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:

  1. 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.
  1. 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.
  1. 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.
  1. 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?
  1. 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.
  1. 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?
  1. 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.
  1. 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.
  1. 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.
  1. 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?
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.

 

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?

The giant dandelion!

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

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.

Further Reading

Lev Tarasov – Calculus – Basic Concepts For High Schools (Starts with and explains  the basic mathematical concepts required to understand calculus. The book is in the form of a dialogue between the author and the student, where doubts, misconceptions and aha moments are discussed.)

Morris Kline – Calculus – A physical and intuitive approach (Builds the concepts in the context of the physical problems that calculus was invented to solve.  A book every physics student should read to get an understanding of how mathematics helps solve physical problems.)

Richard  Courant and Fritz John – Introduction to Calculus Analysis (In 2 Volumes) (Standard college level text with in-depth discussions. First volume is rigorous with basic concepts required to conceptually understand the topics and their applications/implications.)

Quote The Mitr

What is mass renormalization?

A simple explanation of mass renormalization:

The difficulties associated with an infinite rest mass can be successfully overcome in calculation of various effects with the help of mass renormalization which essentially consists in the following. Suppose that it is required to calculate a certain effect and an infinite rest mass appears in the calculations. The quantity obtained as a result of calculations is infinite and is consequently devoid of any physical meaning. In order to obtain a physically reasonable result, another calculation’ is carried out, in which all factors, except those associated with the phenomenon under consideration, are present. This calculation also includes an infinite rest mass and leads to an infinite result. Subtraction of the second infinite result from the first leads to the cancellation of infinite quantities associated with the rest mass. The remaining quantity is finite and characterizes the phenomenon being considered. Thus, we can get rid of the infinite rest mass and obtain physically reasonable results which are confirmed by experiment. Such a method is used, for example, to calculate the energy of an electric field.

– A. N. Matveev, Electricity and Magnetism, p. 16

The Mitr

Emphasis

emphasis | ˈɛmfəsɪs | noun (plural emphases | ˈɛmfəsiːz | ) [mass noun]

1 special importance, value, or prominence given to something: they placed great emphasis on the individual’s freedom | [count noun] : different emphases and viewpoints

2 stress given to a word or words when speaking to indicate particular importance: inflection and emphasis can change the meaning of what is said

• vigour or intensity of expression: he spoke with emphasis and with complete conviction

Emphasis on something means that we want to highlight it from the rest. A common way to do this in text is to italicize or give a boldface or even underline the text. At times colour is added to text to highlight it or colour is added to the background of the text. All these elements of typography work when there is a common background against which these elements standout. Hence emphasise the words as required. But,

If everything is emphasised, the un-emphasised becomes emphasised.

But consider a block of text which is completely emphasised.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Thus we see that the appeal of the emphasis is lost! The only way emphasis will work is to create a background against which it stands out. Let us return to our examples above

 

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

 

For me, personally I have not used underline or the highlight. And recently have shifted to coloured italics as my choice of emphasis.

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

Sometimes this produces very pretty results (at least I am very happy about them 🙂

(ETBB font with OrangeRed  (#FF4500) italics )

In some cases boldface colour also gives very good results:

Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next.

 

Further reading:

Elements of Typographic Style by Robert Bringhurst

The Mitr

Escher on Escher

Recently (read some years back) I read Escher on Escher – Exploring the Infinite. This book gives an insight on how Escher viewed himself and his work. How were his social relations with his family, friends and admirers. Fame and appreciation of his work by a wide circle of people came late to Escher, when he was past his 50s. Escher was a perfectionist, he had almost perfected his craft of making woodcuts, taking it to its limits
as far as his hands and eyes could take. But that was the mere mechanical part of his work, the real part was the idea of the graphic print. The ideas it seems struggled a lot in his mind, making the print itself was the easier part. The ideas came to him, but later he strived for something entirely new, and succeeded.

On of the part of the book “Lectures That Were Never Given” has notes from the talks that Escher was supposed to give in the US of Amerika, but could not because of health reasons. Other include translations of his articles that appear in many of the art magazines and journals. These articles tell us how Escher looked at the work he was doing, and his feelings about other artists works. But he was the most critical about his own work.

This is what he had to say about the ancient cave-painters:

# 12
But his will and his capacity to produce pictorial images were at the least just as strong as ours. Perhaps even stronger because he was in direct contact with nature, which we usually approach by the way of a cultural and educational system that, if not barring the was, certainly obstructs it for us.
# 13
Illustrations are consequently for the graphic artists (mostly) an indispensable link in the chain of activities, but never his goal. That is probably the reason why a graphic artists cannot suppress a feeling of dissatisfaction when presented with an illustration as end result. You see, I don’t give reasons, only statements.
# 15
The above-mentioned elements of repetition and multiplication is /not/ in conflict with this. On the contrary, order is repetition of units; chaos is multiplicity without rhythm.

