Math with bad drawings

An excerpt from the book “Math with Bad Drawings: Illuminating the Ideas That Shape Our Reality" by Ben Orlin

"On a fundamental level, mathematicians do not care about reality. I’m not talking about the odd habits of mathematicians - muttering to themselves, wearing the same trousers for weeks, forgetting their spouse’s names on occasion. I’m talking about their work. Despite the aggressive ad campaign about its “real-world usefulness,” mathematics is pretty indifferent to the physical universe. What math cares about are not things but ideas. Math posits rules and then unpacks their implications by careful reasoning. Who cares if the resulting conclusions - about infinitely long cones and 42-dimensional sausages - don’t resemble physical reality? What matters is their abstract truth. Math lives not in the material universe of science but in the conceptual universe of logic. Mathematicians call this work “creative.” They liken it to art. That makes science their muse. 

Think of a composer who hears chirping birds and weaves the melody into her next work. Or a painter who gazes at cumulus clouds drifting through an afternoon sky, and models her next landscape on that image. These artists don’t care if they’ve captured their subjects with photorealistic fidelity. For them, reality is nothing more or less than a fertile source of inspiration. That’s how math sees the world, too. Reality is a lovely starting point, but the coolest destinations lie far beyond it. Math sees itself as a dreamy poet. Science sees it as a supplier of specialized technical equipment. And herein we find one of the great paradoxes of human inquiry: These two views, both valid, are hard to reconcile. If math is an equipment supplier, why is its equipment so strangely poetic? And if math is a poet, then why is its poetry so unexpectedly useful?"

"The machine, we learned, had a soul"

"In the second match Sedol displayed his newfound respect for AlphaGo by playing careful, flawless Go. It wasn’t designed to wow the 280 million people who would eventually watch the series, but from someone of Sedol’s rank, it constituted nearly unbeatable play, and Sedol exuded a quiet but unmistakable confidence. Then, as the game began to enter its middle phase, AlphaGo did something unusual: it instructed its human attendant to place a black stone in a largely unoccupied area to the right of the board. This might have made sense in another context, but on that board at that moment AlphaGo seemed to be abandoning the developing play in the lower half of the board. This historic move was something that no human would have feasibly played - AlphaGo calculated the probability that a human would play that move at 1 in 10,000. It produced instant shock and confusion among the spectators. Lee Sedol paled, excused himself, and left the room for a full fifteen minutes before returning.

The English-language commentators went silent before one said, with great understatement: “That’s a very surprising move.” At first Fan Hui, who was watching the game with Cade Metz, a writer for Wired magazine, was as befuddled as anyone else. “It’s not a human move,” he told Metz. “I’ve never seen a human play this move.” As Metz would later note, nothing in the 2,500 years of collected Go knowledge and understanding prepared anyone for move 37 of the second game in the series. Except Hui. Since losing to AlphaGo the previous fall Hui had spent hours helping the Google DeepMind team train the software for the match with Sedol, an experience that allowed him to understand how the move connected the black stones at the bottom of the board with the strategy AlphaGo was about to pursue. “Beautiful,” he said, then repeated the word several more times. This was not mere “tesuji”* - a clever play that can put an opponent off guard. This was a work of aesthetic as well as strategic brilliance, possibly even a "myoshu"*. Sedol continued to play nearly flawless Go, but it wasn’t enough to counter the striking creativity the DeepMind software displayed, even after move 37. By the end of the day the big news wasn’t that AlphaGo had won a second game, but that it had displayed such deeply human qualities - improvisation, creativity, even a kind of grace - in doing so. The machine, we learned, had a soul."

* A tesuji (手筋) is a clever play, the best play in a local position, a skillful move.

* Myoushu 妙手) is an "inspired move", a move which turns a game around or otherwise exceeds expectations.

