Archive for August, 2008

Though I have worked on pattern recognition in the past I have always wanted to work with Neural Networks for the same. However for some reason or the other I could never do so, I could not even take it as an elective subject due to some constraints. Over the last two years or so I have been promising myself and ordering myself to stick to a schedule and study ANNs properly, however due to a combination of procrastination, over-work and bad planning I have never been able to do anything with them.

However I have now got the opportunity to work with Support Vector Machines and over the past some time I have been reading extensively on the same and have been trying to get playing with them. Now that the actual implementation and work is set to start I am pretty excited to work with them. It is nice that I get to work with SVMs though I could not with ANNs.

Support Vector Machine is a classifier derived from statistical learning theory by Vladimir Vapnik and his co-workers. The foundations for the same were laid by him as late as the 1970s SVM shot to prominence when using pixel maps as input it gave an accuracy comparable with sophisticated Neural Networks with elaborate features in a handwriting recognition task.

Traditionally Neural Networks based approaches have suffered some serious drawbacks, especially with generalization, producing models that can overfit the data. SVMs embodies the structural risk minimization principle that is shown superior to the empirical risk minimization that neural networks use. This difference gives SVMs the greater ability to generalize.

However learning how to work with SVMs can be challenging and somewhat intimidating at first. When i started reading on the topic I took the books by Vapnik on the subject but could not make much head or tail. I could only attain a certain degree of understanding, nothing more. To specialize in something I do well when I start off as a generalist, having a good and quite correct idea of what is exactly going on. Knowing in general what is to be done and what is what, after this initial know-how makes me comfortable I reach the stage of starting with the mathematics which gives profound understanding as anything without mathematics is meaningless. However most books that I came across missed the first point for me, and it was very difficult to make a headstart. There was a book which I could read in two days that helped me get that general picture quite well. I would highly recommend it for most who are in the process of starting with SVMs.The book is titled Support Vector Machines and other Kernel Based Learning methods and is authored by Nello Cristianini and John-Shawe Taylor.

I would highly recommend people who are starting with Support Vector Machines to buy this book. It can  be obtained easily over Amazon.

This book has very less of a Mathematical treatment but it makes clear the ideas involved and this introduces a person studying from it to think more clearly before he/she can refine his/her understanding by reading something heavier mathematically. Another that I would highly recommend is the book Support Vector Machines for Pattern Classification by Shigeo Abe.

Another book that I highly recommend is Learning with Kernels by Bernhard Scholkopf and Alexander Smola. Perfect book for beginners.

Only after one has covered the required stuff from here that I would suggest Vapnik’s books which then would work wonderfully well.

Other than the books there are a number of Video Lectures and tutorials on the Internet that can work as well!

Below is a listing of a large number of good tutorials on the topic. I don’t intend to flood a person interested in starting with too much information, where ever possible i have described what the document carries so that one could decide what should suffice for him/her on the basis of need. Also I have star-marked some of the posts. This marks the ones that i have seen and studied from personally and found them most helpful and i am sure they would work the same way with both beginners and people with reasonable experience alike.

Webcasts/ Video Lectures on Learning Theory, Support Vector Machines and related ideas:

EDIT: For those interested. I had posted about a course on Machine Learning that has been provided by Stanford university. It too is suited for an introduction to Support Vector Machines. Please find the post here. Also this comment might be helpful, suggestions to it according to your learning journey are also welcome.

1. *Machine Learning Workshop, University of California at Berkeley. This series covers most of the basics required. Beginners can skip the sessions on Bayesian models and Manifold Learning.

Workshop Outline:

Session 1: Classification.

Session 2: Regression.

Session 3: Feature Selection

Session 4: Diagnostics

Session 5: Clustering

Session 6: Graphical Models

Session 7: Linear Dimensionality Reduction

Session 8: Manifold Learning and Visualization

Session 9: Structured Classification

Session 10: Reinforcement Learning

Session 11: Non-Parametric Bayesian Models

2. Washington University. Beginners might be interested on the sole talk on the topic of Supervised Learning for Computer Vision Applications or maybe in the talk on Dimensionality Reduction.