Escher also talks about the influence Bach’s music had on his work. He says after hearing Bach’s Goldberg variation in a concert (this is from the acceptance address for an award which he gave to city of Hilversum):

# 20
That was to Bach to whom I have pledged my heart and my intellect at the same time. Such beauty, of composition as well as of execution, cannot be possibly expressed in words.

Maybe same is also true of Escher’s own work. And the inspiration that he got from Bach was at a deep level, maybe if Bach was a contemporary, Escher wouldn’t have felt that lonely in his life. He says:

# 20
Bach’s music may perhaps provide the occasion to say a few words about my work. I had better not expound on the affinity I seem to have discovered between the canon in polyphonic music and the regular division of a plane into figures with identical forms, no matter how striking it is to me that the Baroque composers have performed manipulations with sounds similar to the ones I love to do with visual images.

Allow me to say only that Father Bach has been a strong inspiration to me, and that many a print reached definite form in my mind while I was listening to lucid, logical language he speaks, while I was drinking the clear wine he pours.

And this is what he has to say about his own work:

# 21
I can’t keep fooling around with our irrefutable uncertainties. It is, for example. a pleasure knowingly to mix up two- and three-dimensionalities, flat and spatial, and to make fun of gravity. Are you really sure that a floor can’t also be a ceiling? Are you definitely convinced that you will be on a higher plane when you walk up a staircase? Is it a fact as far as you are concerned that half an egg isn’t also half an empty shell?
Such apparently silly questions I pose first to myself (because I am my own first observer), and then to others who are kind enough to come and observe my work. It is satisfying to note that quite a few people enjoy this kind of playfulness, and that they aren’t afraid to modify their thinking about rock-solid realities.

And about art itself and the feelings that it manifests in us he says:

# 21
To tell you the truth, I find the concept of “art” a bit of dilemma. What one person calls “art” is often not “art” for another. “Beautiful” and “ugly” are old-fashioned concepts that are only rarely brought into the picture nowadays – maybe rightfully so, who is to say? Something repellant, something that gives you a moral hangover, something that hurts your eyes and ear can still be art!

And he says about himself:

# 21
So I am a graphic artist with heart and soul, but the rating “artist” makes me a feel a little embarrassed.

Next in the book are the “Lectures That Were Never Given”. These are the notes accompanying the slides, the text tells us about the technique and thought and thinking about the work. Escher has interesting way of putting thoughts about his work and the creatures it contains. He suggests to us that the creatures have ideas and behavior of their own.

# 30
On Horsemen and Symmetry Work 67 (glide reflection) The left horsemen, as a creature, was exceptionally obliging and willing. It happens rarely that my subjects so meekly allow themselves to be portrayed in detail.

# 31
While drawing, I feel as if I were a spiritualistic medium, controlled by creatures that I am conjuring up, and it is as if they themselves decide on the shape in which they like to appear.

And the regular division of the plane is a theme which he calls “unusual mania” and its origins.

# 30
I often have wondered at this, for an artist, unusual mania of mine to design periodic drawings. Over the years I made about a hundred fifty of them. In the beginning, that was some forty years ago, I puzzled quite instinctively, apparently without any well-defined purpose. I was simply driven by the irresistible pleasure I felt in repeating the same figures on a piece of paper. I had not yet seen the tile decorations in Al-hambara and never heard of crystallography; so I did not even know that my game was based on rules that have been
scientifically investigated.

And on interpretations of his work, in which people find what they want, religious, spiritualistic and philosophical messages he says this:

# 47 (Reptiles)
I never had any moralizing or symbolizing intention with this print, but some years later one of learned customers told me that it is a striking illustration of the doctrine of reincarnation. So it appears that one can even be symbolizing without knowing it.

And on the self-portraits that he has something to say to us regarding ourselves, ( involving a bit of narcissism, I think) :

# 60 (Hand with Reflecting Sphere, Three Spheres II)
Your own head, or more exactly the point between your eyes, is the center. No matter how you turn or twist yourself, you can’t get out of that central point. You are immovably the focus of your world.

# 61 (Eye)
I choose the features of Good Man Bones, with whom we are all confronted whether we like it or not.

And on Print Gallery, (one of my personal favourites) he says:

# 67 (Print Gallery)
Thus having let our eyes rove in a circular tour around the blank center, we come to the logical conclusion that the young man himself also must be part of print he is looking at. He actually sees himself as a detail of the picture; reality and image are one and the same.

This is something that I can relate to. The life we observe is ultimately the print and we are actually observing ourselves in life as in young man in the Print Gallery. And on perspectives and absurdities of logical opposites he says:

# 73 (Another World)
It may seem absurd to unite nadir, horizon and zenith in one construction, and yet if forms a logical whole.

