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The Fractal Geometry of Nature, Benoit Mandelbrot

My interest in this book is that the author and founder of the theory of fractal geometry described it fairly recently in a paper as the essential introductory text in the area. Fractal geometry is basically an attempt to define mathematically the difference between complex data at separate scales. So if you imagine the coastline of a country, then measure that coastline with a 1 meter ruler and you will get a shorter distance than if you measure it with a 1cm ruler, and again with a 1mm ruler etc etc. It’s taken me a while to read because, having not studied maths for a while the terminology is quite alien, the concepts are simple enough but what I’m really looking for is the tools used to define the differences between scale and so I want to understand the maths properly.

The central importance of fractals to the study of cooperation (or indeed any other social construct) is that it allows you a potential way round a central issue in economics which is that social data is not linear in nature. My interest in looking into psychology and complexity is in seeing how other subjects tackle this problem. To illustrate the point, if you recall the research methods lecture with the economics professor we had the other week he was attempting to model migration patterns by reducing migration data to single values and then add in probabilistic margins for error. This is a typical way for an economist to tackle a complex area, you might have seen Mervin King from the bank of England giving his economic forecast today along the same lines – we know the data is complicated, we have introduced these assumptions and we believe this is a sensible percentage error. Is their another more accurate way to model this complex phenomena?

The approach Mandelbrot takes is to find a scale and measure it as accurately as you can with the tools available, then take as many more scales as you can and calculate the trend of increased or decreased complexity between the scales. This is fundamentally different from what you do in economics, in economics you scale your data up in a linear fashion (e.g. you calculate GDP by adding up the domestic output for each industry sector) which doesn’t account for that scale may be a factor in itself, you then add in a margin for error to account for the fact that you cant understand how the interactions between the actors who produce your data may change with scale.

Now, it’s fair to say that if your data is linear – i.e. one change always has one effect on one thing then there will be no difference in approaches but if by changing one thing has an effect on several things which has an effect on several more then the linear approach quickly gets to rather large margins for error rather quickly. The fractal approach doesn’t.

To summarise, fractal geometry is about understanding the changing shape of data at scale which captures the relationships between many data points. So if you know accurately what happens at one scale and the fractal dimension your data scales by you can predict accurately what your data will look like at larger scales or visa versa.

I’m now going to go look how a psychologist/sociologist attempts to quantify the phenomena they observe as a comparison. Any psychologist want to point out a book for me?

In order to establish whether i can look at economics in sufficient detail to make it a worthwhile exercise (in relation to the question of reputation) i’ve been focusing on that for the last ten days. Things are a bit more promising i think; provided i concentrate on the social capital side of things i’m confident i can tie everything together coherently.

I’ve been making my way through Economics by Parkin, Powell and Matthews, which i’ve found very accessible and easy to read. The authors try to illustrate reasonably complex concepts (for me they are reasonably complex, anyway) with simple analogies, the majority of which for some reason seem to include David Beckham. Below are the key things i’ve got from the first part of the book.

What is Economics? 
It is the social science that studies the choices that individuals, businesses, governments and entire societies make as they cope with scarcity and the incentives that influence and reconcile those choices.

Microeconomics & Macroeconomics
Microeconomics is the study of choices that individuals and businesses make, the way these choices interact in markets and the influence of governments. Macroeconomics studies the performance of the national and global economy.

Two Key Economic Questions
How do choices end up determining what, how and for whom goods and services get produced?
When do choices made in the pursuit of self-interest also promote the social interest?

Trade-Offs and Opportunity Cost
Trade-offs are a way of conceptualising the process of making a choice between alternatives. For example, when you choose to write your IDR blog rather than watchint the One Show you face a trade-off. By writing this blog i am (hopefully) becoming better educated and giving myself a better chance in doing well in this course, which may lead to a better career later down the line. But i am missing the One Show, so i am trading off current entertainment(?!) with my future ‘performance’.  Linked to this is opportunity cost. If i want to go and see ‘Due Date’ this weekend, the cost of the ticket will preclude me from having a pub lunch on Sunday. Therefore, the opportunity cost of seeing Due Date is the pub lunch i won’t have; that is, the pub lunch is the highest valued alternative that i would have done if i did not go to the cinema.

Margins
If i study five nights a week instead of four, and my marks go from an average of 50 to 60, the marginal benefit of that extra night’s study is the difference between my old and new average – 10%. The marginal cost of getting that extra ten percent is the night i lose socialising. In order to evaluate the benefits, i would have to establish whether the extra marks outweigh the cost of socialising less.

Human Nature and Social Interest
There is an economic assumption that humans act in their self interest; that is, they make the choices that get hte most value for them based on their values. A question the book seems very keen on addressing is when self-interested acts are alos in the social interest.

How Economics is Studied
Economics is not an experimental science, ands as such has to be studied through other means. Given that you cannot really conduct bound economic experiments in the laboratory, the book details and describes methods used to study economics. These include Observation and Measurement, Model Building and Testing Models.

I’ve been necessarily brief; there really is a lot of material that i’ve tried to distill down to the core components. Thus far it’s a rewarding task, and i feel quite comfortable with all of the concepts above although i’m fairly sure i had at least an elementary understanding of most of them. I’m going to press on with this book for the next week or so, as it has only touched on social capital and i think this will be the area that i can most strongly link back to my topic area.