What is generalization?
Generalization is looking at the commonalities instead of the differences.
Generalization is disregarding the things that change and focusing on those that do not.
Patterns are all about generalizations. Patterns are anything that happens more than once. So something that does not change. And you can have very general patterns or very specific ones.
For example “2, 4, 6, 8, 10” is a fairly specific pattern. Now if we see two other patterns such as: “14, 16, 18, 20, 22” or “10, 12, 14, 16, 18” we can already make a generalization. What do all these patterns have in common? They are all a succession of even numbers, fairly simple.
This is what we would call a rule. The rule by which these sequences are produced. Now what is the point of rules? What is the point of generalization? The point of a generalization is to be able to complete a pattern that you have never seen before.
If you simply memorize the pattern “2, 4, 6, 8, 10” then that’s all great and stuff, you can now complete the pattern if I give you the number 2 as a starting point. But if I give you the number 24 for example you have no idea what the pattern will be. You can’t create anything new.
So generalization is actually one of the driving powers behind creativity. With the general knowledge of how these patterns are generated I can now give you the number 24 and you will give me back “24, 26, 28, 30, 32”. You can produce loads of new sequences!
Now these sequences of numbers are of course somewhat trivial. But it’s just to illustrate the most basic form of generalization. Let’s take a look at human language. If you observe the pattern of sentences such as: “he went to the store”, “she ran to the exit”, “I walked to the auditorium”, they all have the same sequence. Pronoun -> Verb -> Preposition -> Determiner -> Noun. This would be the generalization that allows us to produce sentences with the same structure.
Of course we may not even know what prepositions or determiners are, yet still we would be very surprised by the sentence “she house to the walked”. These expectations are all unconscious and only surface when they are violated. Now if everyone uses this structure it is much easier to understand what someone is saying since you already know what to expect and can deduce the meaning of a word you don’t even know. Generalizations allow you to narrow down the future possibilities.
The great thing about generalization is that at each level we simply have sequences that we are memorizing and the higher we go the less we have to memorize. Memorizing the specific number sequences from above is pretty tedious, so we generalize and tadaaa! We only have to memorize one sequence, namely “x, x+2, x+2+2, x+2+2+2”.
Now you might say well why do I even have to memorize that complicated sequence I just have to remember the rule add 2. But what are rules anyway other than remembered sequences? If you want to add 2 you think of 2 + 2 = 4 or 3 + 2 = 5 or 7 + 2 = 9. These are sequences you’ve learned and adding 2 to any number is made easy by the way we name our numbers! Imagine you had a completely different symbol for each number, you’d have to do a lot of memorizing. But with our number system you simply have to know the sequence 0 to 9 and that 9 + 1 is 10. It’s all the same. Adding 2 to 355 is no different from adding 2 to 5. Piece of cake.
So generalizing means building up a hierarchy. There are a lot of specific sequences that can happen at the bottom and the higher you go the less different sequences you have. You can explain a single idea in your mind in different words but the idea remains the same. You can have a life goal of wanting to be happy and this can be actualized in so many different ways.
You can memorize a sequence for problem solving such as: “Truly understand your problem and your goal. Divide it into steps and sub-steps until you arrive at a step you can execute. Lay down and cry.” The last part is optional but this is an example for a sequence that you can memorize and try to apply to any problem you are trying to solve! One general sequence for all your problems. Of course the real work is applying this sequence and transforming it into ever more specific sequences that are adequate for your current situation.
Another good example would be story lines or movies. They all have common themes such as a problem or a quest that the protagonists embark on. Then there’s a kind of conflict or bad guy and then at the end we get a happy end or some kind of conclusion/resolution. Again this is just a sequence we get to know and which we memorize. Once we’ve watched a couple of movies we can predict what will happen in them. Expecting a resolution in the end we can use that knowledge and the context of our situation, the type of hero in the movie, the conflict they had, the location/time it takes place, in order to turn it into a specific sequence that we predict! Just like in our sequences of numbers where we simply needed the first number and the general rule to produce the rest of the sequence.
So generalization is a pretty cool thing, it allows us to anticipate things we have never seen before, it allows us to solve problems we have never seen in this way before. It allows the brain to predict its input.
The more general our knowledge, the less we need to memorize, the more we can anticipate. Our world changes, but not quite as much as we may think. Recurring themes, regularities, patterns are always to be found.
Illuminating these laws is what science is all about!