20 November 2010
Even more interesting is the fact that not only the individuals are competing but also the groups/communities they are belonging to are competing against each other, and could happen that two or more members of a group compete against each other, stirring a conflict of interests and eventually some divisions with the group, but that’s less important for this post. To use a mathematical syntagm I learned during the course of Linear Programming done in university, I was wondering what’s the optimum solution in this case. Unfortunately there are a few years gone since University and the few classes on Game Theory and Linear Programming done in school are somewhere in a dick fog. So, I tried to approach the problem logically: what’s the best choice for a given group of groups to win the 9 prices?!
Intuitively it seems that the best win-win situation is when all the winners are belonging to the same group, and let’s say that the group contains only 9 members. Each day each member will receive 9-1=8 votes (a person can’t vote for himself), which for the next 75 days of contest cumulates to 600 votes, which I bet will be more than some of the winners of the prices will win in the end currently. Why 9 members and not more? Because each member added to a group, means that one member of the group will not win, and as I suppose that all the people want to win, the conflict of interests could lead people to sabotage the voting. On the other side several members could sacrifice themselves for the sake of their friends and let’s say they will vote daily without taking part in the contest, thus resulting (n-1) votes for each of the 9 members, each day. It’s quite a simple formula:
Total number of votes = number of days * (number of members-1)
The numbers are ideal ignoring the situations in which one of the members won’t vote and don’t include the additional votes added by other people, external to the group, who like the quote.
A special case of such type of group in which the number of members is greater than the number of winners could be formed for example by the families of the people winning the contest, thus if each family would comprise two members, let’s say husband and wife, the number of votes would be then multiplied again by 9 (just multiply the above numbers by 9). This is the perfect scenario because once a family wins the contest, both husbands will take eventually advantage of the won iPad. There are more variations on this subject, for example when also the members of the family of the competitor participate, in such case the winning group would be ideal when the family of its members is as bigger as it gets.
I wonder how many of competitors use any of the above approaches. I have several reasons to believe that this won’t happen, but who knows?! Anyway, you are free to join the contest and even vote my quote (here), if you like it. Any vote counts and it’s more than appreciated!
PS: The funny thing about voting contests on Internet is that the participants could easily break the rules voting more times per day by using dynamic IP addresses combined with other techniques. On the other side, the trickery could be found if the organizers are having the adequate mechanisms in place. If I remember correctly, there were such cases in the past when surveys or contests were in this way tricked, in several cases the trickery was discovered. Be careful, after the deed, and retribution!
I have the feeling that many have misunderstood maybe what knowledge and wisdom is about, how things are harnessed and evolve in life. Many bloggers, reputed writers and philosophers, believe that the crowds, sometimes referred as the masses or the mob, can’t be wise but rather stupid, thus appeared terms like stupidity of the masses, madness of the masses, etc. They are not so far away from the truth, especially when they are referring to the uneducated masses or to the panic-like effects, however the reality is that even a simple person who worked the land all his life or any did any other type of work and had no time for school could have more wisdom than a phony intellectual who spent all his life on the banks of schools without achieving a grain of wisdom or even knowledge. Again, with the risk of repeating myself, and as many have stressed, data is not information, information is not knowledge, and knowledge is not wisdom, the scale in this order implying a refinement and evolution of the thought process. Wisdom is a Holy Grail, and this not only in respect to spiritual life, but also to daily professional life, as it implies going above the knowledge existing in a certain field, either managerial, engineering, a simple job that pays the rent or any other activity. A simple person could hold his own grain of wisdom valid in his world, and with the eyes of an open mind and some chunk of knowledge from other domains, he might see the patterns a more educated person can’t grasp. For sure such a statement can’t be digested by researchers, especially when it’s almost impossible to express and measure wisdom, being more like a Morgan le Fay. It seems that is more important to touch the rays of wisdom, however it’s difficult to delimit where ends knowledge and begins wisdom, plus the various facets of the two, and from here the almighty confusion. Even if it’s difficult to believe that wisdom could be found at the fingertips of everybody, in definitive each person brings a different range of experiences, data, information and knowledge, different perspective of the same story, different cultural, social, geographical and cognitive aspects, in other words diversity of a wide range and richness. So on one side we are having the wisdom of the individual, even if it doesn’t fit the academic benchmarking for wisdom, but there is still some wisdom in there, and we have a network of people between each exists different grades of relationship (blood relation, friends, co-workers, neighbors, readers of the same material, etc.) with about 6 or less degrees of connectivity. An old English proverb says that "two’s a company, three’s a crowd", and above its relevant meaning, it’s actually more important its value as output of masses’ wisdom. Sayings, stories, verses, songs and other type of cultural manifestation of the crowds, are examples of wisdom, condensed wisdom I might say. Somebody was saying that all the great ideas of mankind were thought with many ages before, nothing more truly, and we are just rediscovering them now through the advances of modern techniques and thought.
