Putting order into your understanding

It seems that sometimes you don't understand something because you have made an erroneous assumption about what it is.
Sometimes too the subject can just be too complicated to understand: you lose track
of the complex structure. This is where, it seems you can tell smarter people from the less fortunate. Prior training can also help make it easier to grasp some concepts
because prior structures act as scaffolding.

But it can also be the case that you don't understand a small subject because you have not put some order into your view of it and you have in fact contradicting views about different parts of it. Or your view might be not sufficiently developed.
In such a case it is a good idea to try to write up your explanation of the subject.
It has often been said that there is no better way to understand a subject that to teach the subject, presumably because it forces you to put some order on the subject.
Without going so far as teaching the subject, writing a small documentation is a good way of putting some order. It follows that thinking is not good enough on its own.
It's like pencil and paper for a mathematician: without pencil and paper most mathematicians are far less efficient.

I do think that there are a lot of professionals out there who do not take the trouble to put some order and clarity into their concepts by writing it up.
As a technical writer I have noticed that I had to help them clear their ideas up.
I think they should have learned to do this on their own, and the gain in productivity thanks to clearer ideas would have offset the time trying to comitt it to paper.

And yet it also seems that there are some ideas that we do not know how to explain, and yet we seem to manage to deal with a lot of the problems in practice.
This can be due to the fact that the ideas are very difficult to express, given the culture at the time which does not provide the support to express these ideas.

Still that should not be used as an excuse not to try.

A good video

I just saw a good video on understanding and teaching. It's even funny in places.
The first is here
I think the take-home message is that the teacher needs to say what the teacher is trying to explain, and get all students to actively engage in solving problems and thus prepare the student for the exam.
That's a very superficial assessment, and I might rewrite this blog.

So you think you have explained something?

I was just reading the description by a computer scientist of how his programming language executes.
I could not help thinking that the description was very incomplete, and yet the author was probably convinced that he had explained it well enough.

This is somewhat troubling:
  Are our minds geared to thinking that we have explained something well enough when this is in fact wrong?

I cannot help to think of how we fall for logical traps.

It seemed to me that the author had gone through the following strategy: he wrote down what came to mind when thinking about the execution of the subject. Yet, because the community in that field is tiny and because there is supposed to be a reference to that subject anyway it seemed to him that he had done enough. This is illustrative of what goes on in a small community of researchers: if you don't understand them then you should go and work with them for a certain time and it will sink in.

But there is another aspect: this being a programming language that is available, one can always go and try it out and it will sink in that way.

One of the things that I am trying to point out is that the explanation must be understood in the context of
what resources there are in the community for further explanation.

Concepts that take a long time to get

In my life I have on occasions found concepts that seemed hard to understand.
In retrospect I think that I had not assimilated the background to prepare myself, but whatever the reason
I'll put commit some of these of these to my blog, because I know that it is going to be hard to ask other people for such concepts. Teachers are the ones who have the biggest collection of concepts that are hard to get because they meet these in their students all the time.

One concept I found very hard to figure out was the notion of datum in geography.

Another concept I had trouble was with Universal Element in Birkhoff and Maclane's book on Algebra.
It was very hard to remember even if the definition was very short, whats more it seems to mix ideas
from different levels that should not be there: an element of a set and category theoretic ideas which I thought should have existed at another level.

The various kinds of joins in SQL were rather hard to get at first. I felt I should "get back to those later".


I also remember a friend having a lot of difficulty explaining what he meant by the "time value of money".
I think it was also because I refused to accept his conceptual starting point.



I do know that a lot of people have trouble with pointers in the C language.

I have been told that students have many problems with the notion of limits in Calculus. I never had problems here.

I have seen peole have huge problems with how loops could work in computer "functional languages".

A priori ideas and metaphors

One of the obstacles to understanding is the existence of incorrect a priori ideas and metaphors.
I offer a technical example:
  In TCP network programming there is an idea of a server and a client. People are often told that a good metaphor for a connection is a telephone call. They might then come to the conclusion that in a communication between two sockets neither is a server because it does not look like there is a server role when you ring someone: "both are in the same situation"

Another one, easier, concerns drag and drop operationson file icons in a Windowing interface.
In some cases it means copy and in other cases it means move. You can imagine that it is not a priori obvious that there should be this distinction.

