New Focus Graphic

A new focus for memory improvement

by Matthew Leitch, 25 October 2001

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A new focus?

Yes! Something very specific and very practical. Not pop psychology, not mnemonics, not imagery, not supplements, not general advice on when to study and for how long, not mindmaps, not neurobics, not high level multi-pass study procedures, not review scheduling, not the subconscious. No gimmicks, no special equipment, all natural. Something new.

This new route helps you learn everyday, meaningful things. It helps make you an ‘intelligent’ person with good powers of understanding. It's not about developing the ability to rote learn lists of items, arbitrary names, and arbitrary numbers.

Instead, it's about what you observe and what you think, what knowledge you build and into what structures. This new route identifies specific thought patterns that are effective for learning a range of common types of information. Whatever else you do to improve learning, you'll perform better with the right thought patterns.

Where did this come from?

In the late 1970s I was a schoolboy when a pop psychologist called Tony Buzan made study skills hot with a television series based on his books. Suddenly mindmaps were everywhere. I also made the effort to review things after 20 minutes, a day, a week, a month, etc and soon did much better at school work, getting impressive ‘A level’ grades.

I was hooked!

I changed my degree choice and went to London University to study psychology. What I have learned in my studies and since then has radically changed my views on what works. I now distrust the myths spread by pop psychologists but I'm frustrated that serious psychologists have failed to apply what is now known in a practical way.

There's a need for technical advice that's practical yet based on serious psychology. I've taken inspiration from William James's ideas on memory, from research on incidental learning, Herbert A Simon's cognitive science, C A Mace's advice on study, Ebbinghaus's painstaking studies of memory, depth of processing theories, and most of all my personal experiences of learning at home, at work, and for exams.

The ideas behind this approach are simple and obvious but are applied in an increasingly sophisticated way to build a powerful and effective learning skill. Here they are.


‘You see but you do not observe, Watson’

Firstly, you won't remember something unless you noticed it in the first place. If you are reading something and just wallowing in it without actually noticing anything specific then you will find you can't remember much at all.

Example 1: Noticing what you see. Imagine you visit a friend's house and see a shelf unit so stylish you want to make one for yourself. You gaze admiringly at it and when you get home you try to sketch what you saw. How high was it relative to its width? How many vertical dividers were there? Were they evenly spaced? How many shelves were there? Were they evenly spaced? What colour were the verticals? What colour were the shelves? Were there legs? If so what were they like? How did the shelves attach to the verticals? How deep was the unit? What were the components made of? How were they joined? Unless you are an artist or carpenter the chances are you didn't even notice most of the facts you needed to sketch even this simple object.

Example 2: More noticing. In entertaining my children I have read endlessly about dinosaurs and must have read the word ‘cretaceous’ at least 100 times. But just now as I started to type ‘cre...’ I realized I'd never actually noticed how to spell the word and sounding it out doesn't help enough. To write this without risk of embarassment I have had to look it up in a book.

When noticing something it is only necessary to think it. Trying to think ‘harder’, ‘pay attention’, ‘concentrate’, be ‘interested’, or to picture or otherwise sense something clearly, or repeating something over and over, or otherwise trying to pummel the information into your brain will only make you unhappy. It won't give you stronger memories. Research on incidental learning shows that an intention to learn is not effective; all that matters is what you think. So make sure your mind is noticing lots of specific points, as explained in detail below.

Reinforcing memories by use

In general, observing/noticing things creates memories and using memories reinforces them. The most useful thought patterns for memory building are those that create new memories while reinforcing old ones.

As soon as something has been noticed the new knowledge is ready to be used. This can be done in several ways. Knowledge is often used in forming new memories, for example. Or you might be researching something for a specific purpose in which case new discoveries will be applied to your problem.

The sad reality of learning is that most of what you set out to learn is wrong and perhaps deliberately misleading so one of the main uses of knowledge is in evaluating the likely truth of what you have been told.

