#BookStudies I began this book as a way to dive into chaos theory, but as I got deeper into the material, I came to realize that I was diving further into familiar territory. As he says later in this book, it is about emergence more than chaos. He describes chaos theory as having a primary tenants of reversibility and pattern formation. ### DS - Pg. IX - Computation of Reality Should Be Simple > It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what foes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the checkerboard with all its apparent complexities. > - Richard Feynman, The Character of Physical Law Once again, it is good to hear from Feynman. > The simplicity of nature is not to be measured by that of our conceptions. Infinitely varied in its effects, nature is simple only in its causes, and its economy consists in producing a great number of phenomena, often very complicated, by means of a small number of general laws. > - Pierce Laplace (1749-1827), Exposition du systeme du monde [[DS - Pg. IX - Computation of Reality Should Be Simple]] ### DS - Pg. XX - All There is to Chaos and Complexity > While doing this, I discovered that it wasn't so difficult after all. Both relativity theory and quantum theory were regarded, when new, as ideas too difficult for anyone except the experts to understand - but both are based on simple ideas that intelligible to the layperson willing to take the mathematics on trust. I ought not to have been surprised to find that the same is true of chaos and complexity. - but I was, and I clearly recall the moment when I finally got the message of what it was all about. As I understood it, what really mattered was simply that some systems("system" is just a jargon word for anything, like a swinging pendulum, or the Solar System, or water dripping from the tap) are very sensitive to their starting conditions so that a tiny difference in the initial "push" you give them causes a big difference in where they end up, and there is feedback, so that what a system does affects its own behavior. It seemed too good to be true - too simple to be true. So, I asked the cleverest person I knew, Jim Lovelock, if I was on the right track. Was it really true, I asked, that all this business of chaos and complexity is based on two simple ideas - the sensitivity of a system to its starting conditions, and feedback? Yes, he replied, that's all there is to it. I think I need to reflect on this conclusion, as it seems to resound. However, there are other sections in the book that I take issue with after reflection. We'll see if this is a similar conclusion. [[DS - Pg. XX - All There is to Chaos and Complexity]] ### DS - Pg. XXI - Surface Complexity Arises Out of Deep Simplicity > In a phrase attributed to Murray Gell-Mann, but echoing the speculation of Richard Feynmann quoted on page ix, the complicated behavior of the world we see around us is merely "surface complexity arising out of deep simplicity." It is the simplicity that underpins complexity, and thereby makes life possible, that is the theme of this book. This is the thesis of the book, and I think it did a good job of helping me understand complexity as emergence. [[Emergence]] [[DS - Pg. XXI - Surface Complexity Arises Out of Deep Simplicity]] ### DS - Pg. 4 - Martin Luthor's Astronomical Hubris > This fool wishes to reverse the entire science of astronomy; but sacred Scripture tells us that Joshua commanded the Sun to stand still, and not the Earth. > - Martin Luthor in reference to Nicolaus Copernicus' Sun-centered Universe, 1539 It pains me to hear Luthor err, but it wouldn't be his first time. He's not Jesus. I do love Galileo's response: > The Bible shows us the way to go to Heaven, not the way the heavens go. [[DS - Pg. 4 - Martin Luthor's Astronomical Hubris]] ### DS - Pg. 10 - And Nobody Laughed > Newton made the Universe seem an orderly place, with no room for interference from capricious gods. You can hear the poison towards religion in his text, but I find it funny the erasure modern scientists perform towards the great Christian minds. He continues in derision in the footnote on this sentence. > It's perhaps worth pointing out that as recently as 1609, when Johannes Kepler realized that something must be holding the planets in their orbits around the Sun, he had called it the "Holy Spirit Force," and nobody laughed. He says no one laughed as a joke, but the men who derived the truths of science were aware they didn't have the whole picture. The Holy Spirit is the worker of miracles, so He must be the one providing the source of science. It makes sense in a way. [[DS - Pg. 10 - And Nobody Laughed]] ### DS - Pg. 61 - Prediction of the Weather > We can predict the weather accurately provided it doesn't do anything unexpected. > - Ian Stewart, Does God Play Dice? Once again, I regret not getting a few paragraphs from the meteorology section of [[Areas/Reading/Books_Bk/Books/Turing's Cathedral - George Dyson/Turing's Cathedral - Dyson|Turing's Cathedral - Dyson]]. [[DS - Pg. 61 - Prediction of the Weather]] ### DS - Pg. 88 - Mandelbrot and Half Dimensions Made of Fractals > Mandelbrot realized that an object like the Peano curve could be described as having an intermediate dimension, in this case, somewhere between 1 and 2. A regular line was still a one-dimensional object, and a plane was still a two-dimensional object, but just as mathematics had to come to terms with the idea that there is an infinity of numbers between every rational number, so it would have to come to terms with the idea that there are entities with intermediate, noninteger dimensions. If the dimension of such an entity is not an integer, then it must be fractional. In order to have a word to describe such entities, Mandelbrot tells us, "I coined the word fractal in 1975 from the Latin *fractus*, which describes a broken stone - broken up and irregular." You can just as well, though, think of it as a contraction of the word "fractional" which, of course, comes from the same Latin root. If there is the potential for a half dimension between 1 and 2, what about 3 and 4? This could have interesting ramifications