My Thoughts on the book

I though this book was quite interesting at some parts, and then quite dry at other times. It was very interesting to learn about chaos and all the disorder around us. The book presented some concepts which I have never even thought of. I would recommend this book to anyone interested in science and learning about new ideas and concepts. The writing style flows well and is filled with numerous examples to explain complex ideas.  It was difficult to read at times, but overall I feel much more knowledgeable about how different systems work and how disorder plays a part in nature. However, from learning this much more, I know that I know very little of what's out there in the world.

Chapter 11:Chaos and beyond

This last chapter simply summarizes the road chaos has taken and materialized in different aspects of the world. First it summarizes the ways different types of system behave. Stating, ‘Simple systems behave in simple ways’ in terms of the way a pendulum behaves, the way an electrical circuit behaves, and populations fluctuate over time. These systems are only simple as long as they are reduced to few laws predicting their behaviour, which is not the case in the real world. Another concept reviewed is that complex behaviours imply complex causes. That is, an unpredictable system must be subject to random external influences.

We are reminded once again that nature forms patterns, of which some are orderly and some are disorderly. Some patterns are fractal, with structures that are self-similar in scale. The study of chaos in nature has given scientists, over the years, a way of examining nonlinear and chaotic systems in ways that have changed the way they view the world. Looking at all the parts that make up a whole system as opposed to just looking at the outward appearance of a system. We live in a world where order is found in disorder, and understanding this relationship will help further our understanding of life beyond our own. 

Chapter 10:Inner Rhythms

I particularly found this chapter to be one of the most interesting chapters in the book. It looks at the chaos found within the human body. First it takes a look at the heart. Even though the cardiac pattern is periodic, there are numerous nonperiodic pathologies which lead to a person’s death. When a doctor listens to a person’s heartbeat, he hears the pounding of fluid. Blood enters the heart through two large veins, the inferior and superior vena cava, emptying blood without oxyen from

 the body to the right atrium. The pulmonary veins empty oxygen-rich blood from the lungs to the left atrium. Blood flows from the right atrium into the right ventricle, and when the ventricles are full, the tricuspid valve shuts. Blood leaves the heart through the pulmonic valve, and enters the lungs through the pulmonary artery. When an artery is blocked, ventricular fibrillation occurs and a person dies. As an arrhythmia, disorders of the heart's regular rhythmic beating, occurs, the heart’s muscles beat in an ncoordinated fashion as it tries to pump blood. The heart cannot stop fibrillating on its own, it needs a jolt of electricity from a defibrillation device. This is because the chaotic motion is stable over time.

Two unsolved problems many people suffer at some point of their lives are jet lag and insomnia. People have a steady sleep-wake rhythm and body temperature cycle which can restores itself after disturbance. In isolation, without daily resetting cues, the temperature cycle is 25 hours, with low temperatures occurring at night. However, experiments by German researchers found that the sleep-wake cycle became independent of one another, as they became chaotic. The experiment subjects would stay awake for twenty hours, and then sleep for ten hours, while being totally unaware of the time if day. After returning to the real world, the time it took for the participants to return to normal varied greatly.

 

After looking at these chaotic behaviours, it is a wonder how the human body works perfectly in disorder. How does the rhythm of the heart suddenly become chaotic and uncontrolled? How do sleep pattern affect the physiology of the body? It is beyond our understanding how much stress our bodies can take before the inevitable happens.

 

Chapter 9: The Dynamical Systems Collective

This chapter looks at the works of a group called the Dynamic Systems Collective,a small group of physicist that formed in 1977. As a group, they sought ways of connecting theory and experiment. One of thequestions they pondered was could unpredictability itself bemeasured? They found the answer in a Russian concept, the Lyapunov exponent. This number provided a measure of topological quantities that corresponded to unpredictability. The Lyapunov exponent provided a way to measure conflicting effects of a system in phase space. It had the ability to provide a view of properties in a systemthat lead to stability ad instability. All, exponent, which were greater than zero, meant there would be stretching, and all exponents less than zero meant there would becontraction in the system. A Lyapunov  exponent of zero meant the system was at some sort of equilibrium.

The Lyapunov  exponent is

                                                   defined as:

 

After learning about this exponent, the Dynamic Systems Collective group related the exponent to other important properties. They looked at the Information theory and its relation to entropy. This came Second law of Thermodynamics, which states that entropy, or disorder, is constantly increasing. For example, if you divided a tub of water, with barriers, in half and filled one half of the tub with ink and the other half with water, and lifted the barrier, the two liquids would start to mix. However, the mixing will never reverse itself, because it continues to drift towards disorder. To evaluate the level of mixing at a particular point in time would require knowledge of the Information theory, which involves quantifying information. With the information theory, results are measured in bits, as opposed to digits or letters. A bit is either zero or one. The Dynamic Systems Collective was able

I found it very interesting how the information theory could be used to quantify and relay none numerical situations in ways that many people can comprehend.

