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Visual Exploration of Complex Networks
jweebo writes "Seed magazine has a story on complexity, and how it can be visually represented with fascinating results. From the article:
'Complexity is everywhere. It's a structural and organizational principle that reaches almost every field imaginable, from genetics and social networks to food webs and stock markets ...Collected here are a few of the many intriguing, and often beautiful, images that illustrate how the whole is more than the sum of its parts.'"
The point of visualizing data is to learn something that you could not do with the raw data. In all of the cases shown in the article (yes, I acually read TFA), I didn't spot an example where it actually showed anything useful.
The first example with proteins: how similar are two proteins? If two shapes are similar (and please, how many proteins where being graphed there? One, two, five?), then you might be able to recognize it. If they are similar shapes, are they always presented in the same orientation in space? Does color have any meaning? Does this graph have any legend? If I gave someone who understood the graphs two proteins, what could he say besides "these are related" and "these are not related"? We already have wonderful programs to compare two proteins and say how similar they are two each other, along with being able to the estimate significance of the measurement.
I'm not sure that the other graphics look more informative. They are all pretty, but if they do not convey information (and not lose a large amount of relevant information), then they are just a nice way to generate patterns for some nerd's tie.
Honestly, of the things that bother me about his book, that's not horribly high on the list. The main problem is, nothing he talks about has any ability to predict behavior either qualitatively or quantitatively.
He makes no mention about how to crossover from a microscopic theory to his cellular automata stuff, so even if you can say 'wow, that looks like seashells' when you're presented with some new physical problem you can't just look up his book and figure out what the equivalent CA model would be.
And he doesn't really cover in any depth the intrinsic qualities of doing things with a highly discretized model compared to continuum modelling. Discretization produces a lot of structure in its own right, and that structure may interfere with certain symmetries that the real system has - e.g. translation invariance, invariance when going to a moving frame of reference, and conservation laws. As such, these models tend to give you things which are highly unstable to noise (Conway's game of life collapses to interlocking horizontal and vertical stripe patterns if you add the slightest bit of noise for instance), or work because things exist within the CA model that actually recover those symmetries (but detecting if you're in the first or second case is again something that needs to be covered) - the spiral defect chaos CA models are an example of this, where you essentially recover some sort of continuum dynamics and the discretization doesn't kill it.
I certainly have respect for the method of CA modelling. It can be incredibly useful in simplifying simulation, especially in the case where the full continuum approach ends up having operators which are very numerically unstable. If you can write a simple CA model for resolving the function of those operators, it can save you a ton of time. But I don't really feel that Wolfram's book gives one the necessary set of tools to do that sort of work. Rather, it might just give you an idea to try to do things that way, which is not a bad thing. It just means that even comparing this to peer-reviewed journal publications isn't meaningful because thats not the sort of publication it is. It's more of a halfway-between of a popular science book and a textbook.