What to notice? – the key question

What to notice, and in what order, is vital to learning. It determines what you know and how useful and long lasting your memories are. What you should notice depends on the structure of knowledge you want to build. The best choice is determined by:

In practice you will not go back to first principles every time you start to learn something. Instead, as your skill develops, you will learn to spot features of the material and your circumstances that immediately tell you what approach to take, based on pre-digested reasoning. So although the reasoning behind some learning strategies is complex, actually spotting when to use the strategies and doing so is easy.

Example 3: Choosing what to notice. Learning your ‘times tables’ is something most educated people have done and are glad to have mastered. Imagine you had forgotten them and had to learn them again. What should you notice? This is a very interesting question.

The structure of the information is a set of tables of figures (I learned up to 12 × 12 so that was 12 tables). Each table has 12 rows. Each row has two numbers separated by a times symbol, then the equals sign, then the answer, e.g. ‘7 × 8 = 56’. The rows are usually in sequence and traditionally they have often been recited in that order. This structure suggests a number of possible ways to structure your knowledge of the times tables and so a number of different things to notice.

The way the knowledge will be used is also important. Typically, you will get two numbers of the three on each row, an operator (either × or ÷), and be asked for the answer. e.g. ‘What's 7 × 8?’, ‘What's 63 divided by 9?’ Almost never will you need to go through the table rows in sequence. It is nearly always random sequence. This suggests that it is worth noticing the numbers that go together e.g. 5 × 7 = 35, but not the sequence of numbers in the answer column for each table e.g. that 56 is followed by 63 in the 7 times table. The answer to X × Y is the same as Y × X so there is no need to notice the order of the two numbers in the question part of each row.

Finally, the materials themselves are just numbers, which the human brain often finds dry and unmemorable. Anything we can do to reduce the workload or make the numbers more interesting or distinctive will help, provided it is relevant and meaningful analysis rather than irrelevant elaboration.

By careful thought it is possible to reduce the size of the memory task, replacing large numbers of plain number facts by smaller numbers of rules, and to ease the remaining memory work. Here's how. It is worth noticing that X × Y is the same as Y × X so the number of facts to memorize is much less than the rows on the tables – only 78 instead of 144. It is worth noticing that the 1, 9, 10, and 11 times tables can be done with simple rules, leaving just 36 rows to memorize. The 5 times table can be derived from halving the 10 times table leaving just 28 to memorize. Six of the remaining are from the 12 times table and easily worked out as 10 times the number plus twice the number. The remaining 22 facts are easier if you notice that six of these are from the two times table so just one addition is needed to work them out if needed. Six more rows have the same answers as others for reasons that are easy to see. e.g. 12 × 2 = 6 × 4 = 3 × 8 = 24. This leaves 10 facts to memorize. For a long time during practice it will be helpful to have quick ways to work out the most tricky rows using nearby results. e.g. if I know that 5 × 7 = 35, I can get to 6 × 7 by adding 7 to 35 to get 42. This eases the way for a further seven facts, leaving 3 more: 3 × 7, 6 × 6, and 12 × 12.

So by working through the tables and rows that are easiest first (e.g. rules based or derived from something already known) it is possible to notice a structure and build a framework in which more and more of the rows can be safely cemented. Practice using the questions in random order will gradually replace rapid calculation by immediate regurgitation.

In later sections I'll go through common structures of memory, when to use them, and what to notice to build them.

Much of our learning time is actually taken up with searching for something worth remembering. It's time consuming and tiring skimming through chapters of stuff that doesn't make sense, isn't useful, or is just plain wrong.

Later I'll come back to the problem of searching but for now just notice that there is never time to notice and think about everything, so there is value in not noticing things.

Building lasting memories

To build lasting memories you need to notice things so you build structures that:

As a rule, the more you notice the more you will learn, though not necessarily a higher percentage of the things you noticed. Retaining a higher percentage depends on what you notice and in what order. Both quantity and quality matter.

