This biography of Paul Dirac, the Nobel winning British physicist who pioneered quantum mechanics, is foremost a mental biography. It is the story of an intuitive, mathematical mind that, using abstract thinking alone, correctly predicted the existence of anti-matter. He did no experiments.
The author chronicles Dirac’s social behavior, his impact on others, his emotional blindness, his insistence on mathematical and theoretic purity. Farmelo makes the case that Paul Dirac had Asperger syndrome, a form of autism. He was mathematically brilliant, but lacked social intelligence – the ability to ‘read’ other people as the complex emotional beings that they are, which is the hallmark of Asperger syndrome. Weak social intelligence can seem like callousness. Dirac’s lack of personal connection seemed to be on purpose, and people were offended and would think him mean. When someone like Dirac is also known to be very smart, what else can explain his manner? Dirac just did not give the personal regard that people seek. He did marry and have children, but his wife came to be very frustrated, and his children did not fare well. He loved watching Cher, but had no other interest in music.
People like Dirac can seem to be like sociopaths, but poor social intelligence is not sociopathy. Sociopaths often have a very strong social intelligence, indeed a powerful ability to understand what others are feeling, what others want. This is what makes them often skillful manipulators. Their lack of empathy allows them to avoid guilt as they use others. They can convey warmth and concern, all the while acting viciously.
This was not Dirac. He could eventually understand people, after using deliberate and careful perception, logic and analysis. And when he did, he could be caring and loyal.
His contributions to physics were substantial. He solved many of the important issues of early quantum mechanics, and won a Nobel Prize, but his later years were not very productive. He insisted on abstract mathematical beauty and was unable or unwilling to engage the rough promise of new experimental results.
Social intelligence uses a great amount of mental capacity, and may be the chief reason our brain’s evolved so large. Weak social mentation can liberate other mental talents, free up ‘disc space’ for other types of mentation, such as visual or spatial thinking. This is the story of the savant, of people like Dirac.
Dirac was lucky to arrive in Niels Bohr’s time. Bohr’s genius was leadership. He had a great managerial intelligence, even though he was a clumsy speaker and writer. He and his loving and intelligent wife fostered an intensely supportive environment for gifted and varied personalities, some with social intelligence and empathy, and some without, Nobel minds like Schroedinger, Einstein, Pauli, Dirac, and Heisenberg. Even Bohr’s son would eventually win a Nobel Prize.
Under Bohr, these great minds unravelled, in a short few years, the mysteries of chemistry and nuclear forces and brought human knowledge to the very edge of what is knowable, a place we have yet to surpass.
https://thinkagainonline.com/wp-content/uploads/2017/10/ThinkAgain-nsq.jpg00Think Againhttps://thinkagainonline.com/wp-content/uploads/2017/10/ThinkAgain-nsq.jpgThink Again2010-09-29 19:13:192010-09-29 19:13:19The Strangest Man
“In the beginning was the Word”, The Gospel according to John 1.1
Energy has been our most powerful explanatory concept, explaining events in the physical world more comprehensively than any other entity . . . so far. Leave aside what energy actually is, it is a derived concept, known only by its effects. No one has actually ever seen energy.
There are other ‘fundamentals’. There is entropy, order, information, and intelligence. They are all different and yet all related, to energy and to each other. Somehow they create the cosmos, everything we see and know. We feel a call for some kind of synthesis. Information may be the key.
We learn from the early studies of heat energy by Ludwig E. Boltzmann, and his laws of thermodynamics, that not all energy is the same, there is useful energy and there is unuseful energy. Useful energy is creative energy, it can do something, it can perform work. In the process of doing something, useful energy somehow becomes stagnant, unuseful energy. This flow from creative to stagnant energy, from useful energy to unuseful energy, creates our known world. The difference between useful and unuseful energy is mysterious. It seems to be information. Useful energy has information. Useful energy may be information.
Entropy is a measure of non-useful energy. High entropy has disorder, low entropy has order. Order is pattern in space and time. Order has non-randomness. Non-randomness is information. Low entropy has order and information. Order and information have useful energy.
There is a paradox about information. It takes more information to describe something that is more random and has less order, something that contains less information. Something containing more information takes less information to describe. In some mysterious way, information denotes an efficiency quality. Quality information has more power, more effectiveness, it has more meaning. Quality information has order and pattern, but other also attributes such as symmetry, balance, rhythm. It is aesthetic. Quality information has truth and beauty. It is artistic.
