Wednesday, March 09, 2016

Programming an HS-1969

We are all programmers even you who don't consider yourselves programmers. We are programmers of the hardest computer of all, the Homo Sapiens, ourselves!


14 years ago my son Rasmus was born. It was a difficult time, partly because he had colic, but mostly because I couldn't understand what this little critter wanted. But, one day while I was changing his diaper he said something that sounded like Aha! Aha, I thought out loud and he reacted with a smile and said Aha, again. This little kid had picked up that every once in a while I actually understood what he was trying to communicate and when I did I said Aha! He liked it so much that he learned to say Aha himself almost before he could say anything else.


We all know what an insight is and that it is a great feeling. Having an Aha-moment feels great! A lot of human progress (all of it?) has its roots in Aha moments.


Einstein is known as a very intuitive scientist. He had a lot of insights and it was not only the special theory of relativity. He proposed the quantum theory of light and the link between mass and energy and got the nobel prize for the photoelectric effect.

When he was shaving in the mornings he always shaved very slowly, because he often had Aha-moments while shaving and was afraid to cut himself with the razor.

Examples of Insights

An insight can help with a lot of things:

  • The punchline of a joke
  • The solution to a crossword puzzle, riddle or rebus.
  • Understanding why people behave the way they do.
  • Resolving inconsistencies in our thinking.
  • Realizing that one problem is similar to another.


More than anything an insight is understanding. It is when the pieces fall together and we finally get how something or someone works.

A Doh moment is also an Aha-moment, but it is when you are realizing something trivial that you believe you should have known all along. An example can be a song you have been singing your whole life and suddenly you realize that you have misunderstood the song all along. Here is a personal example:

Jimmy Hendrix sings: Excuse me while I kiss the sky,
not: Excuse me while I kiss this guy.

Even though the latter would have been more progressive :)

Some Insight Problems

What historical person does "Horobod" symbolize?

A window washer fell from a 40-foot ladder without hurting himself. How is this possible?

Thiss sentence has thre errors? What are they?

Fermat's Conjecture

Fermat conjectured his theorem in 1637 in the margin of Arithmetica. He wrote,

It is impossible to separate a cube into two cubes
or a fourth power into two fourth powers, or in general 
any power higher than the second into two like powers. 
I have discovered a truly marvelous proof of this, 
which this margin is too narrow to contain.

It took 358 years for mankind to come up with this proof and Andrew Wiles spent 7 years of his research time to prove it. Here is how he describes it:

Two More Insight Problems

Turn the pyramid upside down by moving three coins.

Draw four straight lines through all the dots without lifting the pen.

When Do We Get Insights? Bath, Bed, and Bus

Insights can come at any time, but most often when we are not actively focusing on the problem. Wittgenstein famously said that "the key to creative thinking is the three B:s, Bath, Bed, and Bus.

Archimedes got his Eureka-moment when he was lowering himself into a bath and realized that he could measure the volume of an irregular body by lowering it into water and measuring the amount of water that flowed out.

Edison used to take working naps. He would sit down on a chair with two metal balls in his hands and rest. When he fell asleep the balls would fall out of his hands and onto the steel pan he had placed below himself. He was trying to trigger insights which he often got when falling asleep.

Poincaré got one of his greatest ideas when he was about to get on a bus.

At the moment when I put my foot on the 
step the idea came to me, without
anything in my former thoughts seeming to 
have paved the way for it, that the
transformation that I had used to define 
the Fuchsian functions were identical 
with those of non-euclidean geometry.

How do we get insights?

In order to get insight about something you have to prepare for it. It is impossible to get insights into something you know nothing about.

The Four Stages of Creativity

Preparation means to learn about something, to prime your brain. Then do something else. Here are two ways to do this. 1) Study until you get stuck, until you reach an impasse. 2) Study a little every day to keep the subject percolating in your mind.

Incubation starts when we walk away from the problem. It is when our unconscious mind takes over and keeps on working. Some good ways to let go of a problem is to exercise, walk the dog, sleep, relax!

