The University I Want

Another lemma lay slain at her feet, another book was conquered. Knowledge flowed into her from the slain beasts and knowledge made her stronger. She was ready for the tests, and defeating them, advanced levels. She was not quite at the end yet, and she had made some mistakes, had died a few times, but her pace was still good. She was running at the front of the pack and her eyes blazed with determination, the aura of her competence visible from afar.

 

I make no secret of drawing some inspiration from the system of advancement in some games for some of these ideas, but I think this is as much because it plays directly on human psychology as for any other reason. So, then, the title is fairly self-explanatory. I am rather deeply dissatisfied with the current system – I am aware it works well for some, but for others, including myself and some of my acquaintances, it certainly does not. It gets the job done, just barely, but a complete overhaul could do it vastly better. 

In essence, what I want is complete flexibility. An ability to decide everything, with the university serving to merely assess the quality of your decisions. As you might guess, lectures are terribly inflexible creatures, as such they are the first to go. Seminars should follow except in cases where they are absolutely vital to assessment or learning, which I do not think is the case particularly often. Set exam dates and course lengths are also particularly pernicious and should be expelled post haste. With all those gone, I also don't particularly see the need for the distinction of full time versus part time students, or for full-fledged enrolment or tight location restrictions. 

You might be scratching your head wondering what exactly I'm actually leaving in at this point. Well, not much, I'll admit, the format I desire is rather different from most things around. Perhaps it is most similar to some of the standardised tests, such as the SAT. In essence, each student would sign up with a university for a nominal fee, and from then on would have only recommendations, not demands.

The university's primary role would be to offer an extremely extensive list of exams – one corresponding to a logical size of course. Some might cover the full material of a course as it stands right now, others might cover some fraction of that, others yet may be on even narrower topics. The exact logical scope of the content on each exam could be reasonably determined by choosing tight groups of knowledge, as mentioned in the previous post, and perhaps ensuring they are not too small to prevent the student from having to write too many or from getting by with information only stored in the short-term memory. Each student would then be free to come in to the university facility and write any exam at any time. The exam would be randomly generated from a large list of, say, several hundred questions on the covered topics for each individual student. That way even if the questions were publically available at all times, learning enough of them to have questions with which you are familiar appear on the examination would be exceedingly unlikely unless the topics of the exam were extensively studied anyway.

Scores would be assigned for the examination as normal, and would count towards the student's cumulative grade point average weighed by the size of the examination, much as is commonly done now. I would suggest, although this is unessential, that exams could be retaken endlessly, but with some small, and gradually increasing, penalty for each attempt in order to compensate for the increasing probabilities of luck. The university would charge some amount of money to cover the facility, monitoring, and scoring costs for each attempt. While this would encourage an extremely literal form of studying to the test, that is not actually an issue if the tests are constructed to be sufficiently comprehensive. 

This of course brings up the question of what exactly students would study. Each exam would come with recommendations on appropriate materials from the university, and with samples. Discussion groups could also be made available for free, and professors or advanced students could act as tutors or could answer question for some appropriate fees. Some pre-recorded lectures could also be made available, much as they are often available presently, if deemed necessary. 

To have this system be fully compatible with the current system, the attainment of some majors could occur upon the successful completion of a certain set of exams, while honours ranks could be awarded for the achievement of sufficiently high scores on this set. A university might then award an undergraduate degree upon the completion of a sufficient number of exams (weighed by size, of course). 

I'll concede this leaves, the issue of special course types. Courses with labs could be pared down to labs and coursework being performed separately, with the labs having to be scheduled for some restricted periods of the year. Courses with an emphasis on discussion need to be carefully considered – what role does the discussion serve? I believe that it could be in most cases be restated as a requirement of papers to be graded (to be treated in much the same way as exams), with perhaps a smaller discussion component, which could perhaps partially be migrated to an online forum. Regardless, such courses in my experience, are vastly in the minority and workarounds which maximise freedom could be found even for them. For such programs as graduate education and postdoctoral studies, which require research more than course attendance, the course component could be streamlined along this system while research would be done as normal in institutions actually dedicated to it. 

So with the outline done, what does such a system actually accomplish? Never one to be modest, I will say that it makes everything better. Hours and attendance rate become fully flexible, so anyone of any age and occupation may choose to engage in certified education, and have some results to show for it. It allows you to demonstrate any knowledge that you may have acquired through independent study and to do so cheaply. If you learned a natural or programming language on your own you would have an easy way to show that. If you learned large swathes of evolutionary biology or of political science, you could show that too. If you're a history buff, you could perhaps pick up a history major on the cheap. More than that, however, if you are in fact just entering university from high school and wish to learn something in preparation for work, you can do so very quickly. It is entirely conceivable to compress the standard four years of university into a half year for a sufficiently talented and determined individual. Indeed, a new meaningful metric could be added – perhaps GPA per month, providing an alternate, and I would argue potentially superior, metric for someone's capacity to learn. Anyone could take the four years they do now, but someone who wishes to complete her mandatory education all at once would be able to do that as well. It is not uncommon even presently for students to miss a lot of lectures and learn most of a course before the examination, and this system would render such behaviour meaningless and educationally neutral.

On the institutional side, undergraduate education would be much more cost efficient and affordable. Students could engage in it part time while working without the need to save up for long periods of time. Professors would be in a delicate position, however. On the one hand, many would be out of a job, on the other, those who are actually fully dedicated to research would have all the same money allotted to them and more, and would be able to engage in research full time. Indeed, teaching and research have always been something of an odd couple and separating the two may prove advantageous. 