(An excerpt from the book "Whiplash: How to Survive Our Faster Future" by Joi Ito and Jeff Howe - Page 239 - Description of the 2nd Go match between Lee Sedol (18-time world champion) and AlphaGo, an AI computer program developed by Google. It was played in Seoul, Korea in March 2016. AlphaGo won the series 4-1)

Image Credit : Wikipedia

... that recurring dream

A passage from the book "Pale Blue Dot: A Vision of the Human Future in Space" by Carl Sagan

"When I was a child, my most exultant dreams were about flying — not in some machine, but all by myself. I would be skipping or hopping, and slowly I could pull my trajectory higher. It would take longer to fall back to the ground. Soon I would be on such a high arc that I wouldn’t come down at all. I would alight like a gargoyle in a niche near the pinnacle of a skyscraper, or gently settle down on a cloud. In the dream — which I must have had in its many variations at least a hundred times — achieving flight required a certain cast of mind. It’s impossible to describe it in words, but I can remember what it was like to this day. You did something inside your head and at the pit of your stomach, and then you could lift yourself up by an effort of will alone, your limbs hanging limply. Off you’d soar. I know many people have had similar dreams. Maybe most people. Maybe everyone. Perhaps it goes back 10 million years or more when our ancestors were gracefully flinging themselves from branch to branch in the primeval forest."

Ah, finally an explanation of a recurring dream that I been having since early childhood. It seems that this dream is not that uncommon. Perhaps as Sagan says, it is part of our collective memory.

Erasing Death

Dr. Sam Parnia’s book 'Erasing Death' is about recent advances in resuscitation science. When somebody suffers cardiac arrest and the heart stops; brain devoid of oxygen, also closes its shop within seconds. In that case, there is no heart beat, no respiration, no pulse or blood pressure and no neural activity. That person is dead in traditional sense. But as we have all seen in the movies and on the TV, if CPR (cardiopulmonary resuscitation) or artificial respiration and chest compression are applied within minutes, then that person can be brought back to life.

It all started in 18th century Amsterdam, Holland when it was discovered that blowing air into lungs can save people drowning in city canals. But the science of resuscitation truly progressed in the 20th century. In 1960’s and 70’s, electrical shocks to restart the heart (through defibrillator) and administration of certain drugs to boost the blood pressure were added to the repertoire. Hypothermia treatment was included later when it was realized that people who die in cold climate can be revived many hours afterwards. Lower body temperature seemed to preserve cells. ECMO (Extracorporeal Membrane Oxygenation) which is a type of heart-lung bypass device is being successfully used in Japan and South Korea with above 70% revival rates. Post resuscitation treatment and care also proved to be of vital importance in preventing irreversible brain and organ damage.

Now, medical science recognizes that death is not an event but a process. There is a grey zone after death that permits the reversal of this process. This grey area is extending further and further whenever there is advancement in resuscitation techniques. It is also crucial to understand that the original cause of death must be fixed quickly during or after resuscitation otherwise that person will die a second time after a few hours or days of revival. For example, if a person is dying of cancer then his or her recovery doesn't matter as underlying cause of death can not be fixed at present.

Dr. Sam Parnia’s book also deals with the question of near death experiences or NDE’s. Around 10% of people who are revived through resuscitation, report seeing some kind of tunnel or light, reviewing of past life, meeting dead relatives and out of body experiences. These experiences have been dismissed by the majority of scientists as hallucinations. However, Dr. Parnia believes that these may be pointing towards some undiscovered country that lies beyond the present limits of science. He was also part of the AWARE Study during 2008-2012. In this study, several hospitals in USA and Europe were monitored to improve resuscitation efforts and to conduct objective interviews of persons claiming NDE’s. In a number of emergency rooms and cardiac care units, pictures were placed high over the shelves that can only be viewed from above. This was specifically aimed at out of body experiences. It was reasoned that if such claims are for real then those persons should be able to describe those images. In reality, it was found out that out of body experiences are very rare. Only two persons claimed such experiences during the study and no definitive answers were found. So jury is still out on that matter. 

A recent development in this field is EPR (Emergency Preservation and Resuscitation) treatment which was reported in several journals last year. It is in initial stages for trauma patients at a few places in the US. It works by lowering the patient’s body temperature and replacing blood with cold saline solution. By applying EPR, patient will go into a state of suspended animation. Once the damage to the body is repaired, blood will be pumped back and person can be brought back to life. A possible application of this technique could be longer space voyages of future. It would be much more economical and efficient besides psychological reasons to send astronauts in the state of suspended animation and revive them years or decades later. 

All these developments raises several moral and ethical dilemmas. Lines between life and death are being blurred. Are we playing God and interfering with the course of nature? The answer would vary from person to person based on personal beliefs and convictions. But humans started to alter the course of nature when first person was cured through herbs and plants or was given some kind of first aid treatment. Other living being don’t do that. Science of medicine evolved over centuries and new discoveries were made. Modern medicine and surgery techniques, state of art diagnostics, mass vaccinations and organ transplants are extending human lifespan and delaying death all over the world. 3D organ printing is now at initial stages and nanobots are getting ready to roam human body. Humans would keep on adopting such measures to extent life because nature allows us to do that.

