Knowledge Representation

Knowledge Representation 

The frontiers of knowledge are always on the move across many dimensions and perhaps at varying speeds along each of these dimensions. Inter-disciplinary and cross-disciplinary knowledge is becoming more valuable. The question of how to organise and represent human knowledge is an old problem. But now it has assumed critical importance. Our ability to deal with the complex challenges of the future will depend upon our ability to manage knowledge organisation and representation. 

Knowledge representation refers to the technical problem of encoding human knowledge and reasoning  into a symbolic language that enables it to be processed by information systems. In systems biology, knowledge representation is used to infuse data with scientific concepts and understanding in order to maximize its utility for furthering scientific insight.

Here is the link to a good survey article on Knowledge Organisation:

In this piece I draw attention to a few examples. In the future we may have automated Artificial Intelligence  tools for us to do so. 

  • The periodic table
  • Mind maps
  • Knowledge graphs 
  • Data representation 
  • Valency of ideas/concepts
  • Taxonomy/ Classification

The periodic table  (also known as the periodic table of elements) is organized so that scientists can quickly discern the properties of individual elements such as their mass, electron number, electron configuration and their unique chemical properties. Metals reside on the left side of the table, while non-metals reside on the right. Organizing the elements to help further our understanding was first provided by Dmitri Mendeleev.

The periodic table of the elements has their names, atomic number, symbol and mass is color-coded for easier reference by students and researchers.

The periodic table is the most important chemistry reference there is. It arranges all the known elements in an informative array. Elements are arranged left to right and top to bottom in order of increasing atomic number.  Order generally coincides with increasing atomic mass. 

The different rows of elements are called periods. The period number of an element signifies the highest energy level an electron in that element occupies (in the unexcited state). The number of electrons in a period increases as one traverses down the periodic table; therefore, as the energy level of the atom increases, the number of energy sub-levels per energy level increases.

Using the data in the table scientists, students, and others that are familiar with the periodic table can extract information concerning individual elements. For instance, a scientist can use carbon’s atomic mass  to determine how many carbon atoms there are in a 1 kilogram block of carbon.

People also gain information from the periodic table by looking at how it is put together. By examining an element’s position on the periodic table, one can infer the electron configuration. Elements that lie in the same column on the periodic table (called a “group”) have identical valence electron configurations and consequently behave in a similar fashion chemically. For instance, all the group 18 elements are inert gases. The periodic table contains an enormous amount of important information. People familiar with how the table is put together can quickly determine a significant amount of information about an element.

“The disappearing spoon” is a 2010 book about the periodic table written by science reporter Sam Kean. Sam Kean begins this book by explaining the basics of the periodic table and how it works. He explains the set-up of the table and why it is organized the way it is. He emphasizes the importance of its organization and justifies why it must be this way. He discusses how the periodic table would not function if it were not for the layout. He states that an element’s position describes its function and strength. He describes the table of elements as a castle and the elements as bricks to build this castle. He then discusses how the periodic table contains, and is organized into, metals, gases, noble gases, halogens, etc. Here is a link for further information on the periodic table:

Mind maps: 

The Mind Map first conceptualised by Tony Buzan  is an easy way to brainstorm thoughts organically without worrying about order and structure. It allows you to visually structure your ideas to help with analysis and recall.

A Mind Map is a diagram for representing tasks, words, concepts, or items linked to and arranged around a central concept or subject using a non-linear graphical layout that allows the user to build an intuitive framework around a central concept. A Mind Map can turn a long list of monotonous information into a colorful, memorable and highly organized diagram that works in line with your brain’s natural way of doing things.

Mind Mapping is perfect for:

  • Brainstorming and visualizing concepts
  • Presenting and communicating ideas
  • Graphic organizers and electronic note books
  • Running meetings more effectively
  • Outlining reports and documents
  • Simplifying task and project management
  • Writing essays

Software for creating mind-maps:

Knowledge Graphs:

A Knowledge Graph is a model of a knowledge domain created by subject-matter experts with the help of intelligent machine learning algorithms. It provides a structure and common interface for all of your data and enables the creation of smart multilateral relations throughout your databases. Structured as an additional virtual data layer, the Knowledge Graph lies on top of your existing databases or data sets to link all your data together at scale – be it structured or unstructured.

Knowledge graphs are data. They have to be stored, managed, extended, quality-assured and can be queried.

Knowledge graphs:

Data representation: 

Even before we start on Knowledge representation, we have the challenge of data representation. Let’s take a simple problem. Assume that the average distance of the earth from the sun is 93 million miles. Also let’s assume that the speed of light is 186,000 miles per second. The question: how much time does light take to reach from the surface of the sun to the surface of the earth. You may remember it from your school days as about 8 minutes, or you could calculate it by dividing 93000000/186000 to get 500 seconds, which is 8 minutes 20 seconds. Now try to do the same calculation using Roman arithmetic in which the numbers 1 to 10 are written as: I,II,III,IV,V,VI,VII,VIII,IX and X. And then we have L, C, D and M……for 50,100,500 and 1000. Feel free to  search the Internet to find the rules for Roman arithmetic. You will find that not only is it very difficult to write these two numbers, it is impossible to do the division in any reasonable time. 

  • Valency of ideas/concepts

We considered the organisation of the periodic table as a very important reference diagram in Chemistry. Another important concept in Chemistry is valency. The combining capacity of an atom is known as its valency. The number of bonds that an atom can form as part of a compound is expressed by the valency of the element. 

The concept has been extended to the field of linguistics. 