Illumination is the moment of insight.

Verification is optional for many types of insight, but when doing science it is essential. It is when you prove that the insight is consistent with reality.

Your Memory Bank

It is what you have in your memory bank, what you can 
recall instantly that is important. If you have to look it up,
it is useless for creative thinking!
-- Linus Pauling

You cannot have an insight about things that you don't know anything about. If you don't have the raw-material, you have nothing to work with. You cannot Google for insights. Learn everything you can about a subject and then let go, relax!

Deep Learning

Deep learning is more than just knowing things. It is about understanding things. Insights are crucial for this but so is knowing a lot of things.

Working Memory and Long-Term Memory

Working memory, also known as short-term memory is like a blackboard. It is very limited and things have to be erased before we can put something else on it.

Long-term memory, on the other hand, is surprisingly large. We don't know if it has any limit at all.

Learning is essentially to move stuff from working memory into long-term memory.

  • Encoding change the input from our senses into a format the brain can store.
  • Consolidation recoding the memory to fit with other things that we know. This is done largely unconsciously.
  • Re-consolidation is when we recall a memory by reflecting or actually retrieving it. This re-creates the memory and also changes it.

Focused Mode and Diffused Mode

Our brain works in two modes, focused mode and diffused mode. Focused mode allows us to learn in a sequential step-by-step way. This is the mode we need when we are encoding and learning new things. Diffused mode is when we are not focusing on the problem, when our brain is consolidating. This is when we have insights.


A chunk is a piece of information related to prior knowledge. To learn something is to create a new chunk. The more we learn about something the bigger the chunk gets and the easier it is for us to relate it to other chunks. A chunk can be kept in working memory as a single piece, without us having to bring in all the details about it.

Steps to Form a Chunk

  1. Focus your undivided attention on the task.
  2. Understand, figure out what is the main idea and relate it to what you know.
  3. Test yourself to verify that you understand.
  4. Gain context by figuring out not only how but when to use it.

Relate Chunks

To gain better understanding try to relate similar chunks together. A good way to do this is by using metaphors and similes. A simile is when we say something is like something else: Strong as an ox. A metaphor is when we say something is something else: You are my sunshine.

Metaphors transforms the strange into the familiar.
--Twyla Tharp, The Creative Habit

The Theory of Disuse (Forget-to-Learn)

Any chunk of memory has two characteristics, storage strength and retrieval strength. Storage strength is how well the item is learned. Retrieval strength is how accessible the memory is at the time.

Storage strength increases monotonically, while retrieval strength varies with context.

Both retrieval strength and storage strength increases with use.

Retrieval is key. Retrieving causes us to re-learn the memory. And, the harder it is to retrieve the deeper it gets stored in memory. More pain, more gain!

If we see the mind as a forest, a newly learned memory is somewhere in the forest. If we go to retrieve the memory, a path will be created to it. The more you retrieve it the wider the path gets. If we instead look it up, the path doesn't get created.

Memory Strength Matrix

In this 8 minutes long video, Destin from goes through all the variations of a memory can have.

  • When he starts, he knows how to ride a normal bike well. Strong storage and retrieval strength.
  • After a bit of trying, he learns how it works to ride a reversed bike. Weak storage and retrieval strength.
  • He manages to ride the reversed bike but falls as soon as he is distracted. Strong retrieval and weak storage.
  • When he then tries to ride a normal bike again, ha cannot do it. Even though riding a normal bike is strongly stored, it has weak retrieval strength.

Spaced Repetition

Repeated retrieval is the mother of all learning, but it not good to just repeat over and over without a pause. Because then we are leaning too much on working memory. Pausing between repetitions is good for two reasons:

  1. It gives the diffuse mode time to work.
  2. It lets us forget. Remember, we have to forget to learn.

The most efficient way to learn something is to space it out into intervals.

How long should we wait before we try to retrieve a memory? The longer we wait, while not totally forgetting it, the better. The harder the memory is to retrieve the deeper it gets stored.

