I will start by the conclusion!
If you use the "realise then generalise" concept correctly, you might not need to study more than 20% of most of your textbooks/lectures to get almost a complete understanding
The number 20% is just any number; it's just to say that most of any scientific material is usually nothing more than extra explanations, special cases and examples of a general idea or concept. Get that concept right, then you feel that everything else in the material is repeating itself. In other words, you start reading in the book or listening to your professor speaking and you are simultaneously realising and generalising what you are reading or hearing. After a while, you start feeling that you are not reading anything new, the professor is not saying anything new!! You feel you are reading a paragraph which you have never read before, but you already know its content very well!! When this happens, you start reading faster, i.e. skimming the sentences looking for any new piece of information which might add to your knowledge.
If you understand what I've just said, you would guess that the stuff written in books can be divided into essential information and redundant information. If you finish reading/studying a chapter, and you have got the essential part correctly, you have really got EVERYTHING.
EXAMPLE 1
I really want to go in more philosophical thoughts but let me give you some simple examples to build these thoughts on. Consider this short simple paragraph from wikipedia about the (Square root):
"In mathematics, a square root of a number "a" is a number "y" such that y2 = a, or, in other words, a number "y" whose square (the result of multiplying the number by itself, or y × y) is "a". For example, 4 is a square root of 16 because 42 = 16."
The red part is the essential information in this paragraph. If you realise the meaning of this red sentence correctly, then you would consider it a general rule from which you can understand the rest of the paragraph. The green part is a repetition or a clarification for the red part, the yellow part is just a clarification of the word "square" in case you didn't know it, and the blue part is nothing more than an example. When someone reads such a short paragraph, the chances are:
- Guy 1 reads the red part, understands it well, then goes on. When he reads the other parts he keeps saying: "okay okay, yea yea of course, sure! nothing is new!". This guy is great, he realises that the reality of this paragraph doesn't exceed the general statement in the red part. He knows that the information contained in the other parts is redundant; it is adding nothing real.
- Guy 2 reads the red part, gets some unclear understanding of it, then goes on. When he reads the green part he might say: "Ohh!!! yea!! I seeee, that's what they mean by that red part! got it!! ;)". Then he finds nothing new in the blue part. OR he might have better understanding after the red and green parts but still not complete until reading the blue part. This guy is great as well because at the end of the paragraph, maybe even after reading it more than one time, he realises that the whole paragraph is nothing more than the red part which is a general statement.
- Guy 3 reads the red part, the green part, the yellow part and the blue part. He considers these as essential parts carrying different pieces of information. He finishes reading while carrying the whole paragraph over his head. MAYBE glad for being able to understand these three different pieces of information! He stores these in his memory as three different things!! This guy ... well ... hmmm, NO comment!! This guy has actually added three raw strings of an un-understood text to his memory. He understands non of them! If he really understood the red one and the green one, he should've realised that they are the same.
Essential Parts are not Mere Texts
You should store the realised meaning NOT the raw text in your memory. That is, don't store in your memory the text in the red sentence; store its realised meaning. I say realised meaning to differentiate it from the linguistic meaning and I will come to that later on in more details and examples. You can still store the sentence as it is, but while having some kind of imagination of its actual real meaning. Some people might have an image stored in their memories instead of texts, maybe a graph or something else, maybe some discrete words are stored in your memory like (root and square) while having in your memory some kind of an arrow linking between them. You might store in your memory an image which looks like (root2 = square) and you really have a feeling of what this image means in your insides.
If you do this correctly, you end-up storing a small essential clear nice understood pure informative not redundant piece of realised information in your memory while throwing out all redundant texts out. This is the clean pure and clear understanding which you really need. By generalising this pure essential piece of information you might get the answers of many many questions and generate paragraphs and paragraphs of statements and examples. DON'T STORE THE REDUNDANT PARTS IN YOUR MEMORY!!!!
If these non-red parts are not essentials and should not be stored in memory, what are they there filling most of those text books? Why do teachers/professors say these redundant things?
Well, the answer is that the majority of the great guys who realise the actual meaning are of the type (Guy 2). These redundant parts which repeat the same piece of information in many words or give examples are important in many cases to make the essential part clearly understood; they should be seen in that way. They should not be seen as new things. So after reading them and getting the main idea understood clearly, one can throw them from his memory safely.
