The Physics of Getting Sh*t Done: Why Your Productivity Just Got Squared

I had the weirdest conversation with Claude yesterday. I was refactoring a gnarly legacy Express.js API—2,000 lines of callback hell from 2016, no types, no tests, routes scattered everywhere. The kind of thing you look at and think "we should rewrite this... someday." But then I asked Claude a random question about conformal compactification (don't ask), and two hours later we'd accidentally derived a mathematical equation that explains why AI tools make some people 100x more productive while others barely see a difference.

And here's the kicker: it looks almost exactly like E=mc².

No, I'm not joking. And no, I haven't lost my mind. Let me show you.

It Started With a Refactoring Nobody Wanted to Do

We had this legacy API sitting in our repo. Built in 2016 with Express 4, JavaScript (no TypeScript), callback-based async, no error handling to speak of. Routes defined all over the place. Database queries inline in route handlers. The classic "it works, don't touch it" codebase.

A proper refactor would mean:

• • Convert to TypeScript with strict mode
• • Migrate callbacks to async/await
• • Extract business logic into services
• • Add proper error handling middleware
• • Create repository pattern for data access
• • Add input validation with Zod
• • Write comprehensive tests
• • Update all dependencies

I estimated 2-3 weeks of careful, tedious work. Nobody wanted to do it. We all agreed it should be done "someday."

Then I pointed Claude Code at it.

8 hours later: Production-ready TypeScript, proper architecture, 95% test coverage, zero breaking changes.

But that's not the interesting part. The interesting part is why it only took 8 hours instead of 2-3 weeks. Because I started wondering: is there a mathematical way to predict this kind of time savings? Can we turn "AI makes you faster" into an actual equation?

Yeah, I know. That sounds insane. But stick with me, because what we found is actually simple, elegant, and incredibly useful.

Einstein's Equation (The One You Know)

Let's start with the most famous equation in physics:

This equation tells us something profound: a tiny amount of mass contains an enormous amount of energy, because the speed of light (c) is huge, and squaring it makes it astronomical.

One kilogram of matter? That's 90 quadrillion joules of energy. That's enough to power the entire United States for about a month.

The equation works because of that ² symbol. Squaring makes small numbers explode.

Our Equation (The One We Found)

After going down a rabbit hole of spacetime metrics, time compression factors, and parallel processing models, we eventually simplified everything down to this:

Where ε (epsilon) is your skill level on a scale of 1-10.

Let me show you what this means in practice.

The Magic of Squaring

Here's a table showing how productivity scales with skill when you're using AI tools like Claude Code:

Notice what's happening here: skill doesn't scale linearly—it scales quadratically.

Going from skill level 5 to skill level 8 (a 60% increase) doesn't give you 60% more productivity. It gives you 2.56x more productivity (6,400 ÷ 2,500 = 2.56).

This is the same pattern as E=mc². A small change in the variable, when squared, creates massive changes in the output.

Why Does Squaring Happen?

This isn't just math being cute. There are real reasons why skill gets squared when you add AI to the mix:

1. You Can Do More Things At Once

When I was refactoring that API, I wasn't just doing one thing. I had Claude working on:

• • Converting routes to TypeScript while I reviewed controller logic
• • Generating Zod schemas while I refactored services
• • Writing tests while I updated error handling
• • Updating dependencies while I migrated database queries
• • Creating type definitions while I restructured the folder architecture

All simultaneously. A junior developer might use Claude for one thing at a time. An expert orchestrates multiple workstreams in parallel.

Parallel capacity scales with ε² because managing N tasks requires understanding N² interactions between them.

2. Better Prompts = Less Iteration

Skilled users write better prompts the first time. They know what information the AI needs. They catch mistakes immediately. They iterate less.

Less iteration means:

• • Less time wasted
• • Lower AI costs (fewer tokens)
• • Higher quality output

This efficiency compounds with skill level.

3. You Know What's Worth Automating

The most important skill isn't using AI—it's knowing when to use AI and what to ask it to do.

Experts have strategic vision. They automate the right things. They save time on low-value work and reinvest it in high-value thinking.

This strategic advantage multiplies every other advantage.

Real Example: The Legacy API Refactor

Let me break down exactly what happened with that Express.js refactoring:

Time compression: 95% (2-3 weeks → 8 hours)

But here's the thing—I'm probably around an ε = 8 for this kind of work (senior developer, deep TypeScript knowledge, understand API architecture patterns, know exactly what good code should look like).