Even more mysteriously, Quality information creates agency. The robust interactions of information contained in useful energy is intelligence, which becomes life in evolutionary adaptation in the dimension of time, and becomes consciousness in the perception of time itself.
Rather than being just incidental, information may be integral to the Universe, creator even of matter, IT FROM BIT, in the famous words of the physicist John Wheeler, collaborator of Einstein and Bohr, discoverer of the black hole.
” IT FROM BIT symbolizes the idea that every item of the phsyical world has at bottom – at a very deep bottom, in most instances – an immaterial source and explanation; that what we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and this in a participatory universe”. John Wheeler
The computer revolution may be more profound than we even think.
https://thinkagainonline.com/wp-content/uploads/2017/10/ThinkAgain-nsq.jpg00Think Againhttps://thinkagainonline.com/wp-content/uploads/2017/10/ThinkAgain-nsq.jpgThink Again2010-09-24 23:47:252010-09-24 23:47:25What is Information?
Leonardo da Vinci, The flights of the Mind, Charles Nicholl, Penguin Books, 2005.
During his lifetime, Leonardo da Vinci was not considered the greatest visual artist of all time. No, his personal lot was difficult, and endlessly trying. He was an illegitimate son, a homosexual, a genius without peer, and always dependent for financial support on petty, vain, narrow-minded, and falsely pious rich men of medieval Italy. He suffered fools continually.
A genius can’t really know what non-genius is like, and so life is puzzling, other people are baffling. The genius feels oppressively different and lonely and can be driven to seek expression, if not in this life, then for in the future. This is how it was for Leonardo. His work speaks to us 500 years later. His genius was visual, as Mozart’s was sound, his creativity futuristic, astonishing the world to this day.
“My advice is not to trouble yourself with words unless you are speaking to the blind.”
Three paintings: The Lady with an Ermine, La Belle Ferronniere, and Mona Lisa are exquisite masterpieces. Leonardo presents his subjects radiant, unposed, mysteriously bemused, elegant, and subtly but powerfully defiant. We look at them, and they look at us. We sense that they are unmistakenly people, individuals with thoughts, and hurts, and hopes, individuals who have a story. There is a feeling of intrigue, something has happened. Leonardo doesn’t just capture pose, and clothing, and expression, he captures mentation, one can feel them thinking. And they have dignity. Leonardo feels for them, and wants us see and feel for them also. They are prisoners of sorts, sexual prisoners, sold into marriage by their families, to rich, older men. They are confined – perhaps like him – by sexuality, the circumstances of the times, by the mediocrity of the powerful. And so, too, with his Jesus. In The Last Supper, his Jesus is a person, not an icon. This Jesus has resignation, disappointment, regrets, friends, and human needs, and is resigned to being misunderstood.
Leonardo’s paintings are astonishingly few. Late in life he regrets this, yet one senses that an element of purpose limited his output. A subtle protest, perhaps, as if he felt it a blasphemy to give his artistic gifts over to the despicable, undeserving wealthy. He was most proud of his work on medical illustrations, created from laborious dissections of human cadavers, carried out in the hospitals full of the unpretentious, common humanity. He hoped to aid medical knowledge and treatment. This was his way to contribute his talents to the deserving.
Leonardo sensed the mystical in visual experience.
“Observe the flame of a candle and consider its beauty. Blink your eye and look at it again. What you see now was not there before, and what was there before is not there now. Who is it who rekindles this flame which is always dying?”
https://thinkagainonline.com/wp-content/uploads/2017/10/ThinkAgain-nsq.jpg00Think Againhttps://thinkagainonline.com/wp-content/uploads/2017/10/ThinkAgain-nsq.jpgThink Again2010-09-18 21:40:042010-09-18 21:40:04Leonardo from Vinci
The economy has number. The term “economy” is singular, but its properties emerge from a collection of things which are numerous and diverse. And it is important that the definition is always tied to its disparate components. When we create statistical aggregates to describe the economy, we lose information, we change the concept into something that is not real. The economy is not singular. It is a group, a set, of people, transactions, and ideas. And the individual distinctness of its components, though unseen by the analyzing scholar, is precisely the quality that matters.
