simplicity_complexity

Simplicity vs complexity

Simplicity originates from seeing the Essence.

Whether something is considered as simple or complex depends on the level of consciousness. The complex becomes simple when your understanding grows.

The key to understand a problem, a concept or an event in a simple way is to get to the essence of things and see how they fit together as well as how they fit into a bigger picture.

A complex phenomenon can be made simple through (a smart) organization. When intelligently organized, its representation usually yields more effectiveness and efficiency than when the opposite holds.

Such a smart organization it is being practiced in art, math or science by the use or an extension of modularity. Modularity is achieved by building blocks of nested complexity such that simple operations are needed to relate or combine these blocks in a meaningful way.

An example

Let’s consider an example in math of a sum and an integral. First we need to define numbers (natural, integers, rational and real), then a sum of two elements. This is further extended to a sum of multiple elements. Knowing what a sum is, we define a more complex structure which is a series, that is an infinite sum. This can be understood through a limit of partial sums. In order to arrive at a finite number, the series has to be convergent.

The structure of a series is now the basis to define an integral. Having a structure of integral, we can define simple operations and make calculations on the level of integrals forgetting these are infinite summations. And so, we can estimate area or probability by using these high level concepts.

The development of technology, such as app-oriented programming, click-touch-and-connect devices, identification or recognition systems, feeds on such modular organizing principle, similarly as natural languages do.

Complexity and the level of details

This brings us to the view that perhaps all problems can be perceived as problems of complexity. If we don’t now how to approach them, this happens because their formulation escapes our current way of organization, be it thoughts, models, techniques or tools.

Simplicity looks at similarity. We need the similarity in order to find commonalities.
Complexity looks at the differences. We need the differences in order to discriminate. 
A solution which is simple is still an interplay between similarity and difference, yet in the right proportions.

Unnecessary complexity arises when you are on the level of too many details. Details account for variability, individuality, exceptions, forms, partial views and shadows. They make life surely interesting, yet when in abundance, they clutter the view and hide the Essence.

There is no way for you to see the emerging behavior of ants if you with your eyes are on their level. It is hard to solve problems if you dwell in them. It is hard to make a breakthrough if you constantly keep thinking and exploring the views, angles, positions and details.

As you need your 3D perspective to recognize the patterns of ants, you need a different level of consciousness to find your solutions. This comes naturally when you detach and begin to ask the questions that matter.

The simplest choices can make you happy.
The simplest strategies can lead to success.
The simplest solutions can solve the most complex problems.

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Truth originates from basic foundations.
Truth is simple. If it isn’t, then it’s being formulated in a complex way.
Your challenge is to simplify it.

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The photo above comes from a museum in Cardiff, made some time ago.

 

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We learn from others.
We have family and friends.
We have teachers, mentors, supervisors, managers or bosses.
We have colleagues, politicians, media people, musicians, and stars.

We observe. We analyze. We model. We emulate.
We compare to others.

Without perhaps noticing, we keep dancing between two worlds.
One world is defined by Similarity or Sameness.
The other world is defined by Difference.

Similarity is Interdependence, Belonging, Sharing and Being a part of a Group.
Difference is Independence, Individuality and Self.

We want to belong to a family, community or a peer group. We want to be with others, share experiences and have fun. We want to be appreciated. And we want to be loved.

At the same time we want to explore the boundaries of Self. We want to mark who we are by the way we think, we look, we walk or we talk. We want to do things in particular ways, choose our likings, make own decisions and create. Above all, we want to love.

So, we need both, Similarity and Difference, Interdependence and Independence, Individuality and Belonging, to live happily and healthy. No doubt about that.

And the middle way is about the flow between these polarities, between giving and receiving, self-focus and focus-on-others, individual thought and cooperation, being an individual and a part of a group.

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We learn from others. We exist both as Selves and in relations to others.  And we compare.

It is impossible not to compare.

How else can we receive feedback?
How else can we measure progress to a baseline performance?
How else can we evaluate our growth?
How else can we identify the borders we want to transgress?
How else can we test new skills and practices?
How else can we determine which rules or ideas serve us or not?
How else can we define realistic goals?

