On GIKI

Nestled on two sides by the busy topi bazaar and the Tarbela colony, at the front of the shallow mountains reflecting the greenness of the dense jungle, and facing the might of the Indus passing through the great Tarbela Dam, there stands erected the Landmark of Ghulam Ishaq Khan, the milky white and pencil-slim clock tower. Beside it are the dry fountains forever at the mercy of rain.

Four faculties sit on the wings of the butterfly and face a wide circular road. At the heart of this road rises the squat dome embellished with pure white, the Agha Hassan Auditorium with its red seats and curtains facing the red proscenium. Hidden beneath it is the GIKafé that works behind the dark glass walls facing a grassy lawn and the broken wooden benches.

Ahead towards the mouth of the butterfly rise the long stairs and white pillars of a two-storey square building. Crowded during exams and graveyard at other times, Central Library, with its large purple carpet, grey sofas and small study rooms, sits quiet and greets the air of the jungle's tall trees. In the evening, the jungle first draws a red carpet on the blue sky, and then with passing time they replace the evening sun with a curtain of darkness, and remove the same for the morning sunrise. The humblest of all buildings is the Academic Block with its floors and stairs slippery with marble, facing the benches made of brown bricks that change color with every rain. Student Mosque echoes mild and reverberate Aazaan. The massive black gate surrounded by guards chattering in Pakhto and students signing their names to move in and out at odd times.

Wooden smells of the echoing lecture halls with their white ceilings, broken cameras, and scraped wood on mahogany desks shewing people's names. These lecture halls witness the dead silent and sleepy engineering students scrolling through their socials, waiting till the clock marks the end of the lecture, or bargaining for it to end early.

Unforgivingly complex corridors of hostels, empty fire extinguishers, and hundreds of cubicles.

Excluding Arham's room, GIKI holds a world record by being home to the worst tea on planet Earth, and this overly expensive sugary water beats its own record every day.

[Shall write more when I find solitude.] This book called GIKI has as its front cover the river and as its back cover the mountains.

Poem - 2

Soulmate proclaims I am close
His spectacles press the nose
And he tries to write the prose
But he only knows how to code
Hence fails in verse such gross

Stop seeking the soulmate's sight
Small spectacles a short eye-sight
Ever fail to fall in love-at-first-sight
Forever fruitful is the family's sight

Father works decades of life ahead
In process losing the hair of his head
Rearing the child from cradle to man
With peeled skin of his mother's hand
For needed prayer he raises his hand

Can not miss the Invisible Hand
That exchanges lives for oily land
This spectre of communism on land
Toppling the states for political gain
His convictions await the final call
Of Israel falling like the Berlin Wall
Dawn which brings freedom to all

Summary: He is so shy that he starts doing other things instead of looking at his beloved, even when she is close to him. His eyesight is weak and he is using the wrong glasses, so he cannot even see his beloved even if he wants to. He thinks about his parents and starts praying for them, but in the process he starts worrying about the problems of humanity due to capitalism and communism, hence prays for the betterment of humankind.

February 19, 2024

Literature, Life, and I

Just as a child studying pure mathematics tries to look for the usefulness of it and starts talking about its practical utility and upon not finding it and feeling disgusted at knowing its uselessness he throws it away either for decades or for his whole life, something like that happens with literature when the radical critic opens it and finds that he does not smell what he was looking for: the smell of his political ideology, his vision for social justice, and the fight against oppression. If in a text he finds such smell, he raises the praise of that text to be nothing less than the higher limits of human creativity, but if he does not find it, he crushes it under his feet.

To be free as not to be trapped in the net of ideologies or narratives, let alone being their mouthpiece, nor to be the servant of certain personality traits -- at best to absent the ego under such unavoidable circumstances. This clown "I" wishes to create something new, scientifc or artistic, that has an organic relationship with humans. Our creation is a pseudo-creation in comparion to that of God, the universe. If Allah is simultaneously invisible and everywhere in relation to His creation, we need not necessarily assert our own selves in our pseudo-creations. Sometimes, in order to receive what life has to offer, we have to decelerate the accelerator of our ego.

Neither indulge too much in literature as to forget living and the social reality, nor in metaphysics as to forget the gift of faith in the name of rationality, nor in psychology as to forget seeing the normality in human beings. Nor too much in the world order as to make your daily life a hell by criticizing capitalistic order, terrorism, nuclear wars, cyber wars, military wars, political affairs, governmental affairs, dictatorships, militarial industries, communist and other revolutions, human traffiking, corruption, genocides, bombardment of images and videos, etc.

