Connectivism and Connective Knowledge

During our elluminate session today, the conversation turned to discussions of how chaos and complexity impact learning.

As stated in the paper I submitted for this week's reading, both chaos and complexity theory have their roots in the physical sciences. But, we can still broadly apply principles from each theory to social sciences. The shift from Newton's clockwork universe to the world of probability and unpredictability is monumental. I would posit that a similar shift needs to occur in education.

So, I guess the question I would throw out to the group is: In what way is learning complex? In what way is it chaotic?

There is many ways this question can be answered.

Learning is complex in the traditional sense because of the physical location and constraints placed upon learners in a traditional classroom. Also the lack over conversely the abundance of resources, etc...

Learning is then complex regarding the individual learners unique needs or interests, may be completely divergent from the guided curriculum (however basics still need to be learned to function properly in society, and no 1 teacher could modify program to fit each individuals requirements at a K to 12 level)

Learning also becomes complex when looking at each individuals unique learning issues, what road blocks do they have, and why do they have them.

Just like complexity theory, this could go on and on and on... or like the Energizer Bunny...

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Complexity Simplified & applied to learning

If you think of chaotic systems in terms of the path followed by an "actor" through a 'landscape', the unpredictability occurs because you cannot precisely know the forces acting on the actor. This sort of situation can occur if the centres of attraction are moving (or are 'strange attractors') and if there are just very many of them. I find it useful to picture a pinball table with magnets under the tabletop at various points, which may or may not be switched on, and which can be of varying strengths (and, if you want to get more complicated, which can move).

The learner is the pinball, trying to get from point A to point B. Sources of information (nodes, in connectivism terms) are attractors - they have a degree of interest which attracts the learner. What is 'worse' is that the learner subtly changes through interacting with each of the sources, and will be attracted to different extents by the other sources they encounter later.

To try to plot a course (sorry, pun not intended) through this 'learning landscape' a priori would be brave, if not foolhardy. To navigate the landscape succesfully you need to use constant corrections to your course, determining the next step in light of the local terrain. But for many learners, the view of the landscape is obscured (because maps are few and far between) so a mentor (or pilot) can be very useful to guide them through the process, able to take a slightly wider view of the surrounding concepts.

As the number of sources of information (attractors) becomes greater (thanks to the internet) the greater the chance of the complexity, and thus the chaos, affecting the learner. As someone else suggested on the forum, periods of reflection can help with this - similar to taking shelter in a safe harbour on a turbulent sea, or even just lowering the sails and dropping anchor for a while.

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well...
I Participe...really don't think to realize.

CHOAS: In my vocabulary is mean to relationship with other people..In education is similar but share another elements are the reseach, the paper work and work groups...

So similar that's course...many different opinios about many issues.(Choatic)

COMPLEXITY: the complexity it´s to try comprehension the kind of thinking ¿what people think?...this question not to answer. Isn´t simply...

The actors (role)each party to play in the classroom for example, teach and study...in the cybersapace (internet) to role to complety the labor plus tools...y say video, audio and learning objects...

The creative and feedback...is the clue...

Bye,

Juliana Pachón Hernández

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Learning is complex not because of the subject matter but because of the learner. There's emotional connections to learning (mostly based on our early impressions of school and how we did in those learning contexts). Stephen Brookfield talks a lot about the emotionality of the classroom in his book "The Skillful Teacher".

When you get several complex people in a room with different agendas, different expected outcomes and different needs, that I would say is chaotic.

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Glad you asked, George.

Jenny (http://jennymackness.wordpress.com/) asked if this course is chaotic or connected and mentioned your post here. So in answering her question and yours, I have a question for you. Are the two theories that different? As I wrote on Jenny's blog (quoted below) I don't think so:

"I don’t see chaos and complexity as mutually exclusive or as 'either/or' but as functions of each other. The course may seem chaotic to us now because we are still at the point of information overload. We can’t see the design because we don’t yet know the patterns around us, either because of the newness of the concepts or because they are still in the process of emergence. Even George and Stephen don’t know whether or how their differing opinions and patterns will turn out. That’s Complexity. But somewhere, somehow, the pattern will show…if the Chaos Theory is valid. So I think both concepts apply to this course."

So, George, am I "off base" and misunderstanding something (are they different) or are they functions of each other?