What Happened?

" ... A similar attitude settled in the Ottoman Empire. Having conquered most of the world they knew, the Ottomans turned inward, into religious fundamentalism and centuries of stagnation. Mahathir Mohammad, the former prime minister of Malaysia, has said,

”The great Islamic civilization went into decline when Muslim scholars interpreted knowledge acquisition, as enjoined by the Qur’an, to mean only knowledge of religion, and that other knowledge was un-Islamic. As a result, Muslims gave up the study of science, mathematics, medicine, and other so-called worldly disciplines. Instead, they spent much time debating on Islamic teachings and interpretations, on Islamic jurisprudence and Islamic practices, which led to a breakup of the Ummah and the founding of numerous sects, cults, and schools.”

In Europe, however, a great awakening was beginning. Trade brought in fresh, revolutionary ideas, accelerated by Gutenberg’s press. The power of Church began to weaken after a millennium of domination. The universities slowly turned their attention away from interpreting obscure passages of the Bible to applying the physics of Newton and the chemistry of Dalton and others…

Soon, the rise of science and technology in Europe began to weaken the power of China and the Ottoman Empire. The Muslim civilization, which has prospered for centuries as a gateway for trade between the East and the West, faltered as European sailors forge trade route to the New World and the East – especially around Africa, bypassing the Middle East…

The answer to the question “What happened?” is clear. Science and technology happened. Science and technology are the engines of prosperity. Of course, one is free to ignore science and technology, but only at your peril. The world does not stand still because you are reading a religious text. If you do not master the latest in science and technology, then your competitors will.”

Future of Wealth (Physics of the Future by Dr. Michio Kaku)

World as a Riddle

Earth as viewed from Lunar orbit during the Apollo 8 mission - Dec 24,1968

“I’ll never cease to be amazed that the world exists… Circus performers and variety shows will never captivate me in the same way as steppes or rain forest, or the sky’s uncountable galaxies and all the billions of light years that separate them. 

I am more concerned with the world as a riddle than riddles in the world.”

(The Castle in the Pyrenees by Jostein Gaarder)

Image by NASA / Bill Anders - Wikimedia Commons

Socratic Dialogue

"People did not go to Socrates to learn anything - he always insisted that he had nothing to teach them - but to have a change of mind. Participants in a Socratic dialogue discovered how little they knew and that the meaning of even the simplest proposition eluded them. The shock of ignorance and confusion represented a conversion to the philosophic life, which could not begin until you realized that you knew nothing at all.

... the Socratic dialogue was never aggressive; rather it was conducted with courtesy, gentleness, and consideration. If a dialogue aroused malice or spite, it would fail. There was no question of forcing your interlocutor to accept your point of view; instead, each offered his opinion as a gift to the others and allowed them to alter his own perception."

(The Case for God – Epilogue by Karen Armstrong)

This method of the Socratic dialogue was invented nearly two and a half-millennium ago. I wonder how many of our personal, social, cultural, religious, and political conflicts could be resolved if we start to favor such kind of thinking again. The world could become a much better place if we are able to rise above from our standpoint and give ourselves a chance to understand others' point of view.

The Art of Life

       

With the sure and silent touch of his clever fingers he took hold of my pieces, all the old men and young men and children and women, cheerful and sad, strong and week, nimble and clumsy, and swiftly arranged them on his board for a game. At once they formed themselves into groups and families, games and battles, friendships and enmities, making a small world. For a while he let this lively and yet orderly world go through its evolutions before my enraptured eyes in play and strife, making treaties and fighting battles, wooing, marrying and multiplying. It was indeed a crowded stage, a moving breathless drama.

Then he passed his hand swiftly over the board and gently swept all the pieces into a heap; and, meditatively with an artist’s skill, made up a new game of the same pieces with quite other groupings, relationships and entanglements. The second game had an affinity with the first, it was the same world built of the same material, but the key was different, the time changed, the motif was differently given out and he situations differently presented.

And in this fashion the clever architect built up one game after another out of the figures, each of which was a bit of myself, and every game had a distant resemblance to every other. Each belonged recognizably to the same world and acknowledged a common origin. Yet each was entirely new.

