A Disturbing question

Recently a very close friend of mine asked me a very simple question. He heard from many radical fundamentalists that there is a sanction in Islam to kill infidels – meaning the Koran specifically grants the permission to do so. He wanted to know from people who read Koran whether such a statement does indeed exist. Basically his point is very simple – how can other religions coexist with Islam if such a provision does indeed exist in Koran? Of course, this friend of mine is a very fine scholar, so he believed that such claim by fundamentalists must be totally false because no true religion would ever make such a statement.

At a spiritual, metaphysical and philosophical level, such a statement can have many inner meanings, but if it were true – how can other religions co-exist with Islam at a theological level? If every non-Muslim is considered as a non-believer, and if Islam ‘mandates’ its followers that such non-believers should either be converted or killed, how can we even have a dialogue with them?

This is a widespread belief among many people and perhaps their source of discomfort with Islam. My friend told me that someone who read Koran thoroughly must come out strongly against such a widespread belief and make a public statement, providing the relevant references. How many people would have read Koran? If you are a Hindu, or a Christian or a Buddhist – you are not expected to read the holy book of Islam. May be half the Muslims do not know Arabic and so they cannot read Koran themselves.

What use is another newspaper article in any case?

Any sane person like my friend knows intuitively that such a belief has no basis and must be false. Islam apparently means peace and the Prophet called himself the messenger of peace. Therefore, any such belief must be self contradictory.

But, sanity today is an endangered species.

Our knowledge of history comes largely from various propaganda machines and is constructed by what we read about events in the newspapers. Newspapers report only events. Can they report progress, can they report ten thousand years of human evolution, can they even make an attempt to report what a religion and culture is all about?

But, it is a fact that we live in the age of short term memories and information overload. There is just too much information these days – most of it is pure junk – traveling at the speed of light. Short of asking everyone to read Koran – is there any other sane solution to such a wide spread belief?

There is overwhelming evidence in history that kings, leaders and clergy use their power with disastrous effects. Some societies – like some of the Polynesian islands like Easter Island and the Maya Kingdoms completely destroyed themselves largely because of the attitudes of their leaders. In all such cases, Religion was invoked by the leaders and rich people to justify their own ends, and to make people firmly hold on to certain belief systems.

Religion is a very deep rooted value system, and it can be and almost always is exploited by people in power to their advantage, to promote their own vanity or as an instrument to keep people ignorant.

However, religion and culture do not live in history books or buried in historical monuments. They exist for and through the common people. If we meet an average American, we can estimate the American value system, their religion and culture in five minutes of interaction – we may not be able to write detailed analytical essays, but we understand it intuitively. What a religion and culture stands for is represented by its living monuments – the common, average people. If you interact with an Indian – even casually – you get a ‘feel’ of Indianness, if you meet a Buddhist you get a ‘feel’ for Buddhism.

The average, common people – not people in influential positions – like scholars, clergy and leaders – but just average common people – internalize their culture so deeply and radiate their value systems all the time. They do it unknowingly, without any pretence. There is no drama, no cultivated, politically correct or incorrect responses. Their responses are natural.

If you meet a Muslim autoriksha driver in Hyderabad or a Muslim carpet merchant in Bangalore, a Muslim antique dealer in Delhi – what impression do you carry about them? I believe that impression is always correct. My impression is they are very tolerant, graceful, genuinely honest and nice people. To me, that is what Islam is.

Is there a better answer than that? Can any amount of scholastic reports answer such questions better than our own first hand experiences? Why don’t we trust what we observe, what we feel about our own fellow human being? Why do we place an overwhelming reliance on the media and other propaganda machinary?

There is so much of “manufacturing of our concent” that goes on in the world today by our governments, by our leaders and by the multi-billion dollar corporate houses. They have vested interests. Therefore, in today’s world – it is much better to trust our own first hand experience. If we don't then there is a danger that we lose our own innate ability to discern, and become unwitting instruments of manipulation by the powerful.

God is one when religion is dead.