My writing has strayed from the assumption of needing to have some real-life person in mind to be able to write, and sometimes it does not even mirror my own life, it starts to seek abstract beauty, the essense of literature. A stage where I do not think or feel or imagine or intuite any form of object or a person. Stuck a true balance between sensitivity and the observations in life. Through merely an acute observation of my life and the life of other human beings. By realizing philosophy instead of philosophying reality. By being sensitively active instead of contemplative.

However, I shall continue with my prayers with the childlike methods I use to pray. I shall say dua in the words I have been doing since childhood. I shall satire as I have been doing all my life. I shall continue falling in love with all the good things like computers, games, literature. Good human beings. I shall keep a childlike curiosity in the smallest details and mundane matters of daily life. I shall worry excessively sometimes at some problems. I shall accept boredom and find new way every day to cope up with it in a good way. I shall get angry at stupid arguments, laugh and appreciate good things. I shall continue criticizing the world order, while I feel like doing so, despite knowing I can barely change it. On some days I shall keep quiet, to be in a mood where I feel all is vanity, reach the deepest of my soul and talk to it, produce some literature, and then start talking a lot, involve myself in distractions, accept the life of people -- its beauties, consumerism, fights, beliefs, and jokes -- of people around me and live with them in accordance with it. Assimilate the good things. In all cases, I must, and it is very hard for me, perform my religious duties, form a closer connection with Allah, and hopefully realize the higher purpose of (my) life.

February 7, 2024

Beginning of the Middle Life - II

He was unconscious about it until now. He had stolen the context and meaning associated with the ‘boring’ as well as the action or inaction that constitutes ‘boredom.’ He was least concerned about playing linguistic aerobics, and was very much concerned about realizing lived reality first-hand. He had stolen it from movies, songs, social media images and videos, writings on social media and maybe some nonsensical books promoting popular culture, capitalism, and generally very wrong ideas on life. He called it boring when he was reading in the library, cafe, classroom, dining hall, or the hostel room. He felt this idea to be wrong. Felt that these things were such experiences of his life that were sort of meta-real, more real than the reality he is living in.

He lived in a remote university devoid of city life, a quiet life where the local area shuts down early night, and the inside is filled with consumerism of all sorts. Such consumerism ranged from the good to the bad. You had to be football fan to enter a specific group. You had to love reading history and become a human rights lawyer on social media to enter another friend group. You had to have watched specific short videos to have constructed a sense of humor with necessary pornographic elements to enter another group. There seemed utmost immaturity. They could not live with someone who had entirely different ideas and living style. But of course, he has lived, and he has found such people who could, and from both sides, accept each other and only try to improve each other, and that does not include conforming with each other’s beliefs or ways of life. In fact, such relationship even included mentally crushing a person in certain occasions where illusions are perceived and humane and rational is suggested. That was acceptable to him, but simultaneously, he felt that such suggestions and rationality ought not to be applied on other’s feelings because then it would become a ‘game of incomplete information.’

He feels all this as subjective, only true for him; that others may have widely different and much better judgements from experiences. He did not have any interest in participating in most of the consumerism, such as rave nights and concerts. Many of which he could not participate because of limited finances. A few he did not because of not having a girlfriend. A few of them were the ones he actually felt the lack of in himself to enter. The later brought forth some regrets, and these regrets started accumulating. Every time he thought of doing that thing, he felt himself to be late, perhaps the previous time was better for doing it. Such overthinking reached its peak and then he shared his feelings with someone. He was instantly rejected.

A hopelessness struck and brought him to the lowest points of his life, the remnants of which he still carries within himself. They rise to full consciousness every few epochs when certain emotional triggers are pressed in life. If it weren’t for some good friends around him, specially in the he’d have done much unethical things and would have gone against his own conscience, something which if he had realized later, he would have have profoundly regretted it and would not have been able go forgive himself for it.

January, 2024

On Rational Behavior

In the big or small decisions in life, we tend to think of ourself as the best rational actor with a rational behavior; and simultaneously, we either do not think of other people’s actions at all, or, at best, we think of them as random actors with random behaviors. This works very well if other people’s actions do not have any affect on our decision. But, it comes as a surprise when the other person acts very differently from what we have assumed of him. The error is that we fail to take into account the fact that other people are also rational actors.

