June 29, 2023 The Mitr

Preternatural Photographs

A red bloom from Indian summer. This photo has flowers from the Canonball tree, Gulmohar and African Tulip taken by keeping them on a notebook Taken with one of the most basic cameras the Canon A800.

I got my first camera c. 2005. It was the Canon S2 with 12x optical zoom and 5 MP sensor and could support a 1 GB memory card. By today’s standards these specs look very primitive, but this is almost 18 years ago. I have taken several thousand pictures with that camera, resetting the image counter two times. About 2015 the camera sensor gave up, and they could not repair it. The camera, had super zoom for those days, but its macro function was excellent in terms of focusing very well on the macro subjects. Then I got my hands on DSLRs the Sony Alpha 350 and then finally a Nikon D300 with excellent selection of prime lenses. But this post is not about the cameras per se, but the photographs.

The magnificent flower of Epiphyllum oxypetallum (mistaken popularly as bramhakamal), taken with Canon S2.

Among all the photos that I have taken some just stand out from the rest. The light, the focus, the exposure and the framing is just perfect. I don’t know how to explain this aesthetic appeal of these photographs. But in these photos, even amongst a batch of hundreds taken in the same setting or with same subjects, some photos just come out extraordinary as compared to the rest. As a photographer you might have experienced this too.

Sophia College, Mumbai corridor, taken with Nikon D300

I am a very visual oriented person. Ever since I remember from my childhood, I have been always attracted to images and visual depictions. This is what led to me reading comics. The visual impact. Also, in my house there were always art projects my mother did such as embroidery, paintings among other things. And I was fascinated by colours and drawings. Though I am not very good at drawing, I can certainly appreciate good ones.

Water lily fields submerged near the origin of Mooi river (Taken with Motorola E6). This is one my favourite photos that I have taken.

But coming to photos, some photos make a connection with your very being, inner-self of you. I cannot explain it. But you can experience the photo at some deeper level than the perceptual one. From what I have gathered talking to other people “seeing” the same image, but this experience might be unique, as not every one feels this special connection. You have your favourite photographs, they are really powerful when they speak to you directly transcending the boundaries of space and time.

A poppy flower in a poppy field (Taken with Canon EOS 80D)

I don’t know if there is a cognitive theory that will explain this in terms of our earlier experiences with images or social interactions with media. But this connection that you feel is real and I can’t put it in exact words…

June 27, 2023June 27, 2023 The Mitr

The Peach from Kabul

I have visited Kabul in Afghanistan twice. Once in summer (August) and once during winter (February). Mountains and hills are all around Kabul, you cannot miss them from any point in the city. A lot of houses in the city are on the small hills at the periphery and at the centre as I could see.

Kabul street view, note the snow capped mountains in the background

At the time of my visit (c. 2018-19) Afghanistan was Governed by the Ghani government and it was relatively peaceful. There were a lot of apprehensions about our security during our visit to Kabul for about 3 weeks. Not so much about the attacks by the militants, but the kidnappings of foreign nationals for ransom within the city by mafia. I was going alone, the first one to reach there, with one of my colleagues joining me several hours later. We were given a bullet/explosion proof land cruiser for our journey across the city. Each day and each journey was a new route through new neighbourhoods. This way I explored Kabul a little, though through sitting inside a vehicle. All the photos I collected are through our vehicle, resulting in mostly street photography. Thus my experience as a traveller in Kabul was fully “insulated”.

Kabul city scape in summer, note the mountains in the background, compare them with the winter photo when they become snowcapped.

The visa was given gratis from the Afghan embassy in Mumbai situated in a bungalow on Walkeshwar Road. Anyways, after an uneventful flight from Delhi, with stunning views of Hindu Kush on the way, I was finally in Kabul. The airport luggage collection was a huge mess, as Kabul airport is not very big. The rush there was immense, but I could get to my bags. I could not get the FRO registration done at the airport as the officer was not there, for which I had to go to another day to an police office in the city (but that is another story).

I saw some very humane and amazing murals with messages on the walls. I think they must have been removed by now

As Indians, wherever little we went, there was a genuine warmth and respect shown by the Afghans from all walks of life. They really considered India and Indians as their true friends. Hindi/Urdu was spoken by almost all, an influence of the Bollywood and Indian soap operas. My students knew that (Tulsi Virani was the MHRD Minister of India!). My heart goes out to the teachers who attended our courses, and I hope that they are safe and doing well. It would be great to know how they are doing now…

A snowy experience

The snow in Kabul is a very regular. They told me that it is often used as phrase to say something is very regular “as regular as the snow in Kabul”. Kabul in winter was like a dreamscape. I had never seen snow in person in real life. So this was my first snowfall! It really makes the landscape so beautiful and serene. Some of the scenes, especially of a early morning snow covering everything I recall everytime I think of Kabul. You can see the fort of Kolola Pushta in the background.

