I have been away from blogging for two days. I have been finishing that article about technological change seen from an evolutionary perspective, and I hope I have finished, at least as the raw manuscript. If you are interested, you can download it from Research Gate or from my own website with Word Press. Now, as the paper is provisionally finished, I feel like having an intellectual stroll, possibly in the recent past. I am tempted to use those evolutionary patterns of thinking to something I had been quite busy with a few months ago, namely to the financial tools, including virtual currencies, as a means to develop new technologies. I had been particularly interested in the application of virtual currencies to the development of local power systems based on renewable energies, but in fact, I can apply the same frame of thinking to any technology, green energy or else. Besides, as I was testing various empirical models to represent evolutionary change in technologies, monetary variables frequently poked their head through some hole, usually as correlates to residuals.

So, I return to money. For those of my readers who would like to refresh their memory or simply get the drift of that past writing of mine, you can refer, for example, to ‘Exactly the money we assume’ or to ‘Some insights into Ethereum whilst insulating against bullshit’, as well as to other posts I placed around that time. Now, I want to move on and meddle a bit with Bayesian statistics, and more exactly with the source method presented in the posthumous article by reverend Thomas Bayes (Bayes, Price 1763[1]), which, by the way, you can get from the JSTOR library via this link . I want to both wrap my mind around Thomas Bayes’s way of thinking, and refresh my own thinking about monetary systems. I have that strange preference to organize conversations between the dead and the living (no candles), so I feel like put reverend Bayes in conversation with Satoshi Nakamoto, the semi-mythical founding father of the Bitcoin movement, whose article, that you can download by this link, from my Word Press website, contains some mathematical analysis, based on the Poisson probability.

My initial question, the one I had been wrestling with this Spring, was the following: how can a local community develop a local system of green energy, and a local virtual currency, and how can these two help the development or the transformation of said local community? Why do I bother, posthumously, revered Thomas Bayes with this question? Well, because this is what he stated as the purpose of his article. In the general formulation of the problem, he wrote: ‘*Given the number of times in which an unknown event has happened and failed: Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability than can be named*’. The tricky part in this statement is the ‘unknown’ part. When we studied probabilities at high school (yes, some of us didn’t take a nap during those classes!), one of the first things we were taught to do was to define exactly the event that we want to assess the probability of happening. You remember? Read balls vs. black balls, in a closed box? Rings a bell? Well, Thomas Bayes stated a different problem: how to tackle the probability that something unknown happens? Kind of a red ball cross-bred with a black ball, with a hint of mésalliance with a white cube, in family records. In the last, concluding paragraph of his essay, Thomas Bayes wrote: ‘*But what recommends the solution in this Essay is that it is complete in those cases where information is most wanted, and where Mr De Moivre’s solution of the inverse problem can give little or no direction, I mean, in all cases where either p or q are of no considerable magnitude. In other cases, or when both p and q are very considerable, it is not difficult to perceive the truth of what has been here demonstrated, or that there is reason to believe in general that the chances for the happening of an event are to the chances for its failure in the same ratio with that of p to q. But we shall be greatly deceived if we judge in this manner when either p or q are small. And though in such cases the Data are not sufficient to discover the exact probability of an event, yet it is very agreeable to be able to find the limits between which it is reasonable to think it must lie, and also to be able to determine the precise degree of assent which is due to any conclusions or assertions relating to them*’.

Before I go further: in the original notation by Thomas Bayes, *p* and *q* are the respective numbers of successes and failures, and not probabilities. Especially if you are a native French speaker, you might have learnt, at school, p and q as probabilities, so be on your guard. You’d better always be on your guard, mind you. You never know where your feet can lead you. So, I am bothering late reverend Bayes because he was investigating the probability of scoring a relatively small number of successes in a relatively small number of trials. If you try to launch a new technology, locally, how many trials can you have? I mean, if your investors are patient, they can allow some trial and error, but in reasonable amounts. You also never know for sure what does the reasonable amount of trial and error mean for a given investor. You have the unknown event, see? Just as Thomas Bayes stated his problem. So I take my local community, I make a perfect plan, with a plan B possibly up our local sleeve, I take some risks, and then someone from the outside world wants to assess the odds that I succeed. The logic by Thomas Bayes can be a path to follow.

Satoshi Nakamoto, in that foundational article about the idea of the Bitcoin, treated mostly the issues of security. Still, he indirectly gives an interesting insight concerning the introduction of new inventions in an essentially hostile environment. When the simulates a cyberattack on a financial system, he uses the general framework of Poisson probability to assess the odds that an intruder from outside can take over a network of mutually interacting nodes. I am thinking about inverting his thinking, i.e. about treating the introduction of a new technology, especially in a local community, as an intrusion from outside. I could threat Nakamoto’s ‘honest nodes’ as the conservatives in the process, resisting novelty, and the blocks successfully attacked by the intruder would be the early adopters. Satoshi Nakamoto used the Poisson distribution to simulate that process and here he meets reverend Bayes, I mean, metaphorically. The Poisson distribution is frequently called as the ‘probability of rare events’, and uses the same general framework than the original Bayesian development: something takes place *n* times in total, in *p* cases that something is something we wish to happen (success), whilst in *q* cases it is utter s**t happening (failure), and we want to calculate the compound probability of having *p* successes and *q* failures in *n* trials. By the way, if you are interested in the original work by Simeon Denis Poisson, a creative French, who, technically being a mathematician, tried to be very nearly everything else, I am placing on my Word Press site two of his papers: the one published in 1827 and that of 1832 (presented for the first time in 1829).

