a platform for elegant teaching concepts

Some years ago I saw Alan Kays TED talk “A powerful idea about ideas” and am ongoingly impressed by his story about the many different (in terms of their quality and “neuronal sustainability”) ways to teach the Pythagorean theorem.
This notion of looking at different conceptual approaches when conveying something and then choosing the one with the deepest reach (the best neuronal basis for future concepts) really stuck with me and grew into the following idea:
A platform to hone in on the most elegant approaches for teaching scientific concepts that have maximum in-domain depth and cross-domain reach.
Many times throughout the last semesters while studying for subjects like software engineering, theoretical informatics or linear algebra, I had the strong sense that there must be an obvious “symphony of connections” between these subjects – but I would always only get short glimpses of it and professors seem to rarely speak to, or encourage seeing connections to other subjects than their own. There is much going on regarding MOOCs, we have a lot of funding for ‘excellence universities’ in Germany and there are many players in the field of education that do good work.
But what I haven’t seen yet are places where didactics are discussed down to the actual level of which angle and analogies to choose for introducing a concept and how one approach is more meaningful than another one when looked upon solely asking about the quality of the “new neuronal patterns” this approach leaves in the students brain – how well and how sustainable this sets him or her up for comprehending future related concepts. I would imagine these kind of inquiries are happening in the field of didactics, when a textbook is created, when a professors plans their first lecture series after having earned their title etc.?
I am wondering though if it might be interesting to pull this “into the daylight” and into a broader range of participants. So I imagine a platform that is centered around this idea of honing in on elegant approaches for teaching concepts. I read Siddhartha from Hermann Hesse many years ago, there is this one image that fits nicely. It talks about being the stone in the water and letting yourself sink to the ground. No matter what turbulence you go through in the process, eventually you will reach the ground. In that way I imagine different approaches to be compared, deconstructed and reconstructed until the ground of a particular matter is reached – the deepest point in the valley where the river flows the fullest and fastest. Concepts might merge into a higher abstraction and “spines” emerge that tie things together.
On a practical level I imagine the first to invite to such a platform to be educators that are interested in such an experiment and put the future-quality of their teaching before the ways the already do it. Concepts and approaches can be submitted and are all their own entities that are bound together only through links so that maximal ‘recombinability’ is possible and encouraged. Readily developed material is welcome as well as just vague ideas. The structure of the platform encourages – and in part computes automatically – the continuous structuring of all present entities. In the spirit of Christopher Alexander’s pattern language, each entity could have fields for connections to other domains, related analogies, stories etc. The template for an entity is subject to the platforms recursive development itself. Quantitative measures will be introduced that allow for automated computational support in honing in on the most elegant knowledge graph…

graph edge-force play-tool

The prelude of this weekend brought me to remember some earlier musings about the workings of graph layout algorithms. Namely how a graph might behave, if its edges have target-lengths assigned. Deviation from that value cause expanding or contracting forces onto the two nodes it is incident with.

Then, for the rest of the weekend (quite literally) I implemented said algorithm. And… as it always happens, some little extra features around that core functionality found its way in. I am very happy about the result. Despite the lack of applicability I find it quite enjoyable to play around. To see how different setups behave and create strange structures or beatiful ones, symmetric and balanced like a diamond.

Go try it yourself if you wish, here it is.


situating oneself within vector fields

Ok, this one will be a bit all over the place…

Isn’t it peculiar to think what drives people to live their lives. It’s differences, it’s vectors of change that drive us – especially as singular devotions such as religions are fading away. Most parents want that their children have it ‘better’ than they had it. More happiness, less pain, more money, less conflicts with relatives… those are all vectors into a direction, not just points. Of course there are singular drivers (called goals) as well, like a certain career, a project, a family and so on. But what is the context of those? Family, society in the context of its history… biology as a whole eventually? Since there is no absolute scripture that commands us how to live our life we can’t help but orientate ourselves within a vector field of infinitely many possible directions for change, for development, for betterment, for stability and whatever else we call the thing that is supposed to happen at a certain density along a vector.

Situating ourselves within differences seems to be a pretty universal pattern for the human experience, no? One subset of the social space in which this comes to light clearly is for instance the ‘checking each other out’ type of behaviour. You can’t really know instantly if someone is trustworthy so you are ‘filtering’ him through a social field. See how he behaves with others, how others relate to him and maybe tell you about him afterwards. The net of relative positioning needs to tighten before you have an idea of his personality.

We (have to) build compressed representations of things, people, knowledge, etc. as our inner model of it. How accurately this model maps the real thing can vary drastically, depending on the mind that builds the model. This is like data sense-making works… aggregate as much metadata as possible and then have that collapse in a set of entities and identities.

A certain degree of ‘objectifi-ability’ needs to be exhibited (by a person) to allow continuing the outside-in approach of having metadata (reactions, 3rd party opinions…) tighten the representation of identity.