In linguistics, valency or valence is the number and type of arguments controlled by a predicate, content verbs being typical predicates. A major authority on the valency of the English verbs is Allerton (1982), who made the important distinction between semantic and syntactic valency. As we saw in the making of mind-maps, the number of connections of any Ned on the mind map may be considered as its valency. The value of an idea may become higher if it has a higher valency and connected with others. 

  • Taxonomy/ classification :

Taxonomy is the Science and practice of classification of things or concepts, including the principles underlying such classification. While it was originally used for biological classification, the word taxonomy is now used as a synonym for classification. For example, in the field of education Bloom’s Taxonomy is a standardized categorization of learning objectives in an educational context. In the present times, there would be considerable interest in Virus classification, taxonomic system for viruses. In the field of Computing the following are quite important: Folksonomy, classification based on user’s tags and search engine taxonomy, considered as a tool to improve relevance of search within a vertical domain. 

Abraham Maslow first introduced his concept of a hierarchy of needs in his 1943 paper “A Theory of Human Motivation” and his subsequent book Motivation and Personality. This hierarchy suggests that people are motivated to fulfill basic needs before moving on to other, more advanced needs. There are five different levels of Maslow’s hierarchy of needs. Maslow’s hierarchy of needs is also a taxonomy. 

In analogy, the different levels of self-driving cars is also a taxonomy. 

Level 5 (Full Driving Automation)

Level 4 (High Driving Automation)

Level 3 (Conditional Driving Automation)

Level 2 (Partial Driving Automation)

Level 1 (Driver Assistance)

Level 0 (No Driving Automation)

To see the descriptions for each of these levels :

We now have machine learning to do the classification for you. An enhanced version of the universally accepted Dewey decimal classification for all library books and resources, would be evolved for all types of digital content and automated systems for classification, storage and retrieval. This is very important as the amount of data/knowledge is growing exponentially, with user generated content being a large fraction. The goal of such systems is not only classification and storage but more importantly efficient retrieval when needed. 

While the technologies of the day are changing very rapidly, we have more and more knowledge and data which is long-lived and this must be borne in mind. Long-lived digital data collections are increasingly crucial to research and education in science and engineering. A number of well-known factors have contributed to this phenomenon. Powerful and increasingly affordable sensors, processors, and automated equipment (for example, digital remote sensing, gene sequencers, micro arrays, and automated physical behavior simulations) have produced a proliferation of data in digital form. Reductions in storage costs have made it cost-effective to create and maintain large databases. And the existence of the Internet and other computer-based communications have made it easier to share data. As a result, researchers in such fields as genomics, climate modeling, and demographic studies increasingly conduct research using data originally generated by others and frequently access this data in large public databases found on the Internet.

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On being the right size:

On being the right size? 

There has been a lot of discussion on the NEP 2020 recommendations for higher education, and one of the new ideas is to have large Universities. This is stated at “10.1. The main thrust of this policy in higher education is to end the fragmentation of higher education by transforming higher education institutions into large multidisciplinary universities, colleges, and HEI clusters, each of which will aim to have 3,000 or more students. “

It reminded me of an essay that I had read during my School years, “ On being the right size” by JBS Haldane in a book of essays “Possible Worlds and Other Essays” by J.B.S. Haldane published in1927.  Here is a link to the essay for immediate reference. :

Haldane explains the factors that affect the size of an animal and argues that there is an optimum size for every animal. The opening lines of the essay are:

The most obvious differences between different animals are differences of size, but for some reason the zoologists have paid singularly little attention to them. In a large textbook of zoology before me I find no indication that the eagle is larger than the sparrow, or the hippopotamus bigger than the hare, though some grudging admissions are made in the case of the mouse and the whale. But yet it is easy to show that a hare could not be as large as a hippopotamus or a whale as small as a herring. For every type of animal there is a most convenient size, and a large change in size inevitably carries with it a change of form.

Later it says that “And just as there is a best size for every animal, so the same is true for every human institution.”

Just as there is diversity in the animal kingdom, there would be diversity in the nature of educational institutions, and therefore different types of educational Institutions would have different optimum numbers. 

It seems that Dronacharya’s Gurukul had a very high level of excellence with very few students. 

We have pretty much diluted the higher education system with the goal of enhancing the GER to 50%, which again is reminiscent of the statement that “ growth for the sake of growth is the ideology of the cancer cell”. 

A co-ordinated balanced harmonious growth maintaining homeostasis is the principle of sustainable life. 

Similar considerations apply to matters of Governance and administration. In that essay Haldane writes “ I do not suppose that Henry Ford would find much difficulty in running Andorra or Luxembourg on a socialistic basis. He has already more men on his pay-roll than their population. It is conceivable that a syndicate of Fords, if we could find them, would make Belgium Ltd or Denmark Inc. pay their way.” 

In India we have seen that the number of states  have been regularly increasing. ( ) and India today comprises of 28 states and 7 Union territories. 

While most of India’s states were carved out of bigger ones over the years on linguistic lines, some have argued that ease of governance, rather than language, should be the key to the size of state. Those in favour of small states point to the economic growth of Jharkhand, Chhattisgarh and Uttarakhand that were created in 2000. And that of Haryana and Himachal earlier. Small states are easier to govern and people are closer to the decision makers. Smaller states also reduce diversity making policymaking more focused and management easier.

Why not: Some say that small states won’t be economically viable (only states rich in natural resources benefit) and some smaller states have been politically unstable. Bigger states, on the other hand, are about cohesion and stability. Having more states makes the central government’s job more difficult too.