People might be illiterates but could be masters in manual work or in any field that doesn’t involve writing, people might be shy but find incredible creative force when they are talking about or expressing their passions, they could come with unexpected solutions to complex problems when the problems are broken down to their language. Sometimes only by having a real partner of discussion or having somebody to address to, a person arrives to discover new perspectives in the process of externalizing knowledge, come with a new idea or find the solution to a problem. As Mark Zuckerberg remarks, "people have really gotten comfortable not only sharing more information and different kinds, but more openly and with more people - and that social norm is just something that has evolved over time". And very important, people are willing to give their knowledge free if the right context is met, but how do we achieve that?
Coming back to the before mentioned proverb, it gives a minimal definition for what it means a company, with direct and figurative meaning, an association of two people, respectively a crowd, as an association of at least three people. Witty definition in common sense language, much less than the definitions given by the academic literature, isn’t it? It is necessary to say that here the meaning of association is quite rich, implying any type of association made between people who come in contact in a form or another – organizations, ways of transportation, in queue lines, in chat rooms, forums or within the boundaries of a social network, in fact any place in which some type of communication occurs.
Communication is the backbone on which our society is based, and there are so many aspects, but what is important to retain, is the sharing of ideas which occurs between two or more people, the mode in which the communicated data, information or knowledge shape us. There is a micro scale, in which the communication happens between any two people of a group, and a macro scale, in which the communication is regarded as a whole, though the interactions between all the members of a group. In both cases is important how the input is transformed, loosing or gaining content, what each person retains or contributes. Researching the exchange of information occurred at multiple levels in our society is almost impossible, we only observe its effects, how markets change, how fast we receive important or irrelevant information, how meaning is changed voluntarily or involuntarily, altruistically or looking for profit. I’m mentioning this, because without understanding the whole process of communication and all its aspects we can’t use adequately the communication channels and harness the skills of people.
We could say that we are having the potentiality of crowds’ wisdom, but it depends how we harness it. Harvesting doesn’t resume in the ultimate action of taking the results of nature’s work, you have to invest some time in cultivating the seeds, take care of the plants, providing water and the needed care, the right temperature and fertilizer, consider the appropriate time for performing each action in the process. In addition you have to come also with some additional knowledge about the plants themselves, but also about the context, which is the best soil, what it takes to be in agriculture, to build an infrastructure for optimal work, etc. Who says that the same doesn’t apply to individuals and groups too?!
Individuals and groups need to be brought to the required level of education and knowledge in order to rise to the level of the demands. Wisdom involves some degree of knowledge and implicitly of information, the volume depending on the nature of the task at hand. Same you educate a kid upbringing him to a certain level of autonomy by repetitive task increasing in difficulty, upon its degree of understanding and pace, the same should apply to a group too, based on its intrinsic qualities and requirements. In the past years have been attempted to use the masses in order to solve several types of tasks, some with positive, but also many with negative results. If the masses can’t solve a certain type or types of problems, this doesn’t mean that they are dumb and posses no wisdom. An example of such a “failure” is the attempt to predict the trends of the various types of markets by using the masses, though it’s hard to think that such experiments could come with positive results as long there are too many interests and people who want to make profit by influencing the masses. This aspect stresses especially the need for independence, which adds to autonomy and diversity, other two characteristics that needs to be met by the crowds.
It’s also important to address a problem to the right community. I doubt, for example, that a complex problem of physics could be solved by addressing it to a group of sportives, excepting the cases when you talk about sportive physicists. Mentioning people who have knowledge coming from two or more domains, they are quite important, but not necessarily the most important. Depending on the problem at hand, the group should have a set of given properties that would allow it to approach and solve a problem.
There are many more aspects that need to be considered in relation to the crowds, hopefully I will manage to develop the ideas in a series of other posts.