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Hi Ariel,

I agree chaos and complexity are not exclusive - chaos is a feature of complex systems. As for whether the course exhibits complexity, I am not sure. The wiki and the forums provide quite a lot of common ground, which decreases complexity. Even the blogs, whilst it is harder to keep track of them all, only rates as 'complicated' in my view - whilst the actual interplay between 2,200 people would almost certainly rate as being complex, we don't see that because of the low numbers of active contributors (I am not having a dig at lurkers, by the way).

The web and stock markets are complex. Well, certainly the stock markets. With the web, despite the huge number of people involved, most of the emergent behaviours of the system seem fairly predictable to me (not saying that I would have predicted any particular one, but that none have struck me as being chaotic).

I guess we each act to reduce the level of complication of things we interact with (by using our own filters). It is harder to reduce complexity, but we probably also reduce its effects on us by focusing on specific areas of concern. I think that cck08 is probably not complex (in my view) because the range of concepts it deals with is relatively limited, as well as the relatively small number of active contributors at any one time. Of course, this is my filtered, simplified view - taking the larger picture of connectivism (is we assume the theory is 'correct') then cck08 is a concern focused domain of a larger, complex, whole.

I also guess that one thing we might want to do is find ways to help people engage their filters to focus on a domain - it is easier for them to navigate their learning landscape if they have landmarks.

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Pat,

I think if you can identify landmarks, you are in a complex area. If you can't figure out what the landmarks, signals etc are, then you are in chaos.

In the business world, the definition of the scope of many projects is chaotic becasue there are competing agenda's, different interpretations of what needs to be done or what each person understands the problme to be. Some projects I have worked on requires a pre-project to sort through the chaos to come up with some actual potential objectives that can be ranked as being important for the project to explore or not. The Cynefin framework is a good way to aproach a problem area as it can tell you if you are in Chaos land or complex land!

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Hi Bradley,

A quick confession - although I am not using the strict mathematical definitions, I tend towards them here rather than the everyday usage of the words. And when Stephen Downes does that, I challenge it - so now I have to challenge myself about my use of words in their technical sense rather than their everyday sense. Bad Pat!

I am yet to be convinced by the Cynefin framework - probably because it uses everyday meanings of chaos and complexity too.

I guess it comes back to 'my' idea (as in, I thought of it, but I can't claim nobody else had written about it before me) of building up internal filters and applying them (automatically) to everything we perceive. In this case, I interpret chaos and complexity as technical terms. But also, if we are used to everyday.complexity and everyday.chaos then we will see those in the situations we encounter. Personally, I tend to find that any project worthy of the name has a pre-project to make sense of the environment, requirements and desired outcomes before it can start properly. Those which don't require this step are, to me, just 'tasks'.

One thing I have been noticing in posts on the forum recently (maybe I only just noticed it...) is that people (myself included) are tending to draw reference more to their own preferred theory. For me it is my model of mind, and then there are the Cynefin and micro-global framework. Not to mention the communist conspiracy theory, of course, but that was different in aspect as it was present at the start and has, to some degree, died down a little (what.did.I.just.do? I said not to mention it, and what did I do? OK, so I am a fool)

Is this an example of people being drawn to attractors (to use another of my favourite theories!)? If so, are people being drawn to new ones, or do they seem to be entrenched in their views? I think I am open to the ideas of others here - they are certainly interesting and thought provoking - but I have to admit that mostly I have 'only' re-visited long held models and checked to see if they are challenged by the material other people present. Perhaps this is me following the landmark of my objective through the turbulent waters of the learning landscape?

I would love to hear what others think about this...

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puzzle pieces

Perhaps we seek the edges of the puzzle first, then once we have most of it, and it's shaped like a rectangle really, we see it as our puzzle. Then as we learn we try to fit new pieces into it. Unlike a machined puzzle, our puzzles have many different spaces where we can fit the different pieces we learn about. I think we are willing to move individual pieces around inside the puzzle to another place if we think they don't fit where we put them the first time. We may even be willing to see a piece as an edge piece where we didn't think that before. But I don't think we want to rebuild our edges from scratch again, or start the puzzle over on a different table.

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There was once a famous Chinese philosopher called Chon Chow. In his dream he saw a butterfly. When he woke up, he wasn't sure whether he was actually a butterfly living in reality or was merely dreaming himself as a butterly with illusion or fantasy.

What happens if the puzzles don't fall into a pattern? And what happens if someone changes the number of pieces or shape of the puzzles, and that you are not aware of. Do you think you could reveal the whole puzzle at the end?

Is there anything certain in assembling puzzles, just as what we are trying to assemble learning in terms of learning outcomes? Are all things (learning inclusive) real or just an illusion? Is it a matter of perception?