Abstraction, Pattern Recognition and Problem Solving

The Design and the Designer – Part 6

A gap of more than two weeks interrupts the flow. But, the gap is probably required because from here – the approach is very different. Until now, I largely covered a lot of breadth, and was able to give examples in one paragraph – an approach that may not be sufficient from now onwards. It is like getting into the second chapter of a book – by nature, it gets a little deeper and a bit more boring.

The difference between Architecture and Engineering is like the difference between Music and Sound. Architecture is a word that is associated with many disciplines today – we talk of architects of nations, architects of enterprises and corporations, architects of cities, plantation forests, gardens, buildings, computers and information systems. Sometimes, this word is also used in relation to effects produced by an individual or a group of people – architects of success or failure, architects of war and of destiny. After the last Great War, this discipline seemed to have become main stream.

Even though, these days we use the term in its verb form, actually it exists only as a noun. The architect produces architecture – what he does is not architecture, but design. Therefore, the process used is the process of design, but the end product is “Architecture”. All architects are designers of a particular kind.

What does really an architect do?

Let’s consider the traditional architecture of buildings as an example. Even though the structural engineers deride architects as people who basically add unnecessary embellishments that do not have serve any functional purpose, in reality the job of an architect is one of transformation much like the work of an alchemist.

What the alchemist is to science, the architect is to engineering.

His work involves understanding the essence or meaning of space and transforming this understanding into an engineering problem.

Sounds abstruse even to me. We need some detailed explanation.

An architect basically brings meaning to space. An engineer does not make any distinction between kitchen and living room – both are basically enclosed spaces as far as the engineer is concerned. But, for people living in a house, kitchen and living room have very distinct functions, how they relate to these spaces is very different, the time they spend in these spaces is very different. It is the job of the architect to understand the function of a kitchen or a living room, and their relation to the people who use them and then somehow be able to express it in terms of certain ‘spatial’ characteristics – their geometry, placement, the equipment provided in that space. Basically, the architect defines what a kitchen is in certain engineering terms.

In short, the mysterious craft of architecture is very simple to express in words. The architect performs a series of semantic transformations; the last transformation achieves the feat of converting the problem into a structural engineering problem. If the alchemist transforms lead into gold, the architect transforms gold into lead – in a manner of speaking.

The reason why structural engineers do not respect architects is perhaps because of the fact that over the years, the community of architects was successful in creating a set of transformations that are universally accepted and understood, and the engineers themselves understand the difference between the kitchen and living room without the help of an architect. So, they do not see the necessity of an architect for the most common problems like the construction of a house, or a bridge any more.

In short, architects create new abstractions. An abstraction is an information structure – that codifies meaning objectively, an information structure that is universally understood. The power of abstraction is such that – if we have to state in one single line the difference between human being and an animal – we can say that the difference is the ability to come up with an abstraction.

What is an abstraction? A “tree” is an abstraction. ‘A Tree’ does not exist anywhere in the physical world – there are mango trees, there are lemon trees, there are all kinds of other trees, but there is no such entity called ‘tree’ – it is a pure abstraction that exists only in our consciousness. It helps us to group all mango trees, all lemon trees and all other trees in one sweep, and capture the ‘essential treeness’ that all of them share. Similarly, ‘A Man’ does not exist any where except in our consciousness – there is a John, there is a Joe, there is an Adam – but where is ‘Man’?

It took several thousands of years for us to come up with some very simple abstractions that we take it for granted today. One such example is the number system and the simple arithmetic of additions and subtractions. In ancient times, when people did not know the basic math, the methods they used for trading were very funny. If one goat equals two bags of rice (purely a concept of quantity decided by its value, there was really no such thing as ‘one’ goat and ‘two’ bags of rice) and if you want to want to exchange two goats, then what do you if you do not understand what is one and what is two? You give one goat, take two bags of rice, and then give one more goat again and take another two bags of rice. A very cumbersome process indeed – isn’t it?

But, what can people do if they do not know what is one and what is two? The numbers are very powerful abstractions.

An abstraction is valid only if it is completely objective. This condition means that an abstraction must mean exactly the same thing to everyone. The difference between an abstraction and a concept is in how strictly this condition is applied. A concept is not very strict in imposing the condition of objectivity. For example, “world” is a concept – but what I mean by world and what you mean by world can be somewhat different.