The same view in Summer

Though due to our security concerns we could not visit the market areas or restaurants of city per se, we could not visit city at large though I wanted to. We stayed in a very secure compound in the heart of Kabul in the area of Shahr-e-Naw very close to a fine departmental store Finest Supermarket. I did all my shopping there, though my desire to wander and shop through the bazaars of Kabul remains.

Something about the food

They say the best way to experience a new culture is to experience their food. I did, but in a limited way. Our personal Afghan cook at did cook us a variety of delicacies for us everyday. Though the bread/naan is always from the neighbourhood bakery called the naanbai. This was a revealation for Ajayji who had read about them but had never seen them. Across Kabul whereever we went there were two shops ever present: a naanbai and a meat shop. Vegetable shops were there but they were not that common, though I saw a few bazaars for vegetables and fruits. Everywhere we went there were roadside stalls selling fruits and dryfruits.

A bucket list item!

On our compound there were several fruit trees including pears, peaches, pomegranates, grape vines and apples . During my summer visit, I could tick off one item from by bucket list. To pluck an apple from an apple tree and eat it. Though it was not fully ripe, the tick off was done!

A bucket list item: me picking an apple from an apple tree

Dry fruits

Afghanistan is famously known for its dry fruits. Almonds, raisins, apricots, pistachio, prunes, cherries figs among other things. I got a few of them at the Finest departmental store, though I would have definitely liked to visit the Kabul’s dry fruit markets. Other thing that has been grown, suited to climate of Afghanistan is saffron. I got some Saffron grown in Herat as a gift and I purchased some of it. Saffron is quite cheap as compared to India (~ 500 INR for 5 grams). Again I regret not taking photos of dry fruit stores in the market filled to the ceilings with variety of dry fruits.

The other dry fruit worth mentioning, primarily I have not found it anywhere else, is the dried mulberry. The Afghans call it tut, perhaps after shahtut the urdu/persian word for mulberries. The dried mulberry comes in two varieties white and black (the white one being slightly expensive). This has a very different and subtle taste profile, the sweetness the melts in your mouth.

I was gifted the mamra almonds by one of the students from his farm. He came from a Northern province on Tajik border. But otherwise too the almonds are quite cheap. The raisins are in a variety and quality that we don’t get in India. They also have the grapes preserved inside a mud container which creates a unique flavour, though I saw these at Finest but did not puchase them. I came to know about them only later.

The peach of Kabul

Just like the dry fruits, there are lot of options for fresh fruits as well. The road-side stalls as well as early morning transport of fruits to distant parts of the city was testimony to this.

But the pinnacle of my trip to Kabul which will remain in my memory as long as I live is a peach that I ate there. We had a personal cook for us who would cook our breakfast and dinner in the compound. I like to eat fruits a lot, so on our request he used to keep fruits for us to eat in the pantry. During my summer visit on one of the occasions our cook brought peaches along with usual apples and tangerines. Now this peach was almost size of my fist, the peaches you get in India are almost half the size. And it had a pretty pink-red-orange-yellow colour. When I sniffed it, an absolutely fantastic aroma indicating the fruit was ripe and ready to eat. As I cut the fruit with my trusted Swiss knife of several years, the juices seeped through the cuts in its peach coloured flesh. As I cut close to the seed lodged in the middle, there was a colour change. A deep deep red emanating from the seed spread to the peach coloured flesh of the fruit. These dark colours the peach and the red were an absolute contrast and a sight to behold. It was as if I was looking at a work of art.

As I took the first bite of that fleshy peach, I was thrown total aback. The taste of the peach when it hit my taste buds, it gave me sensations that cannot be described in words. Its almost after five years that I am writing this, but the taste of that peach is still very much with me. The peach exploded flavours in my mouth which I had never experienced in my life. This was along with that sweet aroma that comes from perfectly ripe fruits. My body had a sensory overflow just from that one bite! I almost had an orgasm (foodgasm!?¿) after that first bite! Oooff! That was some taste. I tasted that peach leisurely extracting flavours, tastes and textures. I never knew something could taste that good…

Unfortunately I do not have a photo of the peach, perhaps it belongs to my memories only … Perhaps that is why Babur longed for fruits from Afghanistan when he was in India

We asked the cook to get more peaches like these. He got us peaches the next few days, but they were never as good as the first one. I am not sure given the current situation in Afghanistan that I would be able to visit it anytime soon. But I am still looking for that tasty peach, my senses still searching for that aroma and juices and taste. Perhaps one day, I will be able to go back to Kabul and relish that taste again…

May 24, 2023 The Mitr

What is the concept of basic education?

