Time puts order in the happening

My editorial

I am developing on what I have done so far. The process, I believe, is called ‘living’, in general, but I am approaching just a tiny bit of it, namely my latest developments on making a local community run at 100% on green energy (see my latest updates “Conversations between the dead and the living (no candles)” and ‘Quelque chose de rationnellement prévisible’). I am working with the logic of Bayesian statistics, and more specifically with the patient zero of this intellectual stream, reverend Thomas Bayes in person (Bayes, Price 1763[1]). I have those four conditions, which, taken together, define my success:

Q(RE) = S(RE) = D(E) << 100% of energy from local green sources

and

P(RE) ≤ PP(E) << price of renewable energy, within individual purchasing power

and

ROA ≥ ROA* << return on assets from local green installations superior or equal to a benchmark value

and

W/M(T1) > W/M(T0) << a local virtual currency based on green energy takes on the market, progressively

Now, as I study the original writing by Thomas Bayes, and as I read his geometrical reasoning, I think I should stretch a little the universe of my success. Stretching universes allows a better perspective. Thomas Bayes defines the probability of a p successes and q failures in p + q = n trials as E*ap*bq, where a and b are the simple probabilities of, respectively, p and q happening just once, and E is the factor of ap*bq, when you expand the binomial (a + b)p+q. That factor is equal to E = pq/q!, by the way. Thank you, Isaac Newton. Thank you, Blaise Pascal. Anyway, if I define my success as just one success, so if I take p = 1, it makes no sense. That Bayesian expression tends to yield a probability of success equal to 100%, in such cases, which, whilst comforting in some way, sounds just stupid. A universe made of one hypothetical success, and nothing but failures fault of success, seems a bit rigid for the Bayesian approach.

And so I am thinking about applying those four conditions to individuals, and not necessarily to whole communities. I mean, my success would be one person fulfilling all those conditions. Let’s have a look. Conditions 1 and 2, no problem. One person can do Q(RE) = S(RE) = D(E), or consume as much energy as they need and all that in green. One person can also easily P(RE) ≤ PP(E) or pay for that green energy no more than their purchasing power allows. With condition 4, it becomes tricky. I mean, I can imagine that one single person uses more and more of the Wasun, or that local cryptocurrency, and that more and more gets bigger and bigger when compared to the plain credit in established currency that the same person is using. Still, individual people hold really disparate monetary balances: just compare yourself to Justin Bieber and you will see the gap. In monetary balances of significantly different a size, structure can differ a lot, too. Thus, whilst I can imagine an individual person doing W/M(T1) > W/M(T0), that would take a lot of averaging. As for condition 3, or ROA ≥ ROA*, I think that it just wouldn’t work at the individual level. Of course, I could do all that sort of gymnastics like ‘what if the local energy system is a cooperative, what if every person in the local community has some shares in it, what if their return on those shares impacted significantly their overall return on assets etc.’ Honestly, I am not feeling the blues, in this case. I just don’t trust too many whatifs at once. ROA is ROA, it is an accounting measure, I like it solid and transparent, without creative accounting.

Thus, as I consider stretching my universe, some dimensions look more stretchable than others. Happens all the time, nothing to inform the government about, and yet educative. The way I formulate my conditions of success impacts the way I can measure the odds of achieving it. Some conditions are more flexible than others, and those conditions are more prone to fancy mathematical thinking. Those stiff ones, i.e. not very stretchable, are something the economists don’t really like. They are called ‘real options’ or ‘discreet variables’ and they just look clumsy in a model. Anyway, I am certainly going to return to that stretching of my universe, subsequently, but now I want to take a dive into the Bayesian logic. In order to get anywhere, once immersed, I need to expand that binomial: (a + b)p+q. Raising anything to a power is like meddling with the number of dimensions the thing stretches along. Myself, for example, raised to power 0.75, or ¾, means that first, I gave myself a three-dimensional extension, which I usually pleasantly experience, and then, I tried to express this three-dimension existence with a four-dimensional denominator, with time added to the game. As a result, after having elevated myself to power 0.75, I end up with plenty of time I don’t know what to do with. Somehow familiar, but I don’t like it. Dimensions I don’t know what to do with look like pure waste to me. On the whole, I prefer elevating myself to integers. At least, I stay in control.

This, in turn, suggests a geometrical representation, which I indeed can find with Thomas Bayes. In Section II of this article, Thomas Bayes starts with writing the basic postulates: ‘Postulate 1. I suppose the square table or plane ABCD to be so levelled that if either of the balls O or W be thrown upon it, there shall be the same probability that it rests upon any one equal part of the plane or another, and that it must necessarily rest somewhere upon it. Postulate 2. I suppose that the ball W will be first thrown, and through the point where it rests a line ‘os’ shall be drawn parallel to AD, and meeting CD and AB in s and o; and that afterwards the ball O will be thrown p + q = n times, and that its resting between AD and os after a single throw be called the happening of the event M in a single trial’. OK, so that’s the original universe by reverend Bayes. Interesting. A universe is defined, with a finite number of dimensions. Anyway, as I am an economist, I will subsequently reduce any number of dimensions to just two, as reverend Bayes did. As my little example of elevating myself to power 0.75 showed, there is no point in having more dimensions than you can handle. Two is fine.

In that k-dimensional universe, two events happen, in a sequence. The first one is the peg event: it sets a reference point, and a reference tangent. That tangent divides the initial universe into two parts, sort of on the right of the Milky Way as opposed to all those buggers on the left of it. The, the second event happens, and this one is me in action: I take n trials with p successes and q failures. Good. As I am quickly thinking about it, it gives me always one extra dimension over the k dimensions in my universe. That extra dimension is order rather than size. In the original notation by Thomas Bayes, he has two dimensions in his square, and then time happens, and two events happen in that time. Time puts order in the happening of the two events. Hence, that extra dimension should be sort of discrete, with well-defined steps and no available states in between. I have two states of my k-dimensional universe: state sort of 1 with just the peg event in it, and sort of state 2, with my performance added inside. State 1 narrows down the scope of happening in state 2, and I want to know the odds of state 2 happening within that scope.

Now, I am thinking about ball identity. I mean, what could make that first, intrepid ball W, which throws itself head first to set the first state of my universe. From the first condition, I take the individual demand for energy: D(E). The second condition yields individual purchasing power regarding energy PP(E), the third one suggests the benchmark value regarding the return on assets ROA*. I have a bit of a problem with the fourth condition, but after some simplification I think that I can take time, just as reverend Bayes did. My W ball will be the state of things at the moment T0, regarding the monetary system, or W/M(T0). Good, so my universe can get some order through four moves, in which I set four peg values, taken from the four conditions. The extra dimension in my universe is precisely the process of setting those benchmarks.

[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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