What’s an ‘opinion’. It’s an output of your inner model. It’s a shortcut to be able to make decisions without knowing a full system. Very few system can be fully known. An opinion is kind of like a statistical prediction… but then there is the emotional part in it that can be bent so very easily depending on ones traumata, wishes, fears and so on.

What’s the solid ground laws are based on. Obviously a set of moral and ethical learnings from history that tell us how societies become/stay stable, economies prosper, a set of values like personal freedom are protected and so on…

The human experience: suspended in gradients without absolute ground, deploying strategies to tighten enough vectors into something solid that feels like a purpose and a meaning :)

the one rule to install in your world view

A world view of some sort is fundamental to every person. How sophisticated it might be and ones ability to express it – that’s a different story. In a very real way it’s the causal basis of a brain. It’s a physical structure. It’s a graph of vertices (neurons) and edges (synapses). It’s a particular way billions of neurons connect to each other.
What’s really uncomfortable is when this mental basis gets cracks, crumbles or falls apart entirely. In an emotionally safe environment, ideally provided by parents, kindergarten and school, children can form their world view with a lot less hassle than any changes on it cause if they happen later in life. That’s why world views beyond childhood are mostly of additive nature instead of recursively shaped when it comes to their core. Adding, some editing, some suppressing, but rarely fundamental changes. The “costs” are too high of such a deep restructuring.
From the point of system stability it makes sense if a world view is actually working to stabilize itself. The more solid a fundament the easier life decisions become. The ability to ignore dissonances here is not to be underestimated. That ability can outperform almost any other mode of brain operation apart from half-automated basic modes like survival instinct. A brain has to compare the costs of a change to the much cheaper costs of simply ignoring or bending the disturbance into the existing model. These costs can directly be derived from the fundamental (computational) operations one can perform on graphs. Navigating (reading) a graph is by far the cheapest operation, next comes adding, then deleting and finally editing as the operation with the most cycles required. Think about a simple graph and the steps required (the algorithm) for each operation and you’ll see.
Science works the opposite way. As soon as a you encounter an empirical contradiction of your model you are forced to change your model or throw it over board. No matter how attached you are to it. Notice that throwing over board doesn’t necessarily mean the theory is plain wrong, it might just mean you found a case that’s not covered by it and you are thereby invited to find a higher abstraction that encompasses all of the old model plus accounts for what contradicted the previous model. Measurements can’t lie, so all scientific measurements ever taken will always be true, it might (should) just be the case that our models to explain results evolve to more comprehensive ones.
Just imagine the following. Imagine a person that decides at some point of there life that truth is more important than how one feels about it. Just that simple insight. So so radical and so so rarely. Applied as a rule it means to enact the scientific method on ones own model of the world (again, we all have such a model). It means to adapt or change ones world view as soon as one encounters contradictions. It means to be especially careful to ones resonance or sympathy with any topic or opinion because it might just mean that ones world view is in the process if tightening in on itself… maybe just getting one step too comfortable. Imagine how unbearably exhausting this must be, practically ready at any moment to dump your core in favor of the search for the next more comprehensive iteration. The social pressure on such a person would be immense because social fields are always slow to adapt to fundamental character changes of their members, given they stay members. Yet, imagine what an immensely powerful instrument for truth-finding such a person would be. The starting point in terms of age, culture and class is arbitrary as long as that one rule is carved into “mental stone”. That being said of course a person living within a stable and rich infrastructure has to spend way less energy on worrying than a person worrying about how to avoid going to sleep hungry today. If basic needs are not covered it gets almost impossible for a brain to focus on anything else than the next step in surviving.
So if you can, by all means, do install this one rule in yourself and become a system capable of iterating it’s own operating system. It means leaving behind a lot of places of comfort, but you’ll be better off in the long run. Without the rule your world view just does what it’s architecture compels it to, become more dense and evermore resistant to fundamental change. A ship sailing onward on its self-created ocean, only possible to do so because the infrastructure is sophisticated enough to provide – independent of the quality of what’s in your brain. Of course you can find a group that supports your special kind of world view. A group of like minded validate themselves, that’s what they do. Social validation though is worth nothing compared to scientific validation. Worse, social validation can be very dangerous.

