Fringe phenomena, which happen just sometimes

My editorial

I am focusing on the Fintech industry, and I continue studying that report by Pricewaterhouse Coopers, entitled “Global FinTech Report 2017. Redrawing the lines: FinTech’s growing influence on Financial Services” . I started studying this report in my last update in French (see Quatorze mâles avec le gène Fintech ), and, just for the sake of delivering interesting information, I am reproducing, in English, the table with percentages of incidence as regards partnerships with FinTech companies (table 1, below). Still, I want to focus on another topic. Further below, in Table 2, I reproduce the contents of Figure 7, page 8, in that report. It is supposed to show the attitudes that FinTech companies, and incumbent financial institutions have as for working with each other. This is quite a piece of information: simple at the first glance, bloody cryptic when you really think about it. You can see there one of those tables (in the source report this is a graph, but it does not really help), with a structure much more complex than the content it conveys. I want to use this piece of empirical data as a pretext to discuss the mathematical and logical interpretation I would use to tackle this type of information, i.e. poll percentages. Hence, I invite you to scroll through both tables and I invite you to follow up my analysis, below the table no. 2.My editorialMy editorial

Table 1 Incidence of partnerships with FinTech companies, in the PwC survey 2017

Source: “Global FinTech Report 2017. Redrawing the lines: FinTech’s growing influence on Financial Services”

Table 2 When working with Financial Institutions (or FinTech companies), what challenges do you face?

Source: “Global FinTech Report 2017. Redrawing the lines: FinTech’s growing influence on Financial Services”

Good. You’ve rummaged (intellectually, I mean) through both tables, and now I am focusing on table 2. I am giving here my own interpretation of the data at hand, which is not the same as presented in the source report. Firstly, the basic assumption that I can derive from the data in question is that PwC asked both some FinTech companies, and some classical financial institutions, how they get along with each other. The questioning visibly implied that it is not all rose petals and little angels, and there is tough s**t to handle, on both sides. The typical challenges are enumerated in the left column, under the heading ‘Field of cooperation’. Once again, this is a typical case of Ockham’s razor: I have no clue as for how those fields of cooperation have been defined. They could have resulted from open, in depth-interviews, or could have been defined a priori, whatever: I take what I see. They are linguistic pieces of meaning that some people considered intelligible enough to answer questions about, and this is all I need to know at the starting point.

And thus we come by any percentage we want in that table and we ask a legitimate question: “So what?”. Such type of percentages is based on the Aristotelian logic of the excluded third, i.e. anything we encounter in this world can be A or non-A. The supervisor of my Master’s thesis in law, professor Studnicki, used to tease us, his students, with those mindf***ing games in the lines of: “All the phenomena in the universe are either pink elephants or non-pink-elephants. Prove me wrong”. It was bloody hard to prove him wrong. This is probably what made him a professor. Anyway, Aristotelian logic comes handy regarding basic distinctions, as it does not burden us with too many of them. There is just one. Yet, what Aristotle used to train the minds of young, ancient aristocrats requires some deeper understanding. Suppose I ask you: “Do you consider differences in business models as a challenge in cooperating with FinTech companies?”, and you can answer just with a YES or a NO, without any further opportunity to enter into nuanced judgments. I ask the same question to like 100 other people. As a result, X% of them say YES, and Y% = 1 – X% say NO. The 1 – X% part is crucial here: each of the percentages X in table 2 (just as in table 1, by the way) makes a closed universe together with its opposite 1 – X. We call it a logical division, both complete (it covers the whole universe) and separable (no overlapping between the classes defined). Mathematically, we translate it as the probability X% of scoring a success in a trial, versus the 1 – X% probability of suffering a failure. In mathematics, we use the binomial distribution to understand such situations. You can check the mathematical details with Wikipedia (formal, quite complete an exposition) or with the Khan academy .  What I want to discuss is the practical logic behind the equations.