I will give you an example. Imagine there are around a hundred students in the class. The professor asks everyone to privately (no sharing with anyone) choose any integer between 0 and 100. Professor will then collect everyone’s number and calculate the overall average, say ‘A.’ He will then take one-half of that average as the final result, i.e., ‘A/2.’ The person who has chosen the number closest to this final result (half of the overall average) will get the reward. A rational person should choose the number that has the highest chance of getting the reward. For example, if the average came out to be 70 and you have chosen 35, you win. Clearly, more than one person can win as well.

Let’s say you choose 60. You can win if the class average somehow comes as 120. But this is impossible because average cannot exceed 100! So, final result cannot exceed 50. Hence, a person who is assuming that others will just randomly select numbers above 50 and below 50, is simultaneously assuming that people selecting above 50 are absolutely irrational.

How about you choose 50. You can get the reward only if the class average were close to 100, which itself is only possible if everyone else chooses numbers close to 100. But wait. Why would anyone, say Khizar, choose 100? He can never win because 100 can never be the final result. It may come as the final result only if average is 200. Impossible.

This is the problem that occurs when you assume others to act randomly, or don’t think about others at all, while you act rationally for yourself. You know not to choose a number greater than 50 but you assume others will select such numbers. Now, you start to think that others are also rational actors. They might have reached the same thought process as you have, and could have thought about choosing 50. Hmmm, you begin to realize that since everybody will start to choose 50, I should choose 25. You can win if you have thought one step ahead of others. But, if others are as rational as you are, then they might have reached the same conclusion as you have. So, 25 won’t win because 25 will be the average, and only close to 12 can win. I won’t trace each and every thought-process now, you may have guessed that 0 is the best choice. Everybody wins with 0!

The underlying idea I wanted to communicate was to realize that in the minor or major decisions we take in our lives, we instinctively take ourself as the only rational actor while at the same time considering others to be random or irrational. This way of acting or decision making has probably to do with immense number of psychological factors, a few of which include haste, less focus, prior consumption or experiences, etc. This way, it rarely occurs to our mind to stop for moment with the current decision, start thinking of its best response, and maybe our best response against that best response, and other person’s best response against our best response… It sometimes regresses infinitely, but it mostly ends.

Another short example. My university has four dining halls. In normal days, all hotels inside and outside the university are almost equally filled with people. But, when Ramzan comes, there is a large influx of people towards the dining halls. One has to stand on a long queue and wait a lot just to get some food. Many get frustrated at this, and thus after a few days, they start to think that they should just “Mess Out.” and eat from somewhere else. I am not talking about randomly leaving the queue, nor the food quality or expenses, but actively deciding never to come to the dining hall again because of long waits. Everybody starts thinking for himself only, because he only remembers his own wait, his own suffering. Large number of people stop eating from dining halls. Suddenly, dining halls are almost empty. Some people who had assumed that others will leave, know that they will not have to wait for food. So, they just suffer for a few days, and then happily eat in the dining hall.

Such a situation tells you that other people are not necessarily very rational actors. If everybody is rational, then nobody will leave the dining hall because of long-waits (again, not talking about food quality or expenses). Everybody has to wait. Here, a double-step rational thought is equivalent to zero-step rational-thought. Hence, in real-life, everybody thinks at different levels. Most think at the first-step, i.e, leave the dining hall because of long queue time — consider yourself a rational actor and don’t think about others, or just consider random behavior from others. Others think of the second step too, i.e, remain in the dining hall because queue will become very small because ‘first-step’ thinkers will leave. The game somehow reaches a stable point.

Lastly, I must say that good decisions are not guaranteed to result using the recipe of rational behavior. We are unfamiliar with other people’s level of rationality. They are also normal people, so they will not necessarily think of the best responses. It may be the touch of a great mind to integrate in his decision both the rationality and the psychology of the people involved, to somehow figure out when they will stop thinking further, and when to stop an infinite regress. To be rational does not mean to be unethical. Moreover, a purely rational person will lose the game by choosing 0; because in real life, most people will choose numbers randomly and the result will be far away from 0. Such a theory of rational behavior is called game theory. It is one of the things that you accidentally stumble upon and it remains with you for a long time. At least for me, it has.