In form and function the idea of logical opposites forms, much of the basis for Escher’s work. Visit to Al-hambara had a special significance for Escher. Here he found that the Moorish artists had explored the regular division of
the plane, but he lamented that they restricted themselves to abstract geometric forms and not to the anything that is present in nature which he himself felt an urge for.

# 83
After that first Spanish trip in 1922, I became more and more intrigued by the fitting together of congruent figures according to the above-mentioned definition and by the effort to shape this figures in such a way that they would evoke in the observer an association with an object or a living form of nature. (emphasis in original)

# 88
With regard to my present work, this proves to what extent I feel liberated from the graphic arts simply for the sake of graphic arts.

About the graphic artist with which he identified:

# 90
The graphic artist, however, is like a blackbird that sings in the treetop. Again and again he repeats the song, complete in every copy he makes. The more copies people ask him to make, the better he likes it. He hopes the wind will spread his leaves over the Earth, the farther the better – not like the dry leaves in autumn but like feather-light seeds capable of germinating.

And I think Escher has attained this goal which he describes above very well. His works have germinated into new ideas to a new era of graphic artists and others. And on the old techniques of graphic art:

# 90
Consequently, the emphasis falls unjustifiably on process, and one hardly takes into account the actual goal of all that drudgery. No matter how much joy the exercise of a noble craft can bestow, let us not forget that it is a means of repeating and multiplying. Repetition and multiplication – two simple words. The entire world perceivable with the senses will fall apart into meaningless chaos if we could not cling to these two concepts.

On him being called an “expert.”

# 92
A feeling of helplessness comes over me now that I am faced with describing what is meant by this designation. To my unending amazement, however, this is apparently so unusual and in a sense so new that I am unable to identify any “expert” in addition to myself who is sufficiently comfortable with it to give a written explanation.

 

# 93
By doing this they have opened the gate that gives access to a vast domain, but they themselves have not entered. Their nature is such that they are more interested in the way the gate is opened than in the garden that lies behind it. Sometimes I think I have covered the entire domain and trod all the paths and admired all the views. Then all of a sudden I find another new way, and I taste a new delight.

On his explorations of the plane and its drawings

Because what fascinates me, and what I experience as beauty, is apparently considered dull and dry by others. A plane which one must imagine as extending without boundaries in all directions, can be filled or divided into infinity, according to a limited number of systems, with similar geometric figures that are contiguous on all sides without leaving “empty spaces.”

We don’t to master everything required to construct something in order to appreaciate it.

# 94
Just as I do not consider it necessary to know all the tricks of the graphic trade in order to appreciate prints, neither do I believe that one must master in detail the theoretical fundaments of division of planes in order to learn to value this and to accept that it can exert an inspiring influence, as I have experienced.

On the unending nature of many of creations.

# 95
I see it as a means of representing timelessness, the dimensionlessness, that existed before life commenced and that will return when life again ceases.

On the dynamic nature of his drawings and comparison to film and reading of a book.

# 98
The series of static representations achieved a dynamic character due to the time span that was needed to follow the whole story. In contrast to this cinematographically projected images of a film which appear one in the after the other on an immovable place, onto which viewer’s eye remains directed without moving. In the case of both the medieval story in images and the developing pattern of a regular filling of a plane, the images are located next to each other, and timing becomes a factor in the movements made by viewer’s eye as it follows the story from image to image. In this way, holding a strip of film in hand, one observes it image by image, reading a book is also done more or less in the same manner.

 

# 99
Is it possible to make a representation of recognizable figures that has no background? To see only a “figure” is not conceivable because something that manifests itself as a figure, that is, as “thing to be seen,” is limited, whether it is real or not. A limitation also means a separation with regard to something else. That “something else” is the background from which the figure (or object sensation) frees itself.

 

# 100

Imagination and inventiveness, not to mention tenacity, are indispensable for this work. They come to us from “somewhere out there” but we can facilitate their path to us and encourage and
cultivate them in various ways. Among others I found one in writings of Leonardo da Vinchi. This is
the fragment, translated as best I can:

“When you have to represent an image, observe some walls that are besmeared with stains or composed of stones of varying substances. You can discover in them resemblances to a variety of mountainous landscapes, rivers, rocks, trees, vast plains and hills. You can also seen in them battles and human figures, strange facial features and items of clothing, and an infinite number of other things whose forms you can straighten out and improve. It is the same with crumbling walls as it is with the sound of church bells, in which you can discover every name and every word you want.”

Despite all this conscious and personal effort the illustrator still gets the feeling that some kind of magic action is taking place as he moves his lead pencil over the paper. It seems as if it isn’t he who determines the shapes but rather that the simple, flat stain is guiding or impeding the movements of the hand that draws, as if the illustrator were a spiritualistic medium. In fact, he is amazed, not to say taken aback, at what he sees appearing under his hand, and he experiences with regard to his creations a humble feeling of gratitude or of resignation depending on whether they behave willingly or reluctantly.