NP ≈ P + E: Entrepreneurship as Complexity Reduction

In 1961, Sydney Brenner, François Jacob and Matthew Meselson identified messenger RNA as the molecule that carries instructions from genes to ribosomes. The implication followed at once: a cell that reads instructions could be given new ones. Nobody in 1961 could act on it, and it took another sixty years to write instructions that worked as a vaccine.

Nothing about the goal changed in those sixty years. Everything underneath it did.

That gap, between a result you can recognise on sight and one you can actually produce, is the most common shape of hard problems, and entrepreneurship is best understood as the work of closing it.

More than a decade closing these gaps commercially, then five years researching how founders decide under uncertainty. The pattern that follows is what I kept finding in both.

P vs NP to Progress

In 1971 Stephen Cook formalised the question of P versus NP. Leonid Levin reached the same result independently in the Soviet Union. Half a century later it is still open.

P covers problems an algorithm can solve efficiently, where the time required grows polynomially with the size of the input: sorting a list, finding the shortest route between two points on a known map, multiplying two large numbers.

NP covers problems where a proposed solution can be checked quickly by an algorithm, whether or not it can be found quickly. The cases that matter here are the ones where checking is cheap and finding appears not to be. Name a diagnosis to a clinician and confirming it is often a single test with a clear read. Arriving at that name from an undifferentiated patient, with overlapping symptoms and a search space of thousands of conditions, is the part that takes a career to learn and still goes wrong. Technology founders meet the same shape daily. Verifying that a private key opens a given piece of encrypted data takes one operation on a laptop. Producing that key without being handed it is infeasible on every machine ever built, and the security layer of the internet is a bet on that asymmetry holding. It is a bet on something stronger than P ≠ NP, since the hardness has to hold on average and not merely in the worst case.

P sits inside NP. If you can produce an answer quickly then you can certainly check one quickly, so every efficiently solvable problem is also efficiently verifiable. The two are not rival categories. One contains the other.

The open question is whether the containment is strict, whether NP holds anything that P does not. Nobody has proved it either way and the Clay Mathematics Institute has a million dollars waiting. The overwhelming working assumption in the field is that it is strict: there are problems we can recognise but cannot reach.

The problem decides whether a fast method exists. Sorting a list had an efficient solution centuries before anyone built a machine to run one. What moves is reach: what we can build, and how fast we get there. The analogy is structural, and it stops there. In computation the barrier is mathematical. In building it is matter, method and permission.

The E Model

With that boundary drawn, the asymmetry becomes a way to read feasibility as a path rather than a state.

At one end sits the frontier, where you could recognise the answer on sight but cannot yet build the thing that produces it, because the prerequisites do not exist. At the other sits capability: feasible, repeatable and transferable, because they do. The distance between them is not fixed. It closes, and it closes through work.

That work has a name.

NP≈P + E

NP ≈ P + E · Dr. Hafiz Muhammad Ali

Read it as a distance rather than an identity. NP is the result you can recognise, P the result you can produce, and E the work between them. Call that distance the solvability gradient.

E is entrepreneurship: the compounding work that closes it. The engine is reduction, and it advances by engineering the next feasible step rather than the final one.

Which changes the question a strategist should ask. Not who had the idea first, but what chain of reductions finally made this feasible.

E is what the sixty years between the discovery and the vaccine were spent on.

What E Does

A frontier problem becomes a capability when its prerequisite stack is resolved. That is the whole of the movement along the gradient. Not a leap across the distance. The list gets shorter until the distance is gone.

Unsolvable is almost never a claim about impossibility. It is a diagnosis of incompleteness.

The missing piece is usually one of five:

• a critical component: no viable energy source, material substrate or base technology
• a workable architecture: no blueprint for how the parts integrate
• a method of control: insufficient stability, safety or operational precision
• a means of measurement: no way to test or iterate with fidelity
• enabling infrastructure: no manufacturing scale, standards, logistics or regulatory permission

The reduction engine clears them through four mechanics, none of which aims at the finished thing.

1. Decomposition.

   Isolating the bottleneck. The entrepreneur does not solve the problem, they solve the specific constraint that makes it hard. Breaking a vision into discrete, verifiable sub-problems shows which parts of the stack are already solvable and which need targeted invention.

2. Recombination.

   Most breakthroughs are new arrangements rather than new atoms. Much of the work is compiling existing components, often from unrelated industries, into a system nobody had assembled before.

3. Experimentation.

   If the path is unknown, the search space is effectively unbounded. Cheap iterative cycles act as a filter, killing unproductive paths until what remains is small enough to search. You rarely find the answer directly. You eliminate everything else.

4. Institutionalisation.

   The last act of E is to make E unnecessary. Standards, manufacturing protocols and regulatory pathways harden the innovation into infrastructure. At that point the problem has reached the far end of the gradient. It is no longer a discovery, it is a utility.

NP≈P + E

NPThe frontierImaginableVerifiableNot yet feasible

PCapabilityFeasibleRepeatableTransferable

E

1. 01Decomposition
2. 02Recombination
3. 03Experimentation
4. 04Institutionalisation

The gradient is the distance