Nature's Tobin Taxes

It's a tenet of this blog that there are fundamental but little-appreciated similarities between our society and economy on the one hand, and several biological systems such as ecosystems, genetic networks and the brain on the other. We can see this similarity if we conceptualize these systems in terms of one or more currencies that flow among different stocks. For example, we might view the ecosystem as a food web, where each stock is a species, and carbon (the most obvious energy-carrying currency in this analogy) moves into and among these species through processes such as photosynthesis (which moves carbon from the air into plants) and predation (which moves carbon from one animal species to another). Any such summarized view is simplistic of course – the ecosystem really consists of carbon flowing among trillions of individuals. But you have to start somewhere. There is a similarity here with the brain, which consists of trillions of neurons among which flow patterns of chemical and electrical excitation. The currency here is information. Information is also the currency of genetic circuits, which consist of networks of millions of genes, distributed among billions of cells, processing information in terms of how different genes activate or suppress each other in response to various external and internal signals. Against this biological backdrop, economies seem like nothing more than the latest, and probably not the last, in a long line of complex flow networks, albeit one where the currency is … well … currency.

However, a major difference between economies and these natural systems is that the latter are subject to inescapable physical inefficiencies that cap the complexity of the patterns of flow. In ecosystems, a typical predator can ingest only half of the carbon of anything that it eats. Therefore, half of the carbon and energy is lost at each link in the food chain. The rest enters the detritus, where it goes on to cycle among various other species, but even there the laws of thermodynamics (you know, entropy and all that) dictate that a large proportion of energy must be lost each time any organism does any work, including eating other organisms. These natural inefficiencies place a fundamental limit on the length of food chains in ecosystems, and on the total amount of activity and information processing that an ecosystem can carry out. One sign of this limitation is the well-known 'trophic pyramid' pattern, where we find more carbon in the lower levels of the food chain than at higher levels – more plant carbon than animal carbon; more herbivore carbon than carnivore carbon.

Neurons in the brain are also limited in how often they can fire before they become (metabolically speaking) tired, in part because they are ultimately powered by a special fuel called ATP. There are fundamental limits to the concentrations and supply rates of ATP that can be achieved within the human brain, even if we ignore the amount of food that you would need to ingest to produce such huge amounts. The limitations on ATP in turn place limitations on the activity levels of the whole brain, or parts thereof. Interestingly, ATP is also the fuel that powers all processes within all cells, including gene expression and signalling – so the amount and complexity of information transfer in genetic networks is also naturally limited by ATP. It would not surprise me if we one day discovered trophic pyramids in brains and genetic systems, whereby more ATP is used in the lower levels of these biological computational networks.

By contrast, there is no obvious limit on how quickly money can be concentrated in one part of the economy, and money does not get 'used up' as it is cycled around. At first glance then, we would think that, unlike ecosystems, brains or genetic networks, economies could cycle money at any rate, and through networks of limitless complexity. However, governments have decided to impose artificial limitations on the real part of the economy. If I want to give money to anyone in the real economy for any kind of service rendered, I usually have to pay a sales tax. In the UK this is 20% – a more than respectable inefficiency even by nature's standards. If that person makes a personal profit from this transaction, they'll pay a marginal income tax that can be over 50%, which is even worse than a food web! When they go out to spend the rest … in comes that 20% tax again. Not to mention corporation tax and capital gains tax. Presumably, these taxes act like entropy or ATP, dampening both the overall level of activity and the complexity of economic networks. Not that this is necessarily a bad thing – it might make the real economy more stable (see below) and after all, we use (some of) that tax money to do useful things for the good of our society as a whole.

But there are two senses in which one part of our economy – the financial sector – really is without limits. First, if I want to move money into or around the banking system (presumably for some reason), this does not (for some reason) count as a service rendered and I pay no tax. Second, I am also free to make legal deals about my future intent to pay someone else under various circumstances – think, the futures market, insurance, bonds. These binding legal agreements are very real, but are subject to taxes only when executed, if at all. Overall then, the rate that the financial sector can cycle money around within itself, and bind itself up in complex networks of legal agreements, appears to be without limit. As a result we can find some very weird patterns, such as the following: every day, the total amount of trading on the global FOREX market is 15 times larger than daily global GDP. Think about that for a second. Money gets cycled through this one part of the financial sector 15 times for every time it passes through the real economy. The trophic structure of our economy, in other words, shows an extreme opposite pattern to ecosystems – the vast majority of economic activity is carried out by those species furthest removed from primary production.

The limitless complexity of the financial sector might not matter, except for that fact that it affects the real economy and real people, and that limitless networks are known to have a tendency to become highly unstable. It is not hard to understand the stability part. If activity flares up in your brain, ATP limitation will tend to dampen down the ripples as they attempt to spread. If a gene is turned on by mistake, ATP limitation helps to prevent these effects rippling through your body. If a species goes extinct, the laws of thermodynamics help to prevent it causing the whole ecosystem to collapse. In limitless networks though, ripples can quickly spread and amplify, with huge effects on the whole system. For this reason AI researchers (of which I am now one, strangely!) routinely place limitations on artificial neural networks, which, unlike real brains, have no natural limits. Virtual brains with the virtual equivalent of ATP limitation learn faster and are more robust. These beneficial effects of limitation on artificial neural networks raise the possibility that our own neurons might have evolved to become even more limited than they would be from ATP limitation alone.

More to the point, the general effects of limitations on network stability raise the possibility that imposing an artificial tax on financial transactions might help to dampen the often chaotic dynamics of the global financial sector. And this, of course, is my take on the idea of a Tobin tax. According to Wikipedia, economists are still arguing as to whether a Tobin tax would make the global economy more, or less, stable. It will take more than a couple of analogies to answer that difficult question – but I can't help point out that, of the many complex systems that have supported my 39 years on this planet, the global economy is notable for being the least limited, and the least stable.

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