13 November 2010
"Two’s a company, three’s a crowd" (saying)
"The only certainty about following the crowd is that you will all get there together." (Mychal Wynn)
"The man who follows the crowd will usually get no further than the crowd. The man who walks alone is likely to find himself in places no one has ever been." (Alan Ashley-Pitt)
"Crowds are somewhat like the sphinx of ancient fable: It is necessary to arrive at a solution of the problems offered by their psychology or to resign ourselves to being devoured by them." (Gustave Le Bon)
"What if the 'wisdom of crowds' turns out to be the ignorance of the masses? In fact, what if the Internet is a 'really bad thing' for the world and its population?" (Stephen Saunders)
"Men whose counsels you would not take as individuals lead you with ease in a crowd." (Cato)
"The amount of knowledge and talent dispersed among the human race has always outstripped our capacity to harness it. Crowdsourcing corrects that – but in doing so, it also unleashes the forces of creative destruction."
(Jeff Howe, Crowdsourcing, 2008) [via]
"The average man's opinions are much less foolish than they would be if he thought for himself." (Bertrand Russell)
"Men, it has been well said, think in herds. It will be seen that they go mad in herds, while they only recover their senses slowly, and one by one." (Charles Mackay, Extraordinary Popular Delusions and the Madness of Crowds, 1841)
"If it has to choose who is to be crucified, the crowd will always save Barabbas." (Jean Cocteau)
"The mob has many heads but no brains." (Thomas Fuller)
"When a hundred men stand together, each of them loses his mind and gets another one." (Friedrich Nietzsche)
"Truth happens to individuals, not to crowds." (Osho)
"Business today consists in persuading crowds." (T.S. Eliot)
"Opinions are formed in a process of open discussion and public debate, and where no opportunity for the forming of opinions exists, there may be moods, moods of the masses and moods of individuals, the latter no less fickle and unreliable than the former, but no opinion." (Hannah Arendt)
"Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination." (Poincare) [on psychology of discovery, different context but an interesting aspect]
"Quotes are empty and meaningless. It is how they are used that gives them purpose, how the person repeating those words gives them meaning. Good quotes do not offer the author immortality. Instead, they give the author limitless rebirths on the tongues of the masses." (Andy Clark)
"It is proof of a base and low mind for one to wish to think with the masses or majority, merely because the majority is the majority. Truth does not change because it is, or is not, believed by a majority of the people." (Giordano Bruno)
"The adjustment of reality to the masses and of the masses to reality is a process of unlimited scope, as much for thinking as for perception." (Walter Benjamin)
"The wisdom of the masses is not always....wise..." (Jon Stewart)
"In almost every act of our lives whether in the sphere of politics or business in our social conduct or our ethical thinking, we are dominated by the relatively small number of persons who understand the mental processes and social patterns of the masses. It is they who pull the wires that control the public mind." (Edward L. Bernays) [via]
"Only those who leisurely approach that which the masses are busy about can be busy about that which the masses take leisurely." (Lao Tzu) [via]
"Beauty is not defined by the masses but by the opinion of the individual." (Rune Leknes) [via]
"I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the masses." (Johann Kepler) [via]
"We should not listen to those who like to affirm that the voice of the people is the voice of God, for the tumult of the masses is truly close to madness." (Alcuin, Letter to Charlemagne) [via]
"[It] is impossible for us to establish a living vital connection with the masses unless we will work for them, through them and in their midst, not as their patrons but as their servants." (Gandhi) [via]
"Non-cooperation is an attempt to awaken the masses, to a sense of their dignity and power. This can only be done by enabling them to realize that they need not fear brute force, if they would but know the soul within." (Gandhi) [via]
"Educate and inform the whole mass of the people...they are the only sure reliance for the preservation of our liberty." (Thomas Jefferson)
"When distant and unfamiliar and complex things are communicated to great masses of people, the truth suffers a considerable and often a radical distortion. The complex is made over into the simple, the hypothetical into the dogmatic, and the relative into an absolute." (Walter Lippmann) [via]
"Observe the masses and do the opposite." (James Caan)
05 November 2010
A pattern could be considered as a perceptual structure derived from observed similarities existing in the structures existing in a given layer. Following the DIKW pyramid, from data to information, knowledge and further to wisdom and beyond, could be observed various patterns that offer new insights at the respective levels, patterns that could categorize the findings in layers beyond the layers in which they are observed. We could discuss thus about data patterns referring to patterns existing in data, typically aggregated in form of information, information patterns referring to patterns existing in knowledge, typically aggregated in form of knowledge, knowledge patterns referring to patterns existing in knowledge, typically aggregated in form of wisdom and eventually wisdom patterns, referring to patterns existing in wisdom.