The ToI piece on 2nd November 2020:,card-78984959.cms?utm_source=newsletter&utm_medium=email&utm_campaign=timestop10_daily_newsletter

There is another area where the optimum size is important. MOOCs have been a recent phenomenon and even India has created its own SWAYAM. If we do move towards remote e-learning, an interesting question arises that what is the right size of a remote classroom. From a technological perspective, we could be teaching millions simultaneously with a MOOC. But teaching is different from mere broadcasting. And thus the question arises as to what is the optimum number of a taught learning cohort. Yes it can surely be more than the 20 or so in a traditional classroom. 

Dunbar’s number is a suggested cognitive limit to the number of people with whom one can maintain stable social relationships—relationships in which an individual ( the teacher) knows who each person is and how each person relates to every other person. This number was first proposed in the 1990s by British anthropologist Robin Dunbar, who found a correlation between primate brain size and average social group size. By using the average human brain size and extrapolating from the results of primates, he proposed that humans can comfortably maintain 150 stable relationships. Dunbar explained it informally as “the number of people you would not feel embarrassed about joining uninvited for a drink if you happened to bump into them in a bar.”

Proponents assert that numbers larger than this generally require more restrictive rules, laws, and enforced norms to maintain a stable cohesive group. It has been proposed to lie between 100 and 250, with a commonly used value of 150.

I have been using WhatsApp for teaching for some time now. When I started using WhatsApp for teaching, the limit to membership of a WhatsApp group was 100. Now it is raised to 256. A group that is aligned to the Dunbar number. 

Towards the end, I want to share with you some useful practical knowledge on the right size of digital content. The ideal length of online content : The optimal length of all social media update :

From the above articles, I have culled out key insights on what lengths are considered optimum for different social media posts. But these are averages. N a specific context, longer lengths may not only be acceptable, but also desirable. 

  • The optimal length of a tweet — 71 to 100 characters
  • The optimal length of a Facebook post – 40 characters
  • The optimal length of a Google+ headline – 60 characters maximum
  • The optimal width of a paragraph – 40 to 55 characters
  • The optimal length of a domain name – 8 characters
  • The optimal length of a hashtag – 6 characters
  • The optimal length of an email subject line – 28 to 39 characters
  • The optimal length of an SEO title tag – 55 characters
  • The optimal length of a blog headline – 6 words
  • The optimal length of a LinkedIn post – 25 words
  • The optimal length of a blogpost – 1,600 words. 7-minute posts capture the most total reading time on average.
  • The optimal length of a YouTube video – 3 minutes
  • The optimal length of a podcast – 22 minutes
  • The optimal length of a presentation – 18 minutes
  • The optimal length of a SlideShare – 61 slides. Unlike YouTube, where shorter content tends to be more successful, SlideShare users welcome comprehensive content
  • The optimal size of a Pinterest image – 735px by 1102px
  • Beyond the data, there is a bit of opposite advice that many hold as a best practice: Guy Kawasaki’s 10/2/30 rule. It says 10 Slides/ 20 Minutes and 30 Point Font

As you will see if you read through the article, these are inferences from the data of people perusing the content. It may have nothing to do with the effectiveness of the content or content targetted at and meant for a specific group. 

What is the optimal length of a single lecture ?

Since the founding of Western universities in the middle of the 11th century, the lecture has been the traditional means of passing on knowledge. Indeed, the 50-min lecture still holds sway at many institutions. Despite nearly a millennium of usage, the established lecture format has come under more and more scrutiny. It is criticized as being too long to hold a student’s attention based on several authors’ claims that a student’s attention span declines precipitously after 10–15 min. Such observations would support the TED approach of an 18-min limitation.

The current standard length of a lecture period is 60 minutes, sometimes comprised of 60 minutes speaking and other times approximately 45 to 50 minutes speaking and a 15 or 10 minute time slot for question-answers. 

It depends partly on the audience, but above about 20 adults, you usually get the same mix of learning styles/temperaments, so it ends up being much more strongly dependent on the lecturer and his/her style. 

Duration of a WhatsApp learning session:

While there are several pieces on the Internet on what is the optimum size of a blog, tweet, e-mail heading, e-mail length, a video talk ( TED with its 20 minute duration has emerged as a standard), there is none for the length of a WhatsApp course.

I have given a few WhatsApp live sessions of 60minutes, 90 minutes and even 3 hours. I feel about 90 minutes is good. 

That is the standard that I propose to use for my Whatsapp talks. 

Incidentally, while doing the research on this, I found that the average length of a Hollywood popular movie was 101 minutes.  So, there is a good chance that  one of these Whatsapp live courses may become a Blockbuster. 

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The idea of Justice

The idea of justice?

 The Constitution of India begins with the promise  “ to secure to all its citizens: JUSTICE, social, economic and political…….” and this clearly indicates that the idea of justice is multi-dimensional and complex. 

The idea of justice changes with geography and time. Einstein would have appreciated the statement that justice is a function of space-time. 

The Manusmṛiti (मनुस्मृति), is an ancient legal text.  It was one of the first Sanskrit texts to have been translated into English in 1776, by Sir William Jones and was used to formulate the Hindu Law by the British colonial government.