Example 4: Noticing the problem. Many people who struggle with maths do so because they cannot distinguish between different types of problem. It's not surprising since after learning to deal with a new type of problem the normal ‘homework’ is to do several of that type of question. Since all the questions are of the type just taught it is not necessary to spot the type. In an exam, when the questions are mixed, the student is lost and fails. The correct knowledge structure for maths problem solving is a system of ‘condition → action’ pairs (see later) linking types of problem with the most effective strategies to solve them. Poor students only learn the ‘action’ part and their teachers normally do not notice the problem.

Example 5: Noticing enough to identify the information. Suppose you are a trainee stockbroker and read that there are two types of share: Ordinary shares and Preference shares. Is it enough to notice that there are two types of share and that they are Ordinary and Preference? No. That's because there are lots of other ways to classify shares and even this classification could go into more detail, so you also need to notice that this is a top level breakdown based on the legal status of the shares. There's also a lot to remember about each type, but that's another example.

Example 6: Adding some redundancy. Suppose you are a trainee brewer learning the chemical transformations that turn starch into alcohol. On top of the detailed chemical formulae of starch, alcohol, and the intermediate stages, it also helps to notice that there are three stages and that everything but the alcohol and enzymes are carbohydrates i.e. their chemical formula is a number of carbon atoms plus a number of hydrogen atoms and half as many oxygen atoms, rather like a number of water molecules being joined up with a lump of carbon. With these and other general observations in place it is far easier to take in the details and to remember the whole process later.

Example 7: Adding some distinctiveness. Imagine you met two people for the first time one day. They are both young girls with short blonde hair and of similar age, height, build, and dress sense. Their names are Emilia Davies, and Julia Davis. A week later you see one of them again and struggle to remember if she is Emilia, Julia, or was it Emily? Memory has failed due to lack of distinctiveness. Ideally, one should notice distinctive features of the girls and their names so they are less confusible. For example, nose shape and size, eye colour, lip fullness, natural or dyed blonde, skin colour, accent, the fact that the shorter forename goes with the shorter surname, the fact that one is quite different from the popular actress of the same forename and why, and so on.

Supporting links with good reasons is particularly important. I have often seen advice on memory improvement that says associations should ideally be bizarre, unrealistic, and possibly sexual. In fact this sort of artificial association is a last resort useful only when there is no meaningful connection between the two items to be linked – something that rarely happens except in psychology experiments and memory improvement courses. The downside of such associations is that they introduce alien and irrelevant connections into your memory that stop further meaningful learning.

It is much better to find good reasons why two things are linked, or at least why you are not surprised that they are. If good reasons are not available, look for good reasons why they should not be linked and register your surprise that they are. Failing that, look for helpful coincidences that link the items. Failing that, consider some kind of mnemonic or even an artificial link – a desperate last resort.

Example 8: Good reasons. You are an amateur historian preparing to give a talk on the events leading up to the Gulf War. You want to learn what happened and when in order to prepare your talk, give it, and take questions at the end. There are some dates to learn – always a challenge. How should you approach the dates? Writing them on your prompt cards is one good idea, but if you want to get them into your head then the best approach is not to encode the numbers into some kind of concrete image and then form a bizarre image connecting it to some element of the Gulf War story. This will not advance your understanding of the events one bit and if you forget your images then you won't even be able to guess the approximate date. Instead notice how the key dates stack up against the events that happened between them. Look for reasons why things happened on certain days. Consider how long it takes to assemble troops or move an aircraft carrier 1,000 kilometres. Notice what month it was, what day number, what year, what day of the week, what season. Notice how many times longer certain processes took compared to others and consider why. Build up a framework of dates and time periods so that any event or date can be meaningfully considered and its correctness judged. You might even notice errors in your sources.

