The butterfly effect
Apr. 6th, 2021 07:18 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
qatsiBook Review: Chaos - Making a New Science, by James Gleick
A re-read, so perhaps I am more likely to be critical. I first read this as a teenager - probably a sixth former - I remember writing a Pascal program to draw the Mandelbrot set on the school PCs; it took more than half a day, IIRC.
The subtitle of the book refers to the recency of the discipline; there was no canon or history on which to draw. Except that it's not quite true: the Cantor set dates from the late nineteenth century, and the Sierpiński triangle is probably even older. These are among many objects now considered fractals, having infinite measure in some dimension, yet finiter or even zero in others. A more prosaic example is a coastline such as that of the United Kingdom, which may have infinite length (depending on the scale on which you measure it) yet encloses a finite area.
The images are eye-catching, and perhaps the myriad colouring of the Mandelbrot set boundary gives an intuitive hint of "chaos", but the actual science is more about predictability, of things such as the weather or the stock market. Classical physics tends to focus on problems that can be expressed with linear equations, which can be solved. These equations are approximations based on models, but there's an assumption that small non-linear deviations from the model will result only in correspondingly small deviations in results. Chaos theory shows that this is not always the case. In some iterative processes or difference equations, there is a trend for a solution to converge on a single value, from a wide range of initial values (some values leading to faster convergence than others); in other processes, solutions converge on some periodic cycle of values. But in other cases, the "attractors" are neither singular nor periodic, but some strange infinitely varying sequence of values. And when there are multiple attractors for solutions, the mapping from initial value to solutions can have essentially unpredictable and infinitely complex boundaries - such as the fractals described above. Yet more strange are Feigenbaum constants, which seem to occur in behaviour of difference equations otherwise unrelated to each other. When you do more than scratch the surface, you realise how fiendishly philosophical such study might become.
Gleick builds these ideas as a human-interest story, describing the people involved in this emerging field of knowledge. At times it feels a bit forced, the inevitable drive of outsiders against a scientific establishment, finding dismissal, rejection, wilderness before ultimate triumph. Although the science is well described, I did feel it necessary to take a step back to reflect on how some of the disparate threads should relate to each other: this isn't always made clear. It's a difficult subject and Gleick does a fair job, given how unconditioned we are to consider these concepts and possibilities.
A re-read, so perhaps I am more likely to be critical. I first read this as a teenager - probably a sixth former - I remember writing a Pascal program to draw the Mandelbrot set on the school PCs; it took more than half a day, IIRC.
The subtitle of the book refers to the recency of the discipline; there was no canon or history on which to draw. Except that it's not quite true: the Cantor set dates from the late nineteenth century, and the Sierpiński triangle is probably even older. These are among many objects now considered fractals, having infinite measure in some dimension, yet finiter or even zero in others. A more prosaic example is a coastline such as that of the United Kingdom, which may have infinite length (depending on the scale on which you measure it) yet encloses a finite area.
The images are eye-catching, and perhaps the myriad colouring of the Mandelbrot set boundary gives an intuitive hint of "chaos", but the actual science is more about predictability, of things such as the weather or the stock market. Classical physics tends to focus on problems that can be expressed with linear equations, which can be solved. These equations are approximations based on models, but there's an assumption that small non-linear deviations from the model will result only in correspondingly small deviations in results. Chaos theory shows that this is not always the case. In some iterative processes or difference equations, there is a trend for a solution to converge on a single value, from a wide range of initial values (some values leading to faster convergence than others); in other processes, solutions converge on some periodic cycle of values. But in other cases, the "attractors" are neither singular nor periodic, but some strange infinitely varying sequence of values. And when there are multiple attractors for solutions, the mapping from initial value to solutions can have essentially unpredictable and infinitely complex boundaries - such as the fractals described above. Yet more strange are Feigenbaum constants, which seem to occur in behaviour of difference equations otherwise unrelated to each other. When you do more than scratch the surface, you realise how fiendishly philosophical such study might become.
Gleick builds these ideas as a human-interest story, describing the people involved in this emerging field of knowledge. At times it feels a bit forced, the inevitable drive of outsiders against a scientific establishment, finding dismissal, rejection, wilderness before ultimate triumph. Although the science is well described, I did feel it necessary to take a step back to reflect on how some of the disparate threads should relate to each other: this isn't always made clear. It's a difficult subject and Gleick does a fair job, given how unconditioned we are to consider these concepts and possibilities.