Bitcoin and the Blockchain are perhaps the most hyped technology today, rivalling even Artificial Intelligence for extreme predictions and outrageous claims. We need to talk about the ecology.

Bitcoin is a cryptographically-backed, anonymous, pseudo-currency invented by the otherwise unknown Satoshi Nakamoto. It has a dollar value because it is traded on the market, as can be seen here. It is used to trade in everything from lattes to guns, and is always free of jurisdictional monitoring and hence taxation. In other words it enables criminal transactions. The value of Bitcoin has grown quite predictably since its creation. This is not my main problem with Bitcoin.

The Blockchain, on which Bitcoin is built, is a hideously inefficient means of computing a tally of transactions. There are many superb descriptions of how it works, such as the following:

It is sometimes perceived as an intellectually-elegant formulation, provably sharing a settling of a kind of account. However it costs too much. Picture a train of carriages. There is a first carriage, normally with an engine. Other carriages may be attached to this engine. Any human can get on and off the system of carriages at any time, by adding their own carriage, and may insist that everyone else who ever entered a carriage witness this, mathematically, by adding each carriage to their own description of where the carriages are positioned in the train. This is a huge computational load on all the witnesses.

This is the fundamental purpose of the blockchain. It provides a mathematically sound proof that a certain computational task has been performed and does it in such a way that it can be demonstrated by anyone else in the chain.

While the asymptotic nature of Bitcoin is implied in the above it makes sense to put this in context. An asymptote is a limit to which a function can computationally approach. In Mathematics we can use purely analytical techniques to describe the overall behaviour of such functions, indeed these techniques are fundamental to the theory of Calculus. When we have to determine the stepwise approximation numerically matters can become quite complicated and require significant time and effort.

An example of this asymptotic approach, though not necessarily the most correct, is the value of the fundamental constant Π. We learn in school that Π has a value of roughly 3.14, and this suffices for schoolroom exercises. Archimedes created techniques that foreshadowed Newtonian calculus by over a thousand years in his ingenious calculation of this transcendental number‘s digital expansion. We can now determine Π to billions of places of precision, but we will never know it as accurately as its simplest formulation: the area of a circle is Π times the radius squared. In other words, the idea of Π as a proportion is vastly more accurate than any numerical approximation. Bitcoin utilises this asymptotic approach to guarantee that the number of Bitcoins it is possible to calculate has an upper bound of 21 million, and that it gets proportionally harder to do so.

Most, though not all, contemporary encryption relies on one simple and strange fact: it is vastly easier to multiply two prime numbers to get another number than it is to do the reverse. Thus it is easier to multiply 5 and 13 to get 65 than it is to analyse 65 to determine what two prime are its divisors. This gets harder the bigger the number. Why this is so is deep and suggestive and still not properly understood. Indeed the study of prime numbers is perhaps the single greatest motive for the entire subject of Mathematics. They are bizarre, profound, and remarkably useful, far past their role in encryption. In particular Bitcoin, via the Blockchain, uses the very well studied SHA-256 hash function.

As a result all the theoretical constraints outlined above and elsewhere, Bitcoin is inefficient. Like a giant out-of-control paper clip machine it now requires more energy per month for it’s computations than the Republic of Ireland’s. This is a clear signal we are not communicating effectively with regard to distributed proof-of-computational-work schemes. Indeed the very mention of schemes calls the work of Alexander Grothendieck to mind. He would regard this as no soaking of the walnut. (He preferred not to crack a walnut of a problem using advanced techniques but soak it instead in his understanding, so that it might be peeled apart with the fingers of his mind and thereby yield much deeper understanding).

And now we come to the real problem of Bitcoin. It is trying to solve the wrong problem. We have long suffered the Identification/Authentication/Authorisation problem. Even DNA analysis, which can be very accurate, takes significant effort to compute. Adding a requirement of secrecy to this, while constrained by modern understandings, imposes unacceptable computational cost.

Bitcoin solves the wrong problem, badly. We can and will do better, by using more sophisticated Mathematics, to develop more efficient distributed proof of work.

Right now there are far too many exploitative people working in Finance, Computer Science, and even alternative Politics, who are jumping on the Blockchain Bandwagon, and encouraging others to do likewise because they can profit, monetarily, through their comparative sophistication.

Put it another way, no working mathematician I know recommends Bitcoin, yet every single one recommends the study of Number Theory. Who do you trust more? Financiers or Mathematicians?

*Eoin Tierney is the Science editor of Cassandra Voices.*

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