Abstractions, concepts or semantic types – are all information structures. It is a unit of information that retains the meaning of something, and is made accessible to everyone.

What is interesting is how we as humans acquire concepts and abstractions. We do it so naturally – we do not even realize that we are dealing with abstractions and concepts all the time. But, it is an amazingly complex process.

When as children we learn our alphabet – all we are shown is one particular shape of the alphabet. Your teachers writes ‘a’ in your notebook, and you practice recognizing ‘a’ and writing it yourself. That’s about it – after that you can recognize ‘a’ in what ever shape, size and form it appears – and you can recognize ‘a’ instantaneously. What you as a child accomplished is an amazing feat – by understanding one particular ‘a’ – you somehow extracted the ‘a-ness’ and then can apply that understanding of ‘a-ness’ like a flash. You can recognize ‘a’ in which ever font it is written, in millions of different handwriting samples. You do not need to be taught to recognize ‘a’ by going through several thousand samples, and various complex rules of recognition.

Such a simple act of extracting the meaning by understanding from one single illustration and then apply it on the fly to recognize millions of variations is an amazingly human ability – something very difficult for machines to do. Computers cannot even recognize their own hand writing!!

It is easy for a computer to produce millions of different ways of writing – you can type a word into a document, and then change the font any number of times. Computers are quite good at such manipulations. But, they are miserable when it comes to ‘recognition’ – at least until now. Suppose you take a printout of a document – and then use a scanner to scan the same document, connected to the same computer, and then try and reproduce the document in its original form ( a process called optical character recognition) – almost always you get a document with too many ‘errors’. The OCR programs are very complex where as the document creating programs (like Microsoft Word) are relatively simple. The OCR programs use several thousand ‘sample’ character sets, and ‘train’ the computer to recognize the ‘a-ness’. But, till now there is no foolproof method to accomplish this.

What makes us so good at pattern creation, extraction and recognition? Let’s leave that question to psychologists. However, this particular ability is at the heart of problem solving. In a most generalized sense, architecture, design, engineering, diagnosis are all a form of problem solving. Problem-Solving and Design involves an innate ability to recognize and categorize patterns, abstractions and concepts. Patterns, abstractions and concepts require associative thinking.

In the earlier posts, I mentioned about two kinds of thinking, two different processes of problem solving and so on. I tried to make a distinction between demonstrative reasoning, and heuristic reasoning. It is well recognized that the art of problem solving involves heuristic methods – for example, using analogy, generalization, reduction, specialization and so on. We also described in some detail about various forms of non-linear thinking – be it creativity, right brain thinking, lateral thinking, out of box thinking and so on.

Associative thinking and heuristic/plausible reasoning are the most generalized forms of non-linear thinking and problem-solving.

How does associative thinking work really and how can we use it systematically?

Here is a small exercise:

Let’s pick up some word randomly – let’s say it is Sun. Write down ten other words that come to your mind (without thinking) when you think of Sun – for example, star, heat, light, earth, round, fire, red, day, night, energy, Egypt, Japan and so on. Now, how is Sun connected with Egypt? The relationship between these two very different concepts is one association and it is association of some meaning. For example, Egyptians used to worship Sun God. Therefore, the relationship between these two concepts is “worshippers of”.

In the last post, I discussed about four structural relationships – hierarchy, network, hypertext and set. The relationship between Sun and Egypt is none of the four structural relationships. It can – at best – be represented in terms of a hypertext relationship, but it is in fact a “semantic relationship” – it is the inherent meaning that connects these two concepts.

Nasruddin – while solving a logic puzzle uses his associative network to come up with a completely out of the box solution. We need such an associative mental network to work with analogies, to work with induction, to generalize something, and from generalization to specialization and so on.

Another advantage with the associative thinking is that – you can recall your entire memory starting at any point. I suggest doing this as a fun exercise. Start with Sun – and write down all the words that come to your mind, and then for every word connected with Sun, write down all the words you can think of. For example, expand Egypt – something like – desert, pyramids, Africa, Nile, Pharaohs, Moses and so on.