3. Reinforcement Learning, Universitat Freiburg.

4. Deep Learning Workshop. Good talks, But I’d say these are meant for only the highly interested.

5. *Introduction to Learning Theory, Olivier Bousquet.

This tutorial focuses on the “larger picture” than on mathematical proofs, it is not restricted to statistical learning theory however. The course comprises of five lectures and is quite good to watch. The Frenchman is both smart and fun!

6. *Statistical Learning Theory, Olivier Bousquet. This course gives a detailed introduction to Learning Theory with a focus on the Classification problem.

Course Outline:

Probabilistic and Concentration inequalities, Union Bounds, Chaining, Measuring the size of a function class, Vapnik Chervonenkis Dimension, Shattering Dimensions and Rademacher averages, Classification with real valued functions.

7. *Statistical Learning Theory, Olivier Bousquet. This is not the repeat of the above course. This one is a more recent lecture series than the above actually. This course has six lectures. Another excellent set.

Course Outline:

Learning Theory: Foundations and Goals

Learning Bounds: Ingredients and Results

Implications: What to conclude from bounds

7. Advanced Statistical Learning Theory, Olivier Bousquet. This set of lectures compliment the above courses on statistical learning theory and give a more detailed exposition of the current advancements in the same.This course has three lectures.

Course Outline:

PAC Bayesian bounds: a simple derivation, comparison with Rademacher averages, Local Rademacher complexity with classification loss, Talagrand’s inequality. Tsybakov noise conditions, Properties of loss functions for classification (influence on approximation and estimation, relationship with noise conditions), Applications to SVM – Estimation and approximation properties, role of eigenvalues of the Gram matrix.

8. *Statistical Learning Theory, John-Shawe Taylor, University of London. One plus point of this course is that is has some good English. Don’t miss this lecture as it has been given by the same professor whose book we just discussed.

9. *Learning with Kernels, Bernhard Scholkopf.

This course covers the basics for Support Vector Machines and related Kernel methods. This course has six lectures.

Course Outline:

Kernel and Feature Spaces, Large Margin Classification, Basic Ideas of Learning Theory, Support Vector Machines, Other Kernel Algorithms.

10. Kernel Methods, Alexander Smola, Australian National University.  This is an advanced course as compared to the above and covers exponential families, density estimation, and conditional estimators such as Gaussian Process classification, regression, and conditional random fields, Moment matching techniques in Hilbert space that can be used to design two-sample tests and independence tests in statistics.

11. *Introduction to Kernel Methods, Bernhard Scholkopf, There are four parts to this course.

Course Outline:

Kernels and Feature Space, Large Margin Classification, Basic Ideas of Learning Theory, Support Vector Machines, Examples of Other Kernel Algorithms.

12. Introduction to Kernel Methods, Partha Niyogi.

13. Introduction to Kernel Methods, Mikhail Belkin, Ohio State University.This lecture is second in part to the above.

14. *Kernel Methods in Statistical Learning, John-Shawe Taylor.

15. *Support Vector Machines, Chih-Jen Lin, National Taiwan University. Easily one of the best talks on SVM. Almost like a run-down tutorial.

Course Outline:

Basic concepts for Support Vector Machines, training and optimization procedures of SVM, Classification and SVM regression.

16. *Kernel Methods and Support Vector Machines, Alexander Smola. A comprehensive six lecture course.

Course Outline:

Introduction of the main ideas of statistical learning theory, Support Vector Machines, Kernel Feature Spaces, An overview of the applications of Kernel Methods.

Additional Courses:

1. Basics of Probability and Statistics for Machine Learning, Mikaela Keller.

This course covers most of the basics that would be required for the above courses. However sometimes the shooting quality is a little shady. This talk seems to be the most popular on the video lectures site, one major reason in my opinion is that the lady delivering the lecture is quite pretty!