We look to other people for inspiration, mentoring, help or example. Comparing to others gives us the necessary context  for growth. It also enables us to find out what is possible to achieve or whom we may choose to become. However, it gives us a partial view only. The other important view is to compare to ourselves. In a timeline. And we often forget to do that.

We forget to learn from ourselves.
We forget to measure the progress along our own journey.
We forget how much we have developed with respect to the starting point.
We forget our milestones and achievements on the way.

So, if you are tempted to review your progress, look back at who you were a month ago, one year ago, 5 years a go or 20 years ago. Any progress?

If we are not careful, it is easy to compare to others with a diminishing light, focussing on our inferiority. This may lead to thoughts of jealousy, envy, shame or guilt. And from that place, there is only a small step to unhealthy self-criticism and over-beating. If continued, we will likely pick the fruits of self-devaluation, low self-image and low self-esteem.

Now, imagine this.

Next time when you notice a big difference between yourself and others, just at the very moment you are so much tempted to think how unskilled, untalented you are or how much you suck, welcome and cherish a new thought. Do it consciously.

This thought tells you that what you are perceiving as a difference is merely a distinction.

And this distinction makes you – unique You.

You, who is welcome here, loved and appreciated.

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The image above shows a beautiful quilt by Inge Duin. See more of her works on www.ingeduin.nl.

generalization

In the previous post I discussed some aspects of learning a concept from examples. We will now connect it to….

 

Generalization

Generalization is the ability to learn a concept or a class from a set of examples. In short, generalization is our way of capturing sameness or similarity between objects.

By “objects” we understand all kinds of entities, including physical objects, abstractions, experiences and so on that are elements of the class or belong to the concept of interest.

For instance, we can learn a concept of a bicycle with the objects being bicycles, as well as we can learn a concept of driving with the ‘objects’ being driving experiences.

Generalization is a truly remarkable skill of an intelligent mind. It is one of the basic principles of learning.

We are able to learn a general rule and apply it when needed. We are able to classify or categorize not only physical objects, but also ideas, abstractions, events, behaviors, approaches and people. We are able to recognize patterns from examples, determine the essence and categorize experiences.

Generalization is being used daily on all levels in your life. You can apply skills and abilities in the new context exactly because generalization is at work.  It is really powerful.

  • Isn’t that remarkable that once you know how to walk, you are soon able to run?
  • Isn’t that remarkable that once you can drive an individual car, you can drive (nearly) all other cars?
  • Isn’t that remarkable that once you know how to cook a few meals, you can cook a totally new meal, never tried before?
  • Isn’t that remarkable that once you know how to orient yourself with a map, you can follow maps in arbitrary situations?
  • Isn’t that remarkable that once you know a programming or human language, you can learn a different language much faster?

The stages of concept learning

A quilt by Inge Duin

Imagine that you are to learn how to recognize a particular object or to learn a concept. The stages of learning a concept are in fact the stages of generalization. These are:

  1. Typical examples. Study, observation or experimentation with a number of typical examples of the given class.
  2. Finding the patterns: seeing the differences and perceiving similarities. This is made possible because of our ability to compare.
  3. Concept creation. A first mental formulation of a concept of an object/class/notion. Grasping the basic essence. This is made possible because of our ability to reflect.
  4. Atypical examples. Study of atypical, uncommon and otherwise strange examples from the class. Refining of the concept.
  5. Borderline cases. Exploration of the negative examples (i.e. examples from outside of the class), especially of the borderline cases.
  6. Re-definition of the concept.
  7. Abstraction. A new level of understanding. The essence is found.

Abstraction may develop without your conscious intent. It happens naturally when you reach a good understanding of  the class or concept of interest. Such an understanding is built when you engage in active learning, i.e. thinking, experimentation, reflection and evaluation. Abstraction occurs when you develop a mental image/sound or internal feeling of the class.

Some researchers think that such a class representation relies on a single prototype or a set of prototypes that somehow capture the idea of the class. Sometimes a prototype can be defined by a set of features, but it is usually much more than that. Features offer a limited scope and may vary from example to example.

A prototype  is meant to be an internal representation of the class. It likely combines visual, auditory, olfactory and kinesthetic modalities. Moreover, such a representation includes an emotional component, i.e. feelings that the concept evokes in you or emotionally strong events that took place when you had a related experience. In addition, such a representation may be equipped with a graph of structural dependencies and be hierarchical in order to reflect levels of importance or degree of detail.