Unfortunately, we are never taught how to make and keep an associative memory consciously. We are taught how to practice organizing our knowledge using the structural relationships, and we are taught how to use demonstrative (logical) reasoning, even though our brain uses an associative structure to organize its own memory and experiences. We are naturally gifted with the ability to organize and relate to our experience using associative networks. But, we are never taught how to practice it formally. As a consequence, our memory is a very randomly formed associative, semantic network that we cannot use efficiently.

The real trick of problem solving is nothing but consciously organizing our knowledge and experiences as an inner semantic network of concepts and relationships. In other words, if we can make and keep associative networks of our knowledge and experiences, then we have a better chance of becoming better problem solvers.

More on this in the next post.

An Apology

First – my apologies to all the regular visitors of my blog. Last two weeks have been very hectic. I made a promise to myself that I would upload at least two articles every week. Promises are like spoilt children – as soon as you make a promise - somehow, it brings along situations with it and is always bent upon proving that you are not worthy of it.

There are about seventy articles that I planed to write on various topics – I even made a brief abstract about each one of them – but the actual process of writing them down demands a kind of mental and physical discipline that is very hard to command all the time. The natural laziness is always waiting round the corner to catch up with its old friend, and its company is so enjoyable, one tends to forget everything else and spend all the time with that best of friends.

There is a wonderful Sufi story on this theme, published by Idries Shah in his Seeker After Truth. Here is the gist of the story:

A dervish visited a small town in India. He used to give a talk every night, and many people would go to listen to him. The discourse would begin some after dinner and usually lasted for about an hour and half.

An old man would attend the talk everyday along with his grandson. As soon as the dervish starts to speak, the old man would go to sleep. The dervish watched this for a couple of days, and then he called the grandson to him and promised to give him one rupee if he promises to wake up the old man every time he falls asleep.

The next two days, the boy would pinch his grand father whenever the old man dozed off. But, on the third day, the dervish noticed that the old man was snoring as usual.

The dervish called the boy aside and asked him what had happened – “I thought we had a deal. Why did you not keep your grandfather awake today?”

“That’s right. But when I told my grandfather about our deal, he offered me three rupees not to wake him up”.

The first rupee is our desire to do something productive. The other three are – our habits, our natural laziness and the unobserved opposition to truth.

******

Writing is very difficult. I know what to write, it is very simple to make up the outline of the article. The difficulty starts from the time I sit down to write the actual article. As I am writing the first line, the second line has to ‘spring up’ in the mind simultaneously. Otherwise, the flow is lost. I also have to think of the actual sentence at the same time, and the mind has to recall its typing experience. All this is just too much for the mind. It prefers to drift off, my old friend is back – and we go for a smoke break after every paragraph.

Sometimes the exact opposite happens. I can’t catch up with the speed of my thought – I can’t type as fast as I think. Too many thoughts flood my mind, and I just can’t type any more. So, I take a break and have a dialogue with myself. Before I realize, five hours are gone! By that time, there is too much content piled up in the head – I get enough content for another ten articles. I end up with a perpetual backlog.

I also have another difficulty. English is still a foreign language to me. The Indian languages and English are not natural friends. They are in fact quite the opposite. All Indian Languages are free order languages - it is so easy to construct phrases in Indian Languages. In fact, most words are not single words – most of them are phrases.

English does not have that kind of flexibility. So, when most Indians write English – they tend to make up wrong kind of phrases. For example, the meaning between “I am John’s friend” and “I am a friend of John” is quite significant depending on the context. For some strange reason, I always write the sentence in the reverse order, and then I have to do a lot of editing and rewriting.

Take the previous paragraph as an illustration. An Englishman would write almost every line in the reverse order: Most Indians tend to make up wrong kind of phrases when they write English. Depending on the context, the difference between “I am John’s friend” and “I am a friend of John” could be significant.

Can you see my difficulty? The previous paragraph was my first attempt. So, I have to apply the principle of inversion even to my English!! I always look for which sentences need to be reversed to make them right!!