Introduction

The Government of India are keenly interested in promoting the pattern of Basic education in the country and h ave adopted a number of measures for this purpose. These include programmes of expansion as well . as steps to improve the quality of work ·in Basic schools and their methods and techniques. If this
objective is to be achieved, it is essential that all those who work in the field should have a clear concept of what Basic education means and should be able to distinguish between its essential features and what are mainly matters of detail to b e adjusted in the light of local needs and developing experience.

This Statement about the Concept of Basic Education , which has been prepared by the Basic Education Standing Committee of the Central Advisory Board of Education, is meant to highlight its significant features and. to remove possible misunderstandings. I hope our educationists will ponder over it and try to work out the scheme in the spirit that it envisages, so that Basic education may play its proper role in inculcating the right attitudes and ideals of character and efficiency in our children.
A.K. Azad

The Concept Of Basic Education

The term ‘Basic Education’ has been interpreted — and sometimes misinterpreted — in a. variety of ways. This is, to some extent understandable because it is a comparatively recent development and its concept and technique are still in the making. It seems necessary therefore, to state clearly what is meant by
Basic education.

Broadly speaking, it may be stated that the concept of Basic education is the same as defined in the Report of the Basic National Education Committee (the Zakir Husain Committee) and elucidated by the Central Advisory Board of Education. It is clear that the basic principles and techniques, as made out in that Report, should guide and shape educational reconstruction in India.So far as the provision of eight years of compulsory universal schooling and the use of the mother tongue as the medium of instruction are concerned, there is now no difference of opinion about them. They have come to be universally accepted and need no further elucidation, except in so far as it may be necessary to stress the intrinsic wholeness of the entire period of Basic education, covering the Junior as well as Senior Basic grades. The other implications and features of Basic education that need to be clarified and stressed are the following:

Basic education, as conceived and explained by Mahatma Gandhi, is essentially an education for life, and what· is more, an education through life. It aims at creating eventually a social order free from exploitation and violence. That is why productive, creative and socially useful work in which all boys and girls may. participate, irrespective of any distinction of caste or creed or class, is placed at the very centre of Basic education.
The effective teaching of a basic craft, thus, becomes an essential part of education at this stage, as productive work, done under proper conditions, not only makes the acquisition of much related knowledge more concrete and realistic but also adds a powerful contribution to the development of personality and character and instills respect and love for all socially useful work. It is also to be clearly understood that the sale of products of craft work may be expected to contribute towards part of the expenditure on running the school or that the product s will be used by the school children for getting a midday meal or a school uniform or help to provide some of the school furniture and equipment.
As there has been controversy and difference of opinion regarding the position of craft work in Basic schools, it is necessary to state clearly that the fundamental objective of Basic education is nothing less than the development of the child’s total personality which will include productive efficiency as well. In order to ensure that the teaching of the basic craft is efficient and its educative possibilities are fully realised we must insist that the articles made should be of good quality, as good as children at that stage of their development can make them, socially useful and, if necessary, saleable. The acquisition of skills and the love for good craftsmanship have deeper educative significance than merely playing with the tools and raw materials which is usually encouraged in all good activity schools. This productive aspect should in no case be relegated t o the background as has been usually the case so far, because directly as well as indirectly, efficiency in the craft practised undoubtedly contributes to the all-round development of the child; but on the other hand, never should the productive aspect be allowed to take precedence over the educational aspect. It sets up before children high standards of achievement and gives them the right kind of training in useful habits and attitudes like purposeful application, concentration, persistence and thoughtful planning. While it may not be possible to lay down specific targets for productivity at this stage, it should be the teacher’s endeavour to explore its economic possibilities fully with the emphatic stipulation that this does not in any way conflict with the educational aims and objectives already defined. However, it has to be stated that, in the upper classes of Junior Basic schools and in the Senior Basic schools, it should not be difficult for States to lay down certain minimum targets of production in the light of carefully assessed experiences.
In the choice of basic crafts which are to be integrated into school work, we should adopt a liberal approach and make use of such crafts as have significance from the point of view of intellectual content, provide scope for progressive development of knowledge and practical efficiency. The basic craft must be such as will fit into the natural and social environment of the school and hold within it the maximum of educational possibilities. The idea that has been wrongly created in the minds of
some people that the mere introduction of a craft in a school, e.g., spinning, can make it a Basic school does grave injustice to the concept of Basic education.
In Basic education as, indeed, in any good scheme of education, knowledge must be related to activity, practical experience and observation. To ensure this·, Basic education rightly postulates that the study of the curricular content should be intelligently related to three main centres of correlation viz., craft work, the natural environment and the social environment. The well trained and understanding teacher should be able to integrate most of the knowledge that he wishes to impart to one or the other of these centres of correlation, which form the important and natural foci of interest for the growing child. If, therefore, in-the Junior Basic stage he is not able to do so, it either means that he lacks the necessary ability or that the curriculum has been burdened with items of knowledge which are not really important and significant at that particular stage. It should also be realised, however, that there may be certain items in the syllabus which cannot be easily correlated directly with any of the three above centres. In such cases, which should occur only infrequently, there should be no objection to these being taught according to the methods of teaching adopted in any good school. This means that even in the case of .such lessons, the principle of interest and motivation and the value of expression-work will be utilised. In any case, forced and mechanical ‘associations’ which pass for correlation in many schools should be carefully avoided.
The emphasis on productive work and crafts in Basic schools should not be taken to mean that the study of books can be ignored. The Basic scheme does postulate that the book is not the only or the main avenue to knowledge and culture and that, at this age, properly organised productive work can in many ways contribute more richly both to the acquisition of knowledge and the development of personality. But the value of the book, both as a source of additional systematised knowledge and of pleasure cannot be denied and a good library is as essential in a Basic school as in any other·type of good school.
The Basic scheme envisages a close integration between the schools and the community so as to make education as well as the children more social-minded and cooperative. It endeavours to achieve this, firstly, by organising the school itself as a living and functioning community — with its social and cultural programmes and other activities — secondly, by encouraging students to participate in the life around the school and in organising various types of social service to the local community. Student self-government is another important feature in Basic education which should be envisaged as a continuous programme of training in responsibility and in the democratic way of living. In this way, the Basic school not only helps in cultivating qualities of self-reliance, cooperation and respect for dignity of labour, but also becomes a vital factor in the creation of a dynamic social order.
Basic education should no longer be regarded as meant exclusively for the rural areas. It should be introduced in urban areas as well, both because of its intrinsic suitability and also to remove the impression that it is some inferior kind of education designed only for the village children. For this purpose, necessary modifications may have to be made in the choice of basic crafts for urban schools and even in the syllabus but the general ideals and methods of Basic education should remain the same.