2. Some Mathematical Tools for Machine Learning, Chris Burges.

3. Machine Learning Laboratory, S.V.N Vishwanathan.

4. Machine Learning Laboratory, Chrisfried Webers.

Introductory Tutorials (PDF/PS):

1. *Support Vector Machines with Applications (Statistical Science). Click here >>

2. *Support Vector Machines (Marti Hearst, UC Berkeley). Click Here >>

3. *Support Vector Machines- Hype or Hallelujah (K. P. Bennett, RPI). Click Here >>

4. Support Vector Machines and Pattern Recognition (Georgia Tech). Click Here >>

5. An Introduction to Support Vector Machines in Data Mining (Georgia Tech). Click Here >>

6. University of Wisconsin at Madison CS 769 (Zhu). Click Here >>

7. Generalized Support Vector Machines (Mangasarian, University of Wisconsin at Madison). Click Here >>

8. *A Practical Guide to Support Vector Classification (Hsu, Chang, Lin, Via U-Michigan Ann Arbor). Click Here >>

9. *A Tutorial on Support Vector Machines for Pattern Recognition (Christopher J.C Burges, Bell Labs Lucent Technologies, Data mining and knowledge Discovery). Click Here >>

10. Support Vector Clustering (Hur, Horn, Siegelmann, Journal of Machine Learning Research. Via MIT). Click Here >>

11. *What is a Support Vector Machine (Noble, MIT). Click Here >>

12. Notes on PCA, Regularization, Sparisty and Support Vector Machines (Poggio, Girosi, MIT Dept of Brain and Cognitive Sciences). Click Here >>

13. *CS 229 Lecture Notes on Support Vector Machines (Andrew Ng, Stanford University). Click Here >>

Introductory Slides (mostly lecture slides):

1. Support Vector Machines in Machine Learning (Arizona State University). Click here >>

Lecture Outline:

What is Machine Learning, Solving the Quadratic Programs, Three very different approaches, Comparison on medium and large sets.

2. Support Vector Machines (Arizona State University). Click Here >>

Lecture Outline:

The Learning Problem, What do we know about test data, The capacity of a classifier, Shattering, The Hyperplane Classifier, The Kernel Trick, Quadratic Programming.

3. Support Vector Machines, Linear Case (Jieping Ye, Arizona State University). Click Here >>

Lecture Outline:

Linear Classifiers, Maximum Margin Classifier, SVM for Separable data, SVM for non-separable data.

4. Support Vector Machines, Non Linear Case (Jieping Ye, Arizona State University). Click Here >>

Lecture Outline:

Non Linear SVM using basis functions, Non-Linear SVMs using Kernels, SVMs for Multi-class Classification, SVM path, SVM for unbalanced data.

5. Support Vector Machines (Sue Ann Hong, Carnegie Mellon). Click Here >>

6. Support Vector Machines (Carnegie Mellon University Machine Learning 10701/15781). Click Here >>

7. Support Vector Machines and Kernel Methods (CMU). Click Here >>

8. SVM Tutorail (Columbia University). Click Here >>

9. Support Vector Machines (Via U-Maryland at College Park). Click Here >>

10. Support Vector Machines: Algorithms and Applications (MIT OCW). Click Here >>

11. Support Vector Machines (MIT OCW). Click Here >>

Papers/Notes on some basic related ideas (No estoric research papers here):

1. Robust Feature Induction for Support Vector Machines (Arizona State University). Click Here >>

2. Hidden Markov Support Vector Machines (Brown University). Click Here >>

3. *Training Data Set for Support Vector Machines (Brown University). Click Here >>

4. Support Vector Machines are Universally Consistent (Journal Of Complexity). Click Here >>

5. Feature Selection for Classification of Variable Length Multi-Attribute Motions (Li, Khan, Prabhakaran). Click Here >>

6. Selecting Data for Fast Support Vector Machine Training (Wang, Neskovic, Cooper). Click Here >>

7. *Normalization in Support Vector Machines (Caltech). Click Here >>

8. The Support Vector Decomposition Machine (Periera, Gordon, Carnegie Mellon). Click Here >>

9. Semi-Supervised Support Vector Machines (Bennett, Demiriz, RPI). Click Here >>

10. Supervised Clustering with Support Vector Machines (Finley, Joachims, Cornell University). Click Here >>

11. Metric Learning: A Support Vector Approach (Cornell University). Click Here >>

12. Training Linear SVMs in Linear Time (Joachims, Cornell Unversity). Click Here >>

13. *Rule Extraction from Linear Support Vector Machines (Fung, Sandilya, Rao, Siemens Medical Solutions). Click Here >>

14. Support Vector Machines, Reproducing Kernel Hilbert Spaces and Randomizeed GACV (Wahba, University of Wisconsian at Madison). Click Here >>

15. The Mathematics of Learning: Dealing with Data (Poggio, Girosi, AI Lab, MIT). Click Here >>

16. Training Invariant Support Vector Machines (Decoste, Scholkopf, Machine Learning). Click Here >>

*As I have already mentioned above, the star marked courses/lectures/tutorials/papers are the ones that I have seen and studied from personally (and hence can vouch for) and these in my opinion should work best for beginners.