I have a difficulty with the usage of tense as well. I still do not get the difference between the simple past and present perfect tense. The difference between I read the article and I have read the article eludes me all the time. For some strange reason, many Indians have a preference for “have, has, had” – they prefer “I have written a letter” to “I wrote a letter”. I am sure without the help of a grammar book, most of us can’t tell the difference between the two.

So, I end up doing a lot of editing on each article. I pray for the day when I can write effortlessly.

Forgive me for the delay. I will be back tomorrow again and continue the series on Semantics and other topics.

Non-Linear Thinking and Structures

The Design and the Designer – Part 5

In the last post, I made a brief mention of Nasruddin, Heuristics and Non-Linear Thinking. I shall continue in this post on the same theme and establish the role of semantics in Design and Non-Linear Thinking, and explore some techniques of practicing non-linear thinking.

First, here is a very brief synthesis of the previous posts on this subject: In the previous posts, I applied law of 2 and tried to demonstrate the underlying unity of the theme in various disciplines – which is referred to as Plausible and Demonstrative, Creative and Logical, Synthesis and Analysis, Right Brain and Left Brain, Linear and Non-Linear, Heuristic and Rational and so forth. Largely, the conclusion that one can reach is that there are two distinctive types of thinking – which are interdependent on each other, but at the same time have very different functions and applications. We termed the functions of these two types as – recognition of problems and finding solutions to problems. We also presented a few laws of synthesis – from various fields – particularly societies, management, computing science and consciousness.

Before we get into Semantics, let’s examine linear thinking and non-linear thinking in some detail – with some examples and techniques of how to switch from one to another.

Logic – at least the way Socrates and his disciples developed it – is largely linear. This is carried over into mathematics as well. Logic mostly depends on reasoning from evidence. The early Artificial Intelligence (which is neither artificial nor intelligence) applications ran into some problems with the linear reasoning and there are now several attempts to develop non-linear reasoning systems. Such logics in AI are called “non-classical” reasoning systems. Here is a classic example of linear and non-linear reasoning – it involves a very well known logic puzzle.

Three monks and three cannibals were traveling together because of some strange circumstances – even though naturally there cannot be any friendship and trust among such a diametrically opposite groups. If at any time, the cannibals outnumber the monks – they will eat them. Now, they came to a river bank and they had to cross the river. There was only one boat. The boat can only carry two people at a time. Now, your problem is to devise a strategy to transport the monks and the cannibals safely across the river.

The usual linear reasoning system will start with River Bank-1: 3M, 3C, River Bank2: 0M, 0C as the initial state of the system, and will try to devise a series of moves that will establish the desired final state - River Bank1:- 0M, 0C, River Bank2: 3M, 3C. It is a simple puzzle – you start with something like first two cannibals will travel, one will come back, two monks will then go etc., and you can easily arrive at the final state.

Suppose you give the problem to Nasruddin, what do you think he will do? He will listen to your descriptions, and even before you have completed your narration, he will jump from his chair and shout with the excitement of a child “I know, I know - the monks will take the bridge, and the cannibals will take the boat”.

It is a perfectly valid solution to the problem – isn’t it? Then you tell him “look Nasruddin, I did not say that there was a bridge”. Nasruddin will reply, “Well – you did not say that there was no bridge either”. Now, you modify the problem description, and you will add another constraint to the problem – there are no bridges. “Well, in that case, the monks take the helicopter” will be Nasruddin’s answer. By this time, you get very frustrated and shout back at him – “I want you to solve the problem – not avoid it”. But, for Nasruddin, there was no problem there to be solved. Can you see how he eliminates the problem instead of trying to solve it?

No matter, how hard you try, you cannot contain Nasruddin. He will always think of exploiting some constraint that is not included in the problem definition and use that as a means to eliminate the problem.

The AI community in the last thirty years tried and discovered several techniques for “programming Nasruddin type behavior” into the computer programmers – with some reasonable success. I have no intention of boring you with the Non-Monotonic Reasoning systems here. But what is the technique of Nasruddin?