The K-map, as a graphical tool used to represent chunks of information/knowledge and the associations existing between them, is not only a container for patterns, but a pattern itself, and this because the various types of K-maps are attempting to address special patterns in knowledge and its representational layout: chained, clustered, hierarchical, radial or networked. Patterns could be observed in the smallest representational elements existing in K-maps, the way the chunks, called nodes, are associated together forming micro-patterns, and further aggregated in creating macro-patterns. Ignoring the content of each node, and the meaning of associations, but keeping for example the direction of the associations, could be observed several simple patterns:
The above patterns are not necessarily representative, their scope being to provide an idea of what a pattern looks like: sequence (i), parallel sequences (ii), triangle (iii) & (iv), square (v), divergent (vi), convergent (vii) and any combination of them. For example the simplest pattern, the sequence, could be observed in all the other patterns excepting (xii) and (xiii) patterns, and it could include any numbers of nodes. Maybe more difficult to observe, the patterns (vi) and (vii) could be found in (viii) and (ix), in fact the number of emerging or emerging arrows from node could be greater than two. The number of such patterns could be in theory infinite, the nature offering a huge collection of such patterns, while many of the above patterns could be observed in K-maps too, the arrow playing the role of named or unnamed associations. Here are some variations of the above patterns based on concepts and the associations between them:
The concepts (“Concept i”, i=1, 2, 3, 4) from the above diagram stand as placeholders for any concepts that could fit in such patterns. For example “data”, “information”, “knowledge” and “wisdom” are forming a sequence based on same association which could be named “leads to”, “forms”, “aggregated in”, etc. Causality relations could be modeled with such sequences, for example “high data quality” leads to “accurate report”, which leads to “accurate analysis”, which leads to “better decisions”. However causality is more complex, witness being the various Causal Maps available on the Web, for example “theory”, “concept” and “grounding”, respectively “customer satisfaction”, “product quality”, “customer loyalty” and “brand strength” seems to “break” the sequence pattern. Please note that the associations don’t necessarily to be true, they could represent as well an opinion or be rooted in experiments that confirms them. The laws of causality, complexity and patterns are too complex to be debated in here, in fact each person accumulated in time knowledge that matches such patterns.
In the above diagram, could be observed that the examples based on causality are situated at the top, respectively at the bottom of the diagram, in between different types of associations. Is it there any reasons for that? In the moment we asked ourselves such a question, we are already attempting to identify a spatial pattern referring to the positioning in a given area, in this case a diagram. Spatial patterns are at their turn quite complex patterns, we could see it in the world around us. Does the fact that the same distance exists between various points, that forms are contained one in the other or that the associations are dispersed radially from a common point tell us something? What do such patterns represent for us? Sometimes we have to make abstraction of the associations and content and see the macro-forms created by clusters of such patterns in order to discern the patterns. Does it seem too complicated? It isn’t at all. Just look at a poem formed of 4 strophes and a common rhyme. We are ignoring in fact what the words represent, the letters of a word, or the points that form a letter, we consider just the form of the strophes and the endings, that’s such a pattern. In nature there are so many such patterns, some even more simple than we might think of, and here are some examples:
The world of patterns doesn’t stop here, we could associate patterns related to all our senses, resulting thus olfactory, tactile, auditory or kinesthetic patterns. It seems that such patterns are moving beyond our representational sphere, doesn’t it? Not at all, everything could be reduced to a concept and the associations between them, the difficulty residing in how to choose the “best” pattern that reveals the represented knowledge.
02 November 2010
Unfortunately the richness of natural language goes above the capabilities of the current representational tools, for example the temporal, spatial, causal and conditional associations, or the associations between whole propositions are not so easy to represent in many of the K-maps available. Given the rules of syntax, in natural language a proposition is formed typically at minimum of a triple, while a typical proposition could be expressed as one or more such triples. On the other side, a chunk of meaning could be represented as one, two or more triples that span within one or more propositions, same as from a whole text only 2-3 triples could be relevant. As chunks could spread along several propositions, it is necessary to identify the meaningful triples and recombine them in more complex constructs, such a construct being the knowlet.