Recognition

Testing is the next step after you have derived a concept of a class. It is called recognition. A good recognition does not necessarily prove that you have created an accurate and factual concept. The quality of your recognition depends on the quality of examples you consider for testing, i.e. whether they are a mixture of easy (typical) and challenging ones (border cases).

There are two types of errors you can make, called false positive and false negative errors. False positive are examples that you recognize as belonging to the class of interest while in fact they are not the member of that class. An example is an orange recognized as a ball by a child. After noticing such boundary examples you need to update your concept so that you will exclude such cases in the future (e.g fruits are not balls).

The second type of error is the false negative error which occurs when you miss to name a particular object as a member of the class, while in fact it belongs there . This suggests that you have not included a sufficient variety of examples when you were building your concept.

Concept learning is an ongoing process

If you think you learned a concept, you are wrong. We are living in a developing world and this asks us to continuously update, reformulate or even abandon our concepts by taking new developments and personal experiences into account. For instance, the concept of a telephone or TV you learned, say 20-40 years ago, is really outdated by now. Or the concept of friendship (which refers here to the class of friendship experiences) you developed in your childhood is not going to serve you in your thirties or later. You need to update your concepts by more recent examples.

Concept learning and recognition run in cycles

The concepts you develop are never fixed. They are solid, however, in the sense that they are built from concrete examples leading to specific representations of the classes. But, they are subjected to change.

In fact, you are always in the process of concept learning, recognition and concept re-learning, even though you don’t follow it consciously. These two stages are intertwined and you run them in cycles. You learn a concept and you test it. As long as your examples do not contradict your concept or challenge you with novel perceptions, your concept remains unchanged. If, however, you find a surprising example, you will decide whether the concept should to be re-learned or not.

You need to pay attention to noticing these interesting examples and be ready and prepared to modify your learned concept. At some point you will see that novel examples occur for which your concept definition does not work well. These are the moments in which you observe how your false positive or false negative errors increase. So, you are encouraged to include such examples in the concept formation process.

In addition, you may mentally weight your examples depending on some importance factor (that you define for yourself) or the time you collected them. Perhaps, you may even neglect early examples as they are not relevant any longer. For instance, concerning the concept of friendship, you may like to include examples of your friends from your primary school but they may have a much less weight than the examples from your last years of life.

Summary

Generalization supports us in learning on all levels. The use of generalization requires an open mind, however, able and prepared to question and redefine the derived concepts, if needed. Any concept we learn in our life is temporary. We change and the world changes as well. This means that our general rules, concepts and learned ideas are in operation until e.g. we find a surprise or a contradiction. This is a sign that points us to reformulation of the concept or perhaps even abandoning it.

What is essential is the meta ability of a conscious mind to pay attention and to notice outliers. As long as we remain flexible in our learning, open to questioning and re-learning, we will use generalization well.

Practise generalization with a conscious effort.

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Top photo courtesy Fe Langdon, available under the Creative Commons license on Flickr.
The middle image shows a beautiful quilt by Inge Duin. See www.ingeduin.nl for more details.

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Learning and generalization posts:

 

increase intelligence by concept learning

Let’s  look at some basic questions, which are nevertheless insightful:

  • How enthusiastic are you about learning?
  • How flexible are you?
  • How do you keep up with the fast pace of our changing world?

Whatever your answers to the questions above I hope you recognize the importance of intelligence. It helps you to tackle problems more effectively. It facilities a life of growth. It makes difficult choices easier.

Would you like to increase intelligence?

I bet your answer is “yes”.

There is a simple practice you can install in your mind: creating accurate and up-to-date concepts about the surrounding world. By concepts we understand mental representations of an object, idea, activity, living creature or phenomenon. Whatever we see, hear, feel or encounter in our lives, goes through mental processes of our brains.

For instance, when we learn what an apple is, we learn a concept of a class of apples in the from of a mental representation of the encountered apples  or an abstract idea of an apple.

We are people of the patterns

We are people of the patterns. We create patterns in our lives, art, work and products. Whatever we do it bears the very characteristic of our whole being. It’s hardly possible, even if at all, for you to create something that is completely not like you. Try it. And report to me if you are successful, because I will find it extremely interesting ;).

