The Bitcoin economy

The electronic currency Bitcoin has been in the news quite a bit lately since its value has risen from about $10 a year ago to over $650 today, hitting a peak of over $1000 less than a month ago. I remember hearing Gavin Andresen, who is a Principal of the Bitcoin  Virtual Currency Project (no single person nor entity issues or governs Bitcoin) talk about Bitcoin on Econtalk two years ago and was astonished at how little he knew about basic economics much less monetary policy. Paul Krugman criticized Bitcoin today in his New York Times column and Timothy Lee responded in the Washington Post.

The principle behind Bitcoin is actually quite simple. There is a master list, called the block chain, which is an encrypted shared ledger in which all transactions are kept. The system uses public-key cryptography, where a public key can be used to encrypt a piece of information but a private key is required to decrypt it. Bitcoin owners each have a private key, and use it to update the ledger whenever a transaction takes place. The community at large then validates the transaction in a computationally intensive process called mining. The rewards for this work are Bitcoins, which are issued to the first computer to complete the computation. The intensive computations are integral to the system because it makes it difficult for attackers to falsify a transaction. As long as there are more honest participants than attackers then the attackers can never perform computations fast enough to falsify a transaction. The computations are also scaled so that Bitcoins are only issued every 10 minutes. Thus it does not matter how fast your computer is in absolute terms to mine Bitcoins, only that it is faster than everyone else’s computer. This article describes how people are creating businesses to mine Bitcoins.

Krugman’s post was about the ironic connection between Keynesian fiscal stimulus and gold. Although gold has some industrial use it is highly valued mostly because it is rare and difficult to dig up. Keyne’s theory of recessions and depressions is that there is a sudden collapse in aggregate demand, so the economy operates at below capacity, leading to excess unemployment. This situation was thought not to occur in classical economics because prices and wages should fall until equilibrium is restored and the economy operates at full capacity again. However, Keynes proposed that prices and wages are “sticky” and do not adjust very quickly. His solution was for the government to increase spending to take up the shortfall in demand and return the economy to full employment. He then jokingly proposed that the government could get the private sector to do the spending by burying money, which people could privately finance to dig out. He also noted that this was not that different from gold mining. Keyne’s point was that instead of wasting all that effort the government could simply print money and give it away or spend it. Krugman also points out that Adam Smith, often held up as a paragon of conservative principles, felt that paper money was much better for an economy to run smoothly than tying up resources in useless gold and silver. The connection between gold and Bitcoins is unmissable. Both have no intrinsic value and are a terrible waste of resources. Lee feels that Krugman misunderstands Bitcoin in that the intensive computations are integral to the functioning of the system and more importantly the main utility of Bitcoin is that it is a new form of payment network, which he feels is independent of monetary considerations.

Krugman and Lee have valid points but both are still slightly off the mark. I think we will definitely head towards some electronic monetary system in the future but it certainly won’t be Bitcoin in its current form. However, Bitcoin or at least something similar will also remain. The main problem with Bitcoin, as well as gold, is that its supply is constrained. The supply of Bitcoins is designed to cap out at 21 million with about half in circulation now. What this means is that the Bitcoin economy is subject to deflation. As the economy grows and costs fall, the price of goods denominated in Bitcoins must also fall. Andresen shockingly didn’t understand this important fact in the Econtalk podcast. The value of Bitcoins will always increase. Deflation is bad for economic growth because it encourages people to delay purchases and hoard Bitcoins. Of course if you don’t believe in economic growth then Bitcoins might be a good thing. Ideally, you want money to be neutral so the supply should grow along with the economy. This is why central banks target inflation around 2%. Hence, Bitcoin as it is currently designed will certainly fail as a currency and payment system but it would not take too much effort to fix its flaws. It may simply serve the role of the search engine Altavista to the eventual winner Google.

However, I think Bitcoin in its full inefficient glory and things like it will only proliferate. In our current era of high unemployment and slow growth, Bitcoin is serving as a small economic stimulus. As we get more economically efficient, fewer of us will be required for any particular sector of the economy. The only possible way to maintain full employment is to constantly invent new economic sectors. Bitcoin is economically useful because it is so completely useless.

Symplectic Integrators

Dynamical systems can be divided into two basic types: conservative and dissipative.  In biology, we almost always model dissipative systems and thus if we want to computationally simulate the system almost any numerical solver will do the job (unless the problem is stiff, which I’ll leave to another post). However, when simulating a conservative system, we must take care to conserve the conserved quantities. Here, I will give a very elementary review of symplectic integrators for numerically solving conservative systems.

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What counts as science?

Ever since the financial crisis of 2008 there has been some discussion about whether or not economics is a science. Some, like Russ Roberts of Econtalk, channelling Friedrich Hayek, do not believe that economics is a science. They think it’s more like history where we come up with descriptive narratives that cannot be proven. I think that one thing that could clarify this debate is to separate the goal of a field from its practice. A field could be a science although its practice is not scientific.