According to our equation: V = 100 · 8² = 6,400

Meaning I should be seeing roughly 64x productivity improvement. Let's check:

2.5 weeks = 100 hours
Actual time = 8 hours
Compression = 100 ÷ 8 = 12.5x

Wait, that's less than predicted (64x). Why?

Because I spent significant time on strategic decisions Claude couldn't make: architecture review, code quality checks, ensuring backward compatibility, manual testing edge cases. The equation predicts execution speed. Real projects add judgment overhead.

Still: 12.5x faster is transformative. A 3-week project became a 1-day project.

The Uncomfortable Truth

This equation reveals something that makes a lot of people uncomfortable:

This is both good news and bad news:

Bad news: If you're not investing in skill development, you're falling further behind.

Good news: Small improvements in skill create massive improvements in output. Going from ε = 5 to ε = 6 (a 20% skill increase) gives you a 44% productivity increase (3,600 ÷ 2,500 = 1.44).

What Does This Mean For You?

Three practical takeaways:

1. Skill Is The Multiplier

Your ability to use AI tools effectively isn't just about knowing the right prompts—it's about deep skill in your domain. The better you understand your craft, the more leverage AI gives you.

Don't just learn AI. Learn your craft deeply, then apply AI to it.

2. Parallelization Is Key

The real power of AI isn't doing one thing faster—it's doing multiple things simultaneously. Start thinking in terms of "what can I orchestrate in parallel?"

One Claude instance? That's linear improvement. Three parallel workstreams? That's geometric improvement.

3. Strategic Thinking Beats Tool Knowledge

Knowing every feature of Claude Code is less important than knowing which tasks are worth automating. The skill that gets squared is judgment, not technical knowledge.

Ask yourself: "What's the highest-leverage use of my time?" Then use AI to handle everything else.

The Part Where I Blow Your Mind

Remember how I said this started with a question about conformal compactification?

Here's the reveal: Everything I just explained to you in simple terms is actually a simplified version of theoretical physics concepts from general relativity.

Specifically:

• • Time compression (2-3 weeks → 8 hours) maps to conformal compactification(bringing infinity to a finite boundary)
• • Parallel workstreams map to expanding light cones in spacetime (what's causally accessible to you)
• • Skill-squared scaling comes from hyperbolic geometry in the productivity manifold (expert productivity enters a different geometric regime)
• • V = 100·ε² is the simplified form of a complete metric tensor equationthat includes time, skill, complexity, and cost dimensions

Why Does Physics Work Here?

You might be thinking: "Okay, that's cool and all, but why would physics equations apply to productivity?"

Great question. Here's the answer:

Both systems deal with compression of infinity.

In physics, conformal compactification lets us bring infinite spacetime into a finite diagram while preserving important relationships (angles, causal structure).

In productivity, AI tools bring tasks that would take "infinite time" (or at least impractical amounts of time) into finite, achievable timeframes while preserving important qualities (code correctness, creative coherence).

Same mathematical structure. Different application.

The Formula You Can Actually Use

Forget all the physics jargon. Here's what you need to remember:

What This Means for the Future

If this equation is even roughly correct (and our testing suggests it is), we're living through a profound shift:

The returns to skill are becoming geometric, not arithmetic.

In the pre-AI world, being 2x better meant producing 2x more value. Linear.

In the AI-augmented world, being 2x better might mean producing 4x more value (because 2² = 4). Quadratic.

This changes everything about:

• • How we should invest in learning
• • What skills are worth developing
• • How companies should hire and train
• • What "fair compensation" means
• • How teams should be structured

We're not just getting more productive. We're entering a regime where small differences in capability create massive differences in output.

The Punchline

Einstein showed us that mass and energy are the same thing, related by c².

We've (accidentally) shown that in the AI age, your productivity is directly related to your skill, scaled by ε².

Both equations tell the same story: A small quantity, properly amplified, contains enormous potential.

In physics, the amplifier is the speed of light.

In AI-augmented work, the amplifier is you—your skill, judgment, and strategic thinking.

The tools are incredibly powerful. But they're not magic. They're multipliers.

And multiplying zero still gives you zero.

But multiplying expertise? That's when things get interesting.

One Last Thing

This entire exploration—the physics, the equations, the insights—happened because I asked Claude a weird question about conformal compactification while we were refactoring an API.

We went down a rabbit hole. We explored. We discovered something genuinely interesting. And the refactoring? Still got done in 8 hours.

That's the real power of AI collaboration. Not just doing tasks faster, but exploring ideas that you'd never explore alone because they seem too weird, too complex, or too far outside your expertise.

And sometimes, in those weird explorations, you find something beautiful.

Like a simple equation that explains everything:

Skill squared, productivity multiplied.

Now go build something impossible.