manner, being capable of represent for example a linear causality sequence or the points on a scale (e.g. past, present, near future, future or very cold, cold, warm, very warm). I consider scales, also named continuums by [12], a pattern of its own, used to represent a set of ordered concepts, including timelines, transition between two states, scales of values, ordered sets, etc. It is possible to represent together two or more scales/continuums within the same system of coordinates, each scale on an axis of its own. Such a system is called a crossed continuum by [12] and conceptual space by [13].

Multi-Flow Maps

    A Multi-Flow Map is obtained by combining more than one Flow Maps, creating parallel or intersected sequences. Therefore they are useful to represent causes and effects diagrams, more like the well-known Fishbone diagram, the distinction residing in the fact that the multi-flow Maps not necessarily follow a hierarchical structure, multiple effects being possible. In addition the Fishbone diagram has a “methodology” of its own, the causes being identified starting from an observed effect.

    It’s interesting that [10] makes distinction between Multiple Causes Maps and Multiple Effects, which could be taken as particular Multi-Flow Maps.

Brace Maps and Tree Maps

    Brace Maps are the only type of Maps I often saw used in manuals or other type of books, usually for detailing the parts of concepts allowing thus to analyze the parts of a concept and the concept itself. Brace Maps are used also for the classification and grouping of concepts, in Hyerle’s system usually represented using Tree Maps.

    I often used Brace Maps in Mathematical definitions, when the definitions need to be split in parallel threads (left braces), or demonstrations, when multiple threads flow into the final result (right). Even the use is slightly different the principle is somehow similar.

Bridge Maps

    Bridge Maps are used for highlighting analogies between concepts into an inversed Vee-like diagram, which can be repeated for each additional analogy added to the chain, with the comparison concepts on top and the relating factors below. Bridge Maps can be used not only for simple analogies, but also for metaphors.     I expect that in case are needed to be compared multiple related factor types for the same concepts, then it will be created one Bridge Map for each factor type. For such scenarios a simple table could be a better choice, in which the compared concepts form the headers, while the related factors are the actual records. Even more, the concept representing the concept type can be added too, forming a matrix. An example of such matrix can be found in a previous posting on Web’s evolution.     Even if the use of Bridge Maps expresses directly the intent of representing analogies, I find tables or matrixes much simpler to use and non-redundant.

New Patterns, Old Patterns

    The patterns encompassed in Thinking Maps are not new, many of them have been used a few centuries ago, as can be seen from the below examples. In the first figure can be seen the Buenting clover leaf map, woodcut made in 1581 in Megdeburg; it can be regarded as a combination between Circle Map and Bubble Map. In the second figure from Athanasius Kircher’s Oedipus Aegyptiacus can be seen a wonderful complex diagram of the names of God, a combination of a partitioned target diagram (multi-concentric Circle Maps) and Tree Maps. In the third figure, a simple I Chin diagram based on Pa Gua trigrams, a partitioned Circle Map making use of symbols, the same theme being present also in the fourth diagram, which evolves the I Ching model to a representation of the DNA world.

Buenting clover leaf map Athanasius Kircher’s Oedipus Aegyptiacus
Buenting clover leaf map [6] Athanasius Kircher’s Oedipus Aegyptiacus [14]

I Ching DNA/RMA Mandala
I Ching [4] DNA/RNA Mandala [5]


[1] Hyerle, D. (2008). Thinking Maps®: A Visual Language for Learning. In: Thinking Maps®: A Visual Language for Learning, ISBN: 978-1-84800-149-7. [Online] Available from: (Accessed: 23 June 2009)
[2] A. Costa, P. Wolfe, H. Gardner, D. Goldman. The Networking Brain and Mind. [Online] Available from: (Accessed: 7 July 2009)
[3] Learning Prep School. Thinking Maps. [Online] Available from: (Accessed: 7 July 2009)
[4] Zen’s Sekai I. (2007). I Ching. [Online] Available from: (Accessed: 8 July 2009)
[5] The Abysmal. (2006). DNA Codon Mandala. [Online] Available from: (Accessed: 8 July 2009)
[6] Learn NC. Buenting clover leaf map. [Online] Available from:
[7] L. Sachar. Multiple Mapping: Holes. [Online] Available from: (Accessed: 12 July 2009)
[8] Seattle Schools. Thinking Maps. [Online] Available from: (Accessed: 13 July 2009)
[9] SaskEd. Unit Five: Social Development. [Online] Available from: (Accessed: 13 July 2009)
[10] Somers Central School District. ????. Graphic Organizers that Support Specific Thinking Skills. [Online] Available from: (Accessed: 14 July 2009)
[11] Hyerle. D. (2000) Thinking Maps® for Reading Minds. In: A Field Guide to Using Visual Tools. Association for Supervision & Curriculum Deve. ISBN: 978-0871203670. [Online] Available from: (Accessed: 14 July 2009)
[12] G. Petty. (2009). ISBN: 978-1-4085-0452-9. Evidence Based Teaching: A Practical Approach. 2nd Ed. [Online] Available from: (Accessed: 16 July 2009)
[13] Gaerdenfors, P. (2000). Conceptual Spaces: The Geometry of Thought. Massachusetts Institute of Technology. ISBN: 0-262-07199-1.
[14] Cramer, F (2005) Computations of Totality. In: Words Made Flesh – Code, Culture, Imagination. Piet Zwart Institute. [Online] Available from: (Accessed: 16 July 2009)