I challenge you to write a genuine piece of text that is perceived not like yours. Try to cook a meal which is not like yours. Try to make a design that is completely dissimilar with your previous designs. Try to continuously speak or walk in ways that are 100% alien to you. Try to make something creative that is completely different from who you are. Even attempting this feels weird.

The reason is that at any moment we are attracted to specific ideas or concepts that we live by. These are specific patterns. They permeate our whole being including consciousness, feelings and thoughts.

These drive our actions. When we act, take decisions, make judgements or create something, we derive them from our internal resources. Whatever the output, it is going to bear the watermark patterns of who we are.

Because patterns are so prevalent in our lives, we are very efficient at finding patterns and recognizing traits. Finding patterns relies on noticing the differences and perceiving similarities. We learn concepts, classes or categories after having observed the patterns.

Classification / categorization is essential

A class or category is a group or collection of objects, things, events or experiences that have something in common; there is an underlying similarity.

In this light, any given object or experience is a representative of its class. At the same time any given object may belong to multiple classes, nested or not. For instance, there is a class of oaks which is a subclass of leafy trees, which is a subclass of trees.  Or, there is a class of bananas and there is a class of fruits that you like which includes ripe bananas (but not unripe ones).

Without classes or categories, every object and every experience would be novel, interesting and puzzling. No doubt, this would lead you to a thrilling life of ever fresh experiences, yet without understanding and learning. You would not be able to organize your experiences into meaningful ways.

As a result, you would not be able to tell whether something is a carrot, chair or car, or whether it is useful or friendly. You would not be able to survive.

Have you ever observed how a small child learns to recognize an object?

There are two levels to it: unconscious and conscious classes of experience. Before using a language, a very small child forms unconscious classes of objects or experience. He basically goes through a certain experience and recognizes when something similar happens again. This informal grouping relies on some observable similarity.

An example is a child experiencing an enormous joy in a repetition of a certain play; I bet you’ve seen these situations many times. A child may be laughing when you play with him his version of hide and seek (covering his face with a cloth and asking “Where is  Joe?” and then uncovering and saying with surprise “Oh, there he is!”), over and over again. Even after 20 times the child may still be in the same hilarious laugh as after the 1st time. He recognizes from the first movement what it is going to happen and anticipation makes it great.

In the conscious forming of classes, language plays a role, or more specifically, naming. The whole process begins with a child being interested in the chosen object. He finds this object appealing to his senses, so he interacts with it. And he usually plays with the object in all possible ways. He asks for its name. Naming is essential for learning a concept, because a name labels the class, hence it is identified with the class.

Without the name we miss our reference. The name serves therefore as a handle of a bag. It points to or indicates a group of objects or experiences which are in the bag. At the same time, naming assigns an object or experience to a given class.

The child usually collects sensory experiences and explores the object by touch, taste, sound and smell. He interacts with it in multiple ways. It allows him to create an idea of the object, before a concept is learnt. Later he sees another object of the same kind and explores it even more. Then the next example comes. And some more.

What is interesting is that a few examples are often sufficient for a child to build a good-enough, or sometimes even detailed, concept of the object. If a child is really attracted to this object, he begins to recognize objects from the same category. He is actively noticing them in the world around and happily pointing to them at any occasion. For instance, given a few examples of (playing) balls, a child is able to recognize a previously unseen ball. And you know that it is possible even if the features of a ball such as a size, color or material are totally new.

In the days or weeks to come, a child will further refine the concept of a ball. This is the time he will study (i.e. explore) more examples of balls. Hopefully, such a set includes less typical balls as well. These are important for inspecting the boundary cases. What is even more important are the negative examples, i.e. examples which do not belong to the class. Again, a special focus is put on these negative examples which resemble the object of interest in some way, but are not the object.

For instance, a child may see an orange and recognize it as a ball. If you reply that the object is not a ball but an orange (a different name, hence a different class), a child will be prompted to reformulate his concept of a ball, respectively. When he is pointed out to differences, he will learn the essential discrimination about ball-like objects which are not balls.

The effective concept learning takes place in the presence of both uncommon and negative examples. Borderline cases from both sides of the class are crucial for a good formulation of the concept.