It  is variously dated to be from the 2nd century BCE to 3rd century CE, and it presents itself as a discourse on topics such as duties, rights, laws, conduct, virtues and others. The text’s fame spread outside Bharat (India), long before the colonial era. The medieval era Buddhistic law of Myanmar and Thailand are also ascribed to Manu, and the text influenced past Hindu kingdoms in Cambodia and Indonesia (

The Code of Hammurabi is a well-preserved Babylonian code of law of ancient Mesopotamia dated to about 1754 BC. It is one of the oldest deciphered writings of significant length in the world. The sixth Babylonian king, Hammurabi enacted the code. Code of Hammurabi :

Today, approximately 282 laws from Hammurabi’s Code are known. Each law is written in two parts: A specific situation or case is outlined, then a corresponding decision is given.

One of the best known laws from Hammurabi’s code was:

Ex. Law #196: “If a man destroy the eye of another man, they shall destroy his eye. If one break a man’s bone, they shall break his bone. If one destroy the eye of a freeman or break the bone of a freeman he shall pay one gold mina. If one destroy the eye of a man’s slave or break a bone of a man’s slave he shall pay one-half his price.”

Well, Mahatma Gandhi wasn’t on board with that. His quote “an eye for an eye makes the whole world blind” is saying that if we keep punishing those we deem cruel, then we’re no better than the bad guys ourselves. It’s the whole “you can’t solve violence with violence” spiel. Many civilised countries have abolished the death penalty, but blood thirsty societies still crave lynching by mobs and ‘encounters’ by the police. 

Sir Henry James Sumner Maine,  is famous for the thesis outlined in his book “ Ancient Law” that law and society developed “from status to contract.” According to the thesis, in the ancient world individuals were tightly bound by status to traditional groups, while in the modern one, in which individuals are viewed as autonomous agents, they are free to make contracts and form associations with whomever they choose. 

The Idea of Justice is a 2009 book by the Nobel Prize winning economist Amartya Sen. The work is a critique and revision of the philosopher John Rawl’s “ A theory of justice”  (1971). In the book, Sen makes a radical break with the traditional notion of homo economicus, or ‘rational economic man’ as motivated mainly by self-interest. He points out that children have strong notions of fairness and acute aversion to manifest injustice. In his introduction to The Idea of Justice, Sen states that “the strong perception of manifest injustice applies to adult human beings as well (as children). What moves us, reasonably enough, is not the realization that the world falls short of being completely just – which few of us expect – but that there are clearly remediable injustices around us which we want to eliminate.”

One of Sen’s main arguments is that the project of social justice should not be evaluated in binary terms, as either achieved or not. Rather, he claims that justice should be understood as existing to a matter of degree, and should correspondingly be evaluated along a continuum. Furthermore, he argues that we do not need a fully established abstract ideal of justice to evaluate the fairness of different institutions. He claims that we can meaningfully compare the level of justice in two institutions without positing an ideal, transcendental idea of justice. 

Yuval Noah Harari’s “Sapiens” is one of those uniquely breathtaking books that comes along but rarely. It’s broad, but scientific. It seems to be influenced by  Jared Diamond, author of Guns, Germs and Steel and other similarly broad-yet-scientific works with vast synthesis and explanatory power.

One of the reasons why Homo Sapiens dominate the earth is according to Haraki, their ability to imagine intangible ideas such as the idea of human rights. 

In the present digital age driven by Artificial Intelligence, the role of algorithms is an essential element of the applications of the concept of justice. One of the challenges in delivering justice is to distribute a scarce resource to a large population. One of this is going to come up very soon with the availability of the Covid 19 vaccine. Eventually it will be an algorithm that will used for this. 

In the mid nineteen eighties, I had tried to raise the question of whether the random number calculation algorithm of Maruti allocation of cars was violative of Articles 14 of the Constitution of India. 

Weapons of Math Destruction is a 2016 American book written by the Mathematician Cathy O’Neil about the societal impact of algorithms. It explores how some big data algorithms are increasingly used in ways that reinforce preexisting inequality.  

O’Neil, a mathematician, analyses how the use of big data and algorithms in a variety of fields, including insurance, advertising, education, and policing, can lead to decisions that harm the poor, reinforce  racism, and amplify inequality. 

Most troubling, they reinforce discrimination: If a poor student can’t get a loan because a lending model deems him too risky (by virtue of his zip code), he’s then cut off from the kind of education that could pull him out of poverty, and a vicious spiral ensues. Models are propping up the lucky and punishing the downtrodden, creating a “toxic cocktail for democracy.”

She posits that these problematic mathematical tools share three key features: they are opaque, unregulated, and difficult to contest. They are also scalable, thereby amplifying any inherent biases to affect increasingly larger populations.

This year the 2020 Nobel Prize in Economics was awarded for the model /theory of auctions ….. The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2020 was awarded jointly to Paul R. Milgrom and Robert B. Wilson “for improvements to auction theory and inventions of new auction formats.” 

We may expect innovations in democratic processes beginning with choosing the population’s representatives and the algorithms of collective opinions and decision making. 

Algorithms that are ‘just’ is the next step in the ‘idea’ of justice. 

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Utilitarianism : 

During the greater part of this year, across the world, there have been several restrictions on the activities of people, often preventing them from their regular activities that were thought implicit in their freedoms. 

The basis of such decisions is often the principle of utilitarianism. 

Utilitarianism is a theory, which advocates actions that foster happiness or pleasure and opposes actions that cause unhappiness or harm. When directed toward making social, economic, or political decisions, a utilitarian philosophy would aim for the betterment of society as a whole. Utilitarianism would say that an action is right if it results in the happiness of the greatest number of people in a society or a group.