When it comes to recovering a memory we often work by deducing what we think the answer is and looking for it. Noticing good reasons for things increases the likelihood that your deductions will pick up the reasons you noticed and so lead you to the right memories.

Along with good reasons for something being so there will often be reasons why it is not so. Much of what you read or hear is wrong and even deliberately misleading, so many links will be mentally annotated with your own views on why something doesn't follow, allied to your understanding of the reasons the author made the statement you dispute.

Often you need to observe things that are not immediately obvious and that are in fact the result of thinking about the material. This is best done by thinking rather like Sherlock Holmes and reasoning from observations of surface features to less obvious deductions.

Example 9: Holmesian reasoning. When making plans for the day, you need to think about tasks and develop clearer, more analyzed ideas about what the task involves, when it could be best done, what is needed to do it, and so on. You might have a list of ‘to do’ items, each just a few key words perhaps, and want to think them through. You could ask yourself questions like ‘What are the pre-requisites for this task?’, ‘What are the risks?’, ‘What are the uncertainties around this task?’ and so on. Indeed, most books giving advice on how to plan say to do just this. Unfortunately, it's hard work. You stare at the key words, ask yourself the question, and all too often nothing happens. It is much easier to pick out obvious features of the task and see what they suggest. For example, if the task is to ‘talk to Anne about staffing in her department’ you might think ‘Anne – someone I don't know very well, so I'm not sure how she will react to my questions. Staffing – it's a sensitive subject so I should pick a good time, go in gently and check the ground with questions...’ and so on. As the most obvious inferences run dry, or if you don't think you've covered a particular aspect of the task, you can ask yourself questions like ‘What does the fact that this is an emotionally charged situation suggest about the risks involved?’

This kind of reasoning is quick and easy. It flows. Not only that but the reasoning automatically creates memories linked by good reasons. As you practice making such inferences about a type of subject matter you become quicker and able to put more and more observations together to draw more advanced inferences. In Sherlock's case the inferences came so quickly after the initial observation that the reasoning was barely perceptible.

Deciding what approach to take

Deciding what approach to take to learning something is not hard work. With practice it is possible to see at once what type of material it is and immediately move into the right approach. You do not need to go back to first principles but can refer to ready-made inferences triggered by noticing obvious features of the material.

Examples of such inferences are given in the section ‘Applications’ below.

Some useful memory structures

Before looking at practical applications it will help to think about some of the most useful memory structures:


A chunk is a single idea, made by lumping together other ideas. It is not a statement that is true or false, not a question, not an instruction – it says nothing. It is just a chunk. The bigger and more appropriate the chunks already in your memory the quicker you can learn new things. That's because you build new memories out of existing memories so the better your stock of building blocks the quicker you can assemble new and useful memories.

The implications of chunking are simply awesome and a lot of learning is just building up chunks for later use.

Example 10: Chunks. Written Japanese has two types of symbol. First, there are some simple symbols which stand for sounds, as in English. Second, there are pictograms that have meaning but no sounds. These have been borrowed from Chinese and often there are two spoken Japanese words for the pictogram. The pictograms are particularly interesting because many of them are actually very stylized drawings of the objects they refer to. Many pictograms are combinations of such stylized drawings, with parts overlayed to capture more complex meanings. A great way to learn the pictograms is to start with the simple ones that are stylized drawings (thus forming them as chunks), and then move on to pictograms that combine two or more simple signs (thus forming chunks from the simpler chunks).

Chunks are formed when you notice the sub-chunks of which they are formed. This also reinforces the sub-chunks. Lasting, clearly-formed chunks do not form unless you have clearly identified their components.