So what is the optimal time span? Of course scientists have a solution for this. :)

If you have a test and you have decided to study for it three times. The optimal time for the second study session is as described in the table. The last study session should always be the day before the test.

But, spacing out is not the only important thing, context is also important.


Context, under what circumstances are you studying.

Location matters when you are studying. In one experiment, researchers let two groups of people study vocabulary while under water. One group had to take the test under water and the other group had to take the test on land. The group who was submerged got better results than the group who was on land.

In another study, the subjects were studying after smoking marijuana. Same result there, the group who were stoned got better results than the unstoned group.

And the same thing again with music. If students were allowed to listen to the same music that they had used while studying they got better results. It does not matter what kind of music it is, Mozart is not better than AC/DC. Interestingly not listening to music didn't have this effect. Not listening to music does not seem to provide a context.


You may be thinking, "How in the world am I going to get my teacher to allow me to take my tests stoned, under water, while listening to AC/DC?". This is not the point, the point is variation. If we learn under varying conditions our brain gets better at retrieving the information under conditions where we haven't practiced. And you can vary anything:

  • The color of the paper you are writing on.
  • Your mood, are you happy or sad?
  • Inside or outside
  • Morning or evening
  • Sitting still or exercising
  • etc.


Studying the same thing over and over again is called massed practice. It is commonly believed to be good, because it feels like you are learning fast, but it it's an illusion. It is much more effective to interleave your practice even though it doesn't feel that way.

Don't study the same thing over and over, vary the tasks. Don't just learn to calculate the area of a circle over and over, vary the practice with different figures.

In one study children where told to practice throwing bean bags. One group practiced with a distance of three feet. Another group practiced from two and four feet. The day after they had a competition, from three feet. The group which had used interleaved practice won easily even though they had never practiced on this distance.

Desirable Difficulties

The harder it is for us to retrieve the information the better we learn. It is better to attempt to retrieve and be wrong than to not attempt at all as long as we get feedback about what the correct answer is.

Think of learning as exercising. The harder it is, the stronger we get. No pain, no gain!


Testing is a great way to learn mainly for two reasons.

  1. It tells you what you know and don't know.
  2. It is an extreme form of retrieval. It focuses our mind, because when we really want to retrieve the information we try extra hard.

It is even helpful to pre-test what you haven't learned yet. This tells your brain that you are interested in this information and makes it more receptive and focused when you study.

Test come in varying degrees of difficulty.

From easy to hard:

  • Multiple choice
  • Fill in the blank
  • Reply with a sentence
  • Write an essay

Classroom Testing

Multiple studies have shown that students in classes that have many tests, one per week gets better grades than students who only get two tests per semester. A full grade better on average!


It is not necessary to have formal tests. We can verify that we know by asking ourselves and answering questions.

  • Do I understand what this means?
  • What are the basic ideas in this text?
  • Can I explain this to someone else?
  • How does it relate to what I already know?


Sleep is very good for our brain primarily for two reasons. First, being awake creates toxic products in our brain and sleeping cleans them out. Second, while we sleep our brain tidies up and removes unimportant ideas while simultaneously strengthening ideas that it believes are important to you.

Shallow Learning or Perceptual Learning

Shallow learning or perceptual learning is learning without understanding. It is pattern recognition and it is great for categorization. Perceptual learning is active, our eyes or other senses are searching for the right clues automatically and tunes itself. Here are some examples.

Chicken Sexing

To find out what sex a chicken has is very difficult and the experts who can do it cannot describe how they do it in a way that is understandable to an outsider. So how do you learn? By example. Make a wild guess. After each guess, the master chick-sexer gives you feedback.Yes, no, no, yes. And, eventually, you just start to make correct guesses without knowing how.

Flight Training

When a pilot learns to fly by instruments he has six instruments he needs to know. Airspeed Indicator, Attitude Indicator, Altimeter, Vertical Speed Indicator, Heading Indicator, Turn Coordinator.