Because has been discussed in several occasions about chunks of meaning, some examples are necessary in order to understand what is meant by this construct. The simplest chunk of meaning is the concept itself, for example “collective”, “intelligence”, “collective intelligence” and “harnessing collective intelligence” are such chunks. The next logical type of chunk of meaning is a simple triple formed actually from three concepts, for example “harnessing collective intelligence is a web 2.0 principle” is based on “harnessing collective intelligence”, “is a” and “web 2.0 principle”. A minimum of 4 concepts could result in two triples, for example “web as platform and harnessing collective intelligence are web 2.0 principles”, the two triples could be split in different propositions. By adding one more concept we arrive to three triples, and the logic could be followed, resulting several types of patterns.
Is the latest example still a chunk of meaning? Yes, it is because they share together the same object within the same proposition, enclosed in a definition-like clause. Definitions are typically examples of such unitary chunks of meaning, for example let’s consider the definition of K-mapping given by Dr. Ann Hylton:
"Knowledge Mapping is the process of surveying, assessing and linking the information, knowledge, competencies and proficiencies held by individuals and groups within an organization." 
Proposition’s structure could be represented in a K-map resembling a Concept Map as follows:
The representational language depends from person to person and from one KM to another, for example the same proposition could be rewritten as follows:
Here’s another example following a similar structure, this time based on D. Hyerle’s definition for K-mapping:
Knowledge Mapping is “a rich synthesis of thinking processes, mental strategies, techniques and technologies, and knowledge that enables humans to investigate unknowns, show patterns of information, and then use the map to express, build, and assess new knowledge” .
Which KM is better is a matter of personal taste, in theory the radial/hierarchical structures are easier to understand and navigate than the networked structures, though the later category of structures is closer to the structure of knowledge, the way concepts are structured. On the other side it could be problematic to represent the two definitions in the same K-map. Here’s an attempt based on propositions’ structure, respectively by restructuring concepts and associations:
Each of the two approaches comes with its advantages and disadvantages, the first K-map being closer to initial definitions’ formulation, highlighting the concepts found closer to the subject, but more difficult to represent, while the second, more condensed, closer to the representation of knowledge as triples, but keeping less from the initial structure. The maps are not necessarily representative, and neither too elaborate, they represent just the raw representation of two definitions. It would be useful to include multiple definitions in the same K-map, attempting to represent all the attributes of a concept and most representative associations. The downside of such K-maps is that they are more complex and all the consequences deriving from it.
 M. Jafari, P. Akhavan, A. Bourouni, R. H. Amiri, (2009). A Framework For The Selection Of Knowledge Mapping Techniques. Journal of Knowledge Management Practice, Vol. 10, No. 1, [Online] Available from: http://www.tlainc.com/articl180.htm (Accessed:16 October 2010)
 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: http://www.springerlink.com/content/x57121720731381j/ (Accessed: 23 June 2009)
01 November 2010
Associations, in several contexts called relations, are links between concepts, and even if they are labeled or not, explicit or implicit, they have assigned a meaning too. The split between concepts and labels introduces two perspectives:
1. Knowledge broken down to concepts in which some of the concepts function as associations between other concepts.
2. Represented knowledge broken down as labels in which some of the labels function as associations between other labels.
A simple example of association is the one implied by the object agent verb (OAV) construct, also called the object subject verb (OSV), that stands not only at the base of linguistics topology but also at the base of RDF triples (in this context referred as subject-predicate-object, concept-connection-concept or ‘entity-event-entity’) rooted in the linguistics topology. Such constructs are the “is-a” and “has-a” constructs, often used in knowledge representation. For example “whale is a sea mammal” could be expressed as (“whale”, “is-a”, “sea mammal”) and “whale has a tail” as (“whale”, “has-a’, “tail”) in (subject, predicate, object) notation, however representing knowledge as such triples is not an easy task, but the visual representation of such triples with nodes and links reduces the complexity to some degree.
The domain knowledge could be relatively expressed as such isolated triples, but in knowledge representation, in order to reduce the complexity of visualization and navigation, it’s simpler to join such triples when they have common concepts. Thus the two triples could be represented as follows:
The arrow shows in this case the agent, the first label in the sequence being the subject, while the label in between being the predicate. There are maps that don’t make use of arrows, in some cases the radial flow expressing the direction like in the case of Mind Maps, and maps in which there is no direction implied or a bidirectional row implies a bidirectional association, as in the case of synonymy.