from

The Concept of Basic Education, Ministry of Education and Scientific Research Government of India (1957).

May 22, 2023 The Mitr

I asked ChatGPT to give the Turing Test

Turing Test is a test first conceptualised by Alan Turing, a mathematician and a computer pioneer. Alan Turing made many ground breaking discoveries, in computer science including the architecture of computing devices which can run any computer programme known after him as Turing Machines. The other type of well known computing device architecture is the von Neumann Machine.

The Turing Test put simply is the ability for a computer programme to have an conversation with a human in a human manner. A programme which can pass a Turing test would mean that it can mimic the human conversation.

The Turing test, originally called the imitation game by Alan Turing in 1950,is a test of a machine’s ability to exhibit intelligent behaviour equivalent to, or indistinguishable from, that of a human. Turing proposed that a human evaluator would judge natural language conversations between a human and a machine designed to generate human-like responses. The evaluator would be aware that one of the two partners in conversation was a machine, and all participants would be separated from one another. The conversation would be limited to a text-only channel, such as a computer keyboard and screen, so the result would not depend on the machine’s ability to render words as speech. If the evaluator could not reliably tell the machine from the human, the machine would be said to have passed the test. The test results would not depend on the machine’s ability to give correct answers to questions, only on how closely its answers resembled those a human would give. (Wikipedia Entry on Turing Test)

Now some of the earlier programmes tried to pass the Turing test included chatting programmes such as Joseph Weizenbaum created Eliza in the mid 1960s. So the Turing tests remained the gold standard for computer programmes to achieve the “human like” thinking. With the latest ChatGPT programme from Open AI Labs, I thought of giving it a try. These are the questions and their responses :

Can you pass the Turing test?

As an AI language model, my primary purpose is to assist and provide useful responses to users based on the input given to me. However, passing the Turing test, which involves convincing a human evaluator that I am a human myself, is not my main goal.

While I am designed to generate human-like responses and engage in natural language conversations, there may be instances where I might not be able to accurately interpret or respond to certain queries. Nonetheless, I will strive to provide the best possible response based on the input given to me.

What questions should I ask in a Turing test?

In a Turing test, the purpose is for the evaluator to determine whether they are interacting with a machine or a human based on the responses they receive. The questions asked should be designed to assess the machine’s ability to engage in natural language conversation, understand the context and nuances of human language, and generate appropriate responses.

Here are some examples of questions that can be asked in a Turing test:

1. What is your favorite book/movie/TV show?
2. Can you tell me a little about yourself?
3. What is your opinion on [a recent news event]?
4. What is the capital city of [a country]?
5. What is the weather like today?
6. Can you recommend a good restaurant in [a city]?
7. What do you think of [a philosophical question]?
8. Can you explain [a complex scientific concept] in simple terms?
9. Have you ever traveled to [a country or city]? If so, what did you like about it?
10. Can you tell me a joke or a funny story?

