Thomas S. Kuhn – The Structure of Scientific Revolutions

This book is a proof how important interdisciplinary researches are, as it took a historian to bring a whole new aspect to science and scientific works.  Until Kuhn, and even after him, people usually thinks of scientific works as a cumulative field of research. I made this mistake as well, and without reading this book, the concept of paradigms made me surprised and even deeply disappointed in physics and mathematics as well. Though it’s something people can expect in several cases like from the different kinds of geometries, realizing that science is not advancing in a cumulative way can be a shocking experience.

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What most people mean in a cumulative way is that science advance with knowing more and more about the world. What basically Kuhn writes in this book, is that the different eras of science have different worlds – as in different contexts, different rulesets, and they can be quite discrete to each other.

There are periods of ‘normal science’ that are sometimes interrupted by problems they can not explain and produce a crisis situation that changes the framework of the next era. These frameworks and theories limit the problems scientists work with, they do not need to explain everything or cover every possible fields. In very basic terms science advances by avoiding these crisis situations, we could say it tries to have the least possible amount of mistakes instead of having the most possible amount of knowledge.

This is kind of the essence of the book, but it has more interesting details of course. As a historian, Kuhn has countless examples of how different science periods work, how normal science limits the fields of problems to avoid crisises as long as it can, how some revolutions happen in a specific field without altering anything in others, or how the science from thousands of years earlier was fully scientific in it’s given context.

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Douglas Hofstadter – I Am A Strange Loop

Finally a book that proves we are fractals. Joking aside, in a more serious approach Hofstadter states in his book that consciousness can arise from a pattern called a “strange loop”.  The core problem of cognitive science in general is, that how can chemicals and inanimate matter form such thing as consciousness, that seems to be much more complex and chaotic than the machine-like environment of biology and physics. A strange loop is a hierarchy of levels, each of which is linked to at least one other by some type of relationship. In a strange loop hierarchy there is no well defined highest or lowest level, moving through the levels, one eventually returns to the starting point. Self-referential thought patterns, fractals, the ideas behind some works by Escher, certain music pieces like canons are examples for this. In short, a strange loop is a paradoxical level-crossing feedback loop.

The famous Liar’s Paradox (“This statement is false.”) is kind of a strange loop, as the sentence is refering to itself causing a logical paradox, we are oscillating between two levels of it’s hierarchy, always arriving back to another layer.

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One rarely comes across such an exciting book as anything by Hofstadter, his writings are challenging but rewarding. The author has a really gentle way of explaining, I’m pretty sure he must be a really good teacher, but this doesn’t change the fact that his books have such technical depth that is often not so easy to understand, I read this book two times already and probably will need more reads still.  Even if you can’t follow every threads and puzzle pieces, it is enjoyable to rediscover familiar thoughts or get new perspective on things by the concept of a strange loop.  Because as you see from the examples, the actual subject of the book are everyday things, like well-known biology, ancient tales, or famous theorems like Gödel’s.

There are several novel-like parts, the introduction already feels like a biography, and yet it’s the perfect introduction to such subject. Hofstadter mainly explains why he became vegetarian, and how do the consciousness of plants and animals differ greatly. Besides the economic reasons (the land you grow crops for animals to eat later could be used to feed us instead), this part of his book was a great fuel for my vegetarian diet as well. Though eating either plants or animals are killing, the main diference is in consciousness, as plants have no capability of self-refering thoughts. They feel pain, but they don’t know the magic concept of “I”.  Pain is truly a chemical reaction in this level, not a personal phenomena like for animals and especially for humans.

Compared to his earlier book, “Gödel, Escher, Bach”, this one is kind of easier to read because of the biography-like parts. While the first one was filled with technical examples, this latter one is filled with stories of life. If you decide to read any of them, then you may need to read both, the order is not important.

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James Gleick / Chaos

“There’s a fundamental presumption in physics that the way you understand the world is that you keep isolating its ingredients until you understand the stuff that you think is truly fundamental. Then you presume that the other things you don’t understand are details.”

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This book is maybe the most popular one ever written about chaos science and nonlinear dynamics in general. Gleick kind of wrote a non-fiction novel that is very accurate even if non-technical. It’s even a better read than Hawking’s books because it has all the details to understand some concepts without the really lengthy, almost document-like history parts. It may be a personal preference of course, but I’m not that interested in scientists lives than their actual work.

I’m just presuming things of course, but it may be an effect of the online anonymity I’m used to, and the idea that paradigm shifts happen on their own, certain persons just accelerate the advancing tendencies, so in the terms of a historical scale they are not that relevant. You can see it in several places, and I don’t question the genius of great scientists but no work can exist without a strong background, there is no genius without context.

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In general, nonlinear systems and chaos is like everything in physics besides the textbook examples. Turbulence, meteorology, population growth, market prices, but the famous example of Mandelbrot about the coast of Britain can show one how easy is it to find such phenomena in everyday things. The example is about scaling – you ask how long is the given coast, and give an answer in kilometers or miles. With a smaller scale you measure it again, like in inches or centimeters, so the coast seems bigger. Next you could move on and start measuring in nanometers, then so on until the very core of matter.

The problem shows that in nature a circle is not a circle, a coast is not a line, but most of the systems are turbulent, almost chaotic in the sense of physics. This is not the real problem yet even, as you can get quite close values by working with lines and circles, but some things are more sensitive to (their initial) values than others. Friction, weather, fluids… Extremely little changes can lead to entirely different results. This is why chaos is important.

When you talk about this subject, usually you can’t be really technical and careful wording is important. After all, fully understanding this matter takes years of mathematics and physics studies lots of people including myself, don’t have. Non-linearity in general is a concept that is well-defined, but without giving the certain area we use it in, there’s not much to say about it unless you state something like “functions that change in a way that don’t resemble to a line”. Little changes lead to big ones, they have ups and downs, often hills and mountains seemingly randomly, as the output of such a system is not directly proportional to the input.

Actually we meet such things a lot, because even the trigonometric functions or anything with an x on power is in fact, not linear. As these systems change in time, their corresponding differential equations require linearization or other tools so we can handle them.

The book starts with introducing us to Feigenbaum and Lorenz with their adventures in meteorology and modelling weather environment with computers. Gleick carefully avoids real details of the field, that is kind of understandable because of their complexity. He does not skip through important ideas or parts, though. Very early in the book we meet strange attractors and phase space, and they are difficult enough to fill a whole book with fully explaining them, but in elegant manner the author skips the little details to give us a picture of them we can grasp.

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Although these systems seem unpredictable, an approach is finding strange attractors that are like small areas of regular behavior in the mentioned phase space. The phase space is not real space but an abstract map of a whole system. All possible states are represented, with each possible state of the system corresponding to one unique point in the phase space.

Through the stories of people we learn new concepts like fractals, turbulence and the state and frequency changes leading to such behavior, how population biologists use chaos theory as well, and such fields of science discovering the methods of chaos for themselves. Calling it chaos is misleading, the most important thing is that the methods Gleick writes about can predict numerous systems that were believed to be truly chaotic, like signal noise in cable transmissions.

Though being 300+ pages this book is an easy read, so really recommended in my opinion to anyone interested in a (new) field of physics. Yeah, well. It’s not new any more since decades, but still extremely fascinating.

Pictures:
http://mathworld.wolfram.com/LorenzAttractor.html
http://fractalfoundation.org/OFC/OFC-10-4.html

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