The use of arrows and adequate labeling boxes facilitates KM’s understanding, in what concerns the role of labels in a triple, and navigation, in what concerns the flow/direction. As can be seen from the last diagram a subject could be involved in multiple associations, in the same way an object or predicate could be involved in multiple associations too. In the next KM could be observed for example how the same predicated is involved in multiple associations describing the anatomy of a whale.
Whale Knowledge Map (adapted after whale anatomy)
The original representation could function as a K-map as well, though images are more difficult to process than the maps built with adequate software, the later offering also the possibility of conversion to a portable format that could be further processed. In addition the spatial disposition of concepts could play a role as well, in this case being correlated with the disposal within whale’s anatomy. In more complex KMs the use of “background” images is not always easy to embed, in addition the multitude of connections increasing the overall complexity. The form of representation could depend on each person’s preferences, the association could be explicit as well as implicit, and typically only one of them is use. Here are the same “has-a” associations represented with the help of circle map (implicit associations) and bubble map (explicit associations).
|Bubble map||Circle Map|
The “is-a” and “has-a” associations are used in combination with any other types of associations, of importance being especially the causality (A causes B), synonymy (A is synonym of B) or antonymy (A is antonym of B), precedence (A precedes B) or concomitance (A occurs at the same time as B), etc. In fact any verb, substantive or even prepositions could play in theory the role of an association. If the above examples fall in the “verb as association” category, the use of substantives as associations is maybe more difficult to intuit, so here is an example based on whale’s anatomy in which the “has-a” has been replaced with “anatomic part” association:
Between two concepts there could be in theory multiple associations, more than one explicit association, though few are such cases because typically is stressed only the most important/relevant association. In the below image, a part of a KM on “self-transcending knowledge”, could be seen how the “competitive advantage” is involved in two associations with the same concept.Self-transcending knowledge KM part (KM based on  text)
The existence of multiple associations has several other implications in what concerns associations’ type. For example causality implies two inverse associations: “A causes B”, respectively “B caused by A”, in fact dealing with the same meaning associated in different directions by inversion of terms. Such constructs could be confusing, therefore a good practice is to adopt only one of the two associations; the simplest approach is to simply use “A causes B”. A similar type of association is the transposed association, in which from “A imply B” is inferred that “Not-B imply Not-A”. With this we entered in the territory of
deductive reasoning, entailment and of rules of inference. Deductive reasoning could prove to be quite complex and of great use, especially when is intended to infer new associations (inferred associations) based on an existing set of associations. For example if in a KM we have that “A implies B” and “B implies A”, then we could deal with the equivalent association “A equivalent to B”, in mathematical terms expressed as “A=B”. Another simple logical inference is based on the simple rule of inference: if “A imply B” and “B imply C”, then “B imply C”. Implication could be applied also to causality, synonymy and several other types of associations.
The fact is that many of the rules of inference that apply is deductive reason could be used to KMs too, special inference engines could be used for this purpose. Associations between two or more concepts don’t have to be of the same type in order to prove to be useful, or in some cases even if the association seems to be of different types, the meaning they carry could be sufficient to allow an association to participate in inferences, this being valid especially for the associations belonging to the same class of meaning. In addition, associations of the same type and the concepts involved could reveal interesting properties that could be analyzed from the perspective of (superior) algebra or network theory.
Cardinality of Associations
The above representations have one important issue - they don’t reflect the cardinality of concepts, how many elements of the same concept participate in the associations. For example the whale has two blowholes and two pectorial fins, while a table has for legs, etc. In database modeling the associations, actually called relations, include the cardinality (e.g. 1-to-1, 1-to-n, n-to-n) though it just highlights that there is one or multiple records/entities associated in relations. In our case is typically required to specify the actual cardinality. As database model could be regarded as KM too, it’s thus necessary to address both types of cardinality, when they apply.
 A. Kaiser, B. Fordinal. (2010). Creating a ba for generating self-transcending knowledge. Journal of Knowledge Management.Vol.14, no. 6 [Online] 10.1108/13673271011084943
Knowledge could be broken down to concepts and the associations between them, words functioning as links between concepts. A concept could be seen as a unit or chunk of meaning, for example “mother”, “father”, “child”, “home” are a few of the concepts we incorporate in our conceptual vocabulary, the collection of concepts we hold in our mental world. The previous four mentioned examples are just words, though words are just labels, transporters of meaning, and they don’t equate to concepts. A word (written or spoken) same as an image, a symbol or sound are just a representation/externalization of a concept outside of the mental world, we could regarded them simple as labels. Sure, they are strong correlated, and concepts could exist without labels, same as labels could exist without the articulation of a concept in the mental world. In a simpler formulation we could say that:
Label + Meaning = Concept
Meaning and labels are concepts too, fact that makes the definition kind of redundant, but that’s less important as long the overall meaning is understood. In addition the concept of meaning is quite complex, meaning being considered as existing within a given context, a context that carries its own meaning and it’s a concept in itself. More redundancy, isn’t it?