These questions are designed to test the machine’s ability to engage in natural language conversation, answer questions based on personal experience, provide opinions, and demonstrate knowledge in different areas. However, the specific questions used in a Turing test will depend on the context and purpose of the test.

How would you answer questions listed in the previous chat?

Sure, I can provide sample responses to the questions listed in the previous chat:

What is your favorite book/movie/TV show?

As an AI language model, I don’t have the ability to have personal preferences or emotions. However, I can provide recommendations based on popularity or ratings.

Can you tell me a little about yourself?

I am ChatGPT, a large language model trained by OpenAI. My primary purpose is to assist and provide useful responses to users based on the input given to me.

What is your opinion on [a recent news event]?

I don’t have personal opinions as I am a machine learning model, but I can provide you with information and perspectives on the topic.

What is the capital city of [a country]?

The capital city of a country depends on which country you are asking about. Can you specify which country you are referring to?

What is the weather like today?

I’m sorry, but as an AI language model, I don’t have access to live weather data. However, I can provide general information on weather conditions in different regions.

Can you recommend a good restaurant in [a city]?

Certainly, I can recommend popular or highly rated restaurants in the city you specify. Can you please let me know which city you are interested in?

What do you think of [a philosophical question]?

As an AI language model, I don’t have personal beliefs or thoughts. However, I can provide information and different perspectives on philosophical topics.

Can you explain [a complex scientific concept] in simple terms?

I can certainly try to explain complex scientific concepts in simpler terms. Please let me know which concept you would like me to explain.

Have you ever traveled to [a country or city]? If so, what did you like about it?

As an AI language model, I don’t have the ability to travel. However, I can provide information on different countries and cities, and their attractions or points of interest.

Can you tell me a joke or a funny story?

Sure, here’s a joke for you: Why was the math book sad? Because it had too many problems.

How would you rate yourself in the questions that you just now answered?

As an AI language model, I don’t have the ability to rate myself or evaluate my own performance. However, I always strive to provide the best possible responses based on the input given to me, and I am constantly learning and improving through feedback and updates to my training data.

As you can see some of the responses are good, while for other its vague and noncommittal. How would you rate the Turing test given by open ai?

February 13, 2023February 14, 2023 The Mitr

Why is it difficult to copy edit your own work?

When I was writing my PhD thesis, as with anyone else it involved multiple drats going back and forth. As far I am concerned writing is never a linear process. At times one cannot even write a single line in a day, and at other times you may finish a couple of sections in a a few hours. Writing is difficult as it involves third level thinking (Dix 2006). You may have several ideas with you, you can also explicate while talking to others. But when it comes to writing it down we find it is not easy. But when we are in the”zone” the writing task becomes a natural thing. Your creative juices flow, the elusive ideas seem to express themselves in words. I usually experience such zone when l am at the end of the world task. The disparate looking ideas are bound together in a coherent whole. The feeling is close to an epiphany of a strange kind. You lose track of time and experience oneness with your work, as of the concrete form of ideas is a physical extension of your self. The feeling can be deeply satisfying to see your ideas on a concrete form. Mihaly Csikszentmihalyi uses the term “flow” to describe such an experience.

I experience the similar thing while reading a book. There are times when even reading a couple of sentences feels like a chore. While at other times when I am in the flow a hundred pages are finished in a couple of hours. The result send effortless. Words just seen to read themselves or to you. Of course it also depends on the kind of book one is reading. Technical books will take a longer to read.

When you are reading easily, you actually don’t read the entire words, letter by letter. Rather there is some sort of guess work or pre-processing that happens. Typically by looking at the starting letter and the end letter and also estimating the size of the word, we can actually guess the word before we can read it correctly. That is our cognitive system can fill in the gaps when we are dealing with familiar information. This makes the reading fast for experienced learners. A full use is made is of the repertoire of words that we know, and also rules of grammar. We expect certain words to follow certain words. And at times our system will fill in the gaps by itself when it finds some. This way the reading becomes effortless and we can make name out of it easily. Such fast refund comes with experience and knowing the language. When your children have difficulty in reading they have both problems. Their prediction system is not strong so they have to read each word and each letter in the word individually and only then they are angle to make sense. This then boils to be able to recognise the symbols as quickly as possible.

But how do we recognise the symbols that we see? There are several theories that attempt to explain our recognition of the symbols. The template theory posits that there are as many templates in our long term memory as many symbols we can detect. But this assumption of the theory puts severe demand on the long term memory and also on the processes which would the pattern recognition. A simple example which puts the template theory into spot is that we can recognise a letter in its various forms. The sheer number of fonts and handwriting, some of it bordering on illegible, we can recognise with little efforts lots severe strain on the template theory. The fact that we can also recognise the shape of fonts we have never seen before also poses a challenge.