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I am a pacifist but i don’t intend to write here about peace directly. I thought of writing about things related to the monumental tragedy of bombings of Hiroshima and Nagasaki but in a rather indirect way. This is a “Non-Linear” post and is basically in three parts.

I believe August 6 and 9 will remain in human memory for eons for the bombings of Hiroshima and Nagasaki. I am an optimist and i don’t think there will be any large nuclear conflict in the medium term future. On the latter date 63 years ago the city of Nagasaki was obliterated, Leaving 80,000 people dead by the end of 1945 (140,000 dead in Hiroshima) and a large number continued to suffer for a much longer time after that.

[The city of Nagasaki before and after the atomic bombings, Source: Wikipedia]

Threnody For the Victims of Hiroshima

One thing that I have always imagined was thinking about how it would be like to be in a city that gets hit by an Atomic (Fission), Thermonuclear or a Neutron Bomb. And let me tell you it is one thing that is almost impossible to imagine. Also then there are a number of things, like your position and what you were looking at. If you are in the inner radius near ground zero, i don’t think there would be any time to react to anything. Seeing the bomb drop and being present at ground zero is even harder to imagine. Now being somewhere far, say 3-4 Kilometers from ground zero, is again really hard to imagine. It is really hard to think what would go in the mind in a short span of a few seconds if you do  get to see the wave approaching and destroying everything on its way for some moments.

My girl once gifted me a few CDs on my birthday (which was a very sweet gift, but let me not digress), and introduced me to a wonderful quote by Aldous Huxley (1931):

After silence, that which comes nearest to expressing the inexpressible is music.

One of my favorite compositions is “Threnody For The Victims of Hiroshima“, it is a masterpeice by Krzysztof Penderecki. When I first heard it, I thought it was rather creepy. However after hearing it a few times, it started growing on me and it is only sometime back that I started marveling  at the intensity of this composition and admiring the depth it had. One afternoon I got into thinking that it was a composition on which no video cover could be made. It was impossible for me to assign any image to that music, which made a video on it impossible. This is somewhat related to the above paragraph where I expressed my inability to imagine what it would be like during a nuclear explosion on my city. And very rightly so, this composition is dedicated to the victims of the twin bombings.

[All copyrights rest with the composer and the producer ]

A black screen in my humble opinion represents best the composition and speaks a thousand words for the dead and the mentally shocked.

Pale Blue Dot

[Pale Blue Dot: The image of the Earth taken by the Voyager I from a record distance]

Carl Sagan was a wonderful man, an elegant speaker and a man of great learning. I have read almost all books by him and also thoroughly admired and enjoyed the Cosmos television series. One book that I particularly liked was “Pale Blue Dot“, a book based on the photograph by the same name. A photograph taken by the Voyager 1 from a record distance of 6.4 billion Kilometers that shows the Earth as an obscure dot in a beam of scattered sunlight. The video below has Sagan speaking from the book. Having him talk is something else, such is the effect of his voice. I think this is one piece that everyone of us should see once in while!

Such is the beauty of this part that it is worth quoting it:

Look again at that dot. That’s here. That’s home. That’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every “superstar,” every “supreme leader”, every saint and sinner in the history of our species lived there – on a mote of dust suspended in a sunbeam.

The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.

Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.

The Earth is the only world known so far to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment the Earth is where we make our stand.

It has been said that astronomy is a humbling and character-building experience. There is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly with one another, and to preserve and cherish the pale blue dot, the only home we’ve ever known.