Just like the dream and reality that Chon Chow perceived. How could we distinguish between reality and illusion under chaos theory?

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Individual and Group Learning (just like what Chon Chow is perceiving the world) could be chaotic due to the various sources of information and "shared knowledge" under a digital or virtual world.

Learning as a network (with many Chon Chows interacting) could be complex because each Chon Chow is different in their perspectives, and so the sharing of such knowledge is also complex and emergent.

Does it mean that with the use of Chaos Theory, one could understand and perceive patterns out of chaos, whereas with the use of Complexity Theory one could understand and perceive the importance of emergent knowledge as a result of learning with technology and networks?

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Imagine if each of us is a butterfly and could flap our wings, what would be the changes in the atmosphere that may alter the path of a tornado. See butterfly effect below.

The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in a certain location. The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale alterations of events. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different. Of course the butterfly cannot literally cause a tornado.

http://en.wikipedia.org/wiki/Butterfly_effect

Chon Chow (or Chon Tse) was praised as the wisest philosopher in Chinese history, equal in fame to Confucious, but not known to the western world.

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> Does it mean that with the use of Chaos Theory, one could understand and perceive patterns out of chaos, whereas with the use of Complexity Theory one could understand and perceive the importance of emergent knowledge as a result of learning with technology and networks?

To me, these are one and the same thing. And viewed that way, my answer to your question is: yes. Which is why I have depicted knowledge as "recognition".

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Thanks for your great advice and insights. So knowledge is recognition.

And I have further expanded the butterfly effect in education and curriculum development in my blog: http://suifaijohnmak.wordpress.com

For your comment please.

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John

Maybe it depends on how many people in authority you can get to agree with you. Like Miracle on 34th St ( the movie). If you tell people you are Santa Claus you may be locked up as a lunatic or you may convince enough people (who can validate you to others) that you are. Isn't that what we do in order to get people to trust connections with us and our knowledge as experts/"teachers"?

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I am still learning by reflecting between theory and practice - especially on this Chaos Theory. And it seems that there are already a lot of events happening, with queries on curriculum and assessment, and unpredictable learning in our networks in this course CCK08. These seem to reflect the butterfly effect and the application of Chaos Theory.

These findings and observations have been summarised by George in his mid course review.

Observations, applications and validations are the best ways to prove or disprove a hypothesis, statement or theory. I will review such findings and observations at the end of the course.

I don't think it would be wise for me to tell people that I am the Santa Claus, because I'm not.

George and Stephen are our formal teachers for this course, who I respect. And you as my co-learner is also a teacher too, to whom I will respect. And every co-learners too. Thank you.

And I am not trying to ask everyone to agree or disagree with me. So, I could be wrong in my concepts, but I will check and see what's wrong myself. I think what's more important for me is to share and validate our views, checking if it works in our real life. That's my learning by doing - I do it and I understand.

There is also a Chinese saying, whenever there are three of us in company, there is a teacher for me. So, if you have taught me something, I would appreciate your efforts. And in a network, everyone becomes a teacher and a learner. And it may be good to establish such an ideal cooperative relationship with others throughout our life journey. Of course, one could be selective in choosing our teachers and co-learners. That's why we need to develop skills in filtering knowledge and selecting connections.

And I sincerely thank you for your good advice. That's what I think...and that may be my cultural belief. You are welcome to visit my blog.

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Reminds me of "Horton hears a Who". My kinds watched the orginal cartoon version tonight and Horton had to get the Who's to do enough loud yelling that the Wickerson brothers (3 apes) finally heard the message "We are here", and stopped trying to boil the Who's.

The moral? IT takes a will of being persistent and to develop a gras roots following before ideas become mainstream. Maybe Stephen's jet setting lifestyle of making public appearances on networks, open source etc is a good approach.

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I would not say that we must bring order to chaos, nor that we should fit all the pieces. I would say that chaos should be retained because it has a complexity that makes it possible to maintain the orderly balance of the system.

We are a small part of a system where there are multiple contexts, therefore, we can not sort or change the entire system.

We can only strategically select those elements of our context that are necessary to reach our goals and interact with them.

This will produce subtle changes that may partially modify the immediate context and / or general (like the butterfly effect). But with these changes all you do is renew the complexity of chaos.

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Hi Pat,
I have just 'found' you and I like the conepts you use and how you use them. Internal filters - we have those, we cannot recieve everything. There are no unlimited people (except psychotic) but we can try to be openminded. We are practising it here..