Example 11: More chunks. Dinosaur names come in different styles, but many of the best known have very obvious chunks of which they are made. The parts of each dinosaur name have a meaning too, which makes the names easier to remember. For example, ‘oviraptor’ is ‘ovi’ (egg) and ‘raptor’ (robber); ‘ornitholestes’ is ‘ornitho’ (bird) and ‘lestes’ (thief); ‘iguanadon’ is ‘iguana’ (the present day lizard) and ‘don’ (tooth); ‘brachiosaurus’ is ‘brachio’ (arm) and ‘saurus’ (lizard); ‘ornithomimus’ is ‘ornitho’ (bird) and ‘mimus’ (mimic). The names are easier to remember if you notice their parts and the meaning of the parts and the whole, and if that meaning connects with features of the dinosaur itself so that it has the name for a good reason which you have noticed.

Chunks can be combined into larger chunks, but only attempt to lump together two, or at most 3, chunks at a time. Be patient, and notice each chunk you make, and why it exists, and what it is made of.

Example 12: Yet more chunks. Numbers are easier to remember if you can build them up from chunks. For example, 02077411234 is easier if you notice it is in the form of a London telephone number and so begins with 020, that it is an inner London number, hence 020 7, that the next three numbers are the code number for an old type of operational amplifier chip, 741, and that the last four numbers are consecutive starting with 1. So the smallest chunks are 020 7 ~ 741 ~ 1234. To build the number up in one step from here would mean combining three sub-chunks, which is a bit much, so easier to do it in steps, chunking up the 741 and the 1234, then finally doing the 020 7 onto the rest to build the full number. To link 741 and 1234 you have to notice that they go together in a telephone number you want to remember, and try to find some reason why they are sensibly together e.g. it is a commercial number for a chip maker founded 15 years ago. The sequence of chunking could be written as (020 7 ~ (741 ~ 1234)). A more difficult number (for me at least) is 13249786, which has no familiar chunks to it and no reasoning behind the digits. Yet even here the strategy is to break it down into small chunks and group them up in stages to make the full number. It might be done as ((130 + 2)~((500 − 3)~(86)))

Example 13: One more on chunks. The general mathematical equation for a circle is (x − a)2 + (y − b)2 = r2, where a and b are the coordinates of the centre of the circule and r is the radius of the circle. You can build this up in more than one way, which provides useful redundancy. Firstly, try it in a rather literal fashion: (x − a), (y − b), (x − a)2, (y − b)2, (x − a)2 + (y − b)2, r2, (x − a)2 + (y − b)2 = r2. Next, try for more meaning: it's a version of Pythagoras's equation for right angled triangles, link this to its derivation (which is easy if you know it), an x term plus a y term, the terms are squares, the x and y have the coordinates of the circle centre subtracted from them, again link to the derivation, the hypoteneuse is the radius.

Condition → action pairs

These are very useful for building skills. The ‘condition’ part is there to recognize situations, while the ‘action’ part is there to say what to do in that situation. The situation includes your goal(s) and the circumstances you face. Research suggests that many skills one might think of as being ‘algorithms’ are actually built of condition → action pairs, and that this makes us better able to adapt to new situations, and better able to cope with interruptions and working memory failures.

The ‘condition’ part is rarely given enough attention when skills are taught but is at least half the skill.

Example 14: Conditions. When I was taught to play tennis I was shown how to do each type of stroke but not when to use it. Also, I was taught the strokes as if there was some ideal ‘grooved’ stroke that would somehow work regardless of the speed and height of the ball. There was no concept of assessing conditions and taking appropriate action. Watch any public tennis court in the summer around Wimbledon time and you can see people winding up for great strokes in the style of their favourite player, looking good up to the last moment when they have to adapt their stroke half way through to cope with the ball being higher, lower, slower, or further away than they thought.

In fact the skill is much more complex and involves separate decisions about where to run to, what side to hit on, what stroke to use, where to hit to, what spins to apply, and how to adjust the shot to the precise conditions of height, spin, direction, and so on. All these decisions are taken on the basis of many aspects of the situation and goals, including the other player's position, direction, speed, strengths, etc, your own position, direction, etc, the ball's position, direction, speed, spin, height, and so on. There is no time for conscious deliberation so the decisions and adjustments have to be driven by preprogrammed condition → action pairs, some of which have continuous variables in both the condition and action part rather than simple pattern matching.

