The Chow-Faronius Emotional Bank

About one year ago, a friend of mine, Mabel Chow, and I had a series of very interesting discussions about Human Communication and different kinds of relationships between people. A lot of models has been discussed for different kinds of situations, and I will cover more of these topics when I finish writing my complete work on Human Behaviour.

The Chow-Faronius Emotional Bank(something similar to it has most likely been introduced already) is a very simple model for describing the growth of feelings (or emotional values) of a relationship. The model can then be extended to describe even more complicated matters.

Assume that we have a person P, with a set I containing all pieces (discrete) of information about person P. We will now define a function E, that assigns a real number (an emotional value) to every piece of information i.

Definition: For all i belonging to I, we can define a function E that assigns a real number to every i. The image E(i, t) is called the "emotional value" of the information. The t is for time, and shows that the emotional value of something can change over time.

The emotional value is a scalar describing how "emotionally charged" every piece of information is. A natural choice of the range of E(i) is the interval (0, 1), but the function can be defined for any interval on the real axis, and so that a high value corresponds to a high emotional significance. For instance, for most people the E(your name, independent of time) is lower than E(your cat, this morning).

The thing about relationships (with friends, relatives, colleagues, lovers, etc...) is that by spending time with them, you share information, and this information has emotional values. Like a bank where you can invest your money in different shares and funds, people invest emotional values of information in other people and their relationships, and then you may get a good return or a bad one, depending on coincidences and the person. The more emotional valued information you share, the more you can earn on it (due to rates of the bank).

It is also due to this model that you get more hurt if someone close to you. Actually "closeness to someone" could be defined from having the function E(i, t). Closeness could be measured as the sum of all the information you have shared E(i,t). Of course this is only relative to another relationship and its closeness, and it would be very difficult to define an intrinsic way of defining how much you will have chosen so that you become friends.

Corollary: "Love" is just a special instance of a relationship and sharing emotional values.

Of course, one might say that by doing things you might improve your relationship with someone, and one might argue that this is not just abstract information, but a more thorough investigation will reveal to you that by doing things with someone, you actually just change the emotional value of information that have already been sent. Eg. Lovers might do things for each other to heighten the value of the information that they are affectionate.

Some more advanced extensions to this model is the fact that there is a probabilistic factor of the growth of relationships, and that some possible might not happen if the people involved feel that the risk of losing is too great. The last of these is easily treated with Game Theory and the one before is described by a stochastic model, simmilar to Brownian motion. But treating these, is a more advanced subject.

The Mathematical Theory of Writing

The subject of today is quite elementary, and not that remarkable from a mathematical point of view. It is really a special case of my earlier, unpublished, work on Communication and Behavioural Theory. Still it might be of some interest for the uninitiated, so I will devote today to speaking of how to write good texts.

To define a way to talk, in an intuitive manner, about how to make people understand and be interested in what you are telling them about, we need to find a way to measure "the distance" between what you are telling them and what they understand out of it. This is of course done by providing a metric topology, and we must consider the pieces of information that you are sending and them recieving as discrete points. By providing a constant for what the maximum distance between these points are, we can determine how "close" the information you are sending them and the information that they percieve are, and thus determining if the idea is actually transferred.

Different types of texts have different values of the constant (often denoted in topology as the "delta"), for instance Mathematical texts have relatively small deltas compared to other types of texts because of the exact precision of the theorems and logical arguments. Poetry, especially of the abstract kind can have very big deltas, and it is in fact this that can allow the reader for a subjective interpretation.

Even though mathematical texts have relatively small deltas, these still allow for very different interpretations and the restriction of a certain delta can still allow the reader to view things from many different perspectives. Though the delta is specified, the amount of dimensions that the metric topology have is not, and if every property could be represented as a one-dimensional independent component, we could easily add more dimensions and adjust the metric accordingly.

Different types of texts, especially books have different ways that they should be written in as well. We might want to define some quantity measure how intriguing the plot is as a function of how many pages you have read, to provide some examples of writing styles.

Above is shown have a good thriller is written, or rather, how it is planned. Your goal is to have a story that reaches its peak at the end (this is generally a good way for most stories), which this one clearly does. Different rules apply for dramas though, as well as biographies, where you would rather have an even distribution of excitement.