“This is the art of life,” he said dreamily. “You may yourself as an artist develop the game of your life and lend it animation. You may complicate and enrich it as you please. It lies in your hands.” 

(Steppenwolf - Hermann Hesse)

Diversity, Flexibility and Tolerance

I am reading “The Post-American World 2.0” by Farid Zakaria these days. It is a good read and Farid is certainly right in pointing out that rise of the rest is underway. In Zakaria’s words, his book is not about the decline of American power but about the advance of countries like China, India, Brazil and others. It is about the coming decades in which smart nations and cultures will reclaim their rightful place at global stage and would create “a world of enormous cultural diversity and exoticism”.

An interesting passage in this book is about Hindu worldview. I have always been amazed by Hinduism’s ability to survive into the modern times. It is an ancient religion and in a loose sense belongs to a class of beliefs that has now vanished from active service. Old Egyptian, Greek and Scandinavian deities are limited to mythology at present but Hinduism is still followed by more than a billion people. Zakaria’s answer to this riddle is as under:

“Hindus, like Confucians, don’t believe in God. They believe in hundreds of thousands of them. Every sect and sub sect of Hinduism worships its own God, Goddess, or holy creature. Every family forges its own distinct version of Hinduism. You can pay your respects to some beliefs and not to others. You can believe in none at all. You can be a vegetarian or eat meat. You can pray or not pray. None of these choices determines whether you are a Hindu. There is no heresy or apostasy, because there is no core set of beliefs, no doctrine, and no commandments. Nothing is required, nothing is forbidden.”

In his words, “Hinduism is not really a ‘religion’ in the Abrahamic sense of the world but a loose philosophy, one that has no answers but merely questions. The only clear guiding principle is ambiguity. If there is a central verse in Hinduism’s most important text, the Rig Veda, it is the creation Hymn. It reads, in part:

Who really knows, and who can swear,

How creation came, when and where!

Even gods came after creation’s day,

Who really knows, who can truly say

When and how creation start?

Did He do it? Or did He not?

Only He, up there, knows, maybe;

Or perhaps, not even He”

The above lines seems like written by an agnostic philosopher. So perhaps this ambiguity and a very high level of tolerance within Hinduism is the secret ingredient that gives its followers a kind of flexibility to adopt and survive into an ever changing world. 

Zakaria also believes that “Islam in India has been altered through its contact with Hinduism, becoming less Abrahamic and more spiritual. Indian Muslims worship saints and shrines, celebrate music and art, and have a more practical outlook on life than many of their coreligionists abroad.”

Clash versus fusion and synthesis

     "Every age, every culture, every custom, and tradition has its own character, its own weakness and its own strength, its beauties, and ugliness; accepts certain sufferings as matters of course, puts up patiently with certain evils. Human life is reduced to real suffering, to hell, only when two ages, two cultures, and religions overlap."

These lines by the novelist Hermann Hesse were written in his book Steppenwolf nearly a century ago. The idea of the clash of civilizations has also remained prevalent in recent years. It was popularized by Samuel P. Huntington in the late 1990s. Many people still believe that their culture, religion, or way of life is under threat by the opposing forces. Fears of modernization and new technologies are likewise common. 

Although there is no doubt that every civilization and time period has its unique characteristics. However, the notion that conflict or overlapping between cultures, creeds, or distinct eras would result in human sufferings can’t be true in a broader sense. In my view, these are the intersections where ideas, thoughts, morals, beliefs, and norms get challenged. Without these collisions, growth in human thought will be hampered and stagnation would ensue. At these boundaries, new ideas take root, synthesis is achieved and flowers grow.

The mind of God

 Pillars of creation and other star forming regions in the Eagle Nebula (constellation Serpens)

"If we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason - for then we would truly know the mind of God."

Stephen Hawking (A Brief History of Time - concluding passage)

Image courtesy: NASA

There exists a world ...

"The Blue Marble" photograph of Earth, taken from Apollo 17

There exists a world. In terms of probability this borders on the impossible. It would have been far more likely if, by chance, there was nothing at all. Then, at least, no one would have begun asking, why there was nothing.

(Jostein Gaarder - Maya)

Image courtesy: Wikipedia, NASA

So many galaxies, so many stars

Hubble ultra deep field view

"The Universe, as has been observed before, is an unsettlingly big place, a fact which for the sake of a quiet life most people tend to ignore."

Douglas Adams (The Hitchhiker's Guide to the Galaxy)

Image courtesy: Wikipedia