Friday, July 3, 2009

Knowledge Representation in Antiquity

    I must admit that I’m fascinated by the techniques and tools used for Knowledge Representation, especially the ones used in the past, centuries and even thousands of years before. Somebody was saying that nothing is new under the sky, everything existed before, even if it was in a more archaic form of expression, the simplicity doesn’t diminish the importance.

    My fascination is somehow correlated to the fact that many of the representations that can be catalogued under Knowledge Representation are related to philosophical and religious believes, two of the domains that played an important role in the life of the spiritual man from antiquity. Oh, I forgot astronomy or, astrology if you want, the associations of stars in constellations, uniting the dots in a pattern that can be easier memorized and identified, can be considered maybe as a pseudo-technique for Knowledge Representation.

    In my dissertation paper, in a short historical overview of Knowledge Representation structures used over time, I mentioned the Tree of Life representations on stone, ceramic or clay artefacts preserved until now from different cultures, the “arbor porphyriana” or “Porphyrian tree”, genealogical trees dated from 11th century, KRS like representation of Joachim of Fiore [1] or Ramon Llul [2], the Sephirotic Tree central to Jewish tradition, quipas and square of oppositions. Actually, the list of such representation is much bigger; I tried to point only the oldest sources in order to highlight the existence of various such representation techniques. I think that I could have talked more about some representations and add many more examples, though I don’t think it was nor the place and neither the time to do it, for some of them needing to do more research, given their interpretational richness. In the past two weeks I tried to do some research in this direction, I advanced a little in the subject though there is still a long way to go. I realized that for the moment would be impossible to approach the subject in a more structured and professional form, on subjects like the Tree of Life or Sephirotic Tree has been written many books and advanced many theories. As I am interested in the Kabbalistic and Hermetic traditions, some of the mentioned representations were not new to me, their richness of meaning intriguing me, this being also one of the reasons for which I chosen a topic for my dissertation paper related to Knowledge Representation.

    The Sephirotic Tree is actually my first meaningful intersection with a KRS, giving it some thought over time, trying to understand the various interpretations, and believe me, there is a whole set of philosophies based on it. As Frater FP highlights, the Sephirotic Tree became a Meta-Map or Meta-Model for a Meta-System “capable of comprehending other systems within itself”, the Seven Rays and Chakra systems, the astrology itself and Tarot being examples of other meta-models [4]. It is actually interesting to study how such models were formed and evolved, unfortunately all we can is to launch in the blue other more or less fantastic theories. In many sources it is advanced the idea that the Jewish Sephirotic Tree derives from the Egyptian or Assyrian/Babylonian Tree of Life, theory proved by the antique artefacts found, though Trees of Life can be met also Indian or Nazca antic cultures, revealing the universality of such a symbol. These various tree representations could have in theory a unique source, though this supposes the existence of an older culture, why not the Atlanteans, though that’s maybe a little too much SF for this post, unlike you are open for such theories. If no such common source exists, then most probably exist something higher, a collective or archetypal consciousness, same as is possible that people arrived independently to the same truths, so there must be a correlation between the tree and the inner/outer world.

    Other religious representations are centred on trinity, the various types of crosses and shields of trinity being an example in this direction. The oldest shields of trinity I know of are the ones available in Cotton Faustina and Summa Vitiorum manuscripts from 13th century. A second type of representations was transmitted through the intermediary of seals and even coins, their means being lost in the past.

Zodiac [5] Macrobian cosmic diagram [6] Chinese chart [7]

    As I previously mentioned, an important amount of knowledge was transmitted in relation to the stars, zodiacs like the ones present in a 6th century synagogue at Beit Alpha, Israel, cosmic diagrams like the Macrobian diagram from 9th century and sky charts like the Chinese one dated to 7th century seems to be common along the time. Such testimonies of the past are again present on all continents in various forms and styles. Now that we are approaching with rapid steps the year 2012, the end of the world or beginning of a new era after some interpreters of Mayan calendar, a hoax for others, based on moon’s natural cycle, the Mayan calendar spans over a range of 5125 years, between 3113 BC and 2012 AD; jumping over interpretations, it remains the beauty and abstractness of Mayan calendar representations.

