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It would be tempting to solely blame the dictators and the warlords for these wars. One may go one level farther and blame the news and media conglomerates, the entertainment industry, the public relations experts and various other spin-doctors and entertainers, who are continually working to find better and more effective ways for locating or creating sound-bites, sensationalizing the news, and exploiting various forms of devastation, violence, and virtual reality spectacles to numb us all and hooked to the television screens.

On the other hand, those who may not be so much interested in finger-pointing and blaming others for everything that is wrong, may find their cues from Krishnamurti to realize that our own unhealthy patterns of behavior contribute to the mess we have come to hate. We constantly feed them with our thoughts and our deeds. It is interesting to know that Krishnamurti continued his statement as follows:

Now, I started this note by expressing my fascination with the world around us. As knowledgeable as we think we are, it is quite a humbling experience to realize that there is almost an unending depth for exploration to any subject that we'd like to explore.

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Consider, for example, the following (second) question: "What are the characteristics of the best running shoes"? Most of us feel -- with the help of our ego and the inadequate education that we go through, and the aid of the great deal of advertisements we are bombarded with everyday -- that the best shoes are those with the most famous brands like . . . . (replace with your favorite brand name) . . . . Very rarely do any of us consider the simple fact that many of the animals run much faster and much longer than we do, generally, and yet they all do this barefoot. Hence there must be some benefits to barefoot running. You might have heard about a recent book by Christopher McDougal, entitled "Born to Run: A Hidden Tribe, Super Athletes, and the Greatest Race the World Has Never Seen". A couple of years ago, Chris gave a presentation at Google, which is quite entertaining. Chris McDoudal tells us about the story of a fascinating journey that was started when he wanted to find the answer to a very simple question: "Why does my foot hurt?" In fact, barefoot running is fast becoming a fad (and an industry!-) in itself.

What amazes me is that almost anything one can think of is full of mysteries, unanswered questions, unknowns, and unexplored territories, no matter how simple. Here is an illustrative example to drive this point home: Ask the following question from anyone:

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When I ask this question from someone, most hesitate at first, and then start looking for an answer "out there". So, I would continue with the claim that arguably the best thing that I could possibly know in the whole world is "MYSLEF". After all, I have been accompanying, living with, feeling, sensing, ... myself for as long as I remember ... even before I remember! Perhaps some of the first few words that we learn irrespective of our mother-tongue are "I", "me", and "mine", when we are mere babies. Yet, trying to answer the very simple questions "What am I?", "Who am I?" leads to an unending spiral of discovery and frustrating road blocks. Most people answer these questions in a way that is almost meaningless. For instance, consider the concept of "soul" or "spirit". It seems to me that those who believe in the so-called spiritual world and feel some affinity to the concept of soul have packaged all the unknown (some may even say unknowable) about ourselves into a mysterious blob and call it our "soul". Many of these people have long given up the search to understand what it is, cause they feel they already know it :)

Some others, on the other end of the religious spectrum seem to be so arrogant -- not to mention ignorant -- that they deny any and all belief or investigation into the unknown territories as bogus, fraud, or irrelevant. Take for example, Michael Shermer, PhD, the Editor-in-Chief of Skeptics Magazine, who as you can hear at segment 26:58 -- 28:00 in a recent panel discussion, even the existence of mind -- though he has no problem writing about The Mind of the Market! This prophet of the skeptics, through such a denial, moved single-handedly to resolve the Mind-Body Problem -- which has occupied numerous scientists and philosophers for Millennia -- once and for all! For anyone who agrees with Dr. Shermer, I recommend this very interesting and easy to follow 24-lecture program entitled "Brains, Consciousness, and Thinking Machines", by The Great Courses Company.

Interestingly enough, according to the wikipedia:

Some others, on the other end of the religious spectrum seem to be so arrogant -- not to mention ignorant -- that they deny any and all belief or investigation into the unknown territories as bogus, fraud, or irrelevant. Take for example, Michael Shermer, PhD, the Editor-in-Chief of Skeptics Magazine, who as you can hear at segment 26:58 -- 28:00 in a recent panel discussion, even the existence of mind -- though he has no problem writing about The Mind of the Market! This prophet of the skeptics, through such a denial, moved single-handedly to resolve the Mind-Body Problem -- which has occupied numerous scientists and philosophers for Millennia -- once and for all! For anyone who agrees with Dr. Shermer, I recommend this very interesting and easy to follow 24-lecture program entitled "Brains, Consciousness, and Thinking Machines", by The Great Courses Company.

