Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

23.4.18

Freeman Dyson describes his life and science, and his hope for humanity.




Disturbing the Universe – Freeman Dyson (1979)

            While exploring the bibliography section of some of the science books I have read recently, I came across a mention of this book, by noted theoretical physicist and mathematician Freeman Dyson, and thank goodness the amazing M.D. Anderson Library had a copy for me to check out.  I had previously read that Mr. Dyson wrote some very interesting books which did not stick strictly to equations and mathematical rigor, but instead explored the Universe through Mr. Dyson’s inquisitive mind.  These types of books provide a great insight into the minds that have shaped our modern scientific world.

            The preface to this book details the circumstances leading up to its writing.  The Arthur P. Sloan Foundation started a book series.  They requested eminent people, people who were the leaders in their respective fields, to write something for publication.  It could be a small tome on pure mathematics, or a detailed history of a great scientist’s life, or, as in the case with Freeman Dyson, an exploration of his own life in the sciences, mixed in with the wisdom and gathered insights that he developed through his life.  Because of this, the title of the book,  Disturbing the Universe, is very apt.  The story contained within is of Freeman Dyson and the many times in his life where a chance encounter, a choice made, or an accidental experience, have led to a shake-up, a disturbance, in the way he saw and understood the Universe at large. 

            I love how this book begins.  It pays homage to the written word and the human imagination as being the grounds upon which greatness is dreamed of.  Mr. Dyson begins by detailing a children’s science fiction story that really stuck with him from his childhood, The Magic City by Edith Nesbitt.  This story detailed an alternate world, and Dyson mentions one rule that the story’s citizenry needed to heed.  In this world, you are free to choose to use any type of technology available, but, once chosen, the individual would have to use that technology, and ONLY that technology, for the rest of their lives.  For example, should a person choose to use roller skates as a means of transportation, that person, once they chose, would be denied the use of any other transporting technology.  This idea became a metaphor for Freeman Dyson.  He came to understand that any technology that is created by humans has the power to alter anything and everything that comes after its creation.  The scary part is that, as Freeman Dyson explains, 99% of all new technology stays purely as a clever toy for the powerful and rich few.  Only around 1% of all created technology finds a wide use and spreads throughout the human world.  The problem lies in that there is no way to predict what tech will catch on, and what the moral and philosophical implications and repercussions will be.  Once the printing press was invented, there was no shortage of people who sought to destroy or abandon this technology because of the fear that printing presses would allow for the dissemination of ideas and knowledge contrary to what the powers-that-be wish the masses to read or know about.  Freeman Dyson understood that this same problem applies to even seemingly innocuous technology, such as household goods, and not just to new weapons or giant machines.

            Mr. Dyson goes on to discuss his education and development into one of the premier mathematical and theoretical minds of the 20th century.  He details his involvement in the British Air Force during WWII, and how the omnipresent bureaucracy showed him the blind stupidity of man, the illogic of “leadership”, and the brutality of those that send our youngest to die in war.  He saw the stupidity of the Air Force equating mission successes with number of sorties flown, or number of planes involved, and not with whether the target was actually hit, whether the crews came back alive, or whether their methods were pure suicide for these air crews.  The crews were never told the amount of planes and airmen that came back or that died or that were lost.  They were fed lie after lie after lie to keep them motivated to enter unsafe flying targets and get blown the F up over some unseen and unimportant target.  This shaped him very much.  He stated that when he moved to the USA, it was not until the Vietnam war that the people of the USA lost their innocent and naïve belief in the inherent goodness of their leaders.  The British and most of Europe had lost this during the interminable First World War.

            One of my favorite passages deals with Freeman Dyson’s relationship with my idol, Richard P. Feynman.  The two worked together while at Cornell University, and shared a road-trip across the USA.  His descriptions of Feynman and their relationship are so cool.  Freeman Dyson was lucky to work with the greatest minds around, from Feynman to Hans Bethe, to Robert Oppenheimer.  He is very honest in his portrayals of these peers of his.  It is always reassuring to me to hear of how deeply scientists can disagree over issues and still maintain a collegial working relationship and even be very close friends.  More people could learn from such things.

            Much of the latter half of this book deals with the various political and social engagements that Freeman Dyson took up after his main work was complete.  He is candid about his failures and humble about his achievements.  The last chapters deal with Mr. Dyson’s vision for the future of humanity, of life itself, and make for very moving reading.  I wish his vision of our future indeed comes to pass, allowing humans to differentiate themselves by exploring our solar system, creating colonies, and spreading Life through the cosmos.  Dyson has done the math and he feels, much like I do, that, while Life existing on Earth seems to point to the ability of Life to be anywhere in our Galaxy and Universe, the truth may very well be that the myriad conditions needed, not only for cellular Life to develop, but for the planet to be stable enough for Billions of years to allow for the creation of “Intelligent” Life, are only found here on our Planet Earth, out of all the possible worlds of our Multi-verse.  If there are a quadrillion planets in our Universe, and the odds against Life arising are 1 in a quadrillion, then we are indeed alone.  If the odds turn out to be 1 in a septillion or bigger, then the very existence of Life on Earth can be seen as the ultimate miracle and all of our humanity as a blip in the vast expanse of space-time.  I too think we humans have a mandate to spread Life, in all forms, throughout the Galaxy and then the Universe.  I hope Freeman Dyson’s vision comes to pass.  I will definitely be on the lookout for more books by Mr. Freeman Dyson.