The current state of universities seems primarily influenced by their nature at inception, with only a very minimal amount of evolution having taken place since then. While this state may have some merit for certain people, it is certainly not for everyone, and their purpose, goals, and nature need to be rethought from the ground up. The option I seek is the path of maximum freedom and cleanest execution, letting students make their own choices and aim for their own goals, unfettered.

Knowledge and Learning

We travelled upstream against the flow. From the sea, we entered the delta and moved forward, always struggling, pushing against the current. The river branched and we chose to follow it west, travelling with no destination in mind, always pitting ourselves against the strongest flow. It branched again and again, until we faced a mountain, a small rapid current running down its slope. We swung our oars with all our strength but the water was too strong for us and we could make little headway. Stepping out, we turned our oars to spades and started digging a new channel. It would take years, but in time a new stream would flow, with a milder slope, and boats will run along it as far as they can.

 

I think what we could really use sometimes is a comprehensive map of all human knowledge. Not a map of what that knowledge is, mind you, but rather a map of how its bits and pieces are related. While this is a daunting and implausible task, I think it would not be unreasonable to consider how such a thing could be constructed. 

I will primarily first focus on knowledge of mathematics, since it's the clearest of all fields of study, and extend the system to other fields by comparison. In essence, I believe that knowledge is intimately tied to its acquisition, or, more precisely, I would claim that it is tied together by its acquisition. We can consider each little bit of knowledge, a theorem or a lemma say, as a point on a giant field. Then, in our construction, we will have an arrow direct us from one point to one or more others if you can learn the next point with some study once you know this one. Of course, most new bits of knowledge require combinations of several previous bits, so let's say one colour will be one possible combination, and another colour will be a different one. 

As an example, we might be able to learn integration if we understand infinite sums, areas of rectangles, and graphs. Then, we'd have arrows from those things pointing towards integration, and we might colour these arrows red. Then we might alternatively be able to learn, at least indefinite, integration as the reversal of differentiation, so we might have a green arrow pointing from differentiation to integration. To avoid cyclical definitions, however, we should specify that while there can also be an arrow pointing from integration to differentiation, that arrow would have to be red, not green, to signify that you can't learn integration and differentiation from each other without invoking anything else. In fact, if you consider this entire system, you will notice that there can be no cycles – that is, you can't have A learnt from B, which is learnt from C, which is learnt in turn from A. Having such a cycle would mean that you're using circular logic somewhere, which would automatically render such a bit of knowledge invalid unless it has an alternative source that does not involve itself. What you can have, however, is a bit of knowledge that is based on nothing. The only such bits, however, would be the axioms of mathematics, and equivalent things in other fields.  

Next comes perhaps the most important step. We can add weights to the different colours of arrow, with the weight signifying how long it would take to acquire the new bit of knowledge from the previous bits if you follow this route. These could be empirically estimated by having a few people actually learn the information, although these would naturally never go past estimates because of people's varying aptitudes towards different fields or approaches to learning. Nonetheless, with these weights in hand, we can do many things, some merely interesting, some genuinely useful.

On the useful side, we can find the shortest path to learning each bit of knowledge and thus plan out the most efficient route of learning if we have some goal. This could be extremely relevant for empirically designing courses of all levels. For example, bits of knowledge that can all be learned from the same other bits can be grouped into a course or, more widely, a field of study. As another example, knowledge that does not have many requirements but leads to many other possible bits would make good introductory courses.

On the interesting side, it is not uncommon to describe a field of study as "broad" or "deep", and these can now be assigned real definitions. A deep field is one which has a very high weight on at least one bit of knowledge. For example, if it takes a decade of study to learn to grasp some part of string theory this can be considered a very deep field. Conversely, if all you need to understand any particular bit of literature is to know the language and maybe read some commentary, and it only takes a few years in sum, this field might be relatively shallow. A broad field, on the other hand, is one in which the sum of the weights of the deepest (this restriction is needed for the sum to not depend on the number of intermediaries) bits of knowledge is relatively large. For example, if in physics once you knew string theory you knew all physics (wouldn't that be nice?), the field would be relatively narrow. Conversely in literature you may have to take the sum of the weights of all books ever written and all commentary ever written on them for this metric, and this would make it an extremely broad field. Thus, we would have some interesting empirical measures. Others could be made up, perhaps something can be designated "trivia" if it takes very little to learn and isn't a prerequisite for much else, and something might be "easy" if the weights of the arrows to it from its predecessors is low, and "difficult" if the weight is high. 

There are wide individual applications as well. A person might track how far she is on the graph, and compare how much of the same knowledge she and a friend possess and how much of his knowledge complements hers. To efficiently solve some problem, you might assign several people who all have the bits of knowledge that are absolutely essential to the problem, and have very little knowledge in common outside of those, so they can each bring a different perspective or focus on a different aspect. For bragging rights you might take the sums of everything you've learned and see if you're more knowledgeable than someone else. We can also see that someone with very broad knowledge would be a good generalist, and perhaps conversationalist, someone with very deep knowledge a good specialist, and perhaps would be suitable for being a scientist or other researcher. 

On the whole, putting knowledge in a clear structure such as this would be highly advantageous for both understanding it and making any decisions that involve it in an way. From education to employment decisions to conversation or philosophy, a system such as this could facilitate many things, especially as it itself would not need a high weight to learn.