The Geeta of J. Robert Oppenheimer

[J. Robert Oppenheimer, Source: Wikipedia]

J. Robert Oppenheimer is probably best known as the father of the atomic bomb. Oppenheimer was over-educated in a number of fields other than his forte, that was Physics. He was known for his mathematical acumen, erudition over theoretical physics, knowledge of eastern philosophy and languages particularly Dutch and Sanskrit.

On a personal front, Oppenheimer was emotionally troubled almost all his life often slipping into  depression. He was a chain smoker (which ultimately caused throat cancer and subsequent death) and neglected food for long periods in times of emotional and intellectual discomfort. A lot of his colleagues have said Oppenheimer had a self-destructive tendency, and with his insecurities and melancholy he worried his friends. People associated with him generally fell into two categories, ones who thought he was a silent man of great learning and a brilliant genius, while some thought he was unstable and a pretentious person.

General Leslie Groves was appointed the project director of the Manhattan project and inspite of doubts about Oppenheimer being a possible security risk he made him the scientific director. Many of the generals and people in the defense staff have maintained that inspite of Oppenheimer’s communist inclinations and doubts about his loyalty (that time any communist in America was viewed with suspicion, take for example the rise  of Mc-Carthy as an example of the narrow-mindedness prevalent at the time ), Manhattan project would have never been completed without him. He was so indispensable for the project and for keeping the people from diverse backgrounds working on it together.

[Trinity : The first ever nuclear explosion]

Click to Enlarge

After the end of the great war Oppenheimer became an outspoken critic of the arms race and supported the establishment of an international agency that would have been in control of all the nuclear arsenal. He opposed the development of the Hydrogen bomb initially on technical grounds. Increasingly worried about the danger to humanity from scientific discoveries he lectured on peace till his death, and also joined with Einstein, Bertrand Russell and formed what later became the world academy of art and science in 1960. He had to pay for his outspokeness, for decisions he took that appeared to be plagued with confusion, his leftist leanings and the ire of the politicians that he attracted as a result of his outspoken character after the war in the form of a very publicly humiliating hearing in 1954, which resulted in his security clearance being revoked. For the remainder of his life surprisingly Oppenheimer never showed much resentment for the hearing and it seems he took the humiliation rather gracefully.

In a rare recording in 1965 Oppenheimer was persuaded to quote again the phrase from the Bhagwad Gita  that he claimed crossed his mind when he saw the Trinity explosion.

We knew the world would not be the same. A few people laughed, a few people cried. Most people were silent. I remembered the line from the Hindu scripture the Bhagavad Gita, Vishnu is trying to persuade the prince that he should do his duty, and to impress him, takes on his multi armed form and says “now I become death the destroyer of the worlds”. I suppose we all thought that, one way or another.

In this rare footage, Oppenheimer has tears in his eyes, in what seems to be due to intense guilt and regret.

A lot of people think Oppenheimer was a hypocrite, a moral monster who was instrumental in making  the bomb, for scouting for both the locations over which the bomb was eventually dropped and for supporting the development of the Hydrogen bomb and other devices and that he was a person who was a poser, who lectured on peace but yet supported the bomb and its development and even its use in WW-II.

I think this is unfair on the man, for those who have read stuff on Oppenheimer would know that he had a deep interest in some eastern scriptures, particularly the Bhagwad Geeta. It won’t be wrong to assume that the Geeta had a very marked impact on Oppenheimers thinking and his philosophy on life and duty. The ideas in the Geeta in a way marry the seemingly inherent contradictions that were apparent sometimes in what Oppenheimer spoke about and clear the fog over some of his ideas on peace and support for the bombings of Hiroshima and Nagasaki and even scouting for a place for bombing.

The Geeta like many other scriptures is subject to interpretations and obviously Oppenheimer’s interpretation is bound to be different. However his knowledge and his interest in the Geeta were enough for him to formulate a code on ethics and life loosely based on the principles of it. Oppenheimer never said in the open what the importance of the Geeta in his life was, but there is enough circumstantial evidence to show that it was indeed very important.

After the destruction of Hiroshima and Nagasaki he was dispirited by the continuation of the development of nuclear weapons and constantly wrestled with moral and ethical problems as he thought he was instrumental in handing over humanity the means of its own possible annihilation. He at this time revisited the Geeta, his old favorite and drew power from it which steadied him in his work and worldview.