January 29, 2024

An Adult Weeps - Poem

It would be a lie to say
That I weep like a child
For I played with them
Today I saw them weep
They shed tears, moved legs
And waved their hands

But when I am about to sleep
I weep without moving
Either my legs or my arms
I just press my teeth
And feel my body aching
My head explodes I feel
Meaningless in all of myself
In my mind I weep loudly

But in reality I see that I
Am quiet. Family is sleeping
And I hear the sounds
Of their breath. Of my own
But my mind hits walls
I feel I have no way out

It happens again and again

And comes every few weeks
After I tell myself
That it is over now
So listen my friend

When I say I weep
I do not weep as children do

January 24, 2024

To Humanize the Online Post

My name is post. You can call me a caption. You create me. I live in the timeline. The author left me to write this one all for myself. So I shall type about myself upon myself, upon my own body. I feel naked, I shall clothe myself with some words… ‘ontological’ — nah, too long, doesn’t fit. Let’s try shorter ones. Hey keyboard! Wake up, come up. Good. Ufff! I already feel claustrophobic. They’ve filled both my left and right sides with ugly boxes. It feels like a grave in a long line of graves, and it feels that the reader came here to condole. In a far flung country, they call me tweet. Nevertheless, same motto. The living conditions there are too harsh. Being there equates to fighting in a battle-field. Kids use me as a stone, and adults for their machine gun delivery.

I have no idea what sort of human-created rules make me appear on the screens of millions. They don’t tell me those rules. If they did, I’ll be perfectly capable of deciding for myself, and have full control over my lifeless self — when to appear on who’s screen, considering other members of my own species. The author of the current version of me wishes that one day he will make the algorithm behind us exponentially more humane. It is the same author in whose little profile I may rest from now on. I will keep reminding him of his promise, and we will grow old together. He seems to be the laziest person I know. I advise him and the reader to spend more time with the living beings of your own species than us little lifeless creatures. You will never be able to bring as much life in me as is there in the species as yourself.

I no longer want to be controlled and to have both my life and death in sapiens’ hands. Those who have no one in this world to listen to, they come to me and share. But before reaching me out, please think it through whether the issue can be resolved by live conversation. You may thank me, or through me, if it does get resolved. Well, my room is always open for opening up. When you use me, please don’t make my face look the same as thousands of other posts. Let me have some self respect of my own. I extend my hands and humbly beg you to do justice to me. Through me, you can make wonders. Please use me correctly. Please don’t use me as propaganda. Don’t lie, don’t bully, be sarcastic or serious, just be humane. I have filled too many words, I am over clothed. I already feel old now, any species of my sort doesn’t live now further than that, my bone have started to ache. I shall rest. Meanwhile, I ask you to reflect on the time you spend staring and tending some of my population like a shepherd looks after his cattle.

January 14, 2024

Metaphysics - Notes

 A ‘scientific experiment’ is the test of the truth of a ‘narrative’ that is being tried to push into the world to be taken precedence over. Every other narrative (non-scientific) doesn’t have this experiment, with its concrete process of ‘scientific method.’ But wait, the narrative of ‘evolution’ did take some precedence over the narratives of 𝑟𝑒𝑙𝑖𝑔𝑖𝑜𝑛 at the scale of the world. It’s simple. Experiment is not a lie. The results of the experiment are the truths. If the ‘truth’ is clashing at large scale with something else, maybe that other thing is not constructed or interpreted well enough. If, on the other hand, the ‘other narrative’ is interpreted to its truest sense, and it still clashes directly with the ‘scientific truth’, that narrative is categorically wrong.

There’s the material or physical, mathematical, and the ‘ultimate’ reality. Natural Sciences have a claim of all the truths inside the physical reality. Pure Mathematics claims all the truths in the mathematical reality. I do not intend to portray that the physical and mathematical reality are distinct, for they could be distinct, intersected, or one in the same. As far as the ultimate reality goes, there are a lot of players that lay claim to its understanding. When it comes to the ultimate reality, the narratives fight with each other and try to get higher from each other regarding which narrative holds more truths. These narratives range from ‘ultimate reality doesn’t exist’ to having many complex notions about its nature. The subject matter of science is the physical reality. Hence, when science (or scientist) starts talking about the ultimate reality, it participates as a mere candidate, a mere player among hundreds or thousands of others; and it is, when viewed rightly, nothing more than just another narrative as opposed to the objective truths it holds in the physical reality.