(This book can be purchased here:  AMAZON  )

28.2.18

Quantum Gravity, and the history of human exploration into the nature of our Universe






Reality is Not What It Seems: The Journey Into Quantum Gravity – Carlo Rovelli (2014)

            Around a year ago I read and reviewed another book by the Italian physicist Carlo Rovelli.  (Click Here for that Review) That book was a detailed history of the man known as Anaximander, of whom I wrote that he is “the earliest human that we have record of who helped create the logical and rational framework that set the stage for the scientific revolution all humans have experienced over the past 250 years.”  At the time I bemoaned my inability to read his then-current book Reality is Not What It Seems.  Thank goodness for the good folks at the M.D. Anderson Library of the University of Houston.  They acquired the English translation and this is what I managed to stumble across during my browsing.

            Where to start?  This book is an attempt by Mr. Rovelli to discuss the history of our collective efforts to understand what constitutes the fabric of Reality, the elementary nature of our selves and everything that exists.  Beginning with Anaximander, Plato, and Aristotle, Mr. Rovelli describes how each of these ancient geniuses grappled with the substance of reality, and with the ability and limits of the human to comprehend this reality.  He details the amazing and near-miraculous insights from these men that propelled our entire world forward in the quest to understand. Leuccipus and Democritus formed the basis of “atomist” theory, purely through rigorous analytical thought, understanding that all matter is composed of small indivisible parts. Democritus alone was such an amazing thinker.  It is a shame most of his massive output has been lost to history.

            After the initial period of discovery, once monotheistic religions took over the human landscape, progress was effectively halted, and the knowledge of our forefathers was lost in the Western World.  Scientific fact was replaced by dogma and blind faith in the make-believe magic stories of priests and the governments which aligned themselves with religions.  It was after nearly a thousand years of barbaric ignorance that travelers and scholars visited India and brought back the wisdom of the ancient Greeks, knowledge which was critical to creating the modern world we all share.  From this influx of ancient wisdom and science, someone like Isaac Newton was able to understand and explain what he saw as the structure of the Universe.  Newton saw a fiercely deterministic static Universe.  His laws of motion and his invention of the Calculus allowed humans to plot star and planet trajectories centuries in advance, and his mathematics and science helped the Western world shake free of its religion-induced intellectual coma.

            The world as Newton saw it was un-changing, and infinite.  Scientists continued to study the Universe, finding and creating new tools with which to explore.  In the early 1900’s, Albert Einstein proceeded to shake the world to its core, much like Newton had done before.  Einstein understood that there is no static Universe and that everything is constantly in motion relative to everything else.  He was the first human to grasp that time is not a specific thing, existing separate from the Universe.  He saw that we live in an ever-expanding Present.  Einstein also saw that the world is not what Newton stated.  There is no matter and energy floating in empty space.  There is just matter and energy existing in space-time and gravity is merely the deformation of this space-time by massive objects.  All of these things have been verified countless times.

            What Einstein did for the world at large, quantum mechanics did for the world of the very small.  It is an extremely successful theory and its predictions have been validated countless times as well.  Quantum Mechanics shows us that the world is made up of quantum objects, which have probabilistic traits.  One cannot know everything about a proton, unlike in Newton’s time, when it was assumed that this was possible.  This indeterminacy has been proven to exist throughout the Universe at all quantum levels.

            All of this leads into the discussion of Quantum Gravity.  Einstein’s Relativity and quantum Mechanics work together in most ways, but in special cases, such as black holes, or singularities, both theories fall apart.  Gravity can only be calculated in the macro sense, and quantum effects never give definite answers.  To combine these two theories is the current goal of theoretical physicists around the world.  Some have been working on String Theory, which predicts the existence of super-symmetric particles.  These particles have not been seen in experiments at particle colliders.  This lends more weight to Rovelli’s field, which is studying Loop Quantum Gravity, which seeks to study the constituents of gravity, or the quanta of gravity. 

            Light acts as a wave and a particle.  The quanta of light is the Photon.  Gravity seems to act as both a wave and a particle, gravitational waves having been detected as recently as 2016.  Loop Quantum Gravity postulates that the smallest quanta of gravity are actually small closed “loops” as opposed to points.  He goes into a great explanation of his research and of the ways that scientists have arrived at this idea, one which seems to be more promising that String Theory. What a great book.  The Bibliography at the back will keep me happy for a while too.  I wish I could better describe how much is contained within this awesome book,  but you will have to read it for yourself.

(This book is available for purchase here: REALITY IS NOT WHAT IT SEEMS )

20.10.15

Short Stories about Math? YES!