Implicit Essential Part
Sometimes, you can't point out a sentence or many sentences in a text and say that "this is the essential part". Though, the actual long text can be printed in your memory in some kind of an image, a figure, a shape, a something!! or a whatever!! which is pure, clear and essential; in other words, it includes essential not redundant information. See this example:
"How about a novel way of clapping? Stand up with a space of about a hand-span between your feet then bow down until the tips of your fingers touch the tips of your toes. Keep your eyes down staring at your feet. Your elbows are now stretched so your fingers can reach your toes. Bring your palms together while they are extended downwards. Your fingers are opened as much as you can and the hands are tightly brought together such that each finger from one hand is tightly joined with its corresponding finger from the other hand. Fix your back, legs, head and eyes. While keeping your palms tightly joint with stretched fingers, bend your elbows to raise your joint hands up next to your face. Let the tips of your joint thumbs touch your nose. keep the tips of your thumbs attached and touching your nose while moving the rest of your hands away from each other in a way similar to an opening compass (that thing which is used to draw circles!). Now re-bring both hands together in a strong slapping way. Repeat this opening and closing as many times as you like! Make sure that you always close them in a quick strong way to make the sound of clapping. Congratulations!! You are now clapping in a novel way!! Let's call it Bowed Nose Clapping (BNC)."
Well, apart from concluding that you should never try this BNC clapping in front of others because otherwise you might be taken to a mental asylum, if you understand English then you should be able to have some image stored in your memory for this BNC. The red essential piece of information is not a specific sentence or sentences in this long paragraph; it's rather some realisation of the meaning. If you have the right image in your memory now, you don't need to go back to the text to answer questions like: "At what does the BNC clapper stare?", "Which of these can perform BNC clapping? a blind, a deaf, a lame, a dumb, a guy with a lost thumb, and a guy with a lost pinkie (the smallest finger)." If you have the correct realisation of the given text, which is a small simple pure clear imagination, you should answer these questions correctly!
I will discuss those two cases: "a guy with a lost thumb" and "a gut with a lost pinkie". Correct realisation should through out unnecessary extras and flavours which are not the real actual issue behind what you are trying to understand. In other words, it's essential in order to clap in the BNC way to bow, to stare at your toes, and to have your thumbs joint and touching your nose. Nothing in the text is forcing any constraints on having the rest of the fingers; maybe someone has six or four fingers! As long as the essential core image is met, then he is BNC clapping. It's most likely that you have realised this text by an animated image of a person bowing and clapping in that way. The more accurate realisation should have the positions of the thumbs, back, feet, nose and eyes clear while keeping the rest of the details vague, i.e. keep the rest as optional. Nothing says that you can't do that while wearing a Karate kit or a formal suite for example!! So correct realisation allows you to have correct generalisation.
To give a reasonable example (instead of talking about that funny BNC clapping!!!) which shows you how we sometimes put unnecessary constraints on things while we can think in them in a much more general way, look below at this refined version of (EXAMPLE 1) about square roots.
Refining EXAMPLE 1 - Refining the Essential Part
In the same article (Square root) in wikipedia but after some paragraphs of mostly redundant sentences, they say:
"More generally, square roots can be considered in any context in which a notion of "squaring" of some mathematical objects is defined."
Can you understand what they mean in this? I will give you an imaginary example first to understand this sentence in case you haven't. Assume that someone came and told you "the square of the student is the professor". Based on this definition, even if the "student" and the "professor" are not numbers, we can still find the square root of the professor which is equal to the student. This is because that quoted red statement from wikipedia redefines the square root to be "considered in any context in which a notion of "squaring" of some mathematical objects is defined". This kind of general understanding of this mathematical concept "square root" overwrites the more closed understanding which imposes that square roots are only for numbers.
Now once we read this statement and we realise it correctly, we can go back to EXAMPLE 1 above and refine what we understood from it. First, I will "copy-paste" the red essential part from EXAMPLE 1; here it is:
A common example that fits to this redefined general square root but does not fit in the older definition is the square root of matrices. If you don't know this don't worry. It's just that some types of matrices can be (squared) and thus some matrices have (square roots). The matrix is not a number but still has a square root.
As we discussed before, it is still beneficial to write up these details for the reader. This is because in most of the cases the reader is not expected to have this deep understanding just by giving him only that short essential part. Though, you as a reader should always let all of such pieces of text (definitions, explanations, rewordings, examples ... etc) to contribute in providing you with a very clear and clean essential piece of information.
The best understanding of a passage of information happens when you realise what is the real reason behind each result. For example when we say:
You may think of these examples: "English speakers find Chinese hard to learn", what's the reason? just being an "English speaker" is an empty meaning!! Is it because English is written from left to right? Is it because of the way the grammar of English is structured? Is it because of the differences in the systems of alphabet? If you understand the reasons, you can analyse the cases of Spanish, French, Italian, Japanese or Arabic speakers when they want to learn Chinese.
An example from my field of research which you don't need to understand but you will get the idea from is the importance of "the normalisation of microarray datasets" before analysing them. You don't need to understand what these microarray datasets are. I just want to say that if you give me some other type of datasets, then I need to look at its properties. If the properties of the microarray datasets which makes normalisation important also exist in these different datasets, then I should normalise them as well. In other words, I should understand the real reason for the "importance of normalisation" and then consider it in any other application.
