Initial Conditions, Boundary Conditions and the Shape of Life

It's always interesting to me when an idea from one domain refuses to stay in its lane, sort of. Instead it easily lends itself to generalization beyond its source domain if you get the abstractions correctly [and of course not generalize too much]. You see it show up in a few other places, in conversations, in business decisions [and the accompanying results], in the way people and projects succeed or crash and burn. Recently, I caught myself thinking about how differential equations don't just belong in textbooks. They quietly describe careers, companies and even ordinary choices.

The thought came up after a discussion about the typical cash-burning competition startups engage in like there's a prize at the end of the runway. Some of them survive the turbulence. Others get vaporized. And of course it's not exclusively the hardworking ones that win. It happens to be the ones with the right initial conditions working in the right boundary conditions ["right" here making no references to moral standing of course]. It starts to feel like life is a dynamical system with its own constraints and state variables whether we acknowledge them or not.

Where you start: The Power of Initial Conditions

In mathematics [and maybe control systems engineering], initial conditions tell you the state of a system at t=0. They matter because without them, you don't get a unique solution. Translate that to real life and it's almost embarrassingly accurate.

Your initial conditions are:

• where you were born
• what you know
• what you have access to
• who you can call
• the habits you built early [or indeed never built at all]
• and the environments you accidentally grew up in

And it keeps going. For companies, initial conditions include the founding team, product direction, cash in the bank, even the "why" behind the idea. The wrong co-founder is a broken variable inside the system. A product born in a tiny market might be doomed before it even gets the chance to iterate. We praise "hustle", grit, "10x execution". Those matter but they matter inside a trajectory. Initial conditions are the quiet forces that set that trajectory. Some people like to say, "it doesn't matter where you start", Sounds nice and inspirational to those seeking such things. But I think it's mathematically false.

It matters deeply.

But here's the encouraging part: in dynamical systems, you can change your state variables over time. Skills, resources, network. These are not constants, they're more like functions. Basically you can rewrite your initial conditions in slow motion.

What you can't ignore: Boundary Conditions

Boundary conditions are the constraints of the world the equation is allowed to live inside. They sort of define the solvable region. Real life is chock-full of them:

• regulatory wall in finance or healthcare [and the time period within which these rules applied or now apply]
• market limits [some industries just cap out]
• capital constraints [raising VC is a boundary-altering decision]
• time [the most non-negotiable constraint]
• family, responsibility, ethics, health

Boundary conditions don't care about how brilliant you are. They don't argue. They don't bend just because you want them to. In business, regulatory burden is a boundary condition. A fintech startup can't "move fast and break everything" not unless it enjoys million-dollar fines and possibly prison time. And personally? Someone with a sick parent, child or limited health doesn't have the same solution space as a 22-year old with no obligations and a mattress on the floor.

It's not unfair. It's just physics. The trick is: don't pick a problem whose boundary conditions make your desired trajectory impossible.

Trajectories: The life that unfolds from your conditions

When you pick a system in phase space, you get trajectories or lines that represent how things evolve over time. That's the part we typically label "hard work", "strategy", "success", "failure". But what we call "outcomes" are just the visible curve of a system pushed forward by:

• its initial conditions
• the constraints it lives in
• the control inputs it applies over time

Two startups can have equal talent, equal effort, equal passion and one still wins purely because it was solving the right problem inside the right boundaries. Meanwhile, the other might be fighting turbulence born from day zero. Sounds cynical but it's closer to reality than anything else.

This is the system. Initial conditions set your starting trajectory. Boundary conditions define where that trajectory can legally exist. Control inputs are what you actually do inside that space. And the trajectory? That's the story that gets written.

Small differences, large divergences

Chaos theory is famous for the butterfly effect: tiny changes at the beginning can explode into massive differences later. In non-linear systems, trajectories can diverge exponentially with small changes in initial conditions. In the same way, two lives can fork dramatically on tiny early decisions.

In human terms, it looks like this:

• one early friendship becomes a life-long business network
• one wrong market entry wastes four precious years
• one habit [writing, coding, selling, learning] compounds into expertise
• one mistake compounds into debt, burnout or lost opportunity

A person might work ten times harder than another and still get outpaced not because they are less talented but because they began on a tougher trajectory. We often mistake trajectory challenges for character flaws.

But here's the truth:

A difficult starting point is just a difficult equation to solve. It doesn't make you any less of a solver.

The part you actually control

If life is a kind of differential equation then the empowering part is this:

• You can't choose your initial conditions but you can change your state over time
• You can't remove your boundary conditions but you can choose a domain with better boundary conditions
• And once both are clear, you can adjust your control parameters - the actions, decisions and priorities that bend your trajectory toward your expected landing space.

Skill-building is altering your initial conditions, choosing markets is selecting your boundary conditions and execution is effectively shaping your trajectory. Effort matters most when applied in the right system. That's like working hard on the right things.

What's the goal anyway?

Every control system has an objective function, something to optimize for. For some people, it's freedom, for others wealth, mastery, meaning, stability. The question becomes:

Given where I am, and the constraints I'm in, what actions bend my trajectory toward what I value most? Once you think like this, life stops feeling very random [some randomness is good for creativity and innovation] and leans more toward being navigable especially if you're a person of high agency. You don't need perfect star alignment for your initial conditions, all that's required are solvable equations within the correct boundary conditions and a goal you can actually optimize for.

Some closing thoughts

A lot changes when you stop comparing lives and instead compare systems.

You don't particularly need the same initial conditions as someone else. You don't need their market, their industry, their trajectory. You just need the conditions that make your trajectory possible.