# Peace, Somewhat Precisely

In the footnote of my previous essay, titled ‘War, Peace, and Everything in Between’, I wrote about being able to empirically measure how much at peace a country is. I also mentioned that I’d like to write an essay titled ‘Peace, Precisely’ which would have more mathematical rigor. I spent quite some time thinking about it, and in the interim, I am going to write the current essay and call it ‘Peace, Somewhat Precisely’. The premise of this essay is to step in the direction of the final essay by laying a foundation which can perhaps be reused later.

We shall try to come up with a value which defines how peaceful the world, as a whole, is at a given moment in time.

In my essay I mentioned that we can define interactions between two nations that can help us measure, empirically, how much peace there is between them. For example, the amount of trade and commerce among them can be used as an indicator of peace between them. In theory, we can have many such interactions that together help us measure the peace between the two nations. Mathematically, let’s call this a function . The input to this function are all the interactions among the two nations, and the output is a value between 0 and 1, inclusive that indicates the amount of peace. We shall denote this value as . We, therefore, have .

We can now model the nations of the world, and the relationships between them as a weighted, undirected graph. If a nation has an interaction with another nation, there shall be an edge between them. The weight of the edge shall be the value between the two nations. We’ll introduce one more value, , for serenity, which is a measure of the amount of peace within a nation’s borders, and takes on values between 0 and 1, inclusive. We can define similar interactions which can help us measure the peace within a nation. Let’s define a function such that .

Combining the two above, the amount of peace that a nation has is a combination of peace within, and outside its borders. We can, therefore, define a function which combines the value of and . We now have , and can generate a set of -values for all the nations of the world. The -value, mentioned at the begining of the essay, can now be computed from the set of -values. For example, as a median of the set of values.

This is how we can measure the amount of peace in the world. Hypothetically. :P