We could in theory put on a paper all the concepts we know, to be more focused, all the concepts we know related to other concept functioning as topic. Such constructs are similar to the ones of tag clouds, user-generated tags used to describe the content of a web page. Another type of such collection of concepts is the shopping list or any other types of lists.
|Example of tag cloud||Example of shopping list|
Each of the words from the above tag cloud, respectively shopping list, are labels of the concepts they represent. In contrast to the shopping list, the size of the labels used in the tag cloud is proportional with their occurrence, but that’s less important for now. The fact is that both are representing a collection of concepts. More complex collections could be based on concepts derived from scientific works, book indexes are another such of example.
In the above shop list, “movie tickets” is a multipart label for a “single” concept, though it’s composed of the labels of two different concepts – “movie” and “ticket”. In this way concepts/labels could be formed by the aggregation of meaning for concepts, respectively concatenation of labels for labels. In theory we could put together as many of concepts or labels as we wish, though there are some limits imposed by linguistics. In daily life aggregations/concatenations of 2-3 concepts/labels are pretty usual: “knowledge mapping” (= “knowledge” + “mapping”), “knowledge management”, “business intelligence”, “collective intelligence”, “harnessing collective intelligence”, etc. There are also examples of labels encompassing already a concatenation of other labels, words formed with prefixes (e.g.: “un” + ”believable” = ”unbelievable”), affixes (“engineer” + ”ing” = ”engineering”) or hybrid/compound words (e.g. “auto” + ”mobile” = “automobile”) are the simplest examples we used on a daily basis, some of the languages being more abundant than the others in such compounds (e.g. German language is quite rich in such hybrid words). The linguistics and semantic meaning of words offer us a deeper overview on the formation of words and meaning, though we don’t have to go that far. I will just limit myself to mention that a morpheme is the smallest compound of a word, composed at its turn of multiple phonemes, the smallest linguistically distinctive units of sound, and graphemes, the smallest units of written language. In addition words or labels does not necessarily have to respect the rules of language morphology as a whole, one of such compounds that entered in my vocabulary many years ago, comes from the Disney’s musical film Mary Poppins, and those who the movie, probably already intuit what I’m talking about: Supercalifragilisticexpialidocious is formed, according to Wikipedia, from the following morphemes: super- "above", cali- "beauty", fragilistic- "delicate", expiali- "to atone", and docious- "educable", and the sum of these parts signifying roughly "atoning for educability through delicate beauty".
Given the richness of languages in what concerns the morphology, syntax and declension, how do we choose the labels? Also this is a complex topic and my knowledge stops somewhere. I prefer to use the infinitive form for verbs, nominative and singular form for substantives, sometimes called the dictionary forms, and include the prepositions when they change the meaning (English language is full of such constructs). It’s not always so easy to do that, but I try to stick to it whenever is possible. In what concerns the labels formed of multiple other labels I prefer to choose the smallest unit of meaning that defines a concept “uniquely”.
Classes of Meaning
A class of meaning equivalence, shortly class of meaning, comprises all the labels that share the same meaning . Such a class comprises all the synonyms, acronyms and forms of construction of natural language used to label a concept. For example, depending on context, any of the following labels could be considered as belonging to the same class of meaning: abode, apartment, flat, home, mansion or residence. Many of us use acronyms in daily life, with formal or informal character: EOD (End of Day), ASAP (As Soon As Possible), US (United States, Uncle Sam, Upstream, Ultrasound), KM (Knowledge Map, Knowledge Management, Knowledge Mapping, kilometre), etc. The syntagm “forms of construction of natural language” refers primarily to the various elements of orthography hyphenation, capitalization, word breaks, emphasis and punctuation, which introduce some variance in the labelling of concepts. On whether we write “knowledge based” or “knowledge-based”, “center” or “centre”, “Knowledge Management” or “knowledge management”, “class of meaning” or “meaning class”, the various labels refer to the same concept. Normally in a Map would be enough to include only one member of a class of meaning, unless is intended to highlight the synonymy or any other similar association type.