This is Friedrich Hayek’s insight in his famous essay, The Use of Knowledge in Society.
There are two kinds of “knowledge”. There is the scientist’s knowledge, which seeks to understand the economy comprehensively, and the knowledge of the individual agent, who is uniquely aware of his own circumstances. The individual’s knowledge is the disparate element, and the scientist’s knowledge is the conjectural, theoretic attempt to understand a complex system as a singular object.
As Hayek explains:
The sort of knowledge with which I have been concerned is knowledge of the kind which by its nature cannot enter into statistics and therefore cannot be conveyed to any central authority in statistical form. The statistics which such a central authority would have to use would have to be arrived at precisely by abstracting from minor differences between the things, by lumping together, as resources of one kind, items which differ as regards location, quality, and other particulars, in a way which may never be very significant for the specific decision.
When Hayek uses the word “knowledge”, in today’s vernacular he means “information”. We know that useful information is condensed, coded, and patterned. The problem of economic coordination is the problem of transforming information for exchange. And it is the system of price setting, by the natural mechanism of supply and demand, that achieves this end.
It is more than a metaphor to describe the price system as…a system of telecommunications which enables individual producers to watch merely the movement of a few pointers, as an engineer might watch the hands of a few dials, in order to adjust to changes of which they may never know more than is reflected in the price movement.
Thus, the interactions of numerous, disparate, autonomous individuals create economies by responding to supply and demand, communicating with price. Information is exchanged, but the diverse elements of the economic system are preserved.
Recall that Margaret Thatcher famously said: “there is no such thing as society”. Hayek tells us why. She was concerned that being oriented to “society” can lead to ignoring citizens.
Hayek’s reasoning shows how aggregated information (the knowledge of the societal planner) doesn’t have relevance to any individual citizen. The prudent policy maker doesn’t work on “society”, but on the liberty, safety, and opportunity of the individual.
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“His was a low-slung, smallish figure, neither markedly stout nor thin, inclining, if anything, to the latter. The square-cut tunic seemed always a bit too large for him: one sensed an effort to compensate for the slightness of stature. Yet there was also a composed, collected strength, and a certain rough handsomeness, in his features. The teeth were discolored, the mustache scrawny, coarse, and streaked. This, together with the pocked face and yellow eyes, gave him the aspect of an old battle-scarred tiger. In manner – with us simple, quiet, unassuming. There was no striving for effect. His words were few. They generally sounded reasonable and sensible: indeed they often were. An unforewarned visitor would never have guessed what depths of calculation, ambition, love of power, jealousy, cruelty, and sly vindictiveness lurked behind this unpretentious facade.” George Kennan
Imagine Hitler ruling for 30 years, that was Stalin. An intellectual psychopath, Stalin recognized Leninism/Bolshevism for what it was, intellectual justification for brutality, theft, repression, and power. Promoting the destruction of all the social institutions that served to keep the people precariously bound in some element of civil reciprocity was cat nip to the bank robber he was, and the murderer he became.
His feral cunning, callousness, and Machiavellian malevolence brought him from poverty in Georgia to absolute ruler of the largest victorious army in history, and the conquest of much of the Eurasian continent.
Some say that Hitler had difficulty murdering those he had known well. Not so Stalin. He had the cherished wife of his personal valet of some many years, Poskrebyshev, taken and executed. They had a young son, who Stalin would sit on his lap, like a grandpa. The loved wife of Foreign Minister Vaicheslav Molotov, one of the signers of the death sentence for 21,000 Polish officers held at Katyn forest, and Stalin’s closest comrade in rule for thirty years, was imprisoned for ‘disloyalty’. (Molotov ‘abstained’ on the vote in the Politburo about her arrest, and then later apologized to Stalin about his ‘error’ in judgment and never again raised the issue of her case) Mrs. Molotov was eventually released – four years later – after Stalin’s death. Molotov never acknowledged that Stalin may have intended her harm. Anastos Mikoyan, another lifelong comrade, (also a signer of the Katyn death sentence), the USSR representative at JFK’s funeral, saw his two sons imprisoned, also only released after Stalin’s death. Genrikh Iagoda, Stalin’s early NKVD secret police chief, was ‘tried’ and then shot, as were his wife, and his sister. Another sister, and both parents, perished in the Gulag.