And so I have that idea of developing a local power system, based on green energies, possibly backed with a local virtual currency, and I want to assess the odds of success. Both the Bayesian thinking, and the Poisson’s one are sensitive to how we define, respectively, success and failure, and what amount of uncertainty we leave in this definition. In business, I can define my success in various metrics: size of the market covered with my sales, prices, capital accumulated, return on that capital etc. This is, precisely, the hurdle to jump when we pass from the practice of business to its theoretical appraisal: we need probabilities, and in order to have probabilities, we need some kind of event being defined, at least foggily. What’s a success, here? Let’s try the following: what I want is a local community entirely powered with locally generated, renewable energies, in a socially and financially sustainable manner.

‘Entirely powered’ means 100%. This one is simple. Then, I am entering the dark forest of assumptions. Let’s say that ‘socially sustainable’ means that every member of the local community should have that energy accessible within their purchasing power. ‘Financially sustainable’ is trickier: investors can be a lot fussier than ordinary folks, regarding what is a good deal and what isn’t. Still, I do not know, a priori, who those investors could possibly be, and so I take a metric, which leaves a lot of room for further interpretation, namely the rate of return on assets. I prefer the return on assets (ROA) to the rate of return on equity (ROE), because for the latter I would have to make some assumptions regarding the capital structure of the whole thing, and I want as weak a set of assumptions as possible. I assume that said rate of return on assets should be superior or equal to a benchmark value. By the way, weak assumptions in science are the exact opposite of weak assumptions in life. In life, weak assumptions mean I am probably wrong because I assumed too much. In science, weak assumptions are probably correct, because I assumed just a little, out of the whole expanse of what I could have assumed.

Right. Good. So what I have, are the following variables: local demand for energy D(E), local energy supply from renewable sources S(RE), price of renewable energy P(RE), purchasing power regarding energy PP(E), and rate of return on assets (ROA). With these, I form my conditions. **Condition #1**: the local use of energy is a local equilibrium between the total demand for energy and the supply of energy from renewable sources: **Q(RE) = S(RE) = D(E)**. **Condition #2**: price of renewable energy is affordable, or: **P(RE) ≤ PP(E)**. **Condition #3**: the rate of return on assets is greater than or equal to a benchmark value: **ROA ≥ ROA***. That asterisk on the right side of that last condition is the usual symbol to show something we consider as peg value. Right, I use the asterisk in other types of elaborate expressions, like s*** or f***. The asterisk is the hell of a useful symbol, as you can see.

Now, I add that idea of local, virtual currency based on green energies. Back in the day, I used to call it ‘**Wasun**’, a play on words ‘water’ and ‘sun’. You can look up ‘Smart grids and my personal variance’ or ‘Les moulins de Wasun’ (in French) in order to catch a bit (again?) on my drift. I want a local, virtual currency being a significant part of the local monetary system. I define ‘significant part’ as an amount likely to alter the supply of credit, in established currency, in the local market. I use that old trick of the supply of credit being equal to the supply of money, and so being possible to symbolize with **M**. I assign the symbol ‘**W**’ to the local supply of the Wasun. I take two moments in time: the ‘before’, represented as **T _{0}**, with

**T**standing for the ‘after’. I make the

_{1}**condition #4: W/M(T**.

_{1}) > W/M(T_{0})Wrapping it up, any particular event falling into:

**Q(RE) = S(RE) = D(E)**

**P(RE) ≤ PP(E)**

**ROA ≥ ROA***

**W/M(T _{1}) > W/M(T_{0})**

… is a success. Anything outside those triple brackets is a failure. Now, I can take three basic approaches in terms of probability. Thomas Bayes would assume a certain number **n **of trials, look for the probability of all the four conditions being met in one single trial, and then would ask me how many trials (**p**) I want to have successful, out of n. Simeon Denis Poisson would rather have taken an interval of time, and then would have tried to assess the probability of having all the four conditions met at least once in that interval of time. Satoshi Nakamoto would make up an even different strategy. He would assume that my project is just one of the many going on in parallel in that little universe, and would assume that other projects try to achieve their own conditions of success, similar to mine or different, as I try to do my thing. The next step would to be to define, whose success would be my failure, and then I would have to compute the probability of my success in the presence of those competing projects. Bloody complicated. I like it. I’m in.

[1] Mr. Bayes, and Mr Price. “An essay towards solving a problem in the doctrine of chances. by the late rev. mr. bayes, frs communicated by mr. price, in a letter to john canton, amfrs.” Philosophical Transactions (1683-1775) (1763): 370-418

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