Concepts eConsciousness, eLearning and Digital Identity in your profile seem attractive - I begin to follow your blog anf writings.
Heli from Finland

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Hi Pat,

I think you bring up a very important point about how we use and understand technical terms like chaos, complexity and networks. These terms refer to a set of very specific and precise mathematical tools. They also have everyday meanings that we all use in general conversations. I think that we each understand these terms as a varying mixtures of their everyday meaning and our current understanding of the maths behind their technical meaning. We all end up with slightly different views of what these terms mean. That's fine as long as we all acknowledge that we are each using these terms in an imprecise and personal way. The problem arises when we try to use this fuzzy personal use of the terms in a technical manner. I must admit I'm guilty of this because it's fun to speculate on the consequences of applying these ideas to various situations. I think we need to remember that this is just speculation and a bit of a game. It might give us some new incites into our practice. However we should be ready to abandon these ideas if they aren't useful or someone else provide a better version.
I think that using the technical mathematical tools associated with chaos, complexity and networks to study learning and education could provide new and fascinating knowledge. However if this knowledge is to have any lasting value this needs to be done in a rigours and scientific manner by experts in the specific domain who have the mathematical understanding to use these tools correctly.

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	Re: Complexity and chaos... by Pat Parslow - Monday, 20 October 2008, 01:46 PM
	The maths involved is actually relatively easy - 2nd year undergraduate stuff. My problem is time... Show parent \| Reply

Hi Pat,

How many experts in learning and education have archived proficiency in 2nd year undergraduate maths? And of those who have, like yourself, how many have time to carry out these types of studies?
Maybe you could help me out? I'm struggling with Stephens idea of networked knowledge. I understand that a network can store information in the configuration of the links between nodes. So for two nodes there are two possible configurations (either linked or not). For three nodes their are 8 possible combinations. Is there a general formula to work out how many different ways a given number of nodes can be connected? Each configuration can be represented by 1 bit of information so the number of configurations gives an indication of how much information can be represented by the configuration of the network. This can then be used to compare the amount of information stored in the network configuration and the amount of information stored in the nodes. I think this would be an interesting metric for studying connectivist information storage.

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How many experts in learning and education have archived proficiency in 2nd year undergraduate maths?
Not enough, in my opinion! (Just as not enough professionals generally have a good knowledge of mathematics, philosophy, literature, ethics,... could my standards be too high, maybe? - and noting that I do not have expertise in any field, imho)

Information in configuration of the links between nodes
(not that I necessarily agree that this is the only place information can be held)
There may be more than one channel available between two nodes, so even using a binary representation the configuration of the connections for a given set of nodes may be greater than you indicate. For instance there may be some particular significance to me using sign language to talk to you rather than speaking, or for me using Skype rather than the telephone, or typing a letter rather than using handwriting (you couldn't read my handriting..., I can't).
It is also possible to have various parameters associated with a connection - for instance, if the link exists between you and me, it could be that I trust it whole heartedly (I believe your content) but that you don't trust mine (and who could blame you?). The link could also have properties relating to its bandwidth, and possible means of transmission of signals through it (amplitude modulated, if I shout, or frequency modulated if it supports me repeating myself repeating myself a lot). The link can also facilitate easy communication of emotion, or be more emotion limited (lol).

Add in to this that almost any of these parameters can be continuous rather than discrete - I might trust you highly but not quite entirely. I can convey a range of emotions

via the channel, but not quite as many

as I might be able to via another channel.

However, I completely agree that it would be good to study learning networks this way - and indeed other networks - back in 1984 when I started my first attempt at a degree, one of the dissertation projects I was keen to do was to develop a model of the flow of communication in community, initially limited to something like a small office. I have occasionally toyed with simulations, but the main problem really is in finding suitable attributes of real people which you can measure to include as parameters in the model.

I find simulations of this type of thing easier to set up and run than fully fledged theoretical models - largely because of their sensitivity to initial conditions (well, that is a good, and real, reason, but actually it is because I enjoy writing and running simulations). But given fast enough computing facilities we can run this sort of simulation often enough with different parameters to be able to get a good feel of how the system behaves.

<addendum reason="I forgot to answer this question">
I think that for a fully connected network of size n the number of potential connections, C is
C= Sum(1..n-1) = (1/2)(n-1)(n )
and then the number of bits storable in binary connections is 2^C

So the series goes 2, 8, 64, 1024, 32768, 2091752, 268435456 ... which gets big rather quickly. For 2,201 nodes (to pluck a number out of thin air) there would be 2^2421100 (which my computer is insisting is infinity, but I don't really believe it

)
</addendum>

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Pat, you raise a general problem: when is a word a technical term, and if so, in what sense (see force, motion, work, and "THE word" as in "In the beginning there was...")? [Mathematicians of course cheat, by using Greek words instead of English ones, and non-words like "i"].