In the first place, it is legitimate to ask ‘Why the binomial distribution? Why not something like the Gaussian, normal distribution or any other distribution, as we are talking about it?’. Well, we have just A and non-A, happening with the respective probabilities of X%, and 1 – X%. This is all we have. If you calculate the mean of X% and 1 – X%, you always end up with 50%. Any parametric distribution is close to meaningless in such cases. The binomial one is the only practical logic we can apply in order to understand the situation. Thus, we go with the binomial logic. The interviewer asks a sample of people from FinTech companies what do they think about differences in knowledge and skills when working with the incumbent financial institutions (first numerical column in table 2, second row from the bottom); 33% of them say ‘Yes, this is a challenge’ and 1 – 33% = 67% say ‘No problem whatsoever’ or something similar. Provisionally, I label the former answer as a success in the experiment, and the latter as a failure. On 100 trials, the interviewer scored 33 successes and 67 failures. How could it have happened? How could those 33 successes take place on 100 trials? The binomial distribution says that the probability of having k successes on n trials is defined as P(k; n, p) = (n!/k!*(n – k)!)*p^k*(1 – p)^n-k (the exclamation mark means a factorial, i.e. 1*2*…*n etc.). It further means that there is some kind of underlying probability p of having any given respondent saying ‘Yes, this is a challenge’, and there is (100!/33!*(100 – 33)!) = 294 692 427 022 541 000 000 000 000,00    ways of having that underlying probability happening 33 times on 100.

That makes a lot of ways of happening, more than people on Earth. Seeing this number could make you turn intuitively towards an attempt to extract that underlying probability from the equation. Legitimate goal, indeed, and yet I want to attract your attention to something else. If I change the proportion between the number of successes and that of failures, so if I take e.g. the incidence of people from FinTech companies mentioning IT security as a challenge when working with incumbent financial institutions, and I have that 58%, it means that on 100 people interviewed, I have (100!/58!*(100 – 58)!) = 28 258 808 871 162 600 000 000 000 000,00 ways of having that happening, which is two orders of magnitude more than in the previous case. Of course, these (n!/k!*(n – k)!) values are pretty abstract, and still they show an important aspect of the situation at hand: different distributions of percentages in the Aristotelian logic of excluded third correspond to different degrees of variety in the possinble ways those percentages can happen in real life. If I take a question, which yields ‘Yes, you were correct in your intuition, dear Interviewer’ in 98 cases on 100, I have just (100!/98!*(100 – 98)!) = 4 950 ways of having it happening. If I have something like the electoral results of some politicians I know of, i.e. 99% of support from those voters who are sensible enough not to deny their support (happens in some countries), I have barely (100!/99!*(100 – 99)!) = 100 ways it can possibly take place.

Do you understand? The greater the percentage of something that I qualify as a success (generally, the positive happening of that something), the less distinct ways this percentage can occur. Conversely, the less probable is that occurrence, the more distinct ways it can happen. Big, respectable percentages in table 2, like 58% or 48%, mean that whatever are their underlying mechanisms, they are relatively more unified in terms of patterns in human behaviour than the small percentages, like 16%. Small incidences can happen in more ways than big incidences. Counterintuitive? Apparently, yes. Yet, as you think about it, more robust a logic raises its head. If anything happens quite frequently, like atoms happening in the same spot in space-time in the chair I am sitting on, the structure supporting the happening is relatively stable. My chair is stable: I took it to the carpenter, recently, and he fixed that wobbly leg. If something else happens pretty seldom, like an atom of oxygen in the outer space, the supporting structure must be pretty unstable. Here, it becomes logical. Big, stable, central phenomena, which happen in 99 cases on 100, and make me believe there is any point in all that process called ‘living’, are all based on some stable, predictable structures. Fringe phenomena, on the other hand, which happen just sometimes and their sometimes is really choosy in its happening, are based on ephemeral structures in reality.

This is deep philosophy. How could I have got there, starting from those percentages supplied by Pricewaterhouse Coopers? I still wonder.

One more thing. I am working on launching that fully fledged, business-based educational website of my own. If you follow my blog for some time, you can see I am doing by best to stay consistent in documenting my research in a hopefully interesting form. Right now, I am at the stage of crowdfunding. You can consider going to my Patreon page and become my patron. If you decide so, I will be grateful for suggesting me two things that Patreon suggests me to suggest you. Firstly, what kind of reward would you expect in exchange of supporting me? Secondly, what kind of phases would you like to see in the development of my research, and of the corresponding educational tools?