Stalin’s chief rivals for power, Zinoviev, Kamenov, Bukharin, and Trotsky were all executed for false crimes confessed under torture. Many of their wives, children, and parents were also executed, including a teenage son of Kamenov. For many Bolshevik comrades, their real crime, a monstrous crime against humanity, a crime indeed justifiably punishable by death, was their failure, themselves, to bring to trial and to execute Joseph Stalin.
The Strangest Man
/in All, Books, IdeasThe Strangest Man, by Graham Farmelo
This biography of Paul Dirac, the Nobel winning British physicist who pioneered quantum mechanics, is foremost a mental biography. It is the story of an intuitive, mathematical mind that, using abstract thinking alone, correctly predicted the existence of anti-matter. He did no experiments.
The author chronicles Dirac’s social behavior, his impact on others, his emotional blindness, his insistence on mathematical and theoretic purity. Farmelo makes the case that Paul Dirac had Asperger syndrome, a form of autism. He was mathematically brilliant, but lacked social intelligence – the ability to ‘read’ other people as the complex emotional beings that they are, which is the hallmark of Asperger syndrome. Weak social intelligence can seem like callousness. Dirac’s lack of personal connection seemed to be on purpose, and people were offended and would think him mean. When someone like Dirac is also known to be very smart, what else can explain his manner? Dirac just did not give the personal regard that people seek. He did marry and have children, but his wife came to be very frustrated, and his children did not fare well. He loved watching Cher, but had no other interest in music.
People like Dirac can seem to be like sociopaths, but poor social intelligence is not sociopathy. Sociopaths often have a very strong social intelligence, indeed a powerful ability to understand what others are feeling, what others want. This is what makes them often skillful manipulators. Their lack of empathy allows them to avoid guilt as they use others. They can convey warmth and concern, all the while acting viciously.
This was not Dirac. He could eventually understand people, after using deliberate and careful perception, logic and analysis. And when he did, he could be caring and loyal.
His contributions to physics were substantial. He solved many of the important issues of early quantum mechanics, and won a Nobel Prize, but his later years were not very productive. He insisted on abstract mathematical beauty and was unable or unwilling to engage the rough promise of new experimental results.
Social intelligence uses a great amount of mental capacity, and may be the chief reason our brain’s evolved so large. Weak social mentation can liberate other mental talents, free up ‘disc space’ for other types of mentation, such as visual or spatial thinking. This is the story of the savant, of people like Dirac.
Dirac was lucky to arrive in Niels Bohr’s time. Bohr’s genius was leadership. He had a great managerial intelligence, even though he was a clumsy speaker and writer. He and his loving and intelligent wife fostered an intensely supportive environment for gifted and varied personalities, some with social intelligence and empathy, and some without, Nobel minds like Schroedinger, Einstein, Pauli, Dirac, and Heisenberg. Even Bohr’s son would eventually win a Nobel Prize.
Under Bohr, these great minds unravelled, in a short few years, the mysteries of chemistry and nuclear forces and brought human knowledge to the very edge of what is knowable, a place we have yet to surpass.
What is Information?
/in All, Ideas“In the beginning was the Word”, The Gospel according to John 1.1
Energy has been our most powerful explanatory concept, explaining events in the physical world more comprehensively than any other entity . . . so far. Leave aside what energy actually is, it is a derived concept, known only by its effects. No one has actually ever seen energy.
There are other ‘fundamentals’. There is entropy, order, information, and intelligence. They are all different and yet all related, to energy and to each other. Somehow they create the cosmos, everything we see and know. We feel a call for some kind of synthesis. Information may be the key.
We learn from the early studies of heat energy by Ludwig E. Boltzmann, and his laws of thermodynamics, that not all energy is the same, there is useful energy and there is unuseful energy. Useful energy is creative energy, it can do something, it can perform work. In the process of doing something, useful energy somehow becomes stagnant, unuseful energy. This flow from creative to stagnant energy, from useful energy to unuseful energy, creates our known world. The difference between useful and unuseful energy is mysterious. It seems to be information. Useful energy has information. Useful energy may be information.
Entropy is a measure of non-useful energy. High entropy has disorder, low entropy has order. Order is pattern in space and time. Order has non-randomness. Non-randomness is information. Low entropy has order and information. Order and information have useful energy.