Also like i said earlier, the Geeta makes comprehensible some acts of Oppenheimer that were otherwise difficult to grasp for example not only did Oppenheimer build the bomb, he maintained till the end that he did the right thing and yet he always said that he had blood on his hands. Let us try to see that there was no real contradiction in Oppenheimer’s views about peace taking the Bhagwad Geeta as the base. It makes it understandable why a man of such a great persona would become inactive and confused at times and why a man of peace would build the atomic bomb.

Oppenheimer studied Sanskrit at Berkeley in 1933 with Indologist Arthur Ryder and acquired a deeper knowledge of the Bhagavad Gita that he had read in the original tongue. Much later in life Oppenheimer was to call the Geeta the most beautiful philosophical discourse in any known tongue. He kept a copy of the Geeta always at hand on his desk and often gifted the Geeta as a gift to many of his colleagues. often his own translation. An indication of the impression that the Geeta had made on him.

The Geeta is the single most important sacred text for the Hindus and is a piller of Hinduism. The importance of the Geeta in Hinduism is perhaps the greatest as compared to the other scriptures. It is essentially on philosophy, ethics, code of conduct and life and is set in midst of the Mahabharata (to be precise the Geeta is from the Bhishma Parva of the Mahabharata), the longest epic in the world. Things in the Geeta are told in the context of a story of good against evil. The story has a royal family in which all the cousins grow up together but as they grow up to be men they are torn apart due to a quarrel resulting from the royal inheritance. The differences are only resolved by war. Arjuna, the third oldest of the five Pandavas is shown to be a warrior and an archer unparalleled in history.

The geeta begins with Arjuna riding onto the battlefield with lord Krishna, the 8th avatar of Lord Vishnu but on seeing amongst enemy ranks his own friends and relatives, his heart breaks. He is confronted with the prospect of killing his own people and with the fact that if he did not fight it would mean more humiliation for the Pandavas. Depressed by this, he refuses to fight. He is given solace by Krishna, who is being Arjuna’s charioteer.

The geeta has 18 chapters in the course of which Krishna counsels Arjuna on why he should take part in the war. The arguments given are diverse and take care of even the slightest doubts. Inspite of the lengthy nature of his discourse, Krishna’s arguments can be summed up in some very basic points, out of which these seem to have had a major bearing on Oppenheimer’s conduct and view of duty and life :

1. Arjuna is a soldier, his duty is only to fight.

2. Krishna (god or fate) will decide on who lives and who dies, so there is no point in mourning or rejoicing over results. There should be a detachment from the result and one should only focus on the work. “Worry only about the job at hand, don’t worry about what the result would be”.

Oppenheimer’s position was like that of Arjuna before the war. Arjuna was the younger brother of Yudhistra who was more intelligent, a better man than Duryodhana, his cousin who is driven by hate. Duryodhana was so blinded by hate that he tries to kill his cousins, the Pandavas to rule. Krishna’s message to Arjuna was clear. He MUST fight. The message would have been equally clear to Oppenheimer. One other important idea in the Geeta is the idea of duty. Another is of fate, The Geeta espouses that duty and fate should not be mingled together and that one should only focus on his duty and not worry about what is responsibility of others (in his case the politicians and President Truman for example). This and many simple yet profound ideas defined how Oppenheimer acted. He only did his duty as a scientist and as the director, he did what he had to do.

Professor James Hijiya gives a very beautiful commentary of this aspect. I would recommend you to read it (link given below). It is not possible to analyze most of Oppenheimers actions on a blog post. It might need a book. So I would direct all interested to that link. It is short and makes a brisk read for those who get scared by volume. Please read to get the whole point of me mentioning the Geeta of Robert Oppenheimer in this post. I believe that the man who made the atom bomb did not sin. That is my point. And though I greatly admire J. Robert Oppenheimer, that is not the reason why I think that he did not sin, and that he only did his duty.

Recommendations and References:

1. Threnody for the Victims of Hiroshima – Penderecki

2. Pale Blue Dot– Carl Sagan

3. The Gita of J. Robert Oppenheimer – James Hijiya. Click Here >>

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