On how statistical mechanics can make you happier

7000 millions of definitions of happiness

When I first decided to write on happiness and goal achievement, the first thing I wondered was, why 7000 millions of human beings living on planet earth have such a small set of goals in life. Some of these goals might be “I want to raise my children and provide them with a good quality of life”, “I want to get as much money as possible”, “I want to survive and minimize my effort by getting others to work for me”, “I want my soccer team to win the league” or “I want my mother-in-law to get dumb”, among a few others.

Whatever the set of goals the average person aims at, they will not be for sure that different from other’s. I understand that we all, as human beings, have a lot of things in common, what would lead to have many common desires. That would be the reason for not having 7000 millions of different definitions of happiness. However, it catches my eye the recurrent ambitions on people’s mind.

What if we are letting be pushed to adopt imposed goals, or we are inheriting our parents’ definitions, or being so lazy as to not explore the universe before deciding what we want?. For sure it is easier to embrace something already built, but when it comes to define where we will be focusing our efforts on, during the rest of our lives, should we not be exploring a bit more before we set what we want to be or do in life?.

My point is that the set of goals we want to achieve should be something deeply personal and that we all should be devoting more time in finding out what we really want instead of throwing ourselves into a frenetic race without a prior analysis. This post is about goals, how to define them better to increase our chances and how we can establish a relationship between statistical mechanics and the achievement of goals in life. Yes, you heard well, statistical mechanics and happiness have something to do. I will further explain if you continue reading.

Goals and frustration

Given that frustration comes when our most important goals are not met, we should take a closer look at the way in which we define them and how the probability of achievement changes dramatically depending on certain details in our goal definition. It is time to play in a more favourable pitch.


Fig.1 Frustration

Definition of goals in absence of information. A personal experience

When I finished my Physics degree, long time ago, I was really bent on practising as an electronic designer for a living. A good part of my speciality in the degree had been devoted to that field, and I had really enjoyed attending the related subjects. I was not conscious that only a few Spanish companies were doing electronic design at the time, so I had little chances to end up working in that field. In any case I wrote my CV highlighting my skills in that area and I pointed all my effort to become an electronic designer. However, time passed by and nothing happened, so I had to admit eventually that perhaps I should do something different for a living. With a good dose of frustration I started searching for a different job and I got a computing-related job. I did not enjoy at all in my position, but I did not have any other clear direction to point at.

Absence of information

Fig.2 Absence of information

After a year, I went out for some drinks with some friends, and I realized that sometimes you only need to be in the right place at the right time. I came across in a pub with a former gym colleague that I had not seen for years. While ordering some draft beers he asked me about my professional career and if I was enjoying. Of course my answer was no, and he asked me to email him my CV, since there were some vacant positions in his company. For sure he told me what the vacant positions were about, but sincerely, after six or eight beers I did not remember much about our conversation next day. I just found my former colleague email address in the pocket of my trousers and sent my CV to him, without recalling for what, thinking that it could not be worse than the job I had.

I was contacted one month later by someone from Human resources. So, I went for my blind interview without bothering about the company name. I only had the address and my colleague phone number. When I arrived, surprisingly I realized that the company was the second biggest telecom operator in Spain. Hence, I set myself poker-faced and tackled the interview as if I was convinced (actually I had to convince the interviewer) that I had been born for a telecom job. The fact is that surprisingly I got the job, and I have been doing that for a living for over fifteen years.

The right bar at the right time

Fig.3 The right bar at the right time

I quickly started enjoying my new job and I continue enjoying nowadays. Thinking back to the days in which I was setting my professional goals I clearly understood that I had made my decisions based on the little information I had at the moment (I knew about electronic design), but I was lacking in a lot of information (electronic design was not a realistic option in Spain at that time and I did not know that my profile could be retrained for a telecom company). So, I threw myself into defining what I wanted to do in life with a really limited view of the professional reality.

