Burston's Science Book Blog

Going beyond school maths for the first time with the  appearance of partial derivatives and Jacobians.

I didn't read every page of this book, or even close to it, but the chapters that I was interested in were good and avoided a pitfall that this type of text often falls into. By "this type of text" I mean one where each chapter is written by a different author under the general editorship of one or more persons. Frequently such books end up a collection of independent review articles that act neither as a coherent introduction to the subject, nor as a unified whole, often containing repetition of material, omission of important material or explanations that aren't in any coherent order.

So this book avoids all that by proper cross-referencing and good editorship - i.e. making the individual authors work in conjunction with each other, sharing drafts and devoting exceptional effort to the project.

Good job, all involved!

If you are interested in this subject and have a decent background regarding Earth's magnetosphere, I recommend starting with this book.

2-dimensional linear systems; crash revision course in matrices, determinants and traces required!

I had to start over from the beginning but I still think it's an excellent book. Up to this point it's also fairly easy, requiring only A-level maths. It's going to get harder shortly when we progress from one to two dimensional problems, I expect.

This book is so large and dense that it could probably be used to test General Relativity as well as to learn it!

It's gonna use "geometrised" aka "natural" units, which might be easier to do calculations in but are a PITA for learning purposes.

I couldn't help glancing into this before heading to the office this morning. 20p later I reluctantly dragged myself away. It's already provided a neat insight into co-ordinate systems.

Topology joke my brother used to tell:

Q: How can you escape any prison cell, only using mathematics?

A: Simple! Perform a co-ordinate transform such that the outside of the cell becomes the inside and vice versa - you are now free!

The Foreword is by James A. Van Allen. Yes, that Van Allen, the one with the Radiation Belts named after him.

This is a delightful introduction to applied chaos theory and information theory, written by a physicist for other physicists. I found it very accessible, unlike my previous encounters with information theory which were entirely impenetrable.

It's something of a classic, apparently, and I can see why. Not only is it well thought out, planned and executed, there are some delightful turns of phrase, too, e.g:

"The longer a string of text the easier it is to predict the next lette."

How often can you say that about something the author repeatedly refers to as a "paper"? (It's 111p of main text plus appendices...) It is also charmingly set in some ancient mechanical type-writer font with all the equations requiring Greek or integral signs hand-written in before going to press. It's both a shame and a testament to its usefulness that my copy is beaten up and verging on falling apart...

I'm not really reading this in order; Chapters 10 and 11 are what I most need and they are proving very useful.

Utterly fascinating! Also the first time anything to do with information theory was even remotely intelligible to me.

This is not a pop-science book. It's not even a textbook, really. Instead it is a collection of "review arictles." Review articles (for those who don't know) are technical papers that, instead of presenting new research, attempt to summarise the current state of knowledge about some research topic. Hence they tend to assume you already know quite a bit and tend to ignore things like basic definitions, underlying principles and the concept of starting simple and increasing in sophistication.

In other words, you have no hope of understanding this book unless you are already familiar with the basic concepts of magnetospheric science. On the other hand, it collects an awful lot of information about comparative solar system objects's magneto-tails into one place and is therefore areally useful reference volume.

Here's what it's all about: The sun is constantly emitting plasma into space. This is the solar wind, famous from Arthur Clarke's story "Sunjammer". It carries a magnetic field with it and all solar-system objects move through it. Magneto-tails are the distorted magnetic fields generated down-wind of solar-system objects by their interaction with the solar-wind.

Some objects have their own magnetic fields, some don't. Some have atmospheres, some don't. Some have ionospheres, some don't. Size, rotational velocity, distance from the sun, chemical composition - all these factors and more affect the size, shape and dynamics of magneto-tails.

Some magneto-tail facts to amaze the masses:

Jupiter has the largest magnetotail of any solar system object, thousands of times longer than the planetary radius, so long that it stretches out to the orbit of Saturn and probably beyond.

The solar wind is supersonic, so "bow-shocks" form between the solar wind and the surface of planets that have their own magnetic fields. These regions drastically slow down the solar-wind and prevent the surfaces being hugely irradiated by it. Or put another way, we wouldn't exist if Earth didn't have a strong internal magnetic field. Bow-shocks are similar to the shock waves "sonic booms" caused by jets crossing the sound barrier. Earth is creating noise pollution on an interplanetary scale!

Ganymede is the only natural satellite known to have an internally generated magnetic field. It doesn't have a bow-shock because it sits entirely inside Jupiter's magnetosphere where the solar wind has already been decelerated below the speed of sound.

Uranus' magnetotail, instead of being a typical long, stretched out thing resembling a drop of water just about to detach from a leaky tap (faucet) has a corkscrew-like shape. This is because of it's unusual axis of rotation and internal magnetic field orientation.

A comet's tail does not tell you anything about its direction of motion, instead it tells you which way the solar wind is blowing in the same way a flag tells you which way the wind blows.

A plasmoid is an idealised version of a flux rope that would only occur if the magnetic field has a specific orientation.

Further emphasizes our incomplete understanding of magnetotail formation. Jupiter's aurorae are significantly different from Earth's and saturn's. Jupiter's immense magnetotail only partially explained by plasma input from Io (1 tonne per second!).

Solar wind interaction dominates earth's magnetosphere; rotational dynamics dominate Jupiter's; Saturn appears to be between these two extremes.