An Introduction to Connective Knowledge ~ Ste...

An Introduction to Connective Knowledge
By Stephen Downes
December 22, 2005
http://www.downes.ca/cgi-bin/page.cgi?post=33034
This paper provides an overview of connective knowledge. It is intended to be an introduction, expressed as non-technically as possible. Revised and Updated (minor corrections and typos only) and placed in MS-Word Document form, November 27, 2007.Click here. The version that follows below is the original (uncorrected) version).
Yet another article, describing new forms of knowledge asprobablistic, has crossed my desk today, and consequently it seems appropriate at this time to type a few words on the nature of distributed knowledge.
It should go without saying that these are my own thoughts, and this discussion should not therefore be considered an authoritative reference on the subject. Moreover, this is intended to be a brief overview, and not an academic treatise on the subject.
a. Types of Knowledge
You probably grew up learning that there are two major types of knowledge: qualitative and quantitative. These two types of knowledge have their origin in major schools of history and philosophy, the former in the works of the ancientGreeks, and the latter inArabic and then laterRenaissance philosophy.
Distributed knowledge adds a third major category to this domain, knowledge that could be described as connective. A property of one entity must lead to or become a property of another entity in order for them to be considered connected; the knowledge that results from such connections is connective knowledge.
This is more than just the existence of a relation between one entity and another; it implies interaction. Arelation - such as 'taller than' or 'next to' - is a type of quality. It describes a property of the object in question, with reference to a second object. But the fact that I am, say, 'taller than' Fred tells us nothing about how Fred and I interact. That is something different.
This is why it is incorrect to represent distributed knowledge merely as a type of probabilistic knowledge. The logic of probability implies no connection between correlated events; it merely observes a distribution. A connected system will exhibit probabilistic characteristics, but it is not itself probabilistic.
Probabilistic knowledge is a type of quantitative knowledge. It is based on the counting of things (or events, or whatever) and of comparisons between one count and another (one needs only to readCarnap to see this clearly). A poll, for example, gives us probabilistic information; it tells us how many people would vote today, and by inference, would vote tomorrow. But the fact that Janet would vote one way, and I would vote one way, tells us nothing about how Janet and I interact.
Connective knowledge requires an interaction. More to the point, connective knowledge is knowledge of the connection. If Janet votes a certain way because I told her to, an interaction has taken place and a connection has been established. The knowledge thus observed consists not in how Janet and I will vote, nor in how many of us will vote, but rather, in the observation that there is this type of connection between myself and Janet.
b. Interpretation
What we 'know' about the world is irreducibly interpretive. That is to say, we do not through our senses and cognition obtain any sort of direct knowledge about the world, but rather, interpret the sensations we receive. This is true not only of connective knowledge, but of all three types of knowledge.
Consider qualities, for example. We take it as basic or atomic (see people likeAyer for example) that a statement like 'this apple is red' represents a pure and unadjusted fact. However, looking at this more closely tells us how much we have added to our original sensation in order to arrive at this fact:
First of all, the apple itself has no inherent colour.Colour is a property (specifically, the wavelength) of light reflecting off the apple. In different coloured light, the apple will appear to us differently - it appears white in red light, for example, or grey in diminished light. Yet we say the apple is 'red' - standardizing our colour descriptions to adapt to the natural light that surrounds us day to day.
Second, our perception of the apple as 'red' depends on our organizing light patterns in a certain way. When I was a child, thespectrum had six colours - red, orange, yellow, green, blue and purple. As an adult, I find that a seventh - indigo - has been added. It's not that a new colour came into existence when I was twenty, it's that our nomenclature changed. In a similar way, we can divide the colours of the spectrum in numerous ways: 'red', for example, can include shades as varied as 'crimson' and 'cherry'. Or '#ff0000'.
And third, when we say that 'the apple is red' we are drawing on our prior linguistic ability to use the words 'apple' and 'red' correctly and apply them to appropriate circumstances. Indeed, our prior knowledge often shapes our perceptions themselves: were you shown an apple in diminished light, so that all you could see was grey, and asked what colour it was, you would still respond 'red' because of your prior expectations about apples and redness.
Less intuitively so, but equally clearly, interpretation applies to quantitative knowledge as well. It is easy to say that a sentence like 'there are twenty schoolchildren in the yard' is a basic fact, but this all depends on how you classify schoolchildren. Suppose, unknown to us all, one of the children had just been expelled; is our statement now false? Not obviously so. Perhaps one of them is over sixteen - is this person still a child (and hence, a schoolchild)? It depends on your point of view.
Quantification is essentially the enumeration of members of a category or set. Consequently, it depends crucially on how that set is defined. But membership in a set, in turn, is (typically) based on the properties or qualities of the entities in question. So such membership is based on interpretation, and hence, so is counting.