I think the same is true for any type of goal definition we make in life, no matter how much we investigate, we cannot get all the information (do you remember the “non-observable universe” from my previous post “Reality is a complex object II”? http://unveilingthereality.com/2015/03/06/reality-is-a-complex-object-ii/ ). It led me to a different approach, given that I have not all the information I should not make very precise statements about what I want to get, but rather to establish open statements based on principles without specifying many details. It would be the way to define goals according to my main principles, based on what I know, and let the details to get filled in the future with the new things I will come across in life, completing the information that I did not have at the time I defined the goal.

Once shared with you the way in which I came to this conclusion of open definitions for the goals, it is time now for more objective arguments. Let me explain what statistical mechanics has to say on this.

On how statistical mechanics explains how things happen

Statistical mechanics is the branch of the Physics that deals with systems consisting in millions of elements interacting among themselves. The typical system studied by this branch is a gas with millions of molecules exchanging energy. From my point of view there is no any single reason why we could not extract valuable knowledge to be applied to other fields. It is precisely what I am intending with this post.

Statistical mechanics explains clearly why an initial configuration of molecules with ordered positions tends to get as disordered as possible, or why two portions of matter with different temperatures tend to a balanced temperature when they come into contact. The principles in action can be used in other aspects. For example, and it is something that I will address in another post, we could wonder why heat is distributed uniformly among a molecule net but money and power get stuck in certain circles not allowing a balanced society. Both systems can be explained in the same terms and some interesting insights can be withdrawn, like for example to establish a link between the way in which an asset (heat or money) flows within a network and the resultant probability distributions. Obviously the temperature distribution among molecules in a network is not the same as the wealth distribution within the population.

But that is another story, I am focused here to show the mechanism why a system tends to its maximum entropy or disorder and how the same principle may be involved in the process of achievement of our goals. I hope this drop makes you keep reading, welcome to this attempt to explain why our goals are often not met and how we could set a different strategy to improve our chances.

Macrostates and microstates

The definition of macrostate, from the statistical mechanics point of view, is a specific system state that can be described in a few words indicating the general arrangement. For example, in the context of a gas in a box, a macrostate would be an arrangement in which all the gas molecules are set in the left half of the box. The way in which the arrangement is explained is easy and short, “all the molecules are in the left half”. Another macrostate would be “molecules equally distributed between both halves”, that is to say, 50% of the molecules are in the left half and the remaining 50% are in the right half.

The concept of microstate however is an extensive definition of a specific low level configuration meeting a macrostate, by mentioning all the involved elements and their states. For the macrostate “all the molecules in the left half” we only have an unique microstate: (m1=left, m2=lef,….., mN=left), where m1=left refers to the molecule 1 being in the left half. However, in general, a macrostate will consist in a set of microstates. For example, the macrostate “molecules equally distributed between both halves” consists in a large number of microstates, depending on the number of molecules in the gas. Simplifying the experiment, let us consider a box with a gas consisting in only four molecules: m1, m2, m3 and m4. In this case the macrostate previously mentioned will correspond to the following set of microstates:

(m1=right, m2=right, m3=left, m4=left), (m1=right, m2=left, m3=right, m4=left), (m1=right, m2=left, m3=left, m4=right), (m1=left, m2=right, m3=right, m4=left), (m1=left, m2=right, m3=left, m4=right), (m1=left, m2=left, m3=right, m4=right)

So, while the macrostate “all the molecules in the left half” is fulfilled by only one microstate, the macrostate “molecules equally distributed between both halves” is fulfilled by six different microstates. Now, please make a guess on which macrostate has a higher probability to take place, you have got five units of time to provide an answer.

time to guess

Fig.4 Time to make a guess

Well, I assume that your answer was “molecules equally distributed between both halves”, simply because we are used to seeing things going to the maximum disorder. Perhaps you did not know why systems in general behave like that, but you know it now: things tend to go to their most disordered macrostate simply because that macrostate is the one fulfilled by more microstates, and the probability of a macrostate to happen is proportional to the number of its microstates. This is a key knowledge that can help us, not only to understand where physical systems tend to evolve, but why some goals in life are more difficult to get met than others. This is a principle that I would like you to remind since it is really helpful to understand why certain things happen and other things are extremely rare to be seen.