I should not finish this post without talking about myself, not doing it would be weird and dishonest after all of the above. I had a fundamental change of world view initiated in 2011, stable in the next iteration by 2012 and still noticing the ongoing reconfiguration. Very recently I was told something that I have to work to integrate if I want to follow THE rule. So a big chunk of my current model is now labelled as ‘ready for remodeling or phasing out’ and I am expecting this process to happen over the coming years. To be more specific is not in the scope of this post. It helps to write the above observations and thoughts as a way of pep talking myself :) I am not the imaginary person described above, yet I am striving to be it.
Notice that the thoughts expressed in this post are my own, though I would most likely not have them without the influence of Randall Lee Reetz.

providing infrastructure vs. using it

The other day I learned that here in the library at the Uni in Pilsen you can book really nice glass rooms for yourself or for student groups. Additionally you can get a projector and also a laptop should you need one, all free of charge. That’s quite cool and I found myself wanting to use it without knowing what to use it for! :) Which is a reaction I am sure I am not the only one having from time to time? It made me think about these two distinctly different (opposite?) modes of mental operations: providing, securing or enhancing infrastructure vs. just using it to create or do something.
Setting up the structure of a shared Dropbox folder really well, getting a membership card for something, paying an annual subscription… these kind of things I really enjoy sometimes and find myself in an almost obsessive mode of improving infrastructure for myself or others.

Ok, it’s actually ridiculously spoiled to call these things infrastructure as this term is usually used for bigger systems and networks like the water and energy supply network of a country, the roads, the railways, the health system, the educational system and so on. Of course the infrastructure I am referring to above is 100% depending on this big-I Infrastructure.

Let’s look at some synonyms. How about space, canvas or container for infrastructure? Creation or content is what happens within it and which is using and depending on it? And of course there is a blurry boundary between the two. In many cases creations turn into something to build on, that makes them an infrastructure again and so on.

An overly sophisticated infrastructure can certainly intimidate the creation that is supposed to happen with/in it. In a sense of: who am I to create something with all these amazing tools in these amazing spaces that I am provided with. On the other hand, obstacles in bad structures can turn into slingshots for things to crystallize.

What you see often is that companies offer structures and spaces where ‘anything’ is allowed to happen. But actually the space is by means of its very architecture bent towards certain hidden or outspoken goals of the providers. Or think of the interplay of space and creation in competitions companies might offer – often they are so carefully orchestrated by the marketing department that you just get the impression it doesn’t matter at all what kind of content is being created because by the frames it was pre-determined already very heavily and the following celebration with photo and quote of the winner is absolutely interchangeable and served only the purpose of publicity.

Look at this very post. The infrastructure is wordpress, my blog, my history with this blog, my mental outlet of writing here now and then… eventually all that is enabling me to write her. The content is this (little ordered) stream of thoughts poured into the format of a post. After publishing it becomes an actual ‘post’, somewhat objectified, some entity on its own to relate to… so part of the infrastructure of ‘previous posts’ that i’ll be building on with the next one, somehow.

the neuronal activity of your audience

Imagine a classroom where students are hooked up to a system tracking their neuronal activity. This system is able to accurately detect the specific moments when a student looses the connection to what the lecturer is teaching – in a sense of no longer being able to follow because of a lack of understanding, mental overload or any other reason. These moments of disconnection are visible either only for the lecturer or also for all on a dashboard. However, strictly anonymized. It should not be possible to know or even to guess who or which group of people just lost connection. I have no idea if this would technically and especially algorithmically be possible (yet). So as a “backup-scenario” let’s think of a more active setup where students have to press some sort of tiny hidden button to anonymously signalize when they don’t get something.
The point is to have a mechanism where moments of disconnections can surface without any social patterns (too shy and showing off would be too extremes of such patterns) overlaying.
I would imagine this could be extremely annoying for a lecturer because all the time people drop off (and might or might not get back on track without asking questions). But as challenging it might be, the task would be to stop immediately and explain again, explain differently, use other analogies, give examples etc. as long as it takes to keep on going forward with all green lights. Of course confident strategies on the side of the lecturer might emerge where a few red lights are accepted in the belief that they would naturally be collected back onto the boat a little later in the flow of the lecture…
A stoic continuous inquiry into the best approach to explain something would be the resulting attitude I would hope this stimulates in lecturers once they are over the part of being annoyed about constant interruption though red lights. Also I would think very careful attention will have to be given to thematic bridges, jumps or shortcuts of any sorts. It becomes obvious when things that made complete unquestioned sense in the lecturers mind don’t resonate with the students….
I don’t necessarily post this scenario as a criticism of lecturers, rather as a potential tool to help any kind of educator, communicator, or indeed anyone who intends to explain something to someone else, to become more sensitive to the neuronal activity within their audience :)

Erasmus Mundus Joint Programmes

Usually I don’t “advertise” on my blog – but I think the “Erasmus Mundus Joint Programmes” deserve more attention than they seem to get, especially among you people who are thinking about a next step after their Bachelor. I just recently learned that this exists and I find it really worth looking into and know about. Each of the Masters and PhDs is a collaboration between universities, so every semester one gets to study in a different country. I definitely want to do one of the Masters… at this point I am between “Computational Logic” and “Data Mining and Knowledge Management”.

Since the sites from the European Commission (see here the list of Masters and here the list of PhDs) don’t show the countries next to the programme and don’t let you filter beyond category, I coded a little site to fix this shortcoming. I hope it will be useful for some people: benjaminaaron.github.io/FiltertoolErasmusMundus