One might be tempted to say that even though applied instances of counting are based on interpretation, mathematics itself is not. But in my view, this too would be mistaken. For one thing, as people such asMill andKitcher argue, the rules of mathematics depend on empirical verification for their importance: we say that one plus one is two, not out of some innate sense of goodness, but because when we put one sheep together with another, we observe that there are two. Nothing but our observations prevents us from saying that one plus one is three, and in some contexts such a statement makes perfect sense.
c. Emergence
Emergence is a hard concept, but at this point I can gloss it with a simple characterization: emergence is interpretation applied to connections.
There are two (equally valid) ways of thinking about this:
First, we may perceive an actual set of connections linking a group of entities as a distinct whole. For example, when one domino topples another, and so on, in turn, and we observe this from a distance, we may observe what appears to be a wave moving through the dominos. The wave that we observe can be said to be an 'emergent phenomenon' - it is not a property of the dominos themselves, or even of the falling of the dominos, but of the connectedness of the falling - because one domino causes the next to fall, we see a wave.
Second, we may perceive something as a distinct whole and interpret this as a set of connections. For example, when we look at the image of Richard Nixon on the television, we do not perceive the individual pixels, but rather, the image of a person. But our inference goes beyond merely the observation of the person; if asked, we would say that the appearances of the pixels are connected to each other, through the mechanism of having a common origin (Richard Nixon himself) and the mechanism of video broadcasting.
Emergence is fundamentally the result of interpretation. As mystics (and Spinoza) are fond of arguing, everything is connected. At a certain point, as the old saying goes, when abutterfly flaps its wings in China, the result is a thunderstorm in Halifax. But broadcasters in Halifax do not watch butterflies in China in order to predict the weather, because this connection will be of no use to them. Typically, they will look at more intermediate events, themselevs emergent properties, such as waves of air moving through the atmosphere (known locally as 'cold fronts').
In the same way, the observation of sets of connections between entities depends a great deal on what we already believe. That is why we see swans in clouds orfaces on Mars when, manifestly, there are none. We have brought our prior knowledge of connected entities to bear on our interpretations of these phenomena. AsHume would say, our 'perception' of a causal relationship between two events is more a matter of 'custom and habit' than it is of observation.
d. Physicality
We generally think of knowledge as being about facts, and about facts in turn as being grounded in an independent reality, a physical reality. Consequently, it is natural for us to say, for example, that when we see that something is red, that there is a physical basis for that statement, that even if we bring some interpretation to bear, there is some physical fact of the matter than makes the apple red, and not blue.
Certainly, were we not to think of things this way, we would be hard pressed to say anything about anything. Physicality provides us with a substrate on which to hang our interpretations, asKant would say, a necessary condition for the possibility of perception. Physicality moreover offers us a means of sorting between what might be called 'correct' interpretations and 'misperceptions', between reality and a mirage.
All this may be the case, but nonetheless, there is nothing in our interpretations that is inherently based in physical reality, and hence, nothing that precludes our discussion of them without reference to this foundation. Indeed, this has been enormously useful in other domains. Despite the empirical basis of mathematics, it is much more productive and useful to refer to quantity without reference to the physical entities being counted, to (in other words) think of quantity in the abstract. The same is true of quality. Thinking of quality in the abstract leads to Aristotle'ssyllogisms and the basis of categorical reasoning.
Moreover, non-physical entities may have (or be attributed) properties that are themselves (on this theory) based in physical properties. In our ideas and dreams, we think of vivid colours and large numbers. And the ideas are transferable. Consider the concept of 'purple prose' - an expression which is in all cases either meaningless or false, yet of significant utility and meaning.
What is to be learned from this? That the entities in the various categories of knowledge - be they properties or numbers - are themselves not real. When we talk about 'redness', we are not talking about something that has an independent, concrete existence in the world, but rather, in something that exists (insofar as it exists at all) only in our own minds. When we talk about the number 'four', we are not describing somePlatonic entity, but rather, nothing more than our own thoughts or sensations.
That does not make them less 'real'. Our perception of the colour 'red' is as real as any phenomenon in the world. It is merely to distinguish between the perception, which results from a complex of factors, from the physical entity, which ostensively caused it.
In a similar manner, our interpretations of connections is distinct from the actual set of interactions that may exist in the world. Consider, for example,conspiracy theories - the postulation of a complex and inter-related set of people and events leading to the conclusion that someone is out to get you. Such theories, notoriously, have no basis in the physical world. But they may nonetheless be contemplated, and discussed, and passed along, as though they were real. And the experience of a conspiracy theory may be, to the perceiver, every bit as real to the person having the experience.
There is a tendency on the part of readers, whether of[Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, July 25, 2007
I am read two of your articles, An Introduction to Conectivism and one about Technonolgy, they are very good. I got to know about you when I a CEGSA conference last week, here you presented. I will refer people to your wonderful work.