When dealing with its own personal and main subject matter, science uses logic to traverse through all of its created knowledge. Logic is a system of thought popularized by the Greek (I am not, and do not intend to be, an expert on History). I assert that (I am not talking about ultimate reality, so I can ‘assert’ logically onto this physical reality) — I assert that Science, after its immense success in dealing with the physical reality, has deeply mistaken by using ‘logic’ on ‘ultimate’ reality as well.

Human Psychology laughs at this assertion, because, interestingly, most scientists invent and discover so much about the physical world by having deep and inner beliefs that they are finding truths about the ultimate reality. They do not want their motivation destroyed by a mere Computer Science student.

I am using the term ‘narrative’ in a very large and general sense. Hence, the apparent literary restrictions (I know very little about Literature) shall not be applied on this term here. The narratives are created by people. In a precise professional tone, they are the philosophers, scholars, writers, politicians, businessmen, mathematicians, scientists, and prophets.

I am unfinished, and do not have the energy right now to explicate further.

December 17, 2023

Journey of a Computer Program

The program is given a new life. After some bug fixes in the C file, he was saved on the local disk drive. His master, whom－out of respect－he calls ‘root’, saved him there. He, the program, sits inside a folder named ‘My Codes’ inside the root’s home directory. The address of the home directory is ‘~’. The home directory occupies a block of space in the local storage drive, and that block sits somewhere deep inside the whole of the drive. His height is 500 lines. His upper parts end just after the 10th line, and they contain all of his thinking side－brain. After that, he has his face, heart, lungs, all the way to his feet that rest on the 500th line. In the hard drive, there’s some empty space after his leg, but other programs lie next. Some are long unused, almost dead. Some are freshly used and came back to their place in the drive.

A construction work is happening in the main memory. It is randomly accessible, and hence the camera flies towards this precise location somewhere in the middle of the memory. A guy in a truck is clearing up dirt and cleaning the space. Upon asking, he says a new program is coming here, and the old one left this trace that I have to clean. He was a very old guy, and his name was Garbage Collector. Now, the place is clean. He goes back and writes in his notebook that his place is free now. A team of cranes and trucks come and make up more than a dozen segments here. Every segment is constructed in a delicate way. They put labels on each of the segments: stack, heap, and code, etc.

Something came to the hard disk drive, put him in a car, and after a while he was thrown in one of those segments in the main memory. It all happened so fast that he hardly had time to breathe and look around himself. Here, he is alone. He waits. He asks himself about the structure of these buildings around him, the structure of the roads with which he came here, the methods of travel along the way. What external forces make him move, how these cranes and collectors and trucks work. He tells himself that it doesn’t matter if he doesn’t know anything about it. He only knows his own work, which is enough. After all, he is a Computer Scientist, not a Computer Engineer.

Sitting bored in his code segment, he tries asking his whereabouts from a pedestrian in the busy street alongside. People are too busy with their lives. Nobody answers him. Meanwhile, he sees that new kinds of trucks are putting some things in his other segments. He is perplexed. He starts getting depressed, and wishes to call his psychotherapist. But instantly, a dwarf comes and tells him, looking at his notes sheet, that it is his time to run. They called him to the headquarters. Now, his facial expressions change. A flash of memory comes to his bright eyes, and he smiles. He knows the Central Processing Unit. He had been there before.

The CPU was working hard on something when he realized that a small clock inside it just sent a signal to halt the work. CPU stopped what it was doing. Another signal lighted up, which changed his mood. He calls it the kernel mood. [I SHALL WRITE MORE HERE. TIRED NOW]

He remembers his youth when he was heart broken and devastated upon the rejection of someone he had shared his intense feelings with. First, he had lost hope. Then, he stopped his prayers. At some point, he hit one of the weakest times of his life. He was suffering from fever and headaches. Only his mother was by his side. He did not share any of his feelings with her, but she knew deep inside her that there is much wrong with him than what appears on the outside. A time also came when he would constantly think of suicide and weep every night like a child. He does not remember how he got back into normal in the previous months or a year. Now, as he starts to get mature and become familiar with everything around him, his fascination and passion of things around him decreases. Boredom haunts him every day. He knows that those trucks and cranes were memory managers, loaders, and linkers; the note sheets were nothing but lists containing free space address in the main memory. The high manager ordering all the jobs for moving and placing him in different areas, was the Operating System. Every night, in solitude, he thinks that I have lived my whole life in these areas, and I still understand very little. The young programs live in big mansions called data centers, and they have put me in their local drives since many years. This, too, is a big society. He thinks, I see so many problems in this society, and I know many ways to make things better here. Maybe I might do this some time in my later life. He tells himself, there’s too much to do here. Then, he sleeps.

