Buckle up, settle down, and get ready for something exquisite. I am inspired tonight and what I present here should take a while to really sink in.
The primary use case of a computer is to augment human intelligence. We know that much. I feel, however, that in order to build an intelligence augmentation device you really need to understand how intelligence works.
People can only handle a certain amount of information at one time. No matter how smart you are, the amount of simultaneous details you can keep in your head isn't really that high.
You have to build abstractions; and a given abstraction of some concept I will call a symbol.
It is funny how when you are learning new things how we fight building a given symbol. A lot of times, after something becomes clear I am amazed at how concise it turns out in my head. Many times I have really worked hard to figure out why I fought a given concept so hard. Math is usually like this; when we are alert but relaxed we can pay enough attention to really learn it and enjoy the feeling of new concepts bouncing around in our heads.
Given time you get comfortable with a symbol and you start to incorporate it into you view such that you don't even notice it. Then the symbol gets semi-randomly combined with other symbols and if the new symbol is interesting or enjoyable you remember the new symbol. This process continues indefinitely in all of us all the time.
You should take time to learn new concepts that are interesting and different from what you know. As you build layers of abstractions and symbols to really adapt to the new experience you will make associations and new connections between things you have really known for a long time but been unable to see from the new perspective. Thus learning N brand new and different things really teachings N^2 (N-squared) or more new things; intelligence and learning are at least exponential (this relies on the assumption that this really is a very new thing)!
In any case, we all think by making symbols and manipulating them in some sort of systematic fashion.
The symbols you are allowed to make in a programming language, btw, directly relates to how exact and high level of a sophisticated of a concept you can express with it. Higher level programming forces you to make these clearer and higher level abstractions. The type system provides the rules for combining the symbols you make with the programming language.
Now lets talk about programs and get completely specific and practical. Most programs are very limited in the forms of symbols they allow you to make. Here are a few examples of building symbols:
One is an abstraction over a collection of objects. I have all these paragraphs organized in a chapter. Now I can re-arrange these chapters and form a book. That is a literal hierarchy of symbols. You can bet that in order to have a book laid out in a sophisticated manner the author has built a lot of abstractions about what the chapters mean and exactly how the flow of the story wanders through the literature.
Another example would be that I have these groups of formulas in a single excel spreadsheet. In the user's mind, they are going to build some symbol out of that spreadsheet that allows them to reason about its capabilities without knowing every single line of code in it.
Second is the ability to extend a given symbol with new information. This form of abstraction is akin to a master-instance relationship where you are in effect saying "this item is just like that one, but it differs in a few aspects here". Artists really love to use this form to create crazy interesting concepts. Dj's, Hollywood, video game makers all use this form of abstraction to some greater but mostly lesser benefit.
It is very common on the web where you have a templating system so that a given site will have web pages with some standard styles, heading and footing but override a lot of other things. Most systems use templates incorrectly, however. One they aren't supposed to be something you copy and start from. If you can't change the final product by changing the template then you haven't built an abstraction; you have just added more information. In the common case of Word documents, if I have a bunch of documents based on a template I should be able to change the headers in all the documents by changing the header style of the template. This doesn't happen (you might argue that it is safer and that is fine; I am talking about being able to build complex abstractions; this requires re-evaluating concepts that you might already know and thus presents the risk inherent in that you are changing existing symbols you are talking about ensuring that you *can't* damage existing goods which means that real learning or abstracting isn't happening).
You see this in programs a lot where you like a set of programs to have a standard look at feel. You get used to using these programs quickly because you aren't focusing on building new symbols from low level concepts but instead you are understanding the differences between what you are doing and what the other program was doing. Ctrl-C in windows is copy in most programs. This means that while its meaning may be context specific the general mental symbol that stands for copy is consistent across programs. You needed fewer symbols to use the new system.
Lets look at how someone learns a song. You get the main feel of the piece; this is the first symbol you build. Then given this rough, broad symbol you continue adding detail and forming new symbols until you build the song out to a tolerable richness or accuracy of reproduction.
I can't immediately think of a third way of learning anything that doesn't fall into a combination of the two ways I stated before.
This is where orthogonality of concepts really comes in. Clear, orthogonal symbols are composable in ways that rough, non-orthogonal concepts are not. This sucks because creating new symbols, either through grouping or through templating is what learning really is.
Earlier tonight I realized that my picking technique was too strict. Playing guitar, doing some random drill I found out of a book to warm up my hands and clear my mind I realized that I could pick this drill several ways; I didn't need to really develop some strict strategy and pick it the exact same every time. I then tried many techniques to see which ones felt the best; the drill had a lot of jumping from one string to another and to get it to work well I tried a hybrid-alternate picking style where I arpeggiated the jumps. This meant that if the jump was down several strings I used a down-stroke on both strings, and then used alternate up-down picking where I was playing a line of notes on a single string. If the jump was up several strings then I used an up-stroke for both the last string before the jump and the first string after.
Then I realized that I could also pick it with a strict alternate picking style where I could pick down on the top string, thus moving the pick towards a lower string *move completely over the lower string* and then pick up on the lower string. This meant that I was technically doing more than the most minimal amount of work in order to pick the drill but I realized that it allowed my wrist to make a more natural and better timed stroke and I decided since I had the control to do the strict style I liked it better because it felt like the timing was easier.
This was an example where my symbol I had built for picking -- it had to be the most minimal cost route to getting things done -- was way too strict. The truth of the matter is that wrists are damn quick and for most situations easily move the pick fast enough. Doing things in the most comfortable way that allows you to play the notes is more important than mechanical efficiency. Knowing this then gave me a lot more confidence with songs because I started noticing all the places where I really had somewhat inconsistent picking but because I have worked on control so much it doesn't affect my ability to play the song.
This form of abstraction, templatization, becomes to strict when the template has too much information. This means that it eliminates possibilities that really should be valid.
So what is the point of all this? Just for once I am going to ask for some reader-participation. I just gave up a lot to come up with all that above, it has taken me years to figure all this out. So please, if you enjoyed the above explanation lets take it to the next step.
You have two distinct forms of building symbols, aggregation and templatization (or master-instance if you like).
1. Are there other distinct forms of building symbols?
2. How could you apply these ways of building symbols to the programs that we use? An example would be if you had a Word document, are the different ways you can aggregate and templatize the document? We are familiar with document templates, can you have a meta-template where you have a common template across templates? What about aggregations of the templates, what would that imply? Aggregations of pages make a chapter, but under what scenarios do you want to use a page as a template or master of another (revision control comes to mind).
