[MUSIC] Welcome back to the Session B of the lesson dealing with Terrible Simplifiers. Again, we are dealing here with the problems the quantitative analysis has when trying to represent complex systems. The goal of this session is to make you aware of the problem, giving you practical examples, and especially, we want to show the fragility of numbers, when trying to describe complex systems across different scales. So the innate fragility of numbers and the resulting quantifications, depend on the fact that we are never using numbers, we are using the meaning of numbers. And the meaning of numbers really depend on the ability to identify their external reference, what we are measuring, what is the class of things that we are measuring. And also whether we are capable of sharing the meaning with those that are supposed to use the numbers. So, for any formal statement to be meaningful, It has to be transmitted in the expected associative context. Let's explain this point with a very simple example. Let's imagine I ask you to tell me what is the sum of these two numbers. If I would ask your opinions they would have no hesitation to saying this is 240. Whereas if I would ask people using Arab notation for writing numbers, they will tell me that this is 230, the sum of these two numbers. Why is that? Because if you are looking at a different way of writing numbers, this sum could be write like 165 + 65, so that would be 230. So you can never trust the number because even the symbol can be misleading. So when we want to discuss what mathematical relations should we use, which number and which equation. We have to be capable of identifying what is generating the meaning of the number. Let's, for instance, use this sentence, the proposition 1 + 1 = 2 is occasionally useful, and this is written by Whitehead and Russel, in the Principia Mathemetica. And what this means that, for instance, let's imagine that we want to write, use the variable number of a household to describe what happens when two single get married. So if are using number of household, you will have one person living in one house and another person living in one house, that are getting married, and they will become two people living in one house. So if we are making the representation with numbers of this event, the marrying of two in terms of number of households, we will have that 1 + 1 = 1. So again, unless you are capable of understanding the relation of what you are measuring and the type of mathematics that you're using. It is very tricky to assume that you can do the standard operation, one size fits all. Also, another important point is how you're generating data for your number. We can use a joke that has been proposed by in a book about the quality of scientific work. And the joke is this one, there's a skeleton of a dinosaur in the museum and he has written the age of the skeleton, 250 million years. And one day, someone put an eight on the last digit. So the director of the museum said, who did so? And the janitor said, yes, sir I did it because I've been working here for eight years, and I'm trying to keep the age updated. Of course everyone laughed, because this is a joke. But why wouldn't it be possible to do the sum A + B = C? No, there is no rule in mathematics that say it's impossible to sum 250 million to 8. People laugh because there's a problem of the error bar that is in the measurement. And of course the error bar on the measurement of 250 million is so big that 8 doesn't have any meaning. So, but I mean, do we ever consider this type of problem? When we are doing some of what is consumed by a country, or the estimation of CO2 emission, whatever. Because at times, we can see that there are numbers that are summed, that really do not belong to the same class of accuracy in the measurement. Another example that is very popular is the life cycle assessment, that's how much is embodied in something. So this example is very nice because this was, in the 70s, a very hot topic, how much energy is equivalent to one hour of labor, and has been one of the major fiascos of attempt of quantification. Let's see, I'm reporting here a few examples of papers, and you can see that to these papers, the equivalent of one hour of labor can go from 0.4 megajoules to 12 terajoules, it's unbelievable. And let's see how this is happening and why this is happening. What are the factors generating this wide range of values? It is not because scientists are bad or because they are not good at what they are doing. Because all these papers have published in reputable journals through peer reviewed processes. The problem is that there are differences in the pre-analytical choice of defining what is, or how it should be measured, one hour of labor. Let's see, for example, you can say that one hour of labor depends on the energy consumed by the muscle, without even considering the basal metabolic rate. And this will be 0.3 megajoule per hour. Or you can say, that has to be all the energy consumed, either the one consumed by the mass, or also the one consumed by the body mass. And you will get another measurement. And you can said that it would be nice to have all the energy consumed in one day, divided by the eight hours of work, so of course the is more because you have to consider also the energy spent in the hours when you're not working. Then you can add the hours over one year, the energy spent in one year of food again. Divided the hours worked in a year, then you have also vacation, then this is a little bit higher Let's imagine now to expand even more on this scale and we want to look at the whole family and how much is required for keeping a family, and then divide it by the working working hours of the family. Of course, this is more, because we have dependent population. And then you have a first because the level of a family is no longer only the food that matters, but other things. So you could have also an analysis of much fossil energy is used to deliver the food to the family to process and consume, is almost ten to one. So this is an example, we just want to divide by ten, the magnitude of the food. Then we could have another approach, let's imagine all the energy consumed by a society divided the hours of work in the economic sector. And this is one of the official ways of measuring this, and then you would have 200 megajoules per hour. But there is another thing, there is a method developed by H T Odum, a famous ecologist, a genius. That he was proposing to reconsider transforming this to see how much solar energy was required to do the input that we are using, to produce the input that we are using. So we could calculate and embody energy for solar energy. As a matter of fact, there is a person that did it. He's recorded in one of the papers that was shown at the beginning. And then by doing this it will have that this is 12 tera solar energy joules. That is, tera is 10 to the 12. So what is the conclusion here is that If you are looking at the different assessments that we saw before, you have that you go from one hour to one year to millions of years on the top. And then what is important is that you move from assessments that are referring to different type of energies. If you're looking at the muscle maybe these are the biochemical reaction, ATP would be the carrier of energy. If you're going at the household level, you could have either megajoule of food or megajoule of oil. Then you go at the level of the country you will have all equivalent. And if you go at the level of the biosphere you get energy solar equivalent joules. What is the point here? That in reality, there is no energetic equivalent of labor. It is something that cannot be defined, unless you were defining a lot of relation and a lot of agreement on what should be considered to do what. So, you do not have the energy equivalent but you have different energetic equivalent, that could be useful or not depending on what you want to do.