The same might be said of many other sports and other skills where there are variations in conditions that have to be taken into consideration.

Both the condition and action parts will often be built up by chunking.

The full set of condition → action pairs that make up a skill will include at least one pair to say what to attend to in order to spot other conditions. For example, pilots are taught to attend to a small group of key dials/displays in the cockpit and all the rest are there to help in special situations and when the key indicators show there may be a problem.

The knowledge needed to decide what approach to take to learning some new piece of material is itself made of condition → action pairs.

Structured lists

The ability to recall a list of things is occasionally useful in everyday life and invaluable in exams that require written answers. Indeed, some exams I have taken required little other than endless learning of lists.

Lists are also very useful in your own thinking, where it may not be possible to put the knowledge into a better structure. The structured lists can be used as checklists and as temporary parking spaces for results of your thinking. I think of them as a kind of mental scaffolding.

Most information presented to you as a list should not be remembered as a list, because you will rarely need to be able to recall the information in a linear sequence and doing so is harder than giving short responses to cues. For example, the times table is presented as a list but individual rows are used at random when the knowledge is used for mental arithmetic. Another example is learning vocabulary in a language. It is normally presented as a list but what you actually need to know is what each word means. Pub quizzes would not be so popular if the answers were always long sequences because of the concentration needed to recall and say them.

So only learn something as a list if you really need to, such as when you are delivering a speech from memory, or using them in your own thinking.

Learning lists can be difficult but using structured lists (i.e. hierarchical breakdowns) can significantly reduce the difficulty, and allow you to access the parts of the list you need more quickly. Structured lists are even more powerful when they partition the possibilities i.e. when they divide possibilities so that all possibilities are included and included only once.

Example 15: Reordering for memory. In an old text book on computer systems I found a list of types of microfilm, with explanations and drawings of each. The types given are: microfiche, aperture cards, microfilm jackets, filmstrips, and roll film (16mm, 35mm, and 105mm). This list is in no particular order and we can reorder it to make it easier to remember. The idea is to build, step by step, this:

Notice how each breakdown is on some specific basis and that you need to notice what that basis is, because there could be others.

Example 16: Reordering again. Henry Mintzberg wrote a famous article for the Harvard Business Review in 1975 called ‘The manager's job: folklore and fact’ that contrasted what people say managers do (folklore) with what they are actually observed to do (fact). He gives the folklore in a particular order: (1) managers plan in a carefully systematic way, (2) they spend most of their time planning and delegating, (3) they use summary information from information systems as their basis, and (4) management is a science and profession. As if. I find these easier to remember in a different sequence:

In summary, a structured list is a list of structured lists. To learn each list you need to notice:

Sometimes it is also helpful to notice pairs of items together and why they are in the sequence they are in, chaining them together.

Finding a neat way to structure a list involves a combination of top-down thinking with bottom-up thinking, often searching for commonalities or progressions within some or all of the items in the list, and trying to make them into structured lists. It is much easier if you can take notes on a word processor. In view of the memory advantages of lists organized carefully I think it is very poor if a textbook gives lists in no particular order.


The preceding sections have explained that memories are made by noticing things, and reinforced by use. We need to build our memories into structures that are appropriate for the material, the intended use, and the characteristics of the human memory. What we notice and in what order determines how good and long lasting our memories are and how easily the thoughts flow. This means we have to learn what thought patterns are effective for different types of material and intended uses.

Now it is time to look in more detail at some typical applications of these ideas.

Learning a computer language

The main knowledge structure for learning a computer language is the condition → action pair. You need to notice what it is possible to do with the various commands, operators, etc and in what situations, and what you have to type/do to get those results.