It’s natural to talk about K-maps within Knowledge Representation, and extensively within Knowledge Management, domains in which the process of creating a K-map is known as Knowledge Mapping, shortly K-mapping. In essence that’s what K-mapping is about, creating a K-map, however in literature could be found more elaborated definitions. According to D. Hyerle, K-mapping is “a rich synthesis of thinking processes, mental strategies, techniques and technologies, and knowledge that enables humans to investigate unknowns, show patterns of information, and then use the map to express, build, and assess new knowledge” . Within the same context but from a slightly different perspective,  regards it as a “consciously designed communication medium using graphical presentation of text, stories, models, numbers or abstract symbols between map makers and map users”. In the context of K-mapping in organizations, B. Bergeron defines it as the “process of identifying who knows what, how the information is stored in the organization, where it’s stored, and how the stores of information are interrelated” . All the above definitions focus on mapping as a process, knowledge as the object of the mapping process and the context in which it occurs.
The use of various types of K-maps introduces similar concepts, K-mapping being referred as concept mapping when talking about concept maps or when the granularity of a map is at concept level, mind mapping when the focus is Mind Maps or externalization of mental maps, semantic mapping when discussing about semantic maps, process mapping in the case of process maps, etc. Related concepts stress other aspects of K-mapping referring to different levels of abstraction, for example ontology creation or ontology engineering, in this context ontology mapping referring to the mapping between different ontologies. Same happens in the world of the databases in which data modeling or semantic modeling refers at the creation of a data model, while data mapping refers at the mapping between two structures.
As stressed before, the various types of K-maps in use introduce their own creational philosophy, which with a little effort could be raised at the state of methodology. K-mapping as a process could be reduced to input, output and what happens in between. As input for a K-map could be used the various types of media content, mental models, knowledge of experts, discussions outcomes or any other sources of information. As knowledge is not always available at our disposal, searching for knowledge, identifying knowledge is quite a time consuming task, especially when knowledge is not indexed, easily accessible or we don’t exactly know what we are searching for. In general we talk about knowledge acquisition, which refers to the process of extracting knowledge, structuring and organization of knowledge. When creating a K-map we are doing extensively knowledge acquisition, essential in the process of learning. In exchange, when we create K-maps on the mental models, we are externalizing our knowledge, transforming the tacit in explicit knowledge, figuring out or better said evaluating what we stored in our brain, grounding of knowledge by finding meanings, formalizing concepts, finding the best formulation, finding new associations, building on previous knowledge, examine beliefs, integrating, mixing and recombining knowledge, identify patterns in knowledge, patterns of thinking, becoming creative, etc. Also these aspects are part of K-mapping, even if they are not so visible in the process, however they are stressed especially during K-mapping. The structuring and organization of knowledge in K- mapping is done in representational form (visualization), translated into spatial organization or simple aggregation of information, in patterns or models of expressions, and here the various types of K-maps are used as a form of expression. Mapping techniques need to be flexible in order to reflect the representational richness of knowledge, they evolve with experience, “the one who maps” learning with time to take advantage of the appropriate type of K-map or pattern. K-mapping is thus an iterative process, a K-map being evolved during several stages, the final outcome being unexpectedly different than the inputs or expected outcomes.
K-mapping applies to individuals as well as to groups, collaborative or coordinative K-maps involving more complex forms of acquisition, process or visualization, often being involved some forms of negotiation and knowledge sharing from which the output emerges. Collaborative K-mapping seems to be preponderant to the contexts in which the force of the group emerges, mainly economical and scholar organizations, and recently social networks.
 M. Jafari, P. Akhavan, A. Bourouni, R. H. Amiri, (2009). A Framework For The Selection Of Knowledge Mapping Techniques. Journal of Knowledge Management Practice, Vol. 10, No. 1, [Online] Available from: http://www.tlainc.com/articl180.htm (Accessed:16 October 2010)
 B. Bergeron. (2003). Essentials of Knowledge Management. John Wiley & Sons, Inc. ISBN: 0-471-28113-1.
 H. P. Tseng, Y-C. Lin (2008) A Knowledge Management Portal System for Construction Projects Using Knowledge Map. Knowledge Management:
Concepts, Methodologies, Tools and Applications, M.E. Jennex (Ed.). ISBN-13: 978-1-59904-934-2.