One, Nasruddin does not depend on “evidence” as the only way of establishing the existence of something. All formal logical systems depend on evidence as the only means of establishing “truth”. For example, if I tell you that all visitors from Canopus are fools, and you know that Mr. X is a visitor from Canopus, you can confidently establish the truth that this particular Mr. X is a fool. But, there is a catch. Suppose, if this particular Mr. X is not a visitor from Canopus, then what are you going to do? You cannot establish anything. He may or may not be a fool. You can conclude Mr. X’s foolishness, only if you know that he is a visitor from Canopus.

We need facts to recognize truth, but Nasruddin does not rely on such petty things like facts to recognize truth. According to Nasruddin, some thing does not have to be a fact for it to be true. Kurt Gödel proved this mathematically – it is known as Gödel’s incompleteness theorem. The incompleteness theorem states that in any formal system, there always exists a statement which is “known” to be true, but cannot be proved.

Rabindranath Tagore – with the brevity that a poet alone can command – says it beautifully.

“If I say that the earth is flat – you inform me that my near sight is false.
If say that the stars are the fireflies attracted to the moon, the candle of the sky – you inform me that my far sight is false. My dear logician – in your presence, I prefer to be blind”.

*****

The second principle that Nasruddin mastered is the System’s Principle – understand the problem by studying its relationship to the larger environment in which it is only but a part. I wrote about this principle in part 2 of this series of articles.

In the specific case of monks and cannibals – all Nasruddin does is to bring his knowledge of the larger environment to solve the problem. The minute you tell him about the river and the boat, he can think of a bridge. He can bring his knowledge of traveling in the air, or swim in the water. Or, he will say that the monks – using their magical techniques – will vanish and reappear on the other side. Or, he will say that the monks will use their secret herbs and put the cannibals to sleep. His possibilities to come up a solution are infinite.

The study of system level relationships requires knowledge of semantics – or the “meaning” of things. There are basically two types of relationships – structural and semantic. It is important to distinguish between these two types of relationships. Though, in logic and other sciences, we are mostly taught how to study the structural relationships, in fact, our mind works naturally very well with semantic relationships.

A few examples from various fields may be in order here.

In language, grammar defines the structural relationships. In English, a valid sentence must have a subject, a verb, an orbject/predicate. And, there are various rules that define the relationships between various parts of speech. These relationships are basically structural – they govern the structure of the sentence. We can say that water is triangular – it is a grammatically valid sentence, but completely meaningless.

In information systems there are basically four types of structural relationships. By information systems I do not mean just software applications. Any system that organizes knowledge and depends on that organization is an information system. By this definition, societies, cultures, various disciplines of study are all information systems.

The first – and simplest structural relationship is hierarchy. This relationship in information systems is called “IS-A” relationship. A “IS-A” B. This could be interpreted in several different ways:

• B is the parent of A
• B is the boss of A
• B is part of A
• B is subsumed by A
• B is the root of A

Entire systems, organizations, societies are modeled based on this one particular relationship. Most hierarchical structures use this relationship as the primary relationship. The different sections in this blog-page have a parent-child relationship with the master page. There are basically five sub-sections – header, footer, posts, author information, archives – each of them is a “child” of the main blog page. Similarly, many corporations have a hierarchical structure – with the owner of the corporation at the top. The “semantics” of this relationship connotes ownership and protection.

The second structural relationship is network relationship. In such a structure, elements, or objects at the same level can be connected. This is called “sibling” relationship. A “IS-A brother of” B. The relationship basically means that two things are at the same level. It connotes competition and/or collobaration.

There are two other types of structural relationships in information systems hyper-text and groups. Both these relationships are somewhat non-linear relationships, but nonetheless, they are structural relationships.

The Set, and Hyper-Text are more complex structural relationships than a simple hierarchy and a Network. A set uses a function to create a structure. For example, you can say that all integers belong to a set. You can then define a function that determines an integer and therefore, the membership to the set. The members in the set may not have any particular relationship – they have something in common – that’s all. This is how most social groups are formed. The function gives an identity to the set and therefore to all its members. All people “born” in US are “Americans”. “Being born” in the US determines the identity of the set called Americans.