Modern languages are so large that it is unrealistic to try to learn all the commands straight away, so start with the things that are often needed, and move onto the less common techniques later. Not everything is a condition → action pair. Start with the lowest level of simple task and build them up into larger chunks.

Example: HTML. With HTML the earliest points to note (for someone with some knowledge of programming and computers already) might be along these lines:

It's very important to notice the differences between conditions, and to build up conditions and actions patiently by chunking and chunking again if they are complex.

Example: Word processing. In the mid 1980s I had to learn to use the leading word processing package of the day, WordStar, without access to a computer. I bought a small book about how it worked and identified and learned the condition → action pairs. I reinforced them by writing the conditions on one side of small cards and the actions on the other. I could shuffle these cards and test my memory by reading the condition and trying to recall what keys to press. After doing this I finally got access to a computer for an hour. After 50 minutes on the computer I had done everything the package could do and found it all as I expected, even mail-merge. The next time I used the software was in a test of my skill organized by a potential employer who concluded that I knew it ‘standing on my head’. The next time I used it I was paid. I don't recommend learning with cards if you have the software itself available for practice but this example shows that the right memory structure, diligently built, will give you a usable skill and that this is more important than realistic practice.

Identifying the condition part is not always straightforward. With computer languages it is often possible to break down the conditions in a structured list and take notes that show the breakdown. This helps clarify what each condition is, but the list should not be learned as a list.

Example: The 8086 assembly language command set. This long-obsolete chip had a command set small enough to be a convenient example of the systematic breakdown of conditions and the style of note taking that can be used. It is rare to be able to do a comprehensive analysis like this, and even this example is only the lowest level of condition → action pairs. Higher level pairs would build the skill of doing larger, more meaningful tasks. If this seems complicated to you, don't worry. Anyone who has ever mastered assembly language programming has mastered this information, and worse, and probably picked it up in a more muddled way.

Learning something hard

Some things are really tough to understand at all. Normally this is partly the subject itself and mostly the way it is explained. Often it is hard because the source assumes more knowledge than you actually have. What makes something hard is that ideas you need to learn are explained using terms/ideas you don't already know. You have to be aware of this and backtrack where possible. You also have to learn what you can, notice the gaps, and keep searching until you fill them in.

Using your memory effectively is the key to reaching understanding. You must learn things as you go through or you will never understand.

Example: A mathematical definition. For example, a dictionary of mathematics says that a diagonally dominant matrix is ‘a SYMMETRIC MATRIX in which every element in the MAIN DIAGONAL is larger than the sum of the absolute values of the remaining elements of its row.’ I already know what a matrix is, but observe that:

The dictionary says that a symmetric matrix is ‘a square matrix whose entries are symmetric around its main diagonal’ and it gives an example. I already know about square matrices and about diagonals. From the example I can notice that:

Now back to that original definition.

The deductions are important as they use and so reinforce my new memories, create useful redundancy, and give me a headstart in reasoning about diagnonally dominant matrices. Now if I have to learn something more about them I have more chunks and facts to build with and my inferences will be quicker and more numerous.

This example had a happy ending as I was able to go back and find all the explanations I needed. Often this is not possible and learning is, unavoidably, damaged. Well written explanations give you the elements you need in the right order so there is no need to go back. School text books often achieve this. I hope this web page also does.

Searching for something worth learning

A huge amount of ‘learning’ time is actually spent searching for things worth learning. ‘Skimming’ vaguely across pages and pages of stuff is tiring and unproductive. It is better to be surgical.

If you are learning from books, pick the best. Pick books by great writers who think and write clearly, at the level you can keep up with, and have something important and well supported to say.

When inside the book notice the contents listing and main titles and deduce what is talked about in the book. Decide where to look further and go there only. Check some more titles and notice what is talked about. (Avoid books with titles that are riddles rather than clear signals; life's too short.) Decide where to go and go just there. If needed, read the first sentences of paragraphs likely to contain what you want. Deduce what they are about and decided where to read further. It can also be useful to look at illustrations and their captions. Do not be drawn into scanning rapidly across all words in the hope that something will jump out.

