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The Evolution of Life

I work from home as a Software Engineer and I periodically find myself in a bit of a lull with work. The other day I was running some test cases against large data sets to test performance, and while the tests ran I was just pacing in my office. I started doing a little self-reflection and I realized that there’s a lot more I could be doing to push myself in my career. A big goal of mine is to get an online presence together since I avoid social media for the most part. To start, I would like to talk about something that has been on my mind for a while.

What is the Calculus of Life?

Calculus itself is most easily described as the study of continuous change. As something changes over time (usually the output of a function), how does that change change, and what does it imply? This may sound a bit weird, but imagine the slope of a graph. Maybe we don’t care about the slope itself, but rather how the slope changes over time. That's actually half of traditional calculus. Calculus is usually broken into two overarching categories: differential and integral. One concerns itself with the change of slope over time and the other with the accumulation of area. If this intrigues you, check out the fundamental theorem of calculus.

When I say ‘The Calculus of Life,’ I’m really referring to my own idea of Sociocultural Evolution. In other words, I want to analyze the evolution of society and culture, but I want to do so in a way that makes sense to me. Math makes sense to me, and I think the fundamental principles of differential calculus are interestingly applicable to humanity as a species.

Defining a function

Before I really get started, I would like to talk a little bit about functions to set some context for those who haven’t really dealt with them in a while, or maybe struggled with their introduction to functions. You may have seen something like this in the past:

In this case, f is just the function name. We could call it anything we want. We could say Sally(x) = 2x. All this means is that we have a function named Sally that takes one input, x (probably a number), and has an output of 2 multiplied by that input. So if the input is 4 then Sally returns 2 times 4, which is 8. Simple enough.

In order to apply calculus to the study of cultural evolution, we must first come up with a high-level function to analyze. In this case, the input will be time or t. The output will be an image (or description/understanding/whatever) of society and the culture of humanity at the point in time that was input to the function. Check this out:

The ₑ here stands for Earth. This function takes an input of time and spits out an “image” of world culture at that time. We could easily replace “Earth” with “Japan” and look specifically at Japanese culture, for instance.

Now that we have a function to talk about, let's do some (really) high-level calculus.

I am a Jester

As we move forward, please keep in mind that I have no idea what I’m talking about. I think that's really important. I’m going to be talking about some pretty controversial things because I feel that they work as an impactful example for the point that I’m trying to make. In doing so I’m going to make some very heavy generalizations and some rather bold statements. Know this going in; my mindset is one of complete acceptance, love, and a strong belief in the equality of all human beings.


One of the first things most students learn about calculus is limits. When we talk about limits, we are basically talking about what happens to the output of a function as the input of the function approaches some value. Often times we care about what happens as the input approaches special values like zero or infinity. So lets talk about society. Keep in mind that I’m going to make a lot of assumptions about the evolution of humanity based on the current popular beliefs of science.

Humans in our current form are estimated to have been around for just over 200,000 years. As humanity evolves we change more and more rapidly. An important example is slavery. Slavery is estimated to have started after the invention of agriculture roughly 11,000 years ago during the neolithic revolution. Slavery in America was abolished in 1865.

To make the numbers easier to approach, lets talk about things in terms of that 11,000 year ago mark. That means slavery was invented at the 0% mark of human history in this context. Following that, slavery in America was abolished at roughly the 98.6% mark. The civil rights movement didn’t officially begin until the 1950’s. That is roughly the 99.39% mark of our history since the birth of Slavery. In the time since then American culture has changed in extremely significant ways.

The point? For the vast majority of our history humans have been extremely stagnant. It took almost 11,000 years to abolish slavery in America, and it took almost another 100 years for people to really even begin to accept the natural equality of human beings. In just another 40 years, though, I was born into a generation of acceptance, and neither I nor the people I respect and continually associate with consider skin color to be of any importance whatsoever.

Delta T

So lets talk about our function again. If we look at f(11000 years ago) we get an image of society, S, that condones and utilizes slavery. If we look at f(5000 years ago) we get a very similar image in terms of slavery. It isn’t until f(1865) that this really changes in a significant way (at least for arguments sake). So what is delta t? Delta t is the amount of time necessary between images of our culture to produce a significantly different result. Now, keep in mind I’m making all of this up.

As technology becomes more advanced and general education levels rise, our communication as a species does the same. Overall we seem to be heading in a more tolerant direction as a species, whether you’re talking about Race, Religion, or whatever controversial subject you like. As our culture progresses, delta t is decreasing. That means the time between significantly different states of our culture is decreasing at some speed.

So lets actually apply calculus now. What happens to the output of our function as time goes on? Delta T will get smaller and smaller, and it will decrease more and more rapidly. At some point, Delta T will reach 0, or really 1/infinity. So what happens to society when Delta T becomes infinitesimal, or infinitely small?

The Ambiguity of Infinity

Infinity is frustrating. If we take Delta T as 1/infinity at some point in our future, this would imply that society is changing at a infinite pace. In other words, the time between significant cultural changes will be so small that society could never truly remain in a constant state. That doesn’t seem quite right to me. I think there is a critical point at which cultural acceptance will truly exist and humanity will unify as a species. I may be a nihilist, but at least I’m an optimistic one.

I hope this implies that society will at some point reach some sort of scientific utopia. Perhaps everyone is so similar (thanks to genetics?) that we reach some form of unanimity. I don’t like that idea at all. Our differences as people is what excites me. Its what makes life so fascinating and its necessary to preserve. I would hope, instead, that it implies something more natural. So here is my final hypothesis.

At some point in our future, humanity will be so extremely diverse that our differences cease to be a factor in a social context. — Ty The Jester

For some this may invoke an image of colonized planets and hugely diverse alien species. Personally I see a society where everyone is treated equally. Your interactions will be guided by your personality, disposition, and experience, not by meta-factors about yourself. Of course, industry will be replaced by science, but that is another conversation all together.

Why does this matter?

Well, I’m a nihilist. So it doesn’t. Hope you enjoyed reading!

Note: Credit for the image goes to…

Life, the Universe and Calculus

Ishan Mahajan

Written by

Software engineer, musician, and aspiring humanitarian. Call me Ty.

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