“The greatest good for the greatest number” is a maxim of utilitarianism. The 18th and 19th century British thinkers Jeremy Bentham and John Stuart Mill are the key proponents of this philosophy. Utilitarianism holds that an action is right if it tends to promote happiness and wrong if it tends to produce sadness, or the reverse of happiness—not just the happiness of the actor but that of everyone affected by it. At work, you display utilitarianism when you take actions to ensure that the office is a positive environment for your co-workers to be in, and then make it so for yourself.

The three axioms of utilitarianism :

  • Pleasure, or happiness, is the only thing that has intrinsic value.
  • Actions are right if they promote happiness, and wrong if they promote unhappiness.
  • Everyone’s happiness counts equally.

The limitations of utilitarianism: 

  • A limitation of utilitarianism is that it tends to create a black-and-white construct of morality. In utilitarian ethics, there are no shades of gray—either something is wrong or it is right.
  • Utilitarianism also cannot predict with certainty whether the consequences of our actions will be good or bad—the results of our actions happen in the future.
  • Utilitarianism also has trouble accounting for values like justice and individual rights. In contrast to the utilitarian concept, deontology is ethics of duty where the morality of an action depends on the nature of the action, i.e., harm is unacceptable irrespective of its consequences. This concept was introduced by the German philosopher, Immanuel Kant and hence widely referred as Kantian deontology. The decisions of deontology may be appropriate for an individual but does not necessarily produce a good outcome for the society. 

To appreciate this, it is interesting to watch this video by Michael Sandel of Harvard University : What is the right thing to do? : This is a longish video, so I would suggest that you view the first 20 minutes for now. If you find this interesting, you can go ahead and see not only the rest of the video, but the entire series. 

One of the examples in the video is when  a hospital has four people whose lives depend upon receiving organ transplants: a heart, lungs, a kidney, and a liver. If a healthy person is waiting for his check-up in the hospital, his organs could be harvested to save four lives at the expense of his one life. This would arguably produce the greatest good for the greatest number. But few would consider it an acceptable course of action, let alone an ethical one.

So, although utilitarianism is surely a reason-based approach to determining right and wrong, it has obvious limitations. Michael Sandel has very well explained the ideas of consequential and categorical approaches to moral reasoning. 

And here is what Mahatma Gandhi suggested. 

“I will give you a talisman. Whenever you are in doubt, or when the self becomes too much with you, apply the following test. Recall the face of the poorest and the weakest man [woman] whom you may have seen, and ask yourself, if the step you contemplate is going to be of any use to him [her]. Will he [she] gain anything by it? Will it restore him [her] to a control over his [her] own life and destiny? In other words, will it lead to swaraj [freedom] for the hungry and spiritually starving millions?

Then you will find your doubts and your self melt away.”

– One of the last notes left behind by Gandhi in 1948, expressing his deepest social thought.

It would seem that in these days of Big data, Artificial Intelligence and hyper-personalisation it may be more appropriate to apply Mahatma Gandhi’s talisman than the perceived good of many in utilitarianism. 

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What is a paradox?

What is a paradox? 

paradox  is a logically self-contradictory statement or a statement that runs contrary to one’s expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. Many paradoxes arise because there is one or more hidden invalid argument. Most of us have played around with 2×0=5×0, and therefore 2=5. Or it’s generalised version ax0=b x0, and therefore a=b, or the generalised version that all numbers are equal. 

All grown ups ( teachers, elders and parents) have to deal with queries from the children, which often involve resolution of paradoxes ; for example, why does it get colder as we approach a hill station, when as a matter of fact we are getting closer to the Sun? Or when we describe God as omnipotent, omnipresent and omniscient we may be accosted with “If God is omnipotent ( all powerful) can God make/create a stone that he cannot lift ?”. 

Or the following series of arguments on avoiding studying:

The more you study,the more you forget,

The more you forget the less you know,

The less you know the less you forget

The less you forget the more you know

So, why study?

In common usage, the word “paradox” often refers to statements that are ironic or unexpected, such as “the paradox that standing is more tiring than walking”. 

Here is another teaser “If I plan to fail, and succeed in failing, have I failed or succeeded?”

What is a paradox ?

The classification of paradoxes:

According to Quine’s classification of paradoxes:

  • veridical paradox produces a result that appears absurd, but is demonstrated to be true nonetheless.
  • falsidical paradox establishes a result that not only appears false but actually isfalse, due to a fallacy in the demonstration. The invalid mathematical proof that showed all numbers are equal, given in the first para of this article, relies on a hidden division by zero. 
  • A paradox that is in neither class may be an  antinomy which reaches a self-contradictory result by properly applying accepted ways of reasoning. 

There are many well known paradoxes that are analysed and resolved to build better critical thinking skills :

The Abilene paradox :

Zeno’s paradox?

How to resolve the liar’s paradox :

Russell’s paradox:

Curry’s paradox:

The ship of Theseus:

Protagoras’s paradox:

The  Fermi  paradox :

EPR paradox :

15 paradoxes that will blow your mind:

Difference between paradox and a fallacy:

Most paradoxes are fallacies, but some are not, the paradox of the Liar, ( ) for example.