I still (at this stage) find 'network' as in 'networked learning' quite comfortable (but maybe people who are computer engineers may not!), and I find 'connectivist learning' odd. It doesnt work as a conceptual attractor for me (not through lack of trying!).

The same problem arises with "chaos" and "complexity". I think you have to add another layer of tags, or overcodes, and perhaps hyphenate some of this stuff: so, Stephenian-networks differ from Georgian-networks, etc. Or 'networks' (as in Stephen) ....

I really like to use the Cynefin framework, primarily for operational and strategic purposes. I have also tried to make sense of it as epistemology, or to integrate it into the kind of epistemological frameworks that I use. The best I have so far is a draft on "Ontologies, heuristics and strategy" (see the first link on the page at:
http://k-m-etaphors.wikispaces.com/Ontologies), in which I not only find it necessary to tag the 'Roy' v. the 'Dave' senses of terms, but its also necessary to differentiate the ontological v. heuristic v. strategic sense of these versions of the terms!

And Dave Snowden agrees with only some portions of this draft!

So I too "re-visit long held models and check to see if they are challenged by the material other people present" - and hopefully reassemble and adjust my own ideas in the process, which is 'learning' (see Latour on 'reassembling').

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I agree, Bradley.

And let me add that this statement is extensible to any other area of our lives.

I think that the learning process is internal to the individual and, therefore, as has happened throughout life.

Although they have changed their form, in any educational process, there have always been many attractors and distracting (chaos theory).

The person learns when it is able to filter properly to reach your goal. And that filter is more or less powerful depending on the level of prior knowledge of the individual.

A higher level of knowledge, the lowest level of uncertainty and therefore less complexity, less chaos and higher learning.

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Hi George
you have asked: In what way is learning complex? In what way is it chaotic?
My answer is: in many ways, some of them already described. Learning is complex and chaotic because life and world are. And because learning is a social activity, and social activities are complex and chaotic.

I would like to make a distinction: the more the "object" of learning is complex, the more learning is. I partially contradict Jon Kruithof: it can be a question of the subject matter; the more the "object" is simple, limited and localised, the more learning is not complex nor chaotic: learning computer science is chaotic, learning how to attach a file to an e-mail isn't.
But Jon is right: also if the subject is simple human aspects of learning can make learning complex. Question of emotions, of different goals/expectations, of different use of the same terms (it's what Tim Gillibrand note for this discussion: "… we are each using these terms in an imprecise and personal way").

I have appreciated Pat Parslow's propositions. Learning is complex/chaotic as shown by its unpredictability. But then: what the role of teachers? In my experience - as I wrote in a post on my blog - I tried to promote processes (learning experiences) renouncing to know which long-terms effects they can produce.
But I think that we are, rightly, required to produce some verifiable results. If I propose my students to project and realise a web site, I will not be able to know how such a work produce results on the capabilities of each of them, on their planning skills. But I must guarantee that they become able to use an HTML editor and to present a documentation of the work done.
Using Pat's terms: I propose them a landscape to be explored, but I must provide them some landmarks.
It's a question of filters (thanks again, Pat). My task is to help them in growing their own filters, but to do that I have to propose them some filters to make easier their exploration.

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I think that learning muss be allways complex and chaotic.

A good teacher is the teacher who let you thinking about what he/she says.
A great teacher is the teacher who start a process in an individual context (YOU wink

wink

) and he/she doesn´t know really what it is going to be in the futur with this process, because it is a chaotic process.

Learning is allways a path without a predictable end. Learning is movement.
I learn, I know something and that is the little fire that can change all your complex personal context.

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George,

Chaos has always fascinated me because it seemed so wrong to accept anything that was unclear and disorganized. These days, I am finding that being out of my comfort zone and being in chaotic situations is contributing a great deal to my personal and professional development.

I took a course on SCoPE called Developing a Professional Development Collaboratory: August 18-31, 2008.

On August 28, I wrote:

I was just reading an interesting article by Bryan Moseley and Daniel Dustin (2008) called Teaching as Chaos. Chaos theory suggests that chaos exists if we cannot predict behavior or outcomes. According to the article (Moseley & Dustin, 2008), learning in a classroom follows the chaos theory. Would using technology via blended learning fit in with the chaos theory?