Fantasia Mathematica – Clifton Fadiman, Ed. (1958)


            Having just finished a dense and rigorous philosophical treatise, I needed something which would spark my imagination and my intellect.  I found this collection of math-based and math-referencing stories, most of them under 10 pages long, and proceeded to escape into science fiction.

            Clifton Fadiman, the editor of this collection, was inspired to collect this anthology after reading a few short stories that used mathematics as either a plot point or as a crucial element of the characterization.  In 1958 the genre of science fiction was still obscure and marginalized.  Because of this, many of these stories were published once in pulp magazines and then forgotten.  Some of them are from the very masters of the genre, such as Heinlein, Clarke or Bradbury, while others are from writers that have faded into obscurity.

            I remember picking this book up maybe 20 years ago and not finding it interesting enough to finish.  I guess in the intervening decades I have either picked up more mathematical knowledge or I have grown more adult and capable of enjoying a story purely for the intellectual curiosity of it.  Most of these short stories are great fun, and many illustrate mathematical points which are still explored by today’s mathematicians.  Topics range from topology, to extra-dimensional geometry, to geometric proofs.  There is even a back section which contains mathematical poems, limericks, and other such things.

            My favorite story of the bunch involves a mathematician making a bet with the Devil, all dependent on the Devil answering properly whether Fermat’s Last Theorem is true or not.  This conjecture was unsolved for centuries until a lone-wolf mathematician provided a suitable proof.  I have no idea what the math used was, but then again, neither does 99.999% of the population!  At the end of the tale, the Devil sits befuddled, beaten, and sad.  He spent his time learning all the highly complex math required to even tackle Fermat’s Last Theorem, and was not able to comprehend how to go about solving it.  Math wins.

(To read A Subway Named Mobius, one of the short stories from this volume, please click here: http://westongeometry.pbworks.com/w/file/fetch/61244911/SubwayNamedMobius.pdf )

(This book can be purchased here:  AMAZON  ) 

21.9.15

"Life" is a Game with Very Simple Rules





The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge – William Poundstone (1985)

            What a difference a couple of decades make.  I first picked this book up while an undergrad and could only grasp about one quarter of the information provided by Mr. Poundstone.  I am glad that I can read it now with the necessary knowledge and background to be able to make sense of this book.

            I think what confused me in my previous attempt to read this book was that Mr. Poundstone frames the titular discussion within a description and history of a computer game called “Life.”  This game, which starts with a very basic set of ground rules, can and does lead to infinitely different outcomes, some of which function much like cellular life does.  The British mathematician John Conway created this cellular automaton, in 1970.  The game consists of a 2-dimensional field, much like a chess board, whose “cells” can only exist in “on” or “off” states.  (Think binary code of 1’s and 0’s).  At every turn, each “cell” follows a specific and rigid set of rules to determine if it will be “on” or “off” in the next turn.  This goes on and on until the pattern becomes static, or in some non-static equilibrium.

            Having created such a rigid system with minimal rules, Conway was surprised to see the development of patterns, growth, and complexity that resulted solely from the ground rules.  This leads the author to show how the game itself proves that exquisite complexity can arise from a very simple set of ground rules, something that scientists had debated for centuries.  Some people saw the infinite complexity of our Universe and assumed that the creation of such a wide variety of objects and energy must arise from an equally complex set of natural laws.  Others argued that the complexity evident in the Universe could result from a very simple initial state.  It was a shock to see that a simple computer game could model the extreme complexity of cellular life.

            Mr. Poundstone describes the game as recursive, meaning to “relate to or involve the repeated application of a rule, definition, or procedure to successive results.”  Every “round” of the game applies the exact same rules to all areas of the “board.”  The Universe, our Universe, works the same way.  Our Universe is inherently recursive.  The wide range of experience, phenomena, and mystery in our Universe arises from the repeated application of a very small, limited set of “rules” as well.  It is these “rules” that physicists have been seeking for the past 100 years, with good results.

            Having read the book, I found a version of the Life game that works on my phone.  It is so addicting!  I can create any initial state, and hit “go.”  The rules of the game itself create endless new patterns, many of which start to become familiar once you have played the game several dozen times.  Researchers have spent countless hours discovering different aspects of the game of Life that mirror our own natural Universe.  There are static patterns.  There are patterns that oscillate from one state to another indefinitely.  There are patterns that travel across the plane of the game.  There are patterns that create other patterns even!  It is super cool for a rigorous nerd like myself. 

            I am glad I read this book again, and I feel that it provides a great insight into the rise of complexity in our Universe.   Too many people see complexity as evidence of intelligence.  That is a shame because it stunts our thinking.  It keeps us indebted to the idea that only something greater than us could create the world around us.  It also does not impress upon people the risks inherent in any action, and how even the smallest thing can create massive complexity in its wake.  If more people understood this then maybe they would be more responsible with how they raise their kids, treat other living beings, and exploit our natural resources.

(To play the Game of Life online, click here:  http://www.bitstorm.org/gameoflife/

(This book can be purchased here:  AMAZON  )