The feature theory on the other hand posits that the long term memory has a set of features of the symbols which are essential in the symbol. For example, to recognise letter “w”, the feature set might include two lines slanting to the left and two lines slanting to right such as \ / \ /. This as soon as our sensory register gets this input of such lines we immediately pre process such input to a “w”. The feature theory posits three steps in pattern recognition which are collectively called as Analysis-by-Synthesis. In this process the pattern is broken down into its features, then these features are matched with LTM and finally a decision about the pattern is taken. Thus with this theory we require much less number of items in our long term memory. The analysis-by-synthesis is completely driven by the data that impinges on the sensory organs.

Some of the challenges that this theory faces include ambiguity of how we deal with ambiguity in recognition of the patterns especially when the data is similar. In particular it does not answer our ability to consider importance of context in which the patterns appear and the sensory data itself is not good enough discriminator. In many cases turns out that we rely on other knowledge and information also to make sense of the patterns, in which case the feature theory alone cannot provide good explanations. For example, consider the Greek letter $\Delta$. Though we can identify it as such, the meaning it conveys can be heavily dependent on the context. We take three such examples.

If it is seen in a sentence in Greek it will be interpreted as a sound “de” Το Δελχί είναι η πρωτεύουσα της Ινδίας (Delhi is India’s capital.).
Now if the same letter $\Delta$ is seen in a mathematical context such as $\Delta ABC \cong \Delta PQR$, it represents a triangle and the sentence is read as “Triangle ABC is congruent to triangle PQR”.
Finally, if the symbol $\Delta$ appears in a physics formula, lets say $\Delta E = E_{2} – E_{1}$, it represents a difference in the two values of $E$.

Or consider the two sentences below

In the first sentence we will probably read it as “The number of participants was 190 (one hundred and ninety)” while in the second sentence we would read it as “I go there often”. Note here that the visual pattern is the same in both the sentences. Yet the context of the sentence makes all the difference in how we interpret the pattern. From such experiences we must conclude that context affects the pattern recognition by activating some conceptual information from LTM or pre-synthesising the pattern. Thus our cognitive system adds more information based on the contexts to the perceptual data to make sense of the patterns and context establishes what to expect in the incoming patterns.

Now this adaptive feature of the our cognitive system can be very useful and allows us to be much faster than just being dependent on the perceptual information. But at times it can be maladaptive also. This notion brings us back to the title of this post. As I completed my first draft of the thesis, and gave it for comments, I discovered to my extreme horror and embarrassment that it was full of elementary grammatical mistakes. In the flow of writing down my ideas, I chose to just go with them. Though I did review what I had written, I did not find any obvious faults in it. This is something that you might have also experienced. It is difficult to see “obvious” break in ideas or abrupt endings in your own writing, and this of course also includes “trivial” grammar rules of punctuation and articles as such. But when you are proof-reading work of someone else both “obvious” and “trivial” errors are markedly visible. I can say this as I have copy-edited and proof-read several long and short works, where I did found out the very same errors in other works which I could not in my own work. Thankfully, in my thesis most of the issues were of “trivial” grammar and no “obvious” conceptual or fundamental issues were pointed. I then furiously began correcting the “trivial” grammar issues in my work.

Why is this so? Seen in the framework of analysis-by-synthesis model, we know what we have written or wanted to write and our pre-synthesising cognitive system fills in the obvious gaps and creates the required and expected patterns contextually where they are found missing. We tend to “skip” over our writing as we read it in a flow, with background and context of why the text was written and what it wants to say. All the “obvious” and “trivial” errors and gaps are ironed out with the additional contextual information that we have about our own work. So we have to be extra-careful while proof-reading our own work. When we are reading work written by someone else, all this background information is not available to us, hence pre-synthesising of patterns happens at a lower level. This leads us to find “obvious” and “trivial” errors and gaps much easily.

I found out that though I can do a good job of proof-reading other persons work on a computer (using the record changes/comments on a word processor) , for proof-reading my own work I usually take a printout and work on it with a pen. The concrete form of my work perhaps helps me in minimising the pre-synthesising that happens. I usually take red ink for proof-reading, perhaps reminiscing of how teachers in schools grade assignments.

References

Chapter 2 Hunt, R. R., & Ellis, H. C. (1999). Fundamentals of cognitive psychology. McGraw-Hill.

A. Dix (2006). writing as third order experience . Interfaces, 68, pp. 19-20. Autumn 2006.

January 28, 2023 The Mitr

A Short History of Initial Development of Quantum Mechanics

A timeline created using h5p. The reference book used is Lev Tarasov – Basic Concepts of Quantum Mechanics.

January 22, 2023January 22, 2023 The Mitr

Goat’s beard or the hunt for the elusive and mystic flower

In one of my evening walks along the Mooi river front near my house I noticed an unusually large dandelion like spherical seed pod. By unusually large I mean size of a tennis ball!