By
C. J. Setlhong [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, March 23, 2007
It is enormous amount of knowledge -- a wonderful blog topic!
A similar take is available on another new learning blog http://interlinkedlearning.blogspot.com/ [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
, February 22, 2007
Tremendous! Wonderful discussion of knowledge and how it is changing and staying the same all at once. Beleive it or not very usefull for me in my class (elementary)creating wikis using wikipedia and creating content.
Really a masterpiece of the blogosphere! [Comment] [Permalink]
Connective Knowledge
Anymouse, January 26, 2007
If you agree with this basic "carrousel" model combining associationism, concept mapping and yellow sticky notes, I would be interested to further share your thoughts and possible applications:
http://www.pmm.nl/philo/philo.htm
Best regards,
Ron C. de Weijze
Amsterdam, NL
[Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, January 24, 2007
I am a student and need a article in effecting teaching for a research project.
my name is lydia [Comment] [Permalink]

Anymouse, November 18, 2006
... no changes ... no changes ... no changes ... no changes ... no changes ... no changes ... no changes ... no changes ... no changes ... no changes ... no changes ... [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, June 2, 2006
I think it is part of the language that you are using but it is mostly how you think it. Your thoughts just create the knowing. Anna@www.azerivista.com [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Stephen Downes, February 9, 2006
When you say "I would like for you to operationalize the use of 'language' in this paper" can you tell me specifically what you are looking for? I would be happy to clarify, but I need to understand the question. [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, February 8, 2006
I would like to comment on this, especially your ideas on language, but first I would like for you to operationalize the use of "language" in this paper for me. Thanks Danny drdanny@charter.net [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, January 5, 2006
FYI. Leigh Blackall ( http://leighblackall.wikispaces.org )has been invited to talk to ; mLearning - What in the world is web2.0? Implications, predictions and other anecdotes on Thursday 12th January, 2 - 4 pm at the Centre for Learning Innovation, TAFE NSW, Department of education and Training, NSW Australia. See http://www.moblog.co.uk/blog/CLI for live blog on the day. More networked knowledge. [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, January 4, 2006
While it is incredibly dense and hard to understand, the ideas that CS Peirce developed about phaneron has some answers to the questions about the nature of knowledge that you do not touch upon very well. http://cura.free.fr/16peiren.html is a link to a critique of CS Peirce's work. I would also look at this http://www.univ-perp.fr/see/rch/lts/marty/flows_of_signs.htm which talks about the application of Peircian ideas to networks. [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
John Walling, December 30, 2005
Concepts which have given me my framework for the connections between knowledge and reality are: 1) Uncertainty Principal - Heisenberg 2) Cosmology - Dark matter, big bang 3) Eastern religions and duality - yin-yang, energy-matter, particle-waves 4) Darwinian Evolution 5) Cultural Anthropology - Colin Turnbull, Margaret Mead 6) Quantum theory: quantum entanglement, quantum foam of space, etc. 7) Fuzzy Logic - Lotfi Zadeh, Bart Kosko 8) Complexity&Chaos theory - Santa Fe Institute --- One time on the street, a Lyndon LaRouche vendor asked me did I know what was the truth. I answered, "Truth is what you believe." It was not the answer he wanted. I had never spoken that sentence before but the more I thought about it the more I realized I couldn't punch any holes in the statement. Knowledge, truth,&reality are entertwined in ways that we can only glimpse with the intellectual tools at are disposal. [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, December 29, 2005
Excellent article and I particularly like the structure of your explanations. [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, December 28, 2005
Stephen, this is a fascinating essay as so much of your postings are. Thanks for a great year of stimulating and challenging reading - it has certainly helped prevent me getting bogged down in the mundane. Looking forward to an exciting 2006. Karen (Tasmania, Australia). [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, December 22, 2005
Stephen What a delightful essay to end a marvellous year of postings, thoughts and pointers. Why I enjoy your work so much is because it challenges epistemology and ontology in an increasingly connected global network. I hope you enjoyed writing the piece. I will continue to enjoy reading it! It underscores for me that all discourse has many layers of meaning. Best wishes from Australia! Keith [Comment] [Permalink]
Re: An Introduction to Connective Knowledge
Anymouse, December 22, 2005
You say, "For one thing, as people such as Mill and Kitcher argue, the rules of mathematics depend on empirical verification for their importance: we say that one plus one is two, not out of some innate sense of goodness, but because when we put one sheep together with another, we observe that there are two." Not exactly. While it's true that empirical verification is possible, it is not necessary. Proof of the existence of integers, the existence of addition, and that one plus one equals two may be had via axiomatic set theory. Granted, "axiomatic" set theory relies on a set of presumed axioms, and the point of those axioms is to arrive at a theory that is empirically verifiable, but nevertheless, empirical verification is not necessary to argue that one plus one equals two. [Comment] [Permalink]