The learning experience

Learning... what is learning?

I've come to the conclusion, that for me at least, there are three stages to learning and understanding something.


Stage 1.

I know nothing. This is how we all start of course.

Pick a topic, like say playing a musical instrument, cooking or the electromagnetic-spectrum. You start off knowing nothing about it, at least at one stage in your life you do. You are an outsider at this point. Maybe you can watch others perform music, cook a meal, or predict the warming effect of a beam of light.

However to you, its all just a form of magic. You know there is nothing magic about these people, but they just have some sort of gift that you don't possess. I've been in all of these places.

Stage 2.

You learn how to do something. You decide you've come this far, and really its time you knew how to cook. How do you go about fixing it so you can cook? Well there are the obvious ways. You can take a course, you can read a how-to book, you can ask someone who can cook to show you. Gradually you'll get into the zone where you can cook. Cooking in this way is a wrote mechanism. You want to bake a cake, you take down the recipe book, turn to the page, and follow the recipe. You're passingly familiar with the notation. You know what eggs are, and what cups/grams/teaspoons mean as measures. You can cook now. Or at least you can cook if you have a recipe. You also need the ingredients, and if you don't have the balsamic vinegar the recipe requires, you move onto a recipe you have all the stuff for. If you have a recipe that calls for a technique you're not familiar with, you move on until you are back in the familiar.

The same with musical instruments. You learn the musical notation, you press the keys, cover the holes, or depress the strings and with practice slowly you can make music. I have to admit this is as far as I got with my musical studies. To go further, you need enthusiasm, which is probably one of the rarest commodities around - and easily removed by careless remarks.

If you remain at stage 2, you can solve a certain class of problems, and this can be fine for some things. You probably know how to do long multiplication in this way. You take two numbers - you follow a learnt procedure and you get a result. That's good enough for most people, after all, you're mostly interested in the result, not the method.

Stage 3.

This is where things start to happen. To get to stage 3 you need either a natural inclination for the subject, or sufficient enthusiasm to get you to the stage. A good teacher helps too of course.

At stage 3, you sort of transcend the topic. Its where you get to what Robert Heinlein defined, in one of his novels "Stranger in a strange land", to "Grok" the subject.

Its a great feeling when you get to that level, and its difficult to describe what it feels like, but you must have come across it in one discipline or other. A musician who really understands his/her subject, is no longer confined to the notes on the page. They begin to understand the underlying rules to what makes a good performance, and that really the notes are only a guide. Jazz is one form of this.

The same with cooking - OK the recipe demands demerera sugar, but you can see really what is required here is sweetening - and that white sugar will also work, though maybe not as well. Honey, or treacle is also an option here. Yes it says two eggs, but at a pinch one will probably do, if you make up with a little liquid, and perhaps a little raising agent if one is all you have.

Breakthrough

When it happens, a breakthrough to learning can be the most wonderful feeling. Its an epiphany of understanding, and suddenly the murky waters clear, and all that stuff you've been struggling with drops into context. Its not the end of the road by any means, but its suddenly the case you can see what it all means.

I can still recall the day the electromagnetic spectrum broke through for me. I'd been studying physics at school for some years, and I understood that light was made up of colours. I understood you could take pictures of peoples bodies with X-rays. I knew that you could put together electronics in a way that would pick up radio waves. I'd probably even been told these were all part of the same thing. But you can be told, and you can understand! I remember it happening, quite vividly - getting out of the car after my mum had driven me home from school, and there in the driveway of our house, the E-M spectrum suddenly revealed itself to me! It clicked together in my head. Radio waves were just kind of slowed down light waves, and X-rays were just speeded up light waves. Well not really, it was just a difference in energy, but it was a way of visualising it. Now, I could see it made no sense really to say at what frequency do radio waves begin and end - they're all the same thing. Radio waves are just an arbitrary human division. The E-M spectrum had clicked, and looking back, I couldn't for the life of me see why it never had before. It is sooooo obvious.

To really learn something, you need to do it, teach it, or simulate it.

This is where being a good teacher is hard. You can see now how it all works, but can you remember what it was like before it clicked? What makes it click for you, may not make it click for someone else. This is also why you need a deep understanding of a subject to teach it. You need to be able to explain the concept in different ways. You're standing at the top of the mountain, and you can see the path you got there via. However others will stumble and fall on this path, but there are paths all around the mountain. One of these will probably work for someone else. If you only know the path you got there with, you probably can't explain it to others.

Doing it obviously helps in understanding, but I don't think it always allows you to make the jump to stage 3. When teaching, you need to be prepared to look at alternate strategies, which leads you into deeper understanding.

Computer (or other) simulation is almost as good - as the program asks questions you need to know the answer to. OK - what happens when the program gets into this state? What should happen?


Wrap up

Stage 3 - the groking level, is the one to aim for - because it not only allows you to understand and solve problems - but extrapolate it to other similar problems. Stage 2 will get you by if you need to do something, but you're missing out. Stage 1 is ignorance, and life is short so you have to pick what you're willing to be ignorant on, as you can't do all things.