Money is a computational technology: it's the "technical trick" that allows exchanges of goods and services to be delayed and coordinated beyond one-to-one relationships. That's obvious now wherever countries have converted the entire process of "using money" to database transactions; they always were, it was just that we used to use physical objects as counters, with, e.g., anti-counterfeiting measures as the functional equivalent of cryptographical signatures.

Digital money isn't a radical change, but rather a purer expression of what money is, or at least what it's for. It's always been tied up to information, computational power, and solid protocols. Banks have always been able to create money — Italian banking houses have been loaning more than they had in deposits since before the advent of paper money — and they could do this precisely because of advanced (for the times) information processing and communication technologies. The Venetian state might have had the best diplomatic and intelligence archives of Early Modern Europe, but Venetian (and Florentine, Genoese, and Northern-European) traders and bankers invented modern book-keeping.

So what happens when computation becomes exponentially more powerful and ubiquously distributed?

1. If you focus on traditional currency, the net effect is that the State becomes stronger. Cryptographic tools cut both ways: in a cashless society legal tender can be tracked, taxed, issued, and manipulated with whatever level of speed, thorughness, and force the State wants to and is politically allowed to. Money laundering and tax evasion performed through financial institutions is only possible because the political calculation of the relevant states allows it; it's possible to design efficient, convenient cryptographically supported protocols that would make such activities impossible (for extra irony points, they could be based on blockchain protocols, which are nothing less than panoptic transaction ledgers).

2. The other side of the coin (pun not intended) is that setting up pseudo-currencies becomes trivial. There are multiple bitcoin-like cryptocurrencies ---on itself only one of the possible architectures to set up a new currency--- with their impact limited not by the "State capabilities" of the issuing groups (you can essentially download for free the source code of a financial system, and, given the demand, you could have wholly independent financial systems as a service), but either by their ability to entice or enforce their usage, or by the computational properties of the currency being particularly useful to a certain group (e.g., the ability to coordinate economic transactions with relative anonimity is one of the reasons why bitcoin is used, but this is a property that protocols have, not something specific about currencies... precisely because currencies are about protocols).

3. But why have money at all? After all, it forces us to use a one-dimensional representation of value, one that is so limited that we already have to resort to things like stock options to pay people with, which are computationally more expensive: you need to think more about what they are worth and what to do when you have them, which is why they are more precise as incentives, and, according to companies, more useful than "dumb money." And stock options don't even need computers; the more we use complex, contingent, computationally dynamic reward and transfer systems, the larger the part of our economic behavior that's no longer bound by traditional monetary policy. It's not that necessarily money goes away, it's just that it becomes an smaller part of the suite of protocols with which a society chooses what to do.

That said, once you understand an economic system not as a philosophical or moral construct but rather as an algorithm to coordinate behavior and resources, you begin to think whether money isn't too restrictive a design constraint. Imagine the current system, except that you load into an app your skills, preferences, needs, etc (or just give it your Amazon, Google, Twitter, and Facebook passwords and let it figure it out), and it negotiates with the apps of other people and businesses, and arranges for you a combination of freelance work, purchases, and service subscriptions that maximizes whatever you defined hapiness as. That seems like a conceivable if difficult-to-build app.

And here's where it gets interesting: if an entire local economy is using that app, whatever data structure the apps are using to keep track of the value of what you're doing doesn't have to be a single number, and probably, optimally, won't be. The folk reasoning for currency, that bartering becomes exponentially more complex as you need more things and want to trade with more people, is true, but sufficiently complex computers could do it, and we have theoretical reasons to think that there's a chance it'd work better. We don't need to imagine AI-driven communism to picture a money-less society; in a sense, it'd just be a more complex form of capitalism; after all, modern economies would be impossible if we did away with all financial tools other than cash and cash equivalents.

I don't know if that _can_ work, but it's easy to picture a neo-hippie community somewhere in California trying this out not long from now. More interestingly, a place like Singapore could ---and would probably have reason to--- try to implement some of this to try to gain a leg up in economic efficiency to competitors increasingly catching up with them (one of Singapore's key advantages has always been, after all, the quality of its governance; it probably has the best educated, most highly trained government in the world). Or China; their commitment to centralized non-financial social and economic arrangements long predates communism, and even more so capitalism, so an special money-free economic zone, an experiment on "post-capitalism with Chinese characteristics," is not unthinkable.

In any case, these are extreme examples. More simply, with expanded computing power, we have expanded options for distributed, efficient, large-scale coordination protocols, which compete with, and in many cases will substitute, money as a tool. Money might keep working as a sort of universal lingua franca between different protocols, but not an universal one (to some degree this already happens inside most companies, which give employees money so they can interact with the rest of the economy, but that, generally speaking don't use money as an internal coordination tool; ubiquitous computing power allows this to scale as much as you want).

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So what does all of this mean for the inflation during the second semester of 2056?

Or a bit more generally, what will be the impact on monetary policy in general?

A. The immediate observation is that the sort of activities we call monetary policy will be much more efficient: Digital money is so transparent and manipulable that quick, targetted monetary interventions will only be limited by political will (think real-time Fed decision making). Emergent behaviors like purely monetary recessions will be much easier to control when you can, for example, easily, transparently, and automatically issue money valid for a certain period of time, or between certaint entities.

B. At the same time, monetary policy will be much less effective. As computational power and information capabilities distribute away from governments and the financial system, a lot of the coordination functions of money also shift elsewhere. Much of economic behavior will be independent of whatever happens to "real money," and to some degree algorithmically isolated from. Undesired economic equilibria will be harder to get out of.

C. As the limit case, as we get better at ubiquitous computational systems, monetary policy as currently conceived will probably fade into the rest of our information infrastructure as one of the basic services underpinning our _real_ decision-making protocols. It won't go away, and states will have to get it right, but it won't have the role it now has.