How to display knowledge in a topological way

First Question: Can one „Study Off-University“/“Learn Online“ only?

Over the last few weeks/months I’ve been examining the solutions to study and learn with online content.

The point about it is that a lot of universities have much of their content online, but for a complete study of the matter you still need to be „there“. The stuff on the internet is mostly introductory courses only.

But there are as well additional ressources where professors upload their content on their own behalf (e.g. a complete lecture on „Das Kapital„) – and which, if collected – could make a real complete graduation (at least the knowledge, and that’s what I’m talking about).

There are some startups that try to do this like AcademicEarth and NalandaU

But there is missing the „curriculum“ aspect:

„When can I be really sure to have studied this subject thoroughly?“

So I took the curriculum for sociology (my current topic) and started to transfer it.

I tried this in several ways:

1.) As a mindmap

2.) and as a TV-Channel on yubby

3.) As a collection on Evernote (kind of a note taking/bookmark service)

4.) The annotated curriculum itself.

This all is somehow overwhelming if you want to study a subject.

The Mindmap gives no real ordering and TV-Channels provide ordering, but too strict and allow no additional ressources. Evernote gives ordering as well, but there is no real overview and you don’t get the big picture.

Second Question: How can we make it appealing and comprehensive?

I found the best overview in a game! There the knowledge is linked to preconditions and postconditions. E.g you need Pottery, The Sail and The Wheel to discover Trade. Every discovered knowledge yields some inventions – e.g. Mathematics yield the Catapult (amongst other things).

The connections are the important things. They represent how knowledge is made out of other knowledge. How one thought makes possible and evolves into another. I will call this connectedness of knowledge its topology.

If you have a given topology of knowledge, then you can

  • start learning from the „beginning“ and work to the „end“ – which would be what you get in nowadays universities (but the connections are shut away from you and part of the secret knowledge of the wise)
  • start learning from the end towards the beginning. That’s how private tutoring works, where you start with what you’ve got problems and then follow along the lines of the not-understood preconditions. (The connections aren’t revealed to you again).

And now the breakthrough can happen, you describe not only the content, but the connections as well. So that the learner can be a better self-directed teacher.

Here is the first online tutoring system, that realizes this concept – and models the connections:

In the VirtualNerd-Software you can go back and acquire the different preconditions. With these modeled connections they could easily display the topology of this knowledge.

Question 3: Why are the connections hidden, and how can we make them visible?

Today you *know* the connections as soon as you have studied the subject to the end. Then you are one of the wise and savant. But until then the connections reveal only through studying, exploring and discovering them for yourself.

Connections are nowhere modeled. Knowledge may be categorized and tagged (like this part belongs to algebra), but no explicit connections.

I think this has many reasons:

  • Our intellectual culture is linear, because our texts are linear.
  • Connections are ambivalent. This means, that one thing can connected differently under different views. It makes a difference wether I want to connect authors by their research field or by the date of their works.

But we now have the possibility to formulate this, and formulate different transformations into different views – resulting in different views of the same knowledge. Depending on our focus.

If we wouldn’t model it into data separated from the views, then we would quickly realize that our models are incomplete. So if we order it by author, we wouldn’t have the temporal aspect, or the geographical, or we would miss the conversation of the ideas as they emerged during the centuries, or the concepts they contributed.

So modelling *all* relations into one view we would end up with a messy and incomplete view.

I think this is the reason why all tries have failed so far, and are doomed to fail in the future. So that the connections stay unformulated, unexpressed and obscure. Only the knowing have access to form small models and they know the connections.

If we change this, we could switch from stoneage learning (transmitting the facts and letting the learner figure out the connections) to post-stoneage learning. I think this could have a deep impact. The question would shift from: „What knowledge *is* there“, to „How does knowledge interact?“. Leaving the static perspective and transcending into a dynamic one.



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