Is Depth-First Learning a Flawed Approach?

[verty]

Lately I've been trying to educate myself but I haven't had an informed plan about how to go about that. Regardless of what I choose to learn, just about the only way to proceed has seemed to be to gather the materials on that subject and then to read through them, hoping to gain knowledge. This is rather like building a rocket, aiming at the moon and blasting off: if one got to the moon it would be purely coincidental.

In my case, I have been traversing the web of knowledge in a depth-first manner, by which I mean that if I am reading something and have questions, I stop reading and proceed to find the answers to those questions. In seeking the answers to those questions, I find myself faced with ever more questions. As a result, I have at most skimmed over many areas but haven't really picked up all that much along the way.

One way in which I have at least benefitted is that I can now read quickly and am used to books which are written with big words and long sentences.

Evidentally, this method has serious flaws. While a chess playing algorithm might follow a depth-first traversal, the reason for that is (I believe) because computers are typically relatively fast with little storage. A depth-first traversal partitions the space into narrow alleyways, only one of which needs to be investigated at any time.

However, this seems far less applicable to learning. In learning, one does not want to reach an elementary result like that moving a certain pawn is the best move. Rather, one typically wants to build a cognitive structure whereby one can make judgements at any time in the future.

I wouldn't say this concerns problem solving per se, but rather what one needs to engage in problem solving. This is in preparation for problem solving, whereas a depth-first algorithm is solving a specific problem. The aims are different, so adopting a depth-first algorithm towards learning is very likely to be misguided.

So having identified the inapplicability of this approach to learning, let me analyse why it failed. In my meanderings, I picked up a shallow understanding of many different topics, but is that what I wanted? I started out wanting a deep understanding of one topic but found that understanding that topic deeply depended on many different areas of knowledge. I therefore meandered through these different areas, trying to collect what I needed. In the process, I tended to spend more time in these abstract areas than in the topic in which I started. I would only have returned to this main topic with the ingredients in hand.

So in a sense, the only knowledge I was gaining was not in the area in which I wanted to gain knowledge. In fact, I would only gain knowledge in that area after having gained knowledge in these other areas. This poses a slight problem. Typically when one wants to become knowledgeable, the reason for seeking that knowledge is to use it in the near term. I was sacrificing superficial knowledge in this area for a greater understanding in the distant future but this goes against my reason for seeking that knowledge in the first place.

I would like to say that my method was quality-constrained but not time-constrained. It was a method to breadth of knowledge whereas I need a method to expedient and applicable knowledge. If I must limit the scope of my investigations in order to gain the requisite knowledge in a timely manner, then that is what I should do.

With the goal clarified, a method can now be sought. Another result of my meanderings is that having left one area to research another, on returning I discovered that I could not remember all that much of what I had read there before. Certainly it was quicker going over it the second time, but nevertheless that knowledge was at a very transient stage, very imprecise. A result of this is that, by leaving with a very shallow understanding of the area concerned, my meanderings could not be constrained. How should I identify while reading in another area that what I am reading is applicable or not, without having a relatively precise understanding of the area of knowledge I began with? Because I left it in an imprecise state, I was doomed to a very inefficient search for answers to questions I did not yet quite understand. My search was inevitably wider than it needed to be and that which I was gaining was inevitably imprecise.

So I think the first thing to change is this lack of precision. Although I might come upon questions I don't have an answer for, leaving that area with an imprecise understand of what the question entails, what the relevance of the question to the discipline is, would doom me to an unnecessarily wide search. I therefore think that the most important methodological guideline is to ascertain the relevance of a question before trying to answer it.

The way to begin is then to parse over the materials, noting the questions that arise and seeking to ascertain their relevance, before attempting to answer those questions. In constraining the relevance of such a question, it might become so constrained so as to admit only one solution, or at least it should be constrained to such a degree that one can find the answer without too much searching.

This is somewhat analogous to a breath-first traversal. By enumerating the chess-boards after one move, we can prune that list using heuristics that would not be available to a depth-first traversal. In doing so, we constrain the search so as to get more meaningful results per time. By following this approach, more useful knowledge is gained early on because even if there are questions one can't yet answer, one should be able to make a far more informed guess than one would with an imprecise understanding.

I am posting this here because I think that reading such things would have helped me, and so I make it available here in the hope that it might help someone else.

I think self-study is inevitably a difficult endeavour, and without a mentor guiding one, insights are hard-won. Nevertheless, I would like to think that with a good understanding of the methodology of self-study, many more of us could become educated without selling a large portion of our lives to institutions.