When novices try to fly by instruments, they have a hard time understanding what is going on. While they focus on one instrument the other instruments change and it is difficult to get an understanding of what it means. Experts pilots, on the other hand, quickly glance at the instruments and instantly know what is going on.

By simple flash-card training a novice can get as good at instrument reading in one hour that normally takes a thousand hours. This training takes advantage of the perceptual learning ability our brain has for quickly categorizing the information.

Art Recognition

Flash-cards can also be used to learn to categorize painting styles. Without having any other knowledge of the paintings or the painters we can learn to categorize a painting as surrealism, minimalism, or any other style by just practicing over and over.


The biggest obstacle to our learning is ourselves. We have a tendency to do what feels good and not what is good and it is easy to fool ourselves to think that we know something when we actually don't.

Rickard Feynman once said:

The first principle is that you must not fool yourself - and you are the
easiest person to fool!

So how do we fool ourselves?

Illusions of Understanding


Reading a text over and over gives us the illusion that we know the text since we become familiar with it. We recognize the text as we read it. This is not the same as knowing it. The solution is retrieval practice!


Highlighting text is another way we fool ourselves. If we look at a page which is highlighted all over, it is easy to think that we already know it. The solution is retrieval practice!

Looking at the Answer

If we are solving problems, it is very easy to look at the answer before we have actually tried to solve the problem. We look at the answer and we tell ourselves that we could have solved this without looking. The solution in this case is to actually try to solve the problem. Even if we fail to solve it, we learn better than by just looking at the answer.


By Googling instead of trying to retrieve a memory we rob our brain of the extra storage and retrieval strength that come with retrieval. It is better not to remember and let our diffuse mode go to work and let it pop into our head while we least expect it.

Echoing Other People's Words

If you know a text verbatim, in exactly the same words used by someone else, odds are that you don't really know what you are saying. If you cannot explain it in your own words, you are probably fooling yourself.


Another big obstacle to learning is distractions. The brain needs focus time in order to store memories deep enough for later retrieval.

Studies have shown that students who learn while watching TV at the same time may actually know it quite well immediately after studying. But, when tested later their retrieval ability was abysmal.

If you have problems focusing while studying, the pomodoro technique may help you. Set a timer for an amount of time, 20 minutes or half an hour, and vow not to be extracted until the timer rings.


Procrastination is the avoidance of doing a task which needs to be accomplished. It is the practice of doing more pleasurable things in place of less pleasurable ones, or carrying out less important tasks instead of more important ones, thus putting off impending tasks to a later time.


The key to overcome procrastination is to Just Start. Very often the anticipation of doing something is worse than actually doing it.

The writer Dorothy Parker once said:

Writing is the art of applying the ass to the seat.

Solutions to Insight Problems

What historical person does "Horobod" symbolize? Robin Hood

A window washer fell from a 40-foot ladder without hurting himself. How is this possible? He fell from the bottom step.

Thiss sentence has thre errors? What are they? Two spelling errors, and the semantic error that the sentence only has two errors while claiming to have three.

Pyramid solution

9-dots solution


Martin Seligman is the author of the book, Authentic Happiness. He describes how, in a study on creative problem solving, subjects who were put in a good mood produced much better results. Happy people perform better! Increasing happiness, increases the likelihood of insight.

So here is story to put a smile on your face and to increase your creativity.

A priest fell into a well, but managed to get a hold of a
small vine before falling into the abyss. When he had been 
hanging there for almost an hour, he heard a loud thunder and a voice from above.

"This is your God speaking, if you let go of the vine I will save you!"

The priest contemplated this for a while and then he yelled, "Is there anybody
else up there?"


Insights help us to understand and relate things. In order to have more insights we have to learn things deeply and then let go. The best way to learn new things is by retrieval practice. Our biggest obstacle to learning is that we fool ourselves that we know things we don't know. Happy people have more insights, so by seeing the light side of things we not only feel better, we perform better.



Vijay said...

Really nice article... so well written. Look forward to reading more of your posts.

Anders Janmyr said...

@Vijay, I'm glad you liked it.