Interestingly enough, according to the wikipedia:

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Skeptics, and fundamentalists aside, it is pretty clear that not only do we know abysmally little about ourselves, physically, mentally, or emotionally, but -- more often than not -- we are also not even interested in knowing ourselves that well. We don't have the time, patience or interest in finding out what may be causing us some pain. Say you wake up in the morning and you have a headache or a pain in the ...... (fill fill your favorite! pain or frequently sore limb) ...... So, what do we usually do? We go to the medical cabinet or call the doctor or pharmacist to prescribe a medication for us to take in order not to even feel the pain. Why? Because we are not interested and do not have the time to see what may be wrong. We have the meeting to attend, the game to go to, the job to finish, and all sort of other excuses. And this is perhaps the easiest of our problems, which is understanding our physical ailments and pains.

Understanding our emotional, and mental ailments or what makes us tick and do what is way more complicated and takes much more time, attention and dedication than most of us are willing to allocate for it. Then, we wonder why we act so violently, irrationally, and selfishly in the society. No wonder we have been creating so many problems and issues.

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The more I think about these concepts the more I realize that our knowledge and understanding is often so flimsy and so shallow. Let me give another example. Everybody in the primary school learns the concept of integers and is able to fully grasp the concept of a prime number. Over 2300 years ago, the Greek mathematician Euclid knew that there are infinite number of primes. (What is known as) Euclid's proof for the infinitude of Primes, is very simple and elegant. Many more proofs for this fact, are known today. Some of them are listed in this paper.

So, Euclid knew that as you walk up the integer ladder, no matter how far you go or where you are, there are always infinite number of primes ahead of you. Since then, countless number of amateur mathematical enthusiasts as well as professional mathematicians have tried to find a simple way to generate prime numbers or to efficiently identify whether a given integer is prime or not. Think about it for a moment. The numbers have been sitting there for all to investigate. They have never gone anywhere. Yet, we have failed to come up with simple and efficient algorithms that can tell apart the primes from composites. Best known algorithms for finding the first prime number larger than a given integer N, become miserably slow, when N becomes large. Although there are some reasonably efficient algorithms for telling primes apart from composite numbers, they are not practical for many large numbers, say numbers with hundreds of thousands of digits or more. There are also probabilistic and randomized primality testing algorithms that give the answer with high degree of confidence, but they may declare a number prime when it is composite. Although the error rate could be made arbitrarily small, the approach fails to provide a definitive answer, especially for huge numbers which may have millions of digits. A good source of information on prime numbers is The Online Prime Pages, maintained by Professor Chris Caldwell. This link, and this one are some interesting talks on the subject of prime numbers and the patterns in them. Since the dawn of the electronic age, and the advent of public key encryption, studying primes has become increasingly more important. This talk by Whitfield Diffie, at the Computer History Museum, discusses the historical development in the information security, which might be of interest.

So, Euclid knew that as you walk up the integer ladder, no matter how far you go or where you are, there are always infinite number of primes ahead of you. Since then, countless number of amateur mathematical enthusiasts as well as professional mathematicians have tried to find a simple way to generate prime numbers or to efficiently identify whether a given integer is prime or not. Think about it for a moment. The numbers have been sitting there for all to investigate. They have never gone anywhere. Yet, we have failed to come up with simple and efficient algorithms that can tell apart the primes from composites. Best known algorithms for finding the first prime number larger than a given integer N, become miserably slow, when N becomes large. Although there are some reasonably efficient algorithms for telling primes apart from composite numbers, they are not practical for many large numbers, say numbers with hundreds of thousands of digits or more. There are also probabilistic and randomized primality testing algorithms that give the answer with high degree of confidence, but they may declare a number prime when it is composite. Although the error rate could be made arbitrarily small, the approach fails to provide a definitive answer, especially for huge numbers which may have millions of digits. A good source of information on prime numbers is The Online Prime Pages, maintained by Professor Chris Caldwell. This link, and this one are some interesting talks on the subject of prime numbers and the patterns in them. Since the dawn of the electronic age, and the advent of public key encryption, studying primes has become increasingly more important. This talk by Whitfield Diffie, at the Computer History Museum, discusses the historical development in the information security, which might be of interest.

As of this writing, the largest known (and provable) prime is (2^34112609 - 1) which has just under 13 million digit numbers, and was discovered in August 2008, and won the Electronic Frontiers Foundation's $100,000 prize. There are also prizes worth $150,000 and $250,000 for the first 100,000,000 digit and 1000,000,000 digit provable prime numbers. Claim your prize money here, if you can find them.

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So, let me repeat: The numbers have been sitting there for all to investigate. They have never
gone anywhere. Yet, we have failed to come up with simple and efficient
algorithms that can tell apart the primes from composites, or say find a 10,000,000,000 digit prime! Note that according to the Prime Number Theorem there number of primes smaller than or equal to a given number N is roughly N/ln(N), where ln(N) is the natural logarithm of N. In other words, there are a huge number of 100,000,000 digit prime numbers, and many more 1,000,000,000 digit prime numbers. Each of them -- once provable to be prime, of course -- should quality for one of the two prizes stated earlier.

