By Stephen Downes - Stephen's Web. Set Theory: Should You Believe?
I have papers like this in my own notes from my university days. My doubt in mathematics was created when, one day, I was introduced to i, the square root of -1. Imaginary numbers. And I have done enough work in the philosophical foundations of mathematics to agree with the author when he questions some of the basic principles of this 'most certain' of all the sciences. Things like the use of axioms and the concept of infinite sets, for example. And I remember, from my own days, long discussions about the principle of substitutivity. My own view of mathematics is from the Mill and Kitcher school of thought - that it is a description of physical events, or physical operations. Why does this matter. More...

By Stephen Downes - Stephen's Web. Hope for a Troubled World
In contrast to the depressing messages of Monday, watch this video as (in Mark Federman's words) "Paul Hawken describes how the largest movement in the world came into being, and just how large it is: a movement with no name, no particular location, no ideology, and 'not led by a male vertebrate.'" Yes, I am a member of this large movement, and have been for a very long time. It's what gets me up in the morning and allows me to sleep peacefully at night. More...

By Stephen Downes - Stephen's Web. Kindle, XO, Blah, Blah
The debate for and against Kindle continues. I learn from this item that the Kindle screen refreshes so slowly you cannot even have a mouse. Wow. And I agree with Tom Hoffman that no matter what we decide for ourselves, we should not be teaching children to accept the limitations on reading imposed by this technology. Why? I recommend reading Mark Pilgrim's The Future of Reading (A Play in Six Acts). We need to be clear that technology such as the Kindle redefines not just things like reading and writing, but also such previously good (but now immoral) acts of giving, lending and sharing. More...

By Stephen Downes - Stephen's Web. Secret Strategies or Common Sense?
If there is a theme in today's newsletter, it revolves around the conflict between people wanting to use new technologies to form communities and to talk to each other, and advertisers and marketers wanting to take that environment, control it, and monetize it. This article may be a startling revelation to some people, but for those who (like me) are jaded it will be seen as just business as usual. It is a pattern we have seen followed in every arena since the internet was founded: people build an environment, and then it is corrupted by marketers and advertising. More...

By Stephen Downes - Stephen's Web. Naming Aggregations
Terry Anderson isn't so impressed by Dave Snowden's suggestion that 'crew' is a useful category. "A 'crew' is just another name for a group, much as 'team' is often used for a group in business contexts. I like the nautical inference of 'crew', but think the distinction implied by the two criteria above fit as well for many of the forms of 'group' that Jon and I (and others) have addressed." More...

By Stephen Downes - Stephen's Web. Fun
That's the one word title of this summary of the Manitoba edubloggercon just completed. "About 60 people showed up and Andy Mckneil the president of their provincial technology group, organized and paid for the event. Andy also did a great job filming and recording the entire event." More...

By Stephen Downes - Stephen's Web. Conversation As a Radical Act
Interesting diagram looking at the act of communication (online and off, but the implication is more online than off, to me at least). The 'diversity' petal to me speaks to the structure of the network, and I would add things like autonomy, openness and interactivity to that part of it. The 'key issues' speaks to meaning or content, which I've addressed a bit with semantics. But the 'process' part of it is something I haven't spoken a whole lot about: communications, even in networks, can vary greatly in type. In traditional networks, we think simply of a 'signal' being sent from one node to another, but in fact what we send are complex patterns. Handshakes, protocols, syntax, customs, flames, emoticons - these are all ways of representing the forms those patterns take. Viewed from one perspective, these are signals sent from one node to another. Viewed from another perspective, these are patterns of connectivity with emergent meaning (recognizable only from outside) sent from one network to another. More...

By Stephen Downes - Stephen's Web. When Two Tribes Go To War
The post addresses divergent approaches to managing institutional technological requirements - one view being the standard instiututional view, the other being the one standards and systems view. Good discussion, but what stood out as insightful was this: "I now wonder whether it might be better to sometimes leave such gaps unfilled. For as ‘Webdunc' recently commented 'To oversimplify; I don't think I've ever heard of a policy for what to do when you pass a peer/colleague/superior/lecturer/student in the street - why do we need one for online social behaviour?'." More...

By Stephen Downes - Stephen's Web. Why Does This Stuff Succeed?
It's a rant, but we ned more rants like this. Because while on the one hand there is the scepticism - often expressed in these pages - about standardized instruction and instruction-based learning. But there is the other side of the discussion we need to see: the problem of charlatans who have a 'solution' to sell, that 'improves learning' - though they won't tell you how, nor provide any evidence that it does. And we have in common the objectives of seeing our educational system produce, as the author says, "people who understand through hard study of history and philosophy the challenges of self government." Self-discipline and even self-sacrifice are indeed noble virtues, and we would like to foster them. But students often hear of the need for self-sacrifice from an individual or an institution that will take the fruits of that sacrifice merely to enrich or empower themselves. More...