There is a paradox about information. It takes more information to describe something that is more random and has less order, something that contains less information. Something containing more information takes less information to describe. In some mysterious way, information denotes an efficiency quality. Quality information has more power, more effectiveness, it has more meaning. Quality information has order and pattern, but other also attributes such as symmetry, balance, rhythm. It is aesthetic. Quality information has truth and beauty. It is artistic.
Even more mysteriously, Quality information creates agency. The robust interactions of information contained in useful energy is intelligence, which becomes life in evolutionary adaptation in the dimension of time, and becomes consciousness in the perception of time itself.
Rather than being just incidental, information may be integral to the Universe, creator even of matter, IT FROM BIT, in the famous words of the physicist John Wheeler, collaborator of Einstein and Bohr, discoverer of the black hole.
” IT FROM BIT symbolizes the idea that every item of the phsyical world has at bottom – at a very deep bottom, in most instances – an immaterial source and explanation; that what we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and this in a participatory universe”. John Wheeler
The computer revolution may be more profound than we even think.
Leonardo from Vinci
/in All, art, BooksLeonardo da Vinci, The flights of the Mind, Charles Nicholl, Penguin Books, 2005.
During his lifetime, Leonardo da Vinci was not considered the greatest visual artist of all time. No, his personal lot was difficult, and endlessly trying. He was an illegitimate son, a homosexual, a genius without peer, and always dependent for financial support on petty, vain, narrow-minded, and falsely pious rich men of medieval Italy. He suffered fools continually.
A genius can’t really know what non-genius is like, and so life is puzzling, other people are baffling. The genius feels oppressively different and lonely and can be driven to seek expression, if not in this life, then for in the future. This is how it was for Leonardo. His work speaks to us 500 years later. His genius was visual, as Mozart’s was sound, his creativity futuristic, astonishing the world to this day.
“My advice is not to trouble yourself with words unless you are speaking to the blind.”
Three paintings: The Lady with an Ermine, La Belle Ferronniere, and Mona Lisa are exquisite masterpieces. Leonardo presents his subjects radiant, unposed, mysteriously bemused, elegant, and subtly but powerfully defiant. We look at them, and they look at us. We sense that they are unmistakenly people, individuals with thoughts, and hurts, and hopes, individuals who have a story. There is a feeling of intrigue, something has happened. Leonardo doesn’t just capture pose, and clothing, and expression, he captures mentation, one can feel them thinking. And they have dignity. Leonardo feels for them, and wants us see and feel for them also. They are prisoners of sorts, sexual prisoners, sold into marriage by their families, to rich, older men. They are confined – perhaps like him – by sexuality, the circumstances of the times, by the mediocrity of the powerful. And so, too, with his Jesus. In The Last Supper, his Jesus is a person, not an icon. This Jesus has resignation, disappointment, regrets, friends, and human needs, and is resigned to being misunderstood.
Leonardo’s paintings are astonishingly few. Late in life he regrets this, yet one senses that an element of purpose limited his output. A subtle protest, perhaps, as if he felt it a blasphemy to give his artistic gifts over to the despicable, undeserving wealthy. He was most proud of his work on medical illustrations, created from laborious dissections of human cadavers, carried out in the hospitals full of the unpretentious, common humanity. He hoped to aid medical knowledge and treatment. This was his way to contribute his talents to the deserving.
Leonardo sensed the mystical in visual experience.
“Observe the flame of a candle and consider its beauty. Blink your eye and look at it again. What you see now was not there before, and what was there before is not there now. Who is it who rekindles this flame which is always dying?”
Hayek’s Information
/in All, Ideas, PoliticsThe economy has number. The term “economy” is singular, but its properties emerge from a collection of things which are numerous and diverse. And it is important that the definition is always tied to its disparate components. When we create statistical aggregates to describe the economy, we lose information, we change the concept into something that is not real. The economy is not singular. It is a group, a set, of people, transactions, and ideas. And the individual distinctness of its components, though unseen by the analyzing scholar, is precisely the quality that matters.
This is Friedrich Hayek’s insight in his famous essay, The Use of Knowledge in Society.
There are two kinds of “knowledge”. There is the scientist’s knowledge, which seeks to understand the economy comprehensively, and the knowledge of the individual agent, who is uniquely aware of his own circumstances. The individual’s knowledge is the disparate element, and the scientist’s knowledge is the conjectural, theoretic attempt to understand a complex system as a singular object.