in my understanding of the boundaries between dimensions. What does a Peano curve made of boxes look like? How do fractals help us to see the boundary? The Cantor Set becomes the Sierpinski Carpet becomes the Menger Sponge and eventually becomes Cantor Dust. >There once was a Sierpinski gasket Who had a triangular basket He filled it with holes And said with a smile It's lighter and cheaper than plastic - Bing [[DS - Pg. 88 - Mandelbrot and Half Dimensions Made of Fractals]] ### DS - Pg. 122 - Turing Himself > It would be a machine that, in Turing's own words, > can be made to do the work of any special-purpose machine, that is to say to carry out any piece of computing, if a tape bearing suitable "instructions" is inserted into it. Funny that I haven't heard Turing's exact definition until now, even though I read two other books about his machine. I heard paraphrases, but never quotes. [[Areas/Reading/Books/Computer Science/Turing's Cathedral - George Dyson/TC - Pg. 251 - A Universal Machine to Imitate Other Machines|TC - Pg. 251 - A Universal Machine to Imitate Other Machines]] [[DS - Pg. 122 - Turing Himself]] ### DS - Pg. 127 - Turing, The Poisoner > Turing seems to have had an obsession with poison. His biographer Andrew Hodges describes how Turing went to see the movie 'Snow White and the Seven Dwarves in Cambridge in 1938, and was very taken "with the scene where the Wicked Witch dangled an apple on a string into a boiling brew of poison, muttering: 'Dip the apple in the brew. Let the Sleeping Death seep through.'" Apparently, Turing was fond of chanting the couplet "over and over again" long before he suited the action to the rhyme.' Interesting that he was interested in poisons. I might take that and run with it in regards to [[The Basilisk]]. [[DS - Pg. 127 - Turing, The Poisoner]] ### DS - Pg. 175 - Emergence of Complexity Through Buttons - A Potential Answer to When a Table Becomes a Table > We are ready for the next step, and the first real insightt into the emergence of life. Having stripped the study of complexity down to its bare essentials, and having found the same deep truth underpinning things as diverse as earthquakes, the stock market, and the movement of human populations, we discover that it is all built on networks, interconnections between the simple parts that make up a complex system. The importance of such networks in general and their specific importance for the emergence of life, have been investigated by Stuart Kauffman, of the Santa Fe Institute in New Mexico. > Kauffman has a striking analogy that brings out both what we mean by complexity and the importance of networks in emerging complex systems. He asks us to imagine a large number of ordinary buttons, perhaps 10,000 of them, spread out across a floor. Individual buttons can be connected in pairs by thread, but at the start of the though experiment there are no such connections. This is definitely not a complicated system in the everyday use of the term. But the way you connect the buttons turns it into a complex system. You start with just the buttons on the ground and a supply of thread, but with no button connected to any other button. Choose a pair of buttons at random and tie them together with a single thread, and if you happen to choose a button that is already connected to another button, don't worry about it; just use the thread to connect it to another button as well. After you have done this a few times, there will be a small amount of structure in the collection of buttons. Increasingly, you will find that from time to time you do indeed choose a button that is already connected to another button; sometimes, you will even choose a button that already has two connections, and you will link it to yet a third component of what has become a growing network of connections. > The way to tell how interesting this network has become is to pick up a few buttons, one at a time, and count the number of connections they each have with other buttons. Each connected cluster of buttons is an example of what is known as a component in a network; the buttons are examples of nodes, points that connections are connected to. The number of buttons in the largest cluster(the size of the largest component) is a measure of how complex the system has become. The size of the largest cluster grows slowly at first, more or less in a linear fashion as the number of threads connecting pairs of buttons is increased; because most buttons don't have many connections, already there is only a small chance that each new connection will add another button or two to the largest cluster. But when the number of threads approaches and then exceeds half the number of buttons, the size of the largest cluster increases extremely rapidly (essentially exponentially) as each new thread is added, because with most of the buttons now in clusters, there is a good chance that each new connection will link one smaller cluster (not just individual button) to the existing largest cluster. Very quickly, a single supercluster forms, a netowrk in which the great majority of the buttons are linked in one component. Then the growth rate tails off, as adding more threads usually just increases the connections between buttons that are already connected and only occasionally ties in one of the few remaining outsiders to the supercluster. Although the network has stopped changing very much as new connections are made, it is by now, without doubt, a complex system. > In the network, complexity has emerged naturally from a very simple system just by adding more connections, with the interesting activity associated with the changeover occuring all at once, right at the phase transition, where the system is switching from one state to another as a result of a very few final connections being made. By using Obsidian, you are demonstrating Kauffman's experiment of emergent complexity through connection. I do think that Obsidian is an emergence generator, as well as a syntopic study tool. This also links to cancer somehow. [[DS - Pg. 175 - Emergence of Complexity Through Buttons - A Potential Answer to When a Table Becomes a Table]]