Moseley, B., & Dustin, D. (2008, Summer). Teaching as chaos. College Teaching, 56(3), 140-142. Retrieved August 28, 2008, from EBSCOhost database.

On August 30, 2008 I wrote:

Saturday, 30 August 2008, 12:04 PM

I consider information static unless it is activated. Informing educators may be important, but it is not enough. Education and professional development should cause some form of change. Because the change that may occur is unpredictable, it is considered chaotic. However, provoking turbulence and chaos helps get the learners attuned and ready for the research-based information.

Bevan (2006) came up with the chaos theory as he considered the following questions at a secondary school:

1. What research-based knowledge do you use?

2. How do you use it? (p. 55)

The answers to the first questions were:

1. Effective approaches to assessment

2. Improved strategies for revision classes

3. Informed responses to school transfer (from Primary to Secondary)

4. Computers as tools for learning

5. Effective implementation of staff development

The answers to the second were:

turbulence caused by the 'stone in the stream';

resolved, in turn, through channel depth;

the fluidity of the stream: 'water not tarmac'; and

the purposeful direction: 'it goes nowhere'. (p. 60)

I find that causing turbulence can be a good thing if it is well planned and facilitated fearlessly. Has anyone tried the technique or something similar?

Bevan, R. M. (2006, July). Turbulent flow into smooth stream: Transferring research knowledge between academic environments and practitioner contexts. Reflecting Education, 2(1), 55-72. Retrieved August 29, 2008, from http://tinyurl.com/56ndfx

Does this make sense? Is chaos or not being able to predict what will happen such a bad thing? According to Buddhism philosophy, only the present is real. Trying to predict the future takes a person away from reality and into chaos. As long as a person realizes that thoughts about the future are not real, chaos will remain a word with no real significance. .

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I read all the contributions about this subject and I am a bit confused. I agree with Pierfranco for a great deal. Also with others. Before my work as a teacher of professionals, I was a teacher of nurses. I can't see how I have to teach young nurses if there is only chaos and unpredictable learning. Working with competencies and a curriculum for 4 years, there is a lot of steering in the learning of the students I think. Of course they have to do the learning themselves, but I as a teacher brings a lot of what they have to learn in the program. And by testing them with demonstrations, tests, assessments, I will control if they can do the real job with the real patients and clients in the real hospitals. These students learn a lot via the Internet I think and know, but the most important things to learn are in training which each-other and in practice-situations. In groups I think and not in networks. And in complex, but less chaotic situations I think. Of course the real nursing-situation can be very chaotic, but the learning trajectory is better a bit organised? I have to think about this a lot more. And now week 7 is there. So much to learn, so much to do! But still enjoying it very much.

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Hi Sia,

Seeing the comments that were generated in this forum and also in some blogs, it is easy to deduce that the feeling you have is way. Terry Anderson, in Elluminate, spoke of formal and informal learning.

And we must distinguish the type of learning required in each case. It is not the same professional learning (which require specific techniques to perform a specific job) that the informal learning that can be random and whose progress it marks the individual himself.

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> I find that causing turbulence can be a good thing if it is well planned and facilitated fearlessly. Has anyone tried the technique or something similar?

Causing turbulence can be a good thing.

This process is known as 'annealing' in materials sciences, and is basically a process of hardening a metal by heating it.

In connectivism, the process of annealing is used to shake a neural network from 'local minima' to a more stable configuration. This is the process employed by Boltzmann machines, and is one of the four principles of association I've described.

It is less clear to be that it needs to be "well planned". I think that ad hoc turbulence can be as effective as well planned turbulence. But ultimately, this would be subject to empirical confirmation.

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	Re: Complexity and chaos... by Ken Anderson - Monday, 20 October 2008, 10:52 AM
	Hello Stephen. Are the principles of AI transferable to connectivism, or are you talking about connectionism here? Show parent \| Reply

	Re: Complexity and chaos... by Stephen Downes - Monday, 20 October 2008, 11:43 AM
	Which principles do you refer to? Not all of connectionism applies to connectivism; otherwise they would be one and the same theory. Show parent \| Reply

What triggered my question was the reference to "Boltzmann machines". A better question (for my understanding) might be:

What are the differences between connectivism and connectionism?

It appears that one is focused on neural networks (internal), the other on networks of neural networks (external). I confess that my understanding of either concept is extremely limited. I have read your papers and George's statements but I still don't see major differences between the concepts other than the objects they focus on to describe/illuminate.

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