As Hayek explains:
The sort of knowledge with which I have been concerned is knowledge of the kind which by its nature cannot enter into statistics and therefore cannot be conveyed to any central authority in statistical form. The statistics which such a central authority would have to use would have to be arrived at precisely by abstracting from minor differences between the things, by lumping together, as resources of one kind, items which differ as regards location, quality, and other particulars, in a way which may never be very significant for the specific decision.
When Hayek uses the word “knowledge”, in today’s vernacular he means “information”. We know that useful information is condensed, coded, and patterned. The problem of economic coordination is the problem of transforming information for exchange. And it is the system of price setting, by the natural mechanism of supply and demand, that achieves this end.
It is more than a metaphor to describe the price system as…a system of telecommunications which enables individual producers to watch merely the movement of a few pointers, as an engineer might watch the hands of a few dials, in order to adjust to changes of which they may never know more than is reflected in the price movement.
Thus, the interactions of numerous, disparate, autonomous individuals create economies by responding to supply and demand, communicating with price. Information is exchanged, but the diverse elements of the economic system are preserved.
Recall that Margaret Thatcher famously said: “there is no such thing as society”. Hayek tells us why. She was concerned that being oriented to “society” can lead to ignoring citizens.
Hayek’s reasoning shows how aggregated information (the knowledge of the societal planner) doesn’t have relevance to any individual citizen. The prudent policy maker doesn’t work on “society”, but on the liberty, safety, and opportunity of the individual.
Stalin
/in All, Politics“His was a low-slung, smallish figure, neither markedly stout nor thin, inclining, if anything, to the latter. The square-cut tunic seemed always a bit too large for him: one sensed an effort to compensate for the slightness of stature. Yet there was also a composed, collected strength, and a certain rough handsomeness, in his features. The teeth were discolored, the mustache scrawny, coarse, and streaked. This, together with the pocked face and yellow eyes, gave him the aspect of an old battle-scarred tiger. In manner – with us simple, quiet, unassuming. There was no striving for effect. His words were few. They generally sounded reasonable and sensible: indeed they often were. An unforewarned visitor would never have guessed what depths of calculation, ambition, love of power, jealousy, cruelty, and sly vindictiveness lurked behind this unpretentious facade.” George Kennan
Imagine Hitler ruling for 30 years, that was Stalin. An intellectual psychopath, Stalin recognized Leninism/Bolshevism for what it was, intellectual justification for brutality, theft, repression, and power. Promoting the destruction of all the social institutions that served to keep the people precariously bound in some element of civil reciprocity was cat nip to the bank robber he was, and the murderer he became.
His feral cunning, callousness, and Machiavellian malevolence brought him from poverty in Georgia to absolute ruler of the largest victorious army in history, and the conquest of much of the Eurasian continent.
Some say that Hitler had difficulty murdering those he had known well. Not so Stalin. He had the cherished wife of his personal valet of some many years, Poskrebyshev, taken and executed. They had a young son, who Stalin would sit on his lap, like a grandpa. The loved wife of Foreign Minister Vaicheslav Molotov, one of the signers of the death sentence for 21,000 Polish officers held at Katyn forest, and Stalin’s closest comrade in rule for thirty years, was imprisoned for ‘disloyalty’. (Molotov ‘abstained’ on the vote in the Politburo about her arrest, and then later apologized to Stalin about his ‘error’ in judgment and never again raised the issue of her case) Mrs. Molotov was eventually released – four years later – after Stalin’s death. Molotov never acknowledged that Stalin may have intended her harm. Anastos Mikoyan, another lifelong comrade, (also a signer of the Katyn death sentence), the USSR representative at JFK’s funeral, saw his two sons imprisoned, also only released after Stalin’s death. Genrikh Iagoda, Stalin’s early NKVD secret police chief, was ‘tried’ and then shot, as were his wife, and his sister. Another sister, and both parents, perished in the Gulag.
Stalin’s chief rivals for power, Zinoviev, Kamenov, Bukharin, and Trotsky were all executed for false crimes confessed under torture. Many of their wives, children, and parents were also executed, including a teenage son of Kamenov. For many Bolshevik comrades, their real crime, a monstrous crime against humanity, a crime indeed justifiably punishable by death, was their failure, themselves, to bring to trial and to execute Joseph Stalin.