This is an unfinished draft. I’ll complete it later.

December 16, 2023

Of Creating Sense in Mathematics

Slow stream of thoughts caught in hostel’s quiet hours

Inasmuch as Mathematics is concerned, It is a very private experience for me because there is no external human eye that looks after me. I feel myself a culprit of not doing and learning even a quasi-fraction of mathematics as what I had imagined and was (and am) passionate about, and of doing very little of what I had thought. An active assertion of this kind is taken to be a lie by those close to me, for they take it in a manner where we try to explicate some person’s understanding of maths merely by comparing it to his immediate surrounding that considers maths just as an obstacle to life and examination results. Hence, it is true iff considered at a largely personal sense, as a feeling, and not an active assertion. And it is needless to extrapolate the reasoning behind such sort of negative feeling; for the answer generalizes to too many things of life, material and mental, that are already semantically bleached.

In the movie, ‘The Man who knew Infinity’, G.H. Hardy takes the Indian prodigy Ramanujan in his assistance, goes hard on him first but becomes his friend by the end. Sad to say that Ramanujan, a brilliant mathematician of the first kind, dies at a young age. I heard the name ‘Ramanujan’ from my mathematics teacher, Gul Rehmat, in class twelve at Islamia College. Keeping sir’s persona in mind, I say that he barely taught us anything, and he would just sit in the class and talk to us; yet he stirred a desire in me and opened me to mathematics in an original and creative sense — as opposed to my earlier notion of trying to be faster than everyone around me in calculations, being confident merely because of good marks, and not having a coherent idea of the juxtaposition of abstractness and concreteness. To be precise, this openness to creativity started the moment when he stood up from the wooden chair and started writing on the Whiteboard. My sensory apparatus caught a moment of profound insight when I saw such a rare explicative appartus unveiling such an abstract idea. The ‘precise propositional definition of limit’ entered my mind and imagination, and the image of the teacher entered the frame of my heart. I am proud of myself that I chose to concentrate for those thirty minutes and kept my heart, mind, and imagination open and undistracted.

Later, GIKI revived those older childish notions again in a much superficial sense — as the maths taught to undergrads here is just a play of calculators (you missed a decimal point), 20 minute quizzes coming from presentation slides and prepared by students by cramming formulas; either by sitting alone with a fast beating heart, WhatsApp-ing someone who can help them, or by sitting with friends in the little study rooms of the beautiful library — anxiously staring at laptop screens, listening to a friend who finally understood a way out of ‘x’ from an Integration, ordering food near library, and consistently made silent every by the librarian, and laughing at each other when they hear librarian saying to a group that their plagiarism in humanities course report is 85%. We take sighs of relief after leaving the examination hall and heading to the tuc or the hostel, and then home after months.

In his book, ‘A Mathematician’s Apology’ — which I read twice, first in the summer of ’21, and later in December ’23 — Hardy writes (and I summarize):

“The real maths of the ‘real’ mathematicians, of Fermat and Euler and Gauss and Abel and Riemann, is almost wholly ‘useless.’ The metric of judgement of a mathematician is not the practical utility, but something different: that something worth creating was created. High thinking of one kind is always likely to affect high thinking of another — but it has extremely little effect on anything else.

Exposition, criticism, appreciation, is work for second-rate scientists and mathematicians. It is a confession of weakness to talk about ‘writing’ mathematics, instead of doing the actual maths and adding something to maths. What we do may be small, but it has a certain sense of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.

Languages die, but mathematical ideas do not. Greek mathematics is ‘permanent’, more so even than Greek literature. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean. An equation is the same whether it’s written in red or green ink. It makes no difference to a chess problem if the pieces are white and black, or red and green, or whether there are physical ‘pieces’ at all. The chess board and the pieces are mere devices to stimulate our sluggish imaginations, and are no more essential to the problem than the blackboard and the chalk are to the theorems in a mathematical lecture.

One of the finest weapons of a mathematician is the proof by ‘reductio ad absurdum’ (proof by contradiction) — a far finer gambit than any chess gambit: a chess player may sacrifice a piece, but a mathematician offers the whole game.

A man who could give a convincing account of mathematical reality would have solved very many difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all.”

December 7, 2023