To evaluate the clarity and logic of the author notice what is being said and what reasons are being given. It may soon be obvious that the reasons do not support the assertions at all, or not very well. It may also be unclear what is being said. I find I have to abandon most books and magazine articles for this reason.

Some materials for learning have a single structure, repeated over and over, such as a dictionary, a table of vocabulary, a chronological table, and so on. With these materials one decision of how to learn the material is all that is required and then you can settle down to memorize.

But this is rare. More often the source mixes all sorts of structures and types of content, giving you a constant problem of deciding what to learn and how to tackle it. This is the true test of your learning skills.

Example. Fossils. The book ‘Fossils’ by Niles Eldredge (with stunning photographs by Murray Alcosser) is a fascinating study of the evolution and extinction of species. It ranges over many topics and switches between autobiography, scientific reasoning, descriptions of the history of ideas, and so on, making it tricky to study but well worth the effort.

To get the most value out of it I have had to think for almost every paragraph and even every sentence in places, ‘now he's talking about the topic of X’ and ‘the aspect of X he is talking about is Y’. This is a description of the content of the material, and from this I can see what form of material it is and so how to tackle it. Sometimes it's as though I'm sieving the pages for tidbits worth committing to memory – facts, names, reasons, and so on. The author's arguments unfold rather slowly and with digressions so I have to notice things like ‘now he's arguing that Z, and his reasons were A, B, and C.’

Learning your own thoughts

This may seem a strange topic as I have been claiming that we memorize things by thinking. Surely that means we automatically learn our own thoughts? Sadly no.

If you sit down and think deeply about something then the following weaknesses in your memories of that thinking are likely:

Example: Sustainability. Creating a sustainable economy, i.e. a truly environmentally friendly one, is one of the big problems facing our society. One tool for businesses that want to operate in a less unsustainable way is to lease their products to customers rather than selling them outright. Strictly speaking the idea is to provide customers with a service for which they pay, rather than paying for the asset that provides the service. This means you have an incentive to optimize the whole-life efficiency of things you make instead of just their initial selling price. However, it has been suggested that some consumers are reluctant to go along with this because they prefer the security of owning the asset and the feeling that they would still have it if their money ran low because of redundancy or retirement. Does this argument have merit? Is insuring against this a hidden cost of leasing?

All this I have already learned and is the starting point. However, thinking through this problem is going to take some patient analysis. Here are the thoughts, showing how memory building is vital:

At this point some cash flow modelling is done and this would be a long list of observations. At the end of it, the result will be obtained and I need to notice the actions that flow from it, such as remembering to post a reply on a discussion database where this problem was raised, remembering to raise it in a forthcoming seminar, and perhaps deciding to review the goods I purchase to see if they could be leased more economically as well as giving environmental benefits.

The result of all this thinking is a rather complex conclusion and more questions raised. However, in case you're wondering, the answer to the original question is that the sense of security is not a good reason and insurance should not be needed if the user was in a position to buy the asset but chose to lease instead.


The focus of this approach is on what you think, but instead of mnemonics it concentrates on natural, meaningful thoughts that create intelligent understanding. There are no gimmicks. The ideas go beyond general statements about ‘asking yourself questions’ and ‘looking for patterns’ and build up a much more specific and sophisticated skill. I hope you enjoyed this page and get some benefit out of it in future.

These are links to sources on other aspects of memory improvement, some of which I agree with and others I do not:

These are links to other sources having some similarities with the approach taken on this web page i.e. serious psychology applied sensibly:

Acknowledgements: I would like to thank all those who have read this page and commented. I consider every point carefully and often make improvements as a result. I would also like to thank my son Hector for the picture.

About the author: Matthew Leitch has been studying the applied psychology of learning and memory since about 1979 and holds a BSc in psychology from University College London.