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2023-08-30 ~ 5 min read

The Mathematics of Impermanence: Why Your Legacy Might Not Be What You Think


Life has been a rollercoaster lately, full of highs and lows. Life can be complex and life can be simple. Amid all this, I’ve found a renewed sense of presence and contentment. It’s made me question what really lasts in life—beyond the material, beyond the immediate. This post dives into those questions, mixing personal reflection with math and science to explore what our true legacy might be. If you’ve ever wondered what endures in the grand scope of existence, this is for you.

Impermanence, also known as the philosophical problem of change, is a concept addressed in a variety of religions and philosophies. In Eastern philosophy, it is notably significant for its role in the Buddhist three marks of existence.


When we talk about leaving a legacy, buying homes, and accumulating wealth, we often overlook the long-term implications. The notion that our material possessions will eventually fade away and be owned by strangers can be jarring. However, if we pause to analyze these existential questions from a mathematical standpoint, we realize that perhaps the pursuit of “more” isn’t as solid as we once believed. Let’s explore the mathematical underpinnings of these ideas.

Exponential Decay and the Half-Life of Memory

One way to frame the rapid decrease in collective memory about an individual after their death is through the concept of exponential decay. This concept is commonly understood in the context of radioactive elements, which have a half-life—the time it takes for half of the material to decay. Similarly, our memories also have a half-life, a point in time where half the people who knew you or knew of you will have forgotten.

Mathematically, if we denote as the number of people who remember you and as the time that has passed, exponential decay can be described as:

Here, is the initial number of people who remember you, is the base of the natural logarithm, and is the decay constant.

Probability and Genetic Legacy

Let’s consider your genetic legacy. While it’s true that you pass on a percentage of your genes to your descendants, the proportion decreases with each successive generation. This concept is represented mathematically as:

By the time you reach your great-great-great-grandchildren, the genetic share becomes negligibly small ( or about 3.1%). Over the span of 100 years, your genetic footprint becomes diluted in the sea of genes that constitute your descendants.

Entropy and Material Possessions

The Second Law of Thermodynamics posits that the entropy, or disorder, of an isolated system will always increase or remain constant; it never decreases. While this law primarily applies to energy, it can also metaphorically extend to our material possessions. Homes degrade, cars break down, and even the rarest art pieces are susceptible to the slow decay of time. Unless there is a continuous effort to maintain these possessions, their utility and historical significance will likely fade away.

What Really Lasts: The Mathematics of Memetics and Social Impact

Contrary to the ephemerality of material and genetic legacies, social and intellectual contributions—often encapsulated in the form of memes—can have a more enduring, exponential impact. Memetics, the study of how ideas and cultural elements spread, illustrates this phenomenon. These ideas can range from a trivial catchphrase to significant social or technological innovations.

The impact of memetic spread is akin to compound interest, where the benefits accrue exponentially over time. If a powerful idea or meme impacts 5 people initially, and they each go on to share it with 5 more, the impact can be mathematically described as:

Here, represents the number of people you’ve initially influenced, and is the rate at which each person spreads the meme.

Adding Happiness or Positive Thinking to Memetic Impact

To add a qualitative layer to this model, we introduce a “happiness factor” or “positive thinking multiplier,” denoted by . This variable could range from 0 to 1, with 1 being extremely impactful in terms of promoting happiness or positive thinking. The revised Total Impact equation becomes:

This equation signifies that not all memes are created equal; some have a more profound, positive impact on individual and collective well-being.


Given the mathematical certainty of decay and dilution, accumulating material possessions and the desire to be universally remembered by future generations seems increasingly illogical. Instead, actions—or memes—that not only spread but also multiply happiness or positivity could be more meaningful. Here, the happiness factor serves as a crucial variable, reminding us that the quality of our contributions can amplify their longevity and reach.

Through the lens of memetics, it becomes evident that it’s not just about the immediate effect but also the lasting influence our ideas have on shaping minds and cultures. Our most durable legacy may reside here, constantly adapting and spreading long after we’re gone, yet still holding the essence of the initial spark that started it all. And if that spark carries happiness and positivity, its impact could indeed be immeasurable.

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Hi, I'm Eric. I'm a software engineer and data scientist based in Lisbon. You can follow me on Twitter, see some of my work on GitHub,