The thriller is characterized by this discontinuity near the end, which represents a shocking twist in the story such that you realize that the storyline really went the more smooth path of the dashed line. This is often near the end, which is marked with the filled black dot at the end of the graph.

Having a continuous graph is preferable, because it helps the reader to follow what is happening. If there were to many discontinuities, the story would be impossible to follow, and it would seem more like a dadaistic poem. Textbooks are preferred to be as smooth as possible, even though it wouldn't be a measure of the storyline, but instead the trail of thought leading to the ideas, such that they are understandable. Consider as a theoretical experiment taking a Calculus book, and randomly rearranging all the texts and theorems in it, and then try to read it. Even for a devoted mathematician it would be almost impossible to comprehend it, and even less enjoyable.

Also, another important concept for writing books is the initial conditions, telling the reader what level of knowledge is needed to understand it. This applies both to textbooks as well as for novels(eg. series such as Lord of the Rings). If the initial condition for the book is not met, the reader will have a hard time understanding it because of the discontinuity that will arise of the readers progress.

Those are some important things to consider when writing an arbitrary coherent text.

Scio me nihil scire, and some thoughts about mathematical paradoxes.

Socrates said (translated into latin) "Scio me nihil scire" ("I know that I know nothing"). And I feel that this is a good place to start. After two and a half years at Uppsala University, and AARMS Summer School in Mathematics I am quite confident that I know nothing about Mathematics (or Physics). People seem suprised when I tell them this, and some people (especially engineers) seem to think that I am saying that they know more than me then. I feel that we should have this humble approach to any subject we study, even the social sciences. If nothing else, it is at least a more gentle way of interacting with others.

To explain the more philosophical nature of this statement, is that if we assume that I have some amount of information in a set B. And the total amount of information, finite or not is denoted by a set A. Then B is a subset of A, and if we know the size (ie. the cardinality) of both set A and set B, we can get an idea of how much of A is covered by set B. If however, we only know the size of set B, and not of A, this is of course impossible. Many people that assume that they know a lot of Mathematics think that their cover of set A is big, mostly because they feel that their covering is big compared to some "average person measure".

A person that knows what an overwhelming amount of knowledge lies within Mathematics, realizes that if the set A is finite at all, their covering of it is very, very small. Therefore, I believe that many great Mathematicians are very humble of their knowledge, and even though they are the masters of their fields, they still believe that they know nothing about it.

Something else that fascinates me about the statement "I know that I know nothing", could provide us with a simple, very intuitive way of characterizing (in a way) what a paradox looks like.

If we assume, according to the statement that the set A of everything I know only contains one element, and that is that I know nothing. It would make that set empty, contradicting our assumption that I know nothing, which then assumes that A is empty. This is really equivalent to Russel's Paradox, and we are tempted to make the following definition.

Definition: If the intersection between a set A and itself is not the full set, then the definition of the sets are paradoxal.

This really assumes that we are given two ways to define the sets. For instance, let us apply this to the famous "Barber paradox". Assume that there is a small town with exactly one (male) barber, and that he shaves all men that don't shave themselves. We must also assume that all men has to shave. The paradox arises when we consider who shaves the barber?

Let us assume that the barber shaves everyone. Let us also regard the necessary condition that he doesn't shave himself, meaning that he is the same set except one. This means that the intersection between all men who shave and the set where the barber doesn't shave himself but everyone else does, is not the same, so we have arrived at a paradox by the definition. By using this definition we can develop it further and in an obvious manner find many other equivalent ways to express it.

Seeing the geometry

Today, I have decided to start a new blogg, to share my thoughts about Mathematics with anyone who might be interested in reading it. To often I find myself contemplating about the world, and the structures that seem to govern it, and the only way to actually interpret it is through the language of Mathematics.

For me, this blogg is a way to express my ideas and thoughts about the world, but it is also an exercise in thinking and expressing my thoughts, and to see the geometry. If anyone reads it, I hope you enjoy it, and find my thoughts interesting.

I am currently an undergraduate student at Uppsala University in Physics and Mathematics, and I have not yet published anything or done anything important. Some of my thoughts might be wrong, and if so I apologize for misleading you.

If you have any interesting thoughts or comments that you feel the need to share, feel free to mail me at

Please do not send any spam or just messages saying how you don't like this. If you don't like it, then don't read it.

Also, note that the page might not give the best way to display my equations, and for this I am sorry.

Sincerely Håkan Karlsson Faronius