 

 

Chapter 8: Images of Chaos

This next chapter deals with a complex concept which I have not encountered thus far in my education. I find it really interesting and will do my best to explain the idea. First, the complex plan is examined. In a complex plane, numbers from negaive infinite to positive infinite lie on a line stretching from east to west. These are real numbers. There is also a north-south latitude made up of imaginary numbers. These complex numbers are written in the following manner: 2+3i, I signifying imaginary number. Historically, imaginary numbers were invented to answer complex questions, such as “what is the square root of a nrgative number?” Then, the square root of -1 is i, and the square root of -4 would be 2i. This is an example of a complex plane, which is a geometric representation on the complex numbers in the real axis and in the imaginary axis.

In the complex plane, a complex object, the Mandelbrot set is found. TheMandelbrot, named after Benoit Mandelbrot set is a fractal. A fractal is a rough geometric shape which displays self-similarities at various scales, meaning it can be split in

to parts which are all reduced-size copies of the whole object. To graph the Mandelbrot set in a complex plane, first we need to find numerous numbers in the set. To do this, the equation, Z = Z² +  C, is used. Where C is the complex number corresponding to the point being tested, and Z is a number starting at zero. Only the magnitude of Z is used, and not the direction. To calculate themagnitude of a complex number, as add the square of the number’s distance from the x-axis to the square of the number’s distance from the y-axis, and take the square root of the result. As many complex numbers are tested, we can begin to graph the Mandelbrot set.

When thousands of points are plotted an image such as this one with form:

 

After taking time to understand this new idea, I found it really fascinating. There were some aspects of its make up that I didn’t fully understand, but for the most part the concept is not too complex. 

Chapter 7: The Experimenter

This chapter looks at different experiments performed by Albert Libchaber. I will focus on one of his experiments on convection, which I found to be quite interesting.

Libchaber was an intelligent experimenter who spent his days in laboratories. One of his early inventions, which was he used to measure a liquid’s temperature, was called “Helium in a box”. It contained a cell with liquid helium, that was about the size of a lemon seed”. Liquid helium, which was chilled to 4degrees above absolute zero, was put into this cell. There was also a tiny sapphire “bolometer” inside which measured the fluid’s temperature. The cell was embedded in a casing in order to prevent noise ad vibrations to skew his results. Linchaber used electric heating coils and Teflon gaskets to as heat conductors. The liquid helium would enter the system through a reservoir. The entire system was contained in liquid nitrogen to help stabilize temperature. His plan with the experiment was to create convection, the rising of hot gas or liquid, in the liquid helium as he made the bottom plate warmer than the top. 

 The reason Libchaber used liquid helium in his experiment is because it has low viscosity, meaning it will roll with a slight push.  To cause convection in his tiny cell he had to create a temperature difference of a thousandth of a degree between the top and bottom surfaces. Through his design, Libchaber chose dimensions that allowed enough room for only two rolls.  The heated liquid helium would rise in the center turn up and over to the right and descend on the outside edges of the cell. To record his results, he inserted two microscopic temperature probes in the sapphire, ad their output would be recorded by a pen plotter. 

His results corresponded with the Navier-Stokes equation, which relates a fluid’s velocity, pressure, density, and viscosity, is used to represent the nonlinear relationship. The equation describes the process by which when a liquid is heated from below, and the fluid moves in cylindrical rolls. Hot fluid will rise on one side, lose heat, and descend on the other side. However, when the heat is turned up further, there is instability, and the movement along the cylindrical shape is no longer uniform. At even higher temperature, the motion becomes turbulent and chaotic. These are just a few examples of where chaos exists in our world. With nonlinear systems, this chaos can be further observed and interpreted.

This is the most general form of the Navier–Stokes equat

ion :

 

 

where v is the velocity of the flow, ρ is the density of the fluid, p is the pressure, T and  represents forces acting on the body (per unit volume) acting on the fluid and D is the delta operator.

 

 

 

 

 

 

Chapter 6: Universality

One interesting topic presented in this chapter is a colourful debate between Newton and Goethe about the nature of colour. Goethe’s ideas about colour opposed Newton’s in that Newton thought of colour as a static quantity that could be measured in a spectrometer.Goethe argued that colour was a matter of perception. Newton’s experiment using a prism broughthim to his theory. Through his experiment, he witnessed how a prism breaks a beam of white light into rainbow colour, andconcluded that these

 were the components that add up to produce white. He also proposed that these colours corresponded to frequencies. In Goethe’s experiment, he held a prism to his eye and looked through it. He sawno colour at all. Heobserved the same results when looking at a white surface, as he did when looking at a blue sky. He saw uniformity. However, Goethe did witness

 spots on his white surface or blue sky that he concluded to be  “the interchange of light and shadow” that causes colour.  He then went on to explore the ways people perceive shadows cast by different sources of coloured light. One way in which Goethe and Newton differed was that Newton broke light apart and found physical explanations for colour, while Goethe studying paintings and nature looking for holistic explanations of colour. In a sense, I believe that Goethe’s theories were worth more attention than they actually received. Newton’s theory was very much legitimate, but should not be used alone in defining the nature of light. The colours we perceive vary from time to time, and person to person. The scientific theory doesn’t completely describe the real life brightness of colour, which we see, although it did explain the components of the colours we see. Does that mean that there can be a happy medium between the scientific theory and the philosophical idea?