A Hyper-Text relationship is much more interesting relationships. It does not relate two nodes, but instead it relates content from one node to another node. All web pages use this structure extensively. For example, I can provide a link to an article in wikipedia in one of my articles in this blog. This does not mean that this blog as a whole and wikipedia share any relationship; it also does not mean that this article and the wikipedia share any relationship, and it also does not mean that this article as a whole has any relationship to that article in wikipedia. This relationship connotes friendship. There is no function, there is no responsibility, and there is no ownership in this relationship.

Using these four relationships, we can explain almost all “order” in our world. We defined the basic family relationships (parent-child, sibling), groups and friendships.

So, where is the place for Semantic Relationships?

We conveniently left out the most important, most complex, wonderful, problematic and the most beautiful relationship of all– that of the lover and the beloved. None of the above relationships explain that relationship – do they? What is the relationship of a husband and wife? What is the relationship of a teacher and a student? Friendship comes closest, but these relationships transcend friendship.

This is the realm of semantics – which is the topic of next post.

Non-Linear Thinking, Nasruddin and Polya

The Design and the Designer – Part 4

In these series of articles on Creativity and Design, my intention is to explore if there is a “formal” model of creativity. I am not interested in the psychological aspects of creativity, how it works and so on. The Psychology of discovery and invention is wonderfully described by Mihaly Csikszentmihalyi in his classic book called Creativity.

My interest is to discover a method of consciously practicing it. In the last few posts, I tried to provide a basic framework that I am working on. Basically I am trying to bring together all my experience under one unified theme. Design is the name I gave it.

I studied mathematics and more importantly I studied how to ‘do’ mathematics. I studied computer science and information systems – I designed some very large and complex software systems. I studied design theory – product design, appliance design, communication design, aesthetics, user interfaces, ergonomics etc. I studied philosophy – Western Philosophy, Indian Philosophy and Sufi Philosophy. I studied systems thinking. Basically I am a problem-solver. Given any problem, I can come up with some kind of a solution. I met many people who are fantastic problem solvers. Many of these people can almost instantaneously identify a line of attack and can come up with a solution almost immediately.

In my experience, problem-solving can be taught and can be learned – even though we generally think some people are gifted with this ability. But, teaching problem-solving has been one of the toughest problems for the teaching community. There does not seem to be a discipline for teaching problem-solving. Even the most beautiful subject – mathematics – has not addressed this problem.

How are we taught mathematics? The mathematics teacher presents the proof of a theorem in a step by step manner. First, he defines the theorem, and he has the proof in front of him, and all the teacher does is to explain the ‘logical flow’ of the proof. In the course of several years, various problems and solutions are demonstrated as examples, and somehow the student is expected to ‘understand’ problem-solving from these examples. There is no conscious attempt at teaching problem-solving.

The ‘doing’ of mathematics is not taught. This is what makes Mathematics difficult to learn for many people. The best reference works ever written about this are Polya’s books on mathematical method: How to Solve It and Mathematics and Plausible Reasoning. For some strange reason – these books are not part of the mathematics curriculum.

Polya makes a very useful observation. According to him – rightly so – the process of problem solving is a heuristic process. The difficult part of problem solving is to ‘recognize the problem’ correctly. This recognition is not a “rational”, “logical” process. It is very irrational – if you are good at it – you can immediately recognize what the problem really is in an instant, and you decide on the line of attack. How do we normally recognize the problem? We generally use a set of heuristics. For example, you may recognize that the problem is “similar” to another problem you solved before, or you may recognize that the problem belongs to a class of problems that are already solved and so on. These are all heuristics.

Here is an illustration of how heuristics are applied. Archimedes first discovered the formula for calculating the area of the circle. The area of the circle is PI*r2. In Mathematics texts, the proof is presented using some complex coordinate geometric equations. Archimedes proof is rather very simple and can be explained in one line. He drew several lines from the center of the circle to its circumference. Now, the area enclosed by two such lines and the arc of the circle looks like a triangle. The area of the triangle is (base*height)/2. Now, the height in this case is r. And, the base of all the triangles put together is the circumference of the circle – which is 2*PI*r. Therefore, the area of the circle is PI*r2. Beautiful – isn’t it?