Now once we read this statement and we realise it correctly, we can go back to EXAMPLE 1 above and refine what we understood from it. First, I will "copy-paste" the red essential part from EXAMPLE 1; here it is:
"A square root of a number "a" is a number "y" such that y2 = a."Our new refined better understanding makes the essential part to be:
"A square root of "a" is"y" such that y2 = a."Can you notice that dropping the two instances of the word "number" from this essential part does not lose information? It rather makes the information less redundant and more general. The extra bit in the longer one can be understood implicitly and doesn't need to be included in the definition itself.
A common example that fits to this redefined general square root but does not fit in the older definition is the square root of matrices. If you don't know this don't worry. It's just that some types of matrices can be (squared) and thus some matrices have (square roots). The matrix is not a number but still has a square root.
As we discussed before, it is still beneficial to write up these details for the reader. This is because in most of the cases the reader is not expected to have this deep understanding just by giving him only that short essential part. Though, you as a reader should always let all of such pieces of text (definitions, explanations, rewordings, examples ... etc) to contribute in providing you with a very clear and clean essential piece of information.
Realising the Real Reasons Leading to the Results
The best understanding of a passage of information happens when you realise what is the real reason behind each result. For example when we say:
"If you through a cup of glass from the tenth floor from the window to the street then it will be crashed."The result of (crashing) happened because (1) the material of that cup is crash-able, and (2) the force of hitting was enough to crash it! Being from glass satisfies the first reason and being thrown from the window of the tenth floor to the street satisfies the second. The point is that being a "cup" or not a "cup" is not the issue, being from "glass" or not is not the issue, being thrown from the tenth floor, from the window ... etc is not the issue. If you crash a table of plastic with a strong hammer, it will be crashed!! So if you understand the real reasons for the results of crashing from that statement, you will not fall into the trap of misunderstanding.
You may think of these examples: "English speakers find Chinese hard to learn", what's the reason? just being an "English speaker" is an empty meaning!! Is it because English is written from left to right? Is it because of the way the grammar of English is structured? Is it because of the differences in the systems of alphabet? If you understand the reasons, you can analyse the cases of Spanish, French, Italian, Japanese or Arabic speakers when they want to learn Chinese.
An example from my field of research which you don't need to understand but you will get the idea from is the importance of "the normalisation of microarray datasets" before analysing them. You don't need to understand what these microarray datasets are. I just want to say that if you give me some other type of datasets, then I need to look at its properties. If the properties of the microarray datasets which makes normalisation important also exist in these different datasets, then I should normalise them as well. In other words, I should understand the real reason for the "importance of normalisation" and then consider it in any other application.
Levels of Inference from Essential Information
Consider this paragraph about prime numbers; it's the first paragraph in the article (Prime number) in wikipedia:
"A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering."
The red part is the essential part, and it has two sentences which define two things - the prime number and the composite number. The blue part is totally redundant as it has nothing more than examples. The green part is in reality redundant, but it might need a deeper level of understanding of the red essential part in addition to the ability to build on it to be able to understand why the green part is not adding anything new.
From my understanding of the red part, I can see that the green part is nothing by a mere rewording of the red part, or a description of an intuitive inferred meaning of the red part. I will try to let you get my point, but if you don't, just never mind! Just skip the next paragraph if you like!
Any composite number (X) can divide a natural number (a) which is neither itself nor one. This division means that there is another natural number (b) (greater than one) which divides this composite number! Because the result of dividing X by a should be some number which must be natural and greater than one!! It must be!! If (a) is the square root of (X) then (b=a). On either case, this means that we can say (X = a x b). The numbers a and b are natural numbers that are greater than one, so they are either composite or prime. If any of them is prime then that's it from its side, if any of the is composite then it can be divided as done with X itself. These divisions will never result in any number which is not a natural number greater than one!! We will end up with a set of prime numbers if multiplied then we get the original number (X) again! As (X) is finite then this division is finite. This is all IMPOSED by the definitions of the prime and composite numbers in red!
Even if this is right, in many cases, some theoretically non-essential parts need non-trivial inference levels to be understood only from the clean essential part. This makes it more efficient to store this part in memory as if it is an essential part. This depends on the person himself and the complexity of the inferred part. Though, being able to see the link between these parts helps in having a clearer understanding and a better ability to use them.
Last Word
I like to finish up this article by reminding you that I am drafting my own experience, but I am not an educational sciences expert. I have been a student for a long time and I have always taken care of these bits that I have written in this article. These are not ideas that I have just come up with; they are things that have always been rotating in my mind, wondering about my brain cells, and being felt in my consciousness whenever I read any scientific material. This started long time ago in school time, and I can't give any exact time for them. I am sure they were pretty mature in my BSc time.
Having said that, this article might be found useful for some of you and might be seen as mere philosophy by some others. It's just personal opinion!