Microstates, number of variables in a system and probability

This title may be scaring, but I will try to give a painless explanation on this matter. Actually, I need only to provide a generalization of what I have already explained in the previous section. As you already know at this stage, the probability of something to happen depends directly on the number of its microstates. In turn, this number of microstates depends on the number of elements the macrostate consists in. In our example of a gas consisting in only four molecules, the number of different microstates fulfilling the macrostate “molecules equally distributed between both halves” was six. However, this number will get increased dramatically if we increase the number of molecules in the gas. Perhaps it does not come obvious enough, but a way to understand this fact without using mathematical expressions, would be to think about how many different ways there are to organize a set of N elements into two different boxes. As the number of elements get increased there are more possible permutations.

Actually, the real probability of a macrostate to happen depends directly on the number of microstates fulfilling the macrostate divided by the number of total possible microstates for the system. That is the reason why the macrostate “all the molecules in the left half” has a smaller probability in a system consisting in millions of molecules than in a system consisting in only four molecules. This macrostate always has one microstate, but since the probability is that one microstate divided by the total possible microstates, it comes quite clear that as we increase the number of molecules this ordered macrostate becomes more and more rare to be seen.

Therefore, we have two different aspects to take into consideration when we want to figure out whether a macrostate is likely to be seen or not, on the one hand we need to analyse if there are many or a few microstates fulfilling the target, and on the other hand we need to consider if the system is consisting in a large or a small number of variables. If the situation were that the system has only a few variable (like in the case of a gas with only four molecules), even if a macrostate is fulfilled only by a few microstates, the probability to see an ordered macrostate is appreciable and we could bet on that macrostate. However, betting on an ordered macrostate when the system consists in a huge number of variables would be to waste our money.

Ordered macrostate

Fig.5 Ordered macrostate. A few microstates, low probability.

Disordered macrostate

Fig.6 Disordered macrostate. A lot of microstates, high probability.

A relationship between statistical mechanics and goals in life

In this section I would like to establish a relationship between the concepts I have already explained and their impact in the things happening to us in life. When we define a goal, it will be probably complex enough as to need of several aspects or conditions to happen at the same time. For example, our desire of finding a good job will consists in several lower level variables. We all have skills that can be used for earning a life. At the same time it is needed that the fields our skills are related to demand certain amount of employees. It is also necessary that the economy in our country is good enough as to the companies decide to invest in increasing the number of employees. We will need also to find a direct way to contact those companies demanding our skills. Once we have got an interview we will need to impress our interviewer to get the position. We will need also to negotiate well our salary if we want our goal (to get a good and well paid job) got met. So, each complex target in life will be consisting in a set of low level variables or conditions that need to be met at the same time.

In this context, our goal is a macrostate and the set of variables with the necessary values are the microstates. Hence, if we wanted to analyse how feasible is a goal we would need to wonder first what underlying variables are important and the values that those variables must get to fulfil the goal. From this analysis we can figure out if many microstates (out of all the possible ones) fulfil the macrostate (our goal). Even if we do not calculate this quantitatively we can withdraw how feasible our goal is when comparing with the total number of microstates.

This approach can be useful as well to compare, in term of feasibility, two similar macrostates. Sometimes we increase considerable the probability of a goal to happen by redefining carefully the conditions. The smaller number of variables and the more percentage of microstates (out of all the possible ones) the higher probability to success.

How to define goals. Be generic and succeed

From the previous section follows that we need to define our goals in terms of a little number of variables and providing those variables with a high level of flexibility, in terms of the values they can adopt. I mean, the more values each variable can reach, without affecting the fulfilment of the macrostate, the better. By providing flexibility to a variable we increase the number of the successful microstates.

Hence, the success formula is to define goals with a few flexible variables. For example the goal “I want to become an astronaut and go to the moon in a NASA flight” is quite restrictive. Among all the professions on planet Earth probably astronaut is one with the least employees. In addition, we want to fly with NASA, however there are others options like the European ESA and a few more in Russia and China. On the other hand, we want to be an astronaut travelling to the moon. Only a few people in the history have stepped on the moon. Obviously, this target could be substituted with a more generic macrostate having a larger number of microstates: “I want to work in the aerospace industry. This goal, increases the number of successful microstates what make the macrostate far more feasible.     

statistical mechanics devil

Fig.7 Make the statistical mechanics devil work for you

Be specific and bite the dust

From the previous paragraph it might seem that by modifying our specific goals into generic ones we lose a lot in the process. I could think that if becoming an astronaut is my dream why  should I give up without giving it a try?. Should we not be aiming high, instead of being easily pleased?.