A mathematician will not agree to a proof like this – because, the way Archimedes divided the circle into different regions are not exact triangles – they only look like a triangle. Archimedes used a heuristic.

Now, let’s look at the process that Archimedes used to solve this problem. First, for Archimedes, the problem of calculating the area of a circle is a real problem; it is not a theoretical problem. He had to calculate the area of agricultural land for calculating taxes. Second, given a particular circle, he knew how to come up with answer. So, he has some data in hand. He has the areas of different circles in front of him and he was looking for a common “pattern” that explains all the answers. Third, he knew that the two fundamental properties of the circle are its radius and its circumference. The last step is the important one. He asked himself a question – can I formulate this problem in terms of problems that I already know how to solve? In other words, he knew how to calculate the area of a square, a rectangle and a triangle. Now, he is trying to “reduce” this problem to the problem of a square, a rectangle or a triangle. He also knew another important fact about areas – they are always expressed as a product of the two different lengths. He used four different heuristic techniques – generalization, analogy, reduction and induction.

Polya calls this type of reasoning “plausible” reasoning as opposed to “demonstrative reasoning”. Different disciplines may have different names for this. Psychologists call it right brain thinking, designers call it creativity at work, scientist call it intuition at work, systems people call it “systems thinking”. In popular literature, this is called “non-linear thinking”, “out of box thinking” and by many other similar names.

No matter what name you give it – the process of recognizing the problem, and the process of actually solving it involve two different kinds of thinking altogether.

Polya’s books are the best reference works on this subject. He tried to formulate a systematic method of “problem-recognition”. Unfortunately – thanks largely due to the American experiments with modern mathematics – the world today suffers from cultural isolation of mathematics. Polya’s achievement is remarkable. With the precision of a mathematician, he formulated a “dictionary of heuristic”. This means – if you have some patience – you can learn the heuristic thinking like learning the vocabulary from a dictionary.

Another dictionary of heuristic that is particularly enjoyable to read is the collection of Nasruddin Stories. These stories help us to break our usual linear and cause-effect thinking. Even just remembering the stories has the remarkable effect of constructing a different kind of associative memory. The stories ‘just’ pop up by themselves when we need them most.

More than 700 tales of Nasruddin are collected by Idries Shah and are published by Octagon Press. Here is one story of how Nasruddin describes the “two modes of thinking” that we have been talking about:

One day Nasruddin stormed into the tea house and announced with lot of excitement that he discovered a very important truth.

People asked him what it is.

Nasruddin said – “The moon is more useful than the Sun”

Everyone was taken aback, and asked him why he thinks so.

“Because we have more need for light in the night”

Nasruddin Stories make sense at many levels, and it is said that there are at least seven interpretations for each story. Here is one interpretation that is relevant in our context. Moon is the agent of synthesis. He synthesizes the sun light and reflects it back to earth. Sun is the source of light – when he is there – we have no need for light because it there everywhere. Your need is more when something is not available – right?

There are people who are experts at synthesis. Polya synthesized mathematical method, Will Durant synthesized history, Ackoff synthesized management, and Christopher Alexander synthesized Architecture. I am trying to synthesize Design. In order to synthesize a domain, you need to be a super-specialist in that domain and you need to be able to absorb the entire domain completely.

Both modes of thinking co-exist and compliment each other. I am not indicating that synthesis is more “important” or “superior” to analysis. Like the Sun and Moon, they are interdependent on each other. The linear and the non-linear, the creative and the logical, the plausible and the demonstrative co-exist together.

In order to synthesize Design – we need an understanding of Semantics. We have to understand the meaning of things, and how different things relate to each other.

This will be the topic of the next post in this series of articles.

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Nasruddin on cause and effect:

One day Nasruddin was waling along a street with his students. As Nasruddin was walking past a two story building, a man fell down from the first floor – and he fell on Nasruddin. Nasruddin’s neck was badly hurt.

His students asked him what lesson they can draw from this incident.

Nasruddin was in pain and he was now angry at such stupid questions. He shouted – “fools – can’t you see? He falls from the building, and it is my neck that is broken”.