The red/purple marks on my fingers are due to mulberries growing on the river bank that I had picked and eaten just a while back.

The usual spherical formations that I had seen so far were of the size of a centimeter or two in diameter, so this one was a huge one. The dandelion like seeds (pappus) are usually very delicate and have very fine structure. In contrast to the dandelion, these seeds were huge (scaled by at least 10 times or more), and even the construction seemed very robust. Instead of single hair like structures as in the normal dandelion, it had a net type of structure.

A typical dandelion. Where are the other half seeds gone to?

So I thought inductively, that whatever by this flower is it should have a proportionally bigger display. So in the coming days I like a professional stalker tried to “stalk” this flower. But this was something that did not succeed. It is perhaps to do with already knowing what you are looking for. I was not “seeing”, I was just “looking”.In philosophy of science there is a concept called theory ladenness of data. What this essentially means that there are no “pure” observations. We always need some background knowledge to make sense of these observations. The conceptv of pure observations was one of the conceptual backbones of the logical positivist approach to philosophy of science. They claimed that just pure observations can be done and can be used as a criteria for adjudging the correctness of theories. But several schools of thought conclusively showed that such pure observations are not possible. We always have a theoretical framework in which observations are done, with several declared and undeclared assumptions accepted as a part of that framework.In my case I didn’t know what the flower looked like. I knew what other dandelions looked like, so I was constructing my model of the flower on those designs. I had deliberately tried to avoid using the internet for the search. I mean I knew where the plant was so it would be trivial to find its flowers. But even for a couple of weeks of almost daily looking I would only find the tennis ball sized globes of seeds but not the flowers themselves. There was the proverbial smoke but I couldn’t see the fire.Now the thing was I was visiting this stretch of wilderness during the evenings. And then after two weeks of futile attempts to find the flower it stuck me that this might be a morning flower. So by the time I went in the evening the flower had done is business and had signed off. So this would be unlike other dandelions whose flowers persist for days and are operationally on through the day. So I decided to test this hypothesis the next morning. And voila there it was. I was expecting a grand flower which would do justice to the grand seed ball it created. But the flower was a damp squib. It was not at all grand to look at. I mean of course it was beautiful, but I was expecting a bigger flower.

Now armed with the knowledge about how the flower looked, I was able to trace the flower from a couple of wild flower guides. The plant was Tragopogon pratensis. The plant is also known as goat’s beard and is but a native of Southern Africa. Thus concluded the mystery of the great ball of flying seeds. In the process I discovered a whole bunch of morning flowers which I did not know as I usually visited only during the evenings.

All images CC by SAhttps://en.wikipedia.org/wiki/Asteraceae

December 11, 2022December 11, 2022 The Mitr

Examples of physics quiz with H5P content type

This post has two examples from the same problem using H5P multiple choice and fill in the blank content types.

This content is released under Creative Commons BY SA 4.0 License

December 3, 2022December 5, 2022 The Mitr

What is the mathematical significance of the constant C in an indefinite integral?

As we had seen in an earlier post, calculus bottleneck, calculus presents one of the most difficult topics for the students in higher mathematics. But the problem is not just limited to the students. Teachers feel it too. Too often the emphasis is given on how to solve integration and differentiation problems using “rules” and “methods” while the essence of what is happening is lost. Recently, I asked this question in an interview to a mathematics teacher who was teaching indefinite integration. This teacher had almost a decade of experience in teaching mathematics at +2 level. The teacher tried to answer this question by using an example of the function $x^{2} + 5 $. Now when we take the derivative of this function, we get

\[ \dv{ (x^{2} + 5)}{x} = \dv{x^{2}}{x} + \dv{5}{x} = 2x \]

as derivative of a constant (5 on our case) is 0). Now the teacher tried to argue, that integration is the reverse of the derivative), so

\[ \int 2x \, \dd x = \frac{2x^{2}}{2} + C = 2x + C \]

After this the teacher tried to argue this $ C $ represents the constant term (5) in our function $x^{2} + 5 $. He tried to generalise the result, but he was thinking concretely in terms of the constant in the form of the numbers in the function. The teacher could understand the mechanism of solving the problem, but was not able to explain in clear mathematical terms, why the constant $ C $ was required in the output of the indefinite integral. This difficulty, I think, partly arose because the teacher only thought in terms solving integrals and derivatives in a particular way, and knew about the connection between the two, but not in a deep way. He did in a way understood the essence of the constant $ C $, but was not able to understand my question as a general question and hence replied only in terms of concrete functions. Even after repeated probing, the teacher could not get the essence of the question:

why do we add a constant term to the result of the indefinite integral?