I base my reasoning behind setting generic goals in two main points. I have already explained the first one in the section “Definition of goals in absence of information. A personal experience”. There, I explained that defining something without having all the possible information is a way to limit ourselves. Do you remember my own experience and how I could not wish something that I am enjoying now, simply because I did not know of the existence of that possibility?.

The second point is a reflection on the concept “choice”. Choosing is not a concept as positive as it could seem. For me it is the other way around, choosing is a negative concept in terms of selection. To choose is to select what you want, but it is a way to discard the rest of things in the universe. So, choosing discards far more things than the ones are selected. So, the more specific our selection is the less items we are focusing on and the more things we are discarding. So, when changing our goals from specific into generic WE DO NOT LOSE, WE GAIN instead.

Therefore, if by being more generic we increase our chances of meeting our goals and it is, at the same time, a way to open the range of things we can get in life, should we not embrace this approach when it comes to define our objectives?.

Fulfillment of goals in life, an outcome of randomness or our effort?  

Statistical mechanics is based on the random interaction among a huge set of elements. So, the law of all the systems trending to their maximum entropy (macrostate with maximum number of microstates) is a consequence of randomness. We have established a relationship between statistical mechanics and fulfilment of goals. However, what if we consider that fulfilment of objectives is not random but rather an outcome of our efforts. I will not be meaning that fulfilment is either a random or a deterministic process, I will be just pointing out in this section that whatever the underlying nature of the process is, the general conclusion from the previous section remains the same.

Imagine that the process of fulfilment is entirely a deterministic process in which the chances of getting something achieved is directly proportional to our efforts. In this case we will need to put our effort (energy) into driving the variables defining our macrostate to the expected values. Consider now the statement from the previous section: to succeed we need to establish our goals with a few flexible variables. In this situation we will need to focus our efforts on a few variables instead of on a large number of them. So, from this perspective, even if the process is not random we need less energy to get the macrostate fulfilled. On the other hand, if we allow the variables to be flexible, by allowing them to get several values, then the energy consumed in driving each variable to a range of values will be less than driving the same variable to a specific, an unique, value. Therefore, the statement of “be generic and succeed” continues being valid under the assumption of a deterministic world (assumption quite debatable).

Correlation in life

Correlation is the process by which several variables have a relationship among them. Hence, setting one variable with a specific value will lead to determine the value of the others. An additional consideration when focusing our effort in the fulfilment of a goal, would be the presence, or not, of correlation among the variable defining the macrostate (goal). This analysis can be used to take a shortcut in the way to get the goal met.

The variables can be organized in a sort of abstraction scheme depending on how each variable impact the others. The value of a variable could be impacting three other variables in the system. On the other hand other variables could be affecting only other two or one, or even be independent. If in our analysis we determine the most impacting variables we can reduce the system to a smaller set, by considering only the ones impacting the whole system in a higher degree.

It is a way to reduce the energy to be put into the system, a way to direct our effort to the most relevant aspects. I will be addressing the concept of abstraction and how we can get benefits from a correlation scheme in a system in another post. Here, I only want to leave a quick introduction on how we can go a bit further in our strategy to get our goals met.

A quick insight in correlation and abstraction can be found in the link below. They are some of my thoughts on the matter, inserted in Nassim Nicholas Taleb’s facebook page, author of the famous “The Black swan” (1).


A quick summary

If I had to summarize the practical recipe from this post I would say “establish your goals with a few flexible variables, and after that consider if those variables are correlated. If so, reduce the system by focusing on the relevant ones”.

I wish you the best, be generic and enjoy your life.

enjoy your life

Fig.8 Be generic and enjoy your life


  1. http://en.wikipedia.org/wiki/Nassim_Nicholas_Taleb

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