Anybody teaching should try and identify potential a priori ideas so as to correct them.

Communities

It's been a long time, decades since I have read Michael Polanyi's famous book
"Personal Knowledge" but I believe it's relevant.
I shall risk trying to explain some of the ideas that remain:
Knowledge and the attendant understanding is an affair of communities.
The quantum mechanics community is relatively separate from the pure mathematics community etc...
Each community not only has its assertions and theories but they also have
tacit knowledge that is transmitted by living and working in those communities.
You just cant pick up a book and expect to understand easily by turning the pages.
Communities probably even have different criteria for what passes as truth.
It's that deep.

More later.

He doesnt understand how to answer email.

My friend, let's let him hide behind the name Bob, is in his seventies.
Occasionally I send him  email but he doesn't answer back.
Every time I ring him he reminds me that he doesn't know how to answer
email.

This should make you think.
The traditional reaction of many younger is to conclude that he must be senile.
Now he's not stupid, and it's not going to get any better the longer it lasts.
So what's going on?
I dont have the answers, but we could explore some:

• He's getting "computer fright" (is that the right term) and this is getting ingrained. People who get this are also afraid of making a mistake, so they dont explore.
• He realises that once he wants to understand how to reply to email he's going to be learning lots more and he thinks the investment is not worth it.
• He's set in his ways.
• Somebody needs to show him.

Some people get out of it by writing a recipe: press this button and that and follow the recipe rigidly. Clearly this is not understanding.

One point I want to make is that adapting to a piece of technology can appear to require a huge investment, the little bit you learn is only the visible tip of an iceberg of knowledge.
New information always perturbs our system.

What I have just written is a rough draft. What do you think?

Software patterns can be hard to understand at first

Let's take the fashionable concept of Software Design Patterns.
If you read the foundation book by a group known as the Gang of Four, you can be tearing your hair out wondering what on earth they are saying. On the other hand, if you are prepared to put up with the jokes and you know Java then the book Heads First Design Patterns makes the learning much easier because they present the subject from the perspective of a simple task you are given to solve.
The problem with many descriptions of design patterns as they are expressed in the "abstract" is that
they are using English words which are images, but it's very hard to work out how to interpret them.
And yet I get the impression that their authors think that they are being perfectly clear.

So you need a good strategy to understand the concept. A key element is patience, just keep on reading.
I had started but not finished the head-first design patterns book and then went on to read the Wikipedia
articles on individual patterns. It turned out, it seemed that the best strategy for me was to look at the code samples in Java, surmise what was trying to be accomplished and then go back to the "abstract definition".

And then it seems that it's so much easier than what it seemed to be.

Comfortable/Unconfortable concepts

Let's suppose we try to define a concept in mathematics like this:
A set of integers is Moustierian if it contains the integers 6823807439 and 523098064.
I just made this up using random numbers of course, but I would be hiding this from my listener.

In a way it is a trivial but the person that is given this concept will not feel that this is a comfortable concept because he/she will be wondering where on earth did I get those numbers from?
And where did I get that strange name?
So there will be a number of hanging questions, which are like weights attached.

Did I mislabel this blog?

I have let this blog alone for quite a while, but I often think about the subject.
It seems to me that the title of the blog could have been better adapted to the contents that I have put in and will probably put in, namely it's about understanding technical subjects like computing, mathematics, physics and chemistry rather than understanding say the  Chinese philosophy of the 13th century or understanding French philosophers after World War 2. There are common features of course to all subject but I'm not competent enough to discuss these much.
But while I'm on the subject let me mention the shock I had when I came to France, picked up a book by Gilles Deleuze and tried to understand what he was saying. Being used to discussion from English analytical philosophers I was very put off by the French philosopher's style. Lots of anglophones would agree, coming from a world where they had read someone like say Nozick.

If I wanted to read such a French philosopher I would need a strategy, adapted to someone from my culture.
I would have to have been told how the French typically organise their discourse, which is often different to what anglos are used to. And there are the individual words of course, but that is not sufficient.