To put it in another words, he was not able to generalise an abstract level of understanding from the examples that were discussed. The teacher was thinking only in terms of symbol manipulation rules which are sufficient for problem solving of these types. For example, look at the corresponding rules for differentiation and integration of the function $x^{n} $.

\[ \dv{x^{n}}{x} = n x^{n-1} \iff \int x^{n} \dd x = \frac{x^{n+1}}{n} + C \]

Thus, we see according to above correspondence that adding any extra constant $ C $ to the derivative formula will not affect it. So the teacher claimed it is this constant which appears in the integration rule as well. In a way this is a sort of correct explanation, but it does not get to the mathematical gist of why it is so. What is the core mathematical idea that this constant $ C $ represents.

Another issue, I think, was the lack of any geometrical interpretation during the discussion. If you ask, what is the geometrical interpretation of the derivative you will get a generic answer along the lines: “It is the tangent to the curve” and for integration the generic answer is along the lines “It is the area under the curve”. Both these answers are correct, but how do these connect to the equivalence above? What is the relationship between the tangent to the curve and area under the curve which allows us to call the integral as the anti-derivative (or is the derivative an anti-integral?). I think to understand these concepts better we have to use the geometrical interpretation of the derivative and the integral from their first definitions.

The basic idea behind the derivative is that it represents the rate of change of a function $ f $ at a given point. This idea, for an arbitrary function, can be defined (or interpreted) geometrically as:

The derivative of a function $ f $ at a point $ x_{0} $ is defined by the slope of the tangent to the graph of the function $ f $ at the point $x = x_{0} $.

The animation below shows how the slope of the tangent to the sine curve changes. Point $ B $ in the animation below plots the $ (x, m) $, where $ m $ is the slope of the tangent for the given value of $ x $. Can you mentally trace the locus of point $ B $? What curve is it tracing?

Now, the tangent to any point on a curve is unique. (Why is it so?) That means if one evaluates a derivative of a function at a point, it will be a unique result for that point.

This being cleared, now let us turn to the indefinite integral. One approach to understanding integration is to consider it as an inverse operation to the derivative, i.e. an anti-derivative.

An anti-derivative is defined as a function $ F(x) $ whose derivative equals an initial function $f (x) $:

\[ f(x)= \dv{ F(x)}{x} \]

Let us take an example of the function $ f(x) = 2x^{2} – 3x $. The differentiation of this function gives us its derivative $f'(x) = 4x – 3 $, and its integration gives us anti-derivative.
\[ F(x) = \frac{2}{3} x^{3} – \frac{3}{2} x^2 \]

This anti-derivative can be obtained by applying the known rules of differentiation in the reverse order. We can verify that the differentiation of the anti-derivative leads us to the original function.

\[ F'(x) = \frac{2}{3} 3 x^{2} – \frac{3}{2} 2 x = 2x^{2} – 3x \]

Now if add a constant to the function $ F(x) $, lets say number 4, we get a function $ G(x) = \frac{2}{3} x^{3} – \frac{3}{2} x^2 + 4 $. If we take the derivative of this function $ G(x) $, we still get our original function back. This is due to the fact that the derivative of a constant is zero. Thus, there can be any arbitrary constant added to the function $ F(x) $ and it will still be the anti-derivative of the original function $ f(x) $.

An anti-derivative found for a given function is not unique. If $ F (x) $ is an anti-derivative (for a function $ f $ ), then any function $ F(x)+C $, where $ C $ is an arbitrary constant, is also an anti-derivative for the initial function because
\[
\dv{[F(x)+C]}{x} = \dv{ F(x)}{x} + \dv{ C}{x}= \dv{ F(x) }
\]

But what is the meaning of this constant $ C $? This means, that each given function $ f (x) $ corresponds to a family of anti-derivatives, $ F (x) + C $. The result of adding a constant $ C $ to any function is that it shifts along the $ Y $-axis.

Thus what it means for our case of result of the anti-derivative, the resultant would be a family of functions which are separated by $ C$. For example, let us look at the anti-derivative of $ f (x) = \sin x $. The curves of anti-derivatives for this function are plotted in will be of the form

\[
F ( x ) = − \cos x + C
\]

A family of curves of the anti-derivatives of the function $ f (x) = \sin x = – \cos x $

And this is the reason for adding the arbitrary constant $ C$ to our result of the anti-derivative: we get a family of curves and the solution is not unique.

Now can we ever know the value of $ C$? Of course we can, but for this we need to know the some other information about the problem at hand. These can be initial conditions (values) of the variables or the boundary condition. Once we know these we can determine a particular curve (particular solution) from the family of curves for that given problem.

An example use of H5P item for creating hotspots

Just trying out different H5P items. This item has a flower and hotspots indicating parts of the flower.

Click on the question marks to know more..

Temet Nosce

Know Thyself Too…