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Isn't it amazing -- not to mention humiliating -- that after all these years we are still so miserable at locating the primes on the number line? Of course, this is not to trivialize or dismiss a lot of progress that has been made by many of those who have passionately sought to investigate and discover the hidden patterns, properties, rules and principles in various fields. Here, here, here, here, here, here, here, here, and here are some interesting books and monographs on the subject of prime numbers, for example. The fact that we have yet to find an efficient algorithm for factoring numbers into their prime constituents is exploited for secure communication, and lead to the discovery of the RSA Public Key Encryption. The problem of finding the prime factors of an integer, which can be thought of as the reverse operation of multiplying the prime factors to get the product can be stated in its very simple form as follows: Given an integer

*n*which is the product of two prime numbers*p*and*q*, find*p*and*q*. Watch this clip and this one for some more on this and the celebrated P vs. NP problem which is one of the 7 Millennium problems, whose solutions carry $1,000,000 in cash prize, each.
Now, one may even ask whether there are even such things as "the basic rules and principles" in nature, physics, etc. If you think about it carefully, you may realize that it is simply an assumption that there are such things as the basic laws of physics. But of course, many scientists all after these fundamental laws, and some of the most celebrated personalities in the history of science have crafted a set of so-called principles that we have come to accept as the basic, unquestionable, but only for a little while. Because, interestingly enough, every so often another scientist comes along challenging what has been set in stone for Millennia, centuries or decades, and revises the past theories in pretty unpredictable ways. The story of the advancement of science has been a pretty amazing one. There is no reason to believe that what we currently consider a basic law of physics for example continues to be so in a couple of hundred years -- or even decades -- from now. That, to me, is one of the really fascinating aspects of the world we live in.

One of the more interesting and beautifully written non-technical
science books that I have come across is Gary Zukav's book entitled "The Dancing Wu Li Masters". Highly entertaining, inspiring and informative. An abridged
audio version of the book is available here.
It provides an interesting and poetic discussion and summary of the development that lead to the discovery of Quantum Physics for
those who may be interested. A fundamental area of science, which is notoriously incomprehensible. Nobel Laureate in Physics, Richard Feynman said the following at segment 7:45 to 8:10, in a very entertaining and illuminating public lecture delivered at Cornell University in 1964:

-- Richard Feynman |

His, is not the only quote telling us about the great mysteries and unresolved issues about one of the most successful scientific theories of our time. Here are a few more such quotes from prominent physicists and Nobel laureates, uttered in a quantum theoretic context:

Fascinating, isn't it? There are many unresolved question as to what quantum mechanics really means: a fascinating subject, all by itself, referred to as the "Interpretation of Quantum Mechanics." British Physicist and one of the founders of Quantum Theory of Computation, David Deutsch, seems to adhere to a very interesting and controversial interpretation known as the "Many Worlds Interpretation of Quantum Mechanics." Interestingly enough, the emergence of the quantum computation and quantum information, as vital and active areas of research is to some extent due to discoveries in mid 1990s on how to exploit some of the mysterious properties of quantum mechanics to solve some important algorithmic problems remarkably more efficiently than the best algorithm that has ever been devised using classical computing machinery. One of these was the discovery in 1994 by Peter Shor that some of the strange properties of quantum mechanics could be exploited to find an efficient quantum algorithm for solving integer factorization problem. Here is a half hour skit by the self-described "general utility nerd", Doug Sweetster, entitled "The Stand-Up Physicist: "Why Quantum Mechanics is Weird."

-- Erwin Shrödinger |

-- Max von Laue |

-- Niels Bohr |

-- Carlo Rubbia |

It would be fitting to provide an interesting quote from American biologist Edward O. Wilson that I came across a couple of years ago:

Interestingly enough, Edward O. Wilson was recently invited to Montana State University to moderate a very illuminating and sobering panel discussion on the "Prospects for the Human Species." In the introduction before introducing the panelists he made a very interesting comment that deserves to be framed and pondered upon:

From there, things get even more interesting. Each of the panelists provides an opening statement and then the podium is opened for questions from the audience. I highly recommend listening to this program and pondering upon the issues raised. It is somewhat disappointing that at the time of this writing, there have been a grand total of merely 1942 views.

I would like to end this essay with a wonderful song by the late singer and song-writer, Phil Ochs, entitled When I'm Gone. Here, here, here, here, here, here, and here, are some more recent performances by some young -- and old -- performers. Enjoy!

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