Maya Calendars

    It doesn’t makes sense to talk about Knowledge Representation in antiquity without mentioning, at least roughly, a masterpieces of Chinese thought, I Ching, the Book of Changes. Based on 64 hexagrams rooted in yin and yang principles, it presents a beautiful complex Meta-Model, hard to grasp by most of the mortals, and I’m one of them, at least for now.

1. International Center for Joachimist Studies. (????). Joachim of Fiore. [Online] Available from: (Accessed: 13 February 2009)
2. Cahill, M.J. 2005. Graphical Languages – History and Uses. Future Knowledge Group. [Online] Available from: (Accessed: 8 January 2008)
3. S. Weigel. ????. Genealogy, On the iconography and rhetorics of an epistemological topos. Enciclop├ędia e Hipertexto. [Online] Available from: (Accessed: 3 July 2009)
4. Frater FP. 2005. The Magician’s Kabbalah. [Online] Available from: (Accessed: 3 July 2009)
5. TutorGig. 2009. Astrology [Online] Available from: (Accessed: 3 July 2009)
6. Wikipedia. 2009. Flat Earth. [Online] Available from: (Accessed: 3 July 2009)
7. KIDIPEDE. 2009. Chinese Astronomy. [Online] Available from: (Accessed: 3 July 2009)

Finally the Digital Book Reader - Part II

    One month is gone and I had a great time playing with my Sony Digital Reader – overall is a nice experience, reading in the evening before falling asleep became actually more pleasant, the reader weighting less than some of the books I’m having in my small library. As often I’m using the laptop only for reading electronic documents, the Reader helped me to reduce the number of hours spent In front of the laptop, and that’s quite a deal considering the huge amount of time I’m spending daily working on computer. The device proved to be also useful while using the medical bike, being much easier to fix it on the bike than a normal book.

    Excepting the creation of Knowledge Maps with Digital Readers disscussed in the previous post, on my wish list for future Reader devices and services appeared a few more points appeared since then:

    1. A dictionary that would show a definition or synonyms for the highlighted word. The existence of bilingual dictionaries would be a plus, a tool like Babylon on a reading device would be more than appreciated.

    2. The possibility to categorize notes, for example in key-words, concepts, quotes, unknown words, etc. This shouldn’t be limited to predefined categories, custom categories could be used in combination with predefined categories; the user for example could assign a set of categories to a set of buttons for faster response, thus not needing to select a category from a list each time the assignment is done.

    3. The possibility to save multiple bookmarks – now the device stores the last visited page, great thing, though if for example I click on saved notes, the previous bookmark is lost. This could be covered somehow in point 2, though I considered it deserves a place of its own in my list.

    4. Improved view/editing capabilities, right now there are cases in which the Reader fails to select the exact piece of text I want, most probably because of documents’ format, the same could be blame also for the strange display of text when increasing font’s size. This includes cross-page text selections – right now I find it quite difficult to select a text found on two consecutive pages.
    It won’t be bad if the files’ name and other metadata could be modified directly in Reader.

    5. Internet browsing and the possibility to save content on the local device, for beginning read-only capabilities for simple HTML Web pages would do, though, on the long run, it would be nice if a Digital Reader could dispose of read-write capabilities.

    6. A wider digital display to allow at least normal read of small-format books;

    7. A longer battery duration - because I’m using the stick to select text, the energy consume is higher, after a few hours being requested to recharge it. I wonder whether solar energy could be used to recharge Reader’s battery…

    8. Collaboration between content Vendors, right now vendors like Sony and Amazon providing content only for their products, on one side this strengthen their positions on the Readers’ market, though limits the accessibility to content consumers, market which could prove to be more profitable than the one of the Readers.

    9. Global services – I was quite disappointed when I wanted to buy a book and I couldn’t because Sony offers content only for the Canadian and US market. I understand that this is a new market which might not be mature enough, though I think that such Vendors should be a little more aggressive.

    10. Processing tools that allow processing the content created with Readers (e.g. Notes), exporting it for example to other types of files,

    I see the Digital Reader device playing a more important role in learning, not only simple reading, Reader Based Training (RBT) could have maybe the same impact on users as Computer Based Training (CBT) or Web Based Training (WBT) services, on a Reader being maybe more easier to consume such content.