As I close, I want to draw attention to a paradox of present times that arises out of a universally cherished idea, the idea of freedom of choice. It is considered axiomatic that the more choices we have, the better off we will be. So much so that we even have laws to break monopolies in businesses. But in terms of human consumer experience, the more choices available to you, the less satisfied you are with each one. This is the old ‘paradox of choice’. Research shows that when we are presented with more options, we become less satisfied with any particular one we choose. The reason  is that when we have so many options, we have greater opportunity cost in selecting each particular one; therefore, we’re less happy with our decision. Please do watch this video where Barry Schwartz explains the paradox of choice :


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Learning in times of Uncertainty

Learning in uncertain times: 

It is almost universally agreed that we are living in uncertain times that are complex and rapidly changing. This has often been described as the VUCA world ( Volatile, Uncertain, Complex and Ambiguous). It should not be surprising that Complex Problem Solving tops the list of top 10 skills, and creativity has moved up from being at no.10 in 2015 to no.3 in 2020 as identified by the World Economic Forum for both 2015 and 2020:


A simplistic naive response to uncertainty is to deny it or try reduce it—or even better, to try to wish it away. Many scholars however agree that it is essential in our rapidly changing world for young people to develop ‘uncertainty competences’ comprising specific sets of skills, knowledge, attitudes and capabilities needed to deal with uncertainty, ambiguity and complexity in diverse contexts. Intelligence uses what is known to solve problems. Creativity uses what is unknown to discover possibilities.  Learning to handle knowledge uncertainty requires learning environments tolerating, even inviting, uncertainty into the learning process. Maybe we should have an approach of accepting it, and even embracing it, like what Physicists like Max Planck, Niels Bohr, de Broglie and Albert Einstein did to develop the foundations of the new framework built on accepting the inherent ‘uncertainty’ postulated by the Heisenberg Uncertainty Principle in what till then was considered a fully deterministic world. This led to the development of Quantum Mechanics and the resulting technologies leading to the present digital computing age and the coming age of Quantum Computing and Quantum Biology. 

Likewise, in about a decade from now, this uncertainty in our environment may lead to a transformed model of education, a model that I have labelled Learning 321, real learning relevant education for the 3rd decade of the 21st Century. For more details follow this link :

This will be the decade of transformation of India to a respectable place in the knowledge, innovation and creative economy. 

The key elements that comprise this education model dealing with the decade long uncertainty that we may see before we enter another phase of relative stability are the following:

1: The transition to life-long learning. The NEP 2020 recognised the value of pre-school learning and has incorporated it in its scope. But equally if not more important is the learning throughout life, and especially the added years because of longer longevity. Age related demarcation into finite stages of learning as in the NEP2020 is not relevant, as each learner’s developmental journey is unique and on a continuum. Watch this 5 minute video where Bill Clinton, a former President of the USA extolls the imperative of life-long learning:

That this is not just a theoretical idea, has been witnessed here in India during the last months when schools were closed and teachers of all ages, very gracefully transformed themselves from face to face in class teachers to remote online teachers using Zoom, Google Meet, Microsoft Team, Webex and others. They did not depend upon the NCTE mandated syllabus for B.Ed or M.Ed, but learnt from several sources, including colleagues, students and sometimes even their children and grandchildren, which I describe as a “ learning community”. True lifelong learning will put Maslow before Bloom and strive for the highest levels of attainment in both frameworks . 

2: Interestingly the idea that a learning community can manage the “commons” better than either the Government or the private sector was an idea for which Prof Elinor Ostrom was conferred the Nobel Prize in economics in the year 2009. Our teachers, during this pandemic have given one more piece of evidence to support her work. In times of uncertainty it may be a good idea to move from pre-defined learning outcomes to ubiquitous and serendipitous learning . Going forward, learning in uncertain times should be largely  the responsibility of the learning community, rather than bureaucracies or businesses. The citation for her work for which she was awarded the Nobel Prize identified her contribution as : Challenged the conventional wisdom by demonstrating how local property can be successfully managed by local commons without any regulation by central authorities or privatization:

3: For life-long learning to be successful, as a movement , and not just for some outliers,learners must have a disposition and ability of self-learning. Many enlightened thought leaders have said that any attempt at instruction is futile. Gibbons said “ But the power of instruction is seldom of much efficacy, except in those happy dispositions where it is almost superfluous”. This was quoted by Richard Feynman in his famous “ lectures on Physics”. The professor-poet Robert Frost said “ I am not a teacher, I am an awakener”. The skill of learning to self-learn, includes building learning power ( Guy Claxton) and developing critical thinking skills. In times when there is great uncertainty, we should follow John Holt who had said that we should foster a love of learning, and the ability to learn very well.

Just like in the case of self-driving cars, where the SAE ( Society of Automotive Engineers) have approved 5 levels, self-directed learners may also be at different levels. If we treat autonomous learning as a skill similar to a language skill, we may use the 9 bands like in the IELTS framework or the 6 levels like in the CEFR. Or we could draw an analogy to a learning maturity level like the 5 levels of the CMM framework. The skill of Ultralearning will be essential at the topmost levels of being an Autonomous learner. This has interesting consequences for the cost of education. The more a learner can learn on one’s own, the less the cost of the person’s education. The more external help needed for learning, the higher the cost of education. There will therefore be an economic value to developing self-learning power. What is worth self-learning ?

4: Developing Foresight: If the purpose of learning is to be future-ready, then the starting point is to have some idea of the future trends. Knowing the future with any measure of accuracy would be very difficult, but an appreciation of the mega-trends is perfectly feasible. Today I will do what others won’t… so tomorrow I can do what others can’t said Elon Musk.