Abstraction

Although the example of a ball sounds simple, the same steps take place for learning the concepts behind more complicated things such as dogs, cars, flowers, airplanes, or particular meals, as well as activities such as cooking, running or playing. What is remarkable, is the step in which a child takes the concept to an abstract level by becoming to know what is the essence of the object or concept. I believe such an abstraction is the basis for our fast intelligent recognition skill that we so much rely on in daily life.

For instance, when my toddler was exploring the world around, attracted to airplanes flying above, he only started to recognize them when he was able to name them. He learned the concept well.

Recently, he has surprised me by the following. In the garden he found two wood planks of different lengths. He put them across, kept them in this alignment in his hand above his head and started to run around the garden. While doing so, he was making humming noises and joyfully shouting that there was an airplane flying.

I understood he made an important step. He was able to bring the understanding of what an airplane was to the next level in which he saw its basic essence. He was able to emphasize a few features essential for an object to be considered as a plane: a particular shape, noise and movement in the air. This is the skill of abstraction applied to in a creative way.

You learn concepts from examples

If you observe others and yourself, and explore of how we learn, you will discover that we learn concepts or classes from examples. Moreover, in an ideal scenario, we actually follow the process described above. And what is more, we are able to learn them from a few examples only, usually three to five. Just ask yourself:

  • How many times do you need to hear your friend speaking in order to recognize her voice?
  • How many examples do you need to be to tell whether a cathedral is gothic or not?
  • How many examples do you need to recognize an impressionist painting?
  • How many coffees do you need to smell or drink in order to learn what a cappuccino is?
  • How many passionate people do you need to interact with in order to recognize a passionate one?

A few examples are often enough. Of course, it does not necessarily mean that you will make no errors when a recognition should occur. There may be difficult borderline cases, changed circumstances, previously unseen mixtures of objects or other situations which may lead us to a wrong assignment. But a few examples are sufficient to get an idea behind the concept. However, you will need many more examples especially near the border cases in order to refine the concept well for arbitrarily difficult examples.

For instance, you may need to hear your friend speaking when he is ill in order to better recognize his voice over the phone in arbitrary circumstances. You may also need many more examples in order to recognize particular sub-cases of the given classes.

Whatever the case, remember to collect a wide spectrum of examples from the class as well as from outside of the class. Otherwise, your concept would either be too narrow or too wide. What you want is a well-formulated, tight (but not too tight) concept, because it will facilitate your learning.

Well-learned concepts increase intelligence

There is no doubt about it. Remember, any concept you hold, whether it is about concrete objects in the world, scientific discoveries, your skill or experiences, it is your building block for the synergistic working of other concepts.  It has a direct influence on the quality (read: happiness, joy, fulfillment) of your life.

For example, the concept you have learned about computers links to your ability of using them effectively or not, or the concept you created about love has a huge impact on the way you create your relationships.

The more factual representation of your concept, the better it serves you to build other concepts and make intelligent choices. The better your concepts, the better your ability to plan and act accordingly. Both recognition and prediction directly rely on the goodness and accuracy of concepts you have created.

Well-learned concepts and well-learned classes are formulated based on all examples (or experiences) with the emphasis on uncommon situations or outliers.

Take your time to inspect your most important concepts about yourself and life.

Learn them anew.

Practical strategy

How do you practically implement the learning of accurate concepts? It’s simple. I will summarize it below:

  1. You learn concepts from examples.
  2. The quality and representativeness of the examples/experiences you use for concept learning is essential.
  3. If you learn a new concept, choose your examples wisely. You need examples that cover a wide range of situations and boundary cases. You will often need as little as 3-5 typical examples and a variable number of boundary examples.
  4. Be open and willing to reformulate your concept when you notice an example that is different, strange or otherwise appealing. What you want is a tight description but wide enough to accommodate what is the gist of the concept.
  5. If you have a concept formulated (e.g. about entrepreneurship, working-out, cars, kids, faith, money, Rembrandt paintings, mountaineering, buying houses etc), inspect which examples or experiences you used to create it. Remove outdated examples that no longer serve you and use more recent examples. Mentally re-crete your concept again by finding patterns, similarities and differences, between the examples you collected. Just think about it and get new insights.
  6. Do it with every new concept you learn.

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The image above shows a quilt by Inge Duin. See www.ingeduin.nl for more details.

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