I can't spare the time and money to study further at university, and I imagine that many others can't. There is the matter than studying gives one a qualification, but it is my potentially naive hope that if one were to submit articles to journals and such, that would also be a good qualification. Whether this is true or not is a matter for another day, and it is an opinion for which I would not like to argue. If it turns out in the future than I must study, then so be it. Even if that were to be the case, I don't see that as a good reason not to seek to become more knowledgeable on one's own, if one has a method that works.

 

[-Job-]

The way i see it the learning process consists of merging two graphs, the one that you possesses and which consists of your entire knowledge, and the one that you're taking in, which consists of whatever you're learning.
The graph that you're taking in will have nodes that you already possess, in which case they will be easily merged, and nodes that aren't yet in your graph of knowledge and which happen to be the new topics that the subject you're learning relies upon.
I think naturally we try to avoid having these dead-end nodes by expanding them and any nodes they rely upon, recursively, in a depth-first manner.
The reason is that a graph with dead-end nodes, by which i mean nodes with a very small degree, is a graph that can deteriorate over time. In all likelyhood these dead-end nodes are dropped over time because they're not frequently accessed, and then forgotten. When these nodes go away they might make new dead-end nodes, which through the same process go away as well leading to deterioration of your "graph of knowledge".
So i think you should follow an incomplete depth-first algorithm when learning. You should learn something about the topics your subject relies on, without being exhaustive, just enough to get the idea. If in the future you need to know more about these other subjects there's no reason why you can't come back and study them more thoroughly.

 

[verty]

But in order to know how the question you have which lies in another domain is relevant, I think you must forgo answering that question until you see how it fits in, what effect it has. Otherwise you could spend a lot of time trying to understand only to learn later that it wasn't relevant. That's a sure way to forget a dead-end node, it shouldn't have been investigated.

In other words, we should judge which questions need answering in light of their relevance to the matter at hand, and we can only do this by investigating the matter at hand until we can perceive the relevance of the question.

 

[kant]

But in order to know how the question you have which lies in another domain is relevant, I think you must forgo answering that question until you see how it fits in, what effect it has. Otherwise you could spend a lot of time trying to understand only to learn later that it wasn't relevant. That's a sure way to forget a dead-end node, it shouldn't have been investigated.

In other words, we should judge which questions need answering in light of their relevance to the matter at hand, and we can only do this by investigating the matter at hand until we can perceive the relevance of the question.

I don t think your method would work. If i am getting your point, you are saying that when one encounter a problem that he/she can t solving, then one should access it, and see if it is worth spending more time on it. Most of the time in schools, more students don t master everything in each section, or chapter. The student just have to learn "enough" of the ideas to move on to the next section, or chapter.

It is always relavant on what one studies. For someone to study philosophy, english literature is different from studying math, and physics. I do think one needs to learn literature based studies from the universites.

 

[verty]

I basically mean we should gather the questions before we answer them, judge them heuristically and then pursue them to the degree that we think they are relevant.

 

[CuriousArv]

this site might help..you have probably already visited it.

www.improvehuman.com[/URL]

 

[verty]

That looks like a great site. I like that article about automaticity in problem solving, it foretells that we should learn one thing well before moving on because otherwise that incomplete knowledge will hamper us in the future. That isn't to say that one should learn everything well, but that one should pick the most important and relevant discipline and then master it before moving on. As things become automatic, that'll free up time for other things, but trying to take on too many things at once will mean that none of them get done well.

I hadn't really thought about it in that way before but it does seem relevant to learning, in that one should learn to learn well before moving on to learn other things. Having learned how to learn automatically, how to process incoming information automatically and in the correct way, I think the most time will be freed up because it'll mean that one can separate the wheat from the chaff and only concentrate on the vital details.

 

[verty]

Continuing this trend, I have come to see that critical thinking consists of 3 concerns. The first two of these concern identifying and taking into account bias. The third concerns critically analysing the import of the evidence being presented.

Learning is learning from evidence, but bias can distort the learning process. Personal bias is the first concern of critical thinking, because if one is biased, one will not be able to think reliably and what one learns will not be reliable knowledge. Part of the learning process will therefore be observing one's own attitude and reaction to what one is witnessing. This comes before the matter of whether such an attitude or reaction is justified or not, because if one is biased then what justification one could give must depend on unbiased reasoning.