To have an idea of where the frontiers of Knowledge are headed one needs to look up the progress reports of leading research enterprises and think tanks. Following the awards and citations of Nobel Prizes in each of the 6 areas of Physics, Chemistry, Physiology or Medicine, Literature, Peace and Economics, the Field medal in Mathematics and the Turing Prize for Computing will give a good idea of where the frontiers of new knowledge in different domains are moving. The economic manifestations of the progress in human knowledge is often seen in reports of organisations such as the World Economic Forum, the World Bank, the OECD and various similar organisations.

The 2 main drivers of change in the education domain right now are the 4th Industrial Revolution to which attention was drawn at the World Economic Forum 2016 at Davos by it’s founder Prof Klaus Schwab, and the 4th Education Revolution which is the title of a recent book by Anthony Seldon. 

In its January 2020 meeting at Davos  it was estimated that about a billion people in the world have to be re-skilled‬.

A very recent report from McKinsey on managing in uncertainty. Here is the link : When nothing is normal: Managing in extreme uncertainty 

5: Technology ( especially Artificial Intelligence ) must be used to empower both the teacher and the learner. The goal has to be to promote individuation ( a term introduced by the Psychologist Carl Jung) as opposed to homogenisation, which is the averred goal of all National Education Policies. At a fundamental level, the common thread through much of current technology is Information which can provide answers to profound complex questions. What is the information content of the genome? The human brain? A black hole? The universe? Time and again, the concepts and laws of information reveal breathtaking insights into the workings of nature, even as they lay the foundation of astounding new technologies.

It is important that all educators are conversant and familiar with these technologies, and some are fluent with them. The adoption of technology in education should be spearheaded by educators, as suggested by Anthony Seldon in his recent book “ The fourth Education Revolution”. 

6: The origins of Artificial Intelligence lie in the Turing test. Seventy years after it was proposed, we should embrace its spirit and should be certifying the learning outcomes achieved by a learner irrespective of the learning path or trajectory  pursued. The management of such credentials could be as digital badges if they are not high stake or through Blockchains if they are more highly  valuable credentials. The issue of limited seats in any educational Institute thus becomes redundant. Ridiculous situations like needing to get 100% marks at School leaving level to get admission to Bachelor degree courses will become a thing of the past. One should be able to learn whatever one wants to the level that the person can attain. We could easily do away with IIT-JEE, NEET and such other barriers. 

7: Unlike what some may hasten to  infer, the role of teachers will not become less but more important. The teachers will in fact be central to the new learning ecosystem, and will be the key drivers of the next education revolution. The New Education Policy 2020 gives a big push to the practice  of Heutagogy and encouraging learners to become self-directed learners. The NEP 2020 at para 4.6 says: The key overall thrust of curriculum and pedagogy reform across all stages will be to move the education system towards real understanding and learning how to learn – and away from the culture of rote learning as is present today. The goal will be to create holistic and well-rounded individuals equipped with key 21st-century skills. All aspects of curriculum and pedagogy will be reoriented and revamped to attain these critical goals.

Teachers will be more important than ever before. The reason is that while an expert can demonstrate his or her expertise, a teacher can transform an ignorant person to an informed person, a knowledgeable person and eventually an expert. Like machines that help make other machines, a teacher is a lifelong learner who creates other lifelong learners. Learning anywhere will be the new norm. Learning at School or learning at home ( under lockdown) are actually special cases of learning anywhere. Similarly teachers will be able to teach from anywhere. An extension of anywhere learning would be everywhere learning. The mobile phone will be the access device for anytime everywhere learning. First you learn to use the mobile, then you use the mobile to learn. 

8: Since the Constitutional obligation of the state to provide right to education remains largely unimplemented, in these times of the pandemic it may be a good idea to go to the directive principles and invoke Article 51A(h) to the fundamental duty of the citizen “to develop the scientific temper, humanism and the spirit of inquiry and reform”, and it is the learning community referred to at point no.2 that will facilitate the implementation of this. At one level this refers us to the well known method of Socratic questioning, or the shastrartha or samvad in our own tradition. The reference to humanism becomes even more important in the coming age of Artificial Intelligence. Max Tegmark in Life 3.0 has drawn attention to this, as has Joseph E Aoun President of the NorthEastern University in his book “ Robot-proof education” where he used the word ‘humanics’ as an attribute for humans in analogy to robotics. But humanism suggests a larger scope. Developing the scientific temper involves an appreciation of the Quantum view of the world. As said in the beginning of this piece, mankind progressed substantially by not being afraid of but by understanding the realities. Once one appreciates wave-particle duality, it will be easier to accept the teacher-learner duality implicit in the lifelong learning model. All students while at School need to be introduced to the Quantum Magic, appreciate the key Quantum concepts and be ready to embrace  Quantum Computing and the emerging area of Quantum Biology. This is in alignment to the announcement of substantial allocations in this year’s budget to Quantum Technologies. 


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Resources for self-learning:

Resources for self-learning: 

1: Self-Directed Learning: A Four-Step Process

2: Some useful resources for an educator : Some useful resources for educators

3: Twenty steps towards more self-directed learning :

4: Becoming self-taught ( a how to guide):

5: Thirteen ways to become a better learner in 2020:

6: Learning how to learn by Barbara Oakland (17 minutes):

7: Google talk by Barbara Oakland (1hour 10 minutes):

8: Marty Lobdell : Study less, study smart (1 hour):

9: Independent studying with mind-maps :

10: Want to learn better: start mind-mapping:

11: Make It Stick By Peter C. Brown 

12: Ultralearning By Scott Young

13: Using Chatbots to become a better self-learner through conversational quizzes :

14: Lectures aren’t just boring, they’re ineffective too:

15: Why learning Science fails to make its way into practice :


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What is worth learning?