To me what defines a science is whether or not it strives to ask questions that have unambiguous answers. In that sense, most of economics is a science. We may never know what caused the financial crisis of 2008 but that is still a scientific question. Now, it is quite plausible that the crisis of 2008 had no particular cause just like there is no particular cause for a winter storm. It could have been just the result of a collection of random events but knowing that would be extremely useful. In this sense, parts of history can also be considered to be a science. I do agree that the practice of economics and history are not always scientific and can never be as scientific as a field like physics because controlled experiments usually cannot be performed. We will likely never find the answer for what caused World War I but there certainly was a set of conditions and events that led to it.

There are parts of economics that are clearly not science such as what constitutes a fair system. Likewise in history, questions regarding who was the best president or military mind are certainly  not science. Like art and ethics these questions depend on value systems. I would also stress that a big part of science is figuring out what questions can be asked. If it is true that recessions are random like winter storms then the question of when the next crisis will hit does not have an answer. There may be a short time window for some predictability but no chance of a long range forecast. However, we could possibly find some necessary conditions for recessions just like cold weather is necessary for a snow storm.

Michaelis-Menten kinetics

This year is the one hundred anniversary of the Michaelis-Menten equation, which was published in 1913 by German born biochemist Leonor Michaelis and Canadian physician Maud Menten. Menten was one of the first women to obtain a medical degree in Canada and travelled to Berlin to work with Michaelis because women were forbidden from doing research in Canada. After spending a few years in Europe she returned to the US to obtain a PhD from the University of Chicago and spent most of her career at the University of Pittsburgh. Michaelis also eventually moved to the US and had positions at Johns Hopkins University and the Rockefeller University.

The Michaelis-Menten equation is one of the first applications of mathematics to biochemistry and perhaps the most important. These days people, including myself, throw the term Michaelis-Menten around to generally mean any function of the form

f(x)= \frac {Vx}{K+x}

although its original derivation was to specify the rate of an enzymatic reaction.  In 1903, it had been discovered that enzymes, which catalyze reactions, work by binding to a substrate. Michaelis took up this line of research and Menten joined him. They focused on the enzyme invertase, which catalyzes the breaking down (i.e. hydrolysis) of the substrate sucrose (i.e. table sugar) into the simple sugars fructose and glucose. They modelled this reaction as

E + S \overset{k_f}{\underset{k_r}{\rightleftharpoons}} ES \overset{k_c}{\rightarrow }E +P

where the enzyme E binds to a substrate S to form a complex ES which releases the enzyme and forms a product P. The goal is to calculate the rate of the appearance of P.

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Talk in Taiwan

I’m currently at the National Center for Theoretical Sciences, Math Division, on the campus of the National Tsing Hua University, Hsinchu for the 2013 Conference on Mathematical Physiology.  The NCTS is perhaps the best run institution I’ve ever visited. They have made my stay extremely comfortable and convenient.

Here are the slides for my talk on Correlations, Fluctuations, and Finite Size Effects in Neural Networks.  Here is a list of references that go with the talk

E. Hildebrand, M.A. Buice, and C.C. Chow, `Kinetic theory of coupled oscillators,’ Physical Review Letters 98 , 054101 (2007) [PRL Online] [PDF]

M.A. Buice and C.C. Chow, `Correlations, fluctuations and stability of a finite-size network of coupled oscillators’. Phys. Rev. E 76 031118 (2007) [PDF]

M.A. Buice, J.D. Cowan, and C.C. Chow, ‘Systematic Fluctuation Expansion for Neural Network Activity Equations’, Neural Comp., 22:377-426 (2010) [PDF]

C.C. Chow and M.A. Buice, ‘Path integral methods for stochastic differential equations’, arXiv:1009.5966 (2010).

M.A. Buice and C.C. Chow, `Effective stochastic behavior in dynamical systems with incomplete incomplete information.’ Phys. Rev. E 84:051120 (2011).

MA Buice and CC Chow. Dynamic finite size effects in spiking neural networks. PLoS Comp Bio 9:e1002872 (2013).

MA Buice and CC Chow. Generalized activity equations for spiking neural networks. Front. Comput. Neurosci. 7:162. doi: 10.3389/fncom.2013.00162, arXiv:1310.6934.

Here is the link to relevant posts on the topic.

New paper on neural networks

Michael Buice and I have a new paper in Frontiers in Computational Neuroscience as well as on the arXiv (the arXiv version has fewer typos at this point). This paper partially completes the series of papers Michael and I have written about developing generalized activity equations that include the effects of correlations for spiking neural networks. It combines two separate formalisms we have pursued over the past several years. The first was a way to compute finite size effects in a network of coupled deterministic oscillators (e.g. see here, herehere and here).  The second was to derive a set of generalized Wilson-Cowan equations that includes correlation dynamics (e.g. see here, here, and here ). Although both formalisms utilize path integrals, they are actually conceptually quite different. The first formalism adapted kinetic theory of plasmas to coupled dynamical systems. The second used ideas from field theory (i.e. a two-particle irreducible effective action) to compute self-consistent moment hierarchies for a stochastic system. This paper merges the two ideas to generate generalized activity equations for a set of deterministic spiking neurons.