So there must be a core of reasoning devoid of bias, and any other bias must be justified by appeal to this rational core. If one is biased, one must at least be able to evaluate the matter in a nonbiased way in order to justify that bias. In a sense, one must put one's bias aside at least until one has rationally viewed the situation and determined the relative merit and scope of a biased view of the matter.

Therefore, the learning method will rely on unbiased evaluations first and foremost, and in a sense, if a biased attitude is justified in some way, that is something to be learned. I therefore think we can and should eliminate all bias from the learning method itself, whether or not we hold (hopefully justified) biased opinions otherwise.

The second concern for critical thinking is identifying and evaluating any bias of the speaker's viewpoint. Whether we are engaged in a conversation or participating in a forum discussion or reading a book, any bias in the attitude of the speaker will need to be justified rationally and to do that we must first come to an understanding of the subject concerned. Only when we can justify to ourselves whether a biased opinion is valid do we earn the privilege of holding one.

Part of our learning method will therefore be to factor out any bias from the medium we are studying. By doing so, anything we conclude from what we are learning should be that much more reliable.

The third concern for critical thinking is to the relevance of what we are learning about. Part of our learning method must be to see how the evidence correlates with or contradicts what we have previously learned. I think this should be an active process that we engage in as we learn, rather than something we do at a later stage, because we will thereby be able to extract the most value from the evidence at hand. As we come upon those parts that are more relevant to our former knowledge, those parts might form a bridge to the more abstract material. Even if some of the material is beyond our current understanding, that which we have gained will have made the process worth the while.

So in light of these considerations, I think our learning method is much like an attitude towards learning. It is a mode of thinking and perceiving where we consciously eliminate and factor out bias and where we bring our former knowledge to bear on the evidence at hand, in the pursuit of new insights.

Developing an evolved learning method can, I think, make us better people generally.

 

[CuriousArv]

I am wondering the following about independent learning. If you have all the data available, such as is the case when you are solving puzzles like rubix cube can anybody eventually work out the solution through deduction? I am not even sure if this is a good question, I just happen to be playing around with a rubix cube and I've been writing down observations, testing them to see if they are 'truths' and progressing. Is this how an intelligent person like a scientist thinks about problems, just faster? The reason I ask this is because according to IQ descriptions I have read from MENSA, it says above 125 IQ, one is self-teaching. So does this mean that if you fall below this sort of figure, that you are reallly crippled to identify truths and therefore some problems will be impossible?

 

[Panda]

You need to take into account the way the brain works. As far as I understand you can crudely divide your memory into short term and long term memory which are stored in separate areas. Short term is rapidly accessed but has few links to other memories, long term has many links but is accessed slower.
I suffer with Dyslexia and as such have a poor link between the short and long term memory. I cannot learn by reading a subject, as the subject goes into the short term memory, and is then lost for a time and then appears in long term memory long after I needed it.
If you read a subject then you can remember it, and when tracking off on a sideline it is still there, but after a time it drops out of short term memory.
If you read a subject at a low level thoroughly and applied it then it and its applications will be solidly linked in the long term memory. You can then go to the next layer of complexity in the subject, and the basics are available from long term memory leaving short term memory to absorb the new information.
You seem to be setting out to learn the alphabet but after looking at A is for Apple then sidelined into complex gramma rather than accepting that A is for Apple and moving onto B is for Boobs.
Of course you may have a mind that has much better short term memory than long term in which case you will not be able to learn through conventional means, in the same way that I couldn't as I would forget what A stood for by the time I'd realized the meaning of B.

 

[CuriousArv]

How are decisions made? For some things like computer programs I need to completely rely on deduction, logic etc... whereas with people I look at identifying social patterns and make decisions with this is mind. Is there a universal way of making decisions. Is there such a thing as decision making theory..a subject devoted to working out how to make decisions, types of decisions and their applicability in different situations?

 

[CuriousArv]

is poker for example a good place to understand how to make decisions and get an idea of different types of decisions and practise decision making? It combines psychology and logic..subjective and objective... If it is so..i wonder if poker should be made part of a school curriculum!

 

[CuriousArv]

If you are really keen on a subject but your aptitude for it is not great whereas in something else your motivation is really low but your aptitude is brilliant? what should you choose? Is the best course of action to realign your motivations with your aptitude area and then start from scratch here? Is this how child should be guided?

 

[Moonbear]

This thread doesn't seem to have anything to discuss. It is just a personal accounting of what one person found to be a good learning strategy. Such topics are best posted in the personal blogs available here. It is certainly not philosophy. I am locking this now to give the OP a chance to copy the content to a blog, and will delete it in a few days.