What is worth learning ?

What is worth learning actually changes over time and we have seen this in recent times when the once most coveted engineering and management qualifications seem to be completely unwonted. 

To appreciate this, it is interesting to imagine a food scarce society. In a food starved society the principle of survival would be to eat as much as you can whenever you get a chance to eat because you don’t know when your next meal is going to come. However in a food abundant society,  this principle will lead to obesity and consequential diseases. The same thing holds true about learning. 

When learning resources and opportunities are scarce and not easily available then whenever you get an opportunity to learn you must learn as much as you can because you don’t know when you’ll need it. But when learning resources are easily accessible, as is the situation today, a learner has to be discerning about what is important and valuable. Like one’s wealth portfolio is a carefully chosen mix of asset classes, an educated person’s knowledge portfolio is a suitable mix of a number of knowledge assets and skills. 

Please watch this video where I speak on this theme about 3 years back:

And read these articles on the same theme. 

I am sure that you would have your own thoughts and opinions on what is worth learning, especially with regard to children at School, the young in higher education and the grown ups who need to learn as well. 

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Attributes of a successful self-learner:

Attributes of a successful self-learner:

Since the adjective we are using for self-learners here is ‘successful’ an immediate point of reference should be Stephen R. Covey covered and his book, The 7 Habits Of Highly Effective People

The first three habits are about the transition  from dependence to independence  (i.e., self-mastery):

1 – Be proactive.

2 – Begin with the end in mind

3 – First things first

The next three habits are about interdependence(e.g., working with others):

4 – Think win-win

5 – Seek first to understand, then to be understood

The final habit is that of continuous improvement and adequate preparation

7 – Sharpen the Saw; Growth

Some of the biggest traps for an individual learner that prevents them from self directed learning are:

  • They wait for things to happen, someone to come and provide training, give them a project or assign a mentor
  • They believe it’s someone else’s responsibility to enable learning for them at their job 
  • Approach learning with the mindset of “only to get ahead”. Such people deal with constant anxiety on “how to catch up” and they never truly learn  
  • Lack confidence  to get out of their comfort zone. They develop their own wall of constraints in mind that holds them back 
  • Fear choices due to profusion of content. Such people get stuck at “where to start”
  • Self justifying excuses around lack of time to learn anything new by keeping too busy 

Many people wait for something to happen or someone to take care of them. But people who end up with the good jobs are the proactive ones who are solutions to problems, not problems themselves, who seize the initiative to do what is necessary, consistent with correct principles, to get the job done

These barriers created by the individual in their own mind leads to rational lies to self and a self-fulfilling prophecy around lack of learning in their current environment and work. 

It is not enough to learn, but as Alvin Toffler had said, one has to be able to learn, unlearn and re-learn, all of which become elements of successful self-learning. 

And this is a link to a blog from Brian Tracy, a great motivator and coach :

I have no special talents. I am only passionately curious. – Albert Einstein

I stay with a problem longer……

आचार्यात् पादमादत्ते पादं शिष्यः स्वमेधया ।

सब्रह्मचारिभ्यः पादं पादं कालक्रमेण च ॥

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Why self-learning?

Why self-learning?

Whenever we think of learning, we associate it with a classroom and a teacher at the head of the class, in what has often been called ‘the sage on the stage’ model. The ‘lecture’ which may of about 40 minutes at School, about an hour at University and sometimes of almost 90 minutes in professional courses is the primary activity. There maybe supplementary laboratory, tutorials, seminars, projects or study visits, but the ‘lecture’ is the primary mode. There are enough research studies alluding to the ineffectiveness and limitations of such lectures, and in particular that most learners “zone out” after the first 10 minutes of the lecture. Active learner engagement fares better in learning effectiveness, because learning is not a spectator sport.

Self-learning, described by Malcolm Knowles as a process in which individuals take the initiative without the help of others in diagnosing their learning needs, formulating goals, identifying human and material resources, and evaluating learning outcomes”. 

The way children learn is called pedagogy, the learning process for adults is called Andragogy and the learning approach of the self-directed learner is called Heutagogy. Heutagogy is the study of self-determined learning …

The world of self-learning can be a little daunting. However, if we want to achieve our aspirations and stay relevant in an ever-changing world, self-learning is critical to us in the 21st Century.

The New Education Policy 2020 gives a big push to the practice  of Heutagogy and encouraging learners to become self-directed learners. 

The NEP 2020 at para 4.6 says: The key overall thrust of curriculum and pedagogy reform across all stages will be to move the education system towards real understanding and learning how to learn – and away from the culture of rote learning as is present today. The goal will be to create holistic and well-rounded individuals equipped with key 21st-century skills. All aspects of curriculum and pedagogy will be reoriented and revamped to attain these critical goals.

It is not only the ineffectiveness of lectures, it seems that even the attempt to teach is a futile endeavour. The famous historian Edward Gibbons had said “But the power of instruction is seldom of much efficacy, except in those happy dispositions where it is almost superfluous.”I am not a historian and had seen this quoted by Richard Feynman in his famous “ Lectures in Physics”. The famous poet and Professor Robert Frost had said “I am not an educator….I am an awakener”. We need to re-awaken the inherent desire to learn that traditional education stifles.

Edward T Hall, the anthropologist said “The drive to learn is as strong than the sexual drive. It begins earlier and lasts longer”. Again I am not an anthropologist and this is quoted in “ Schools that learn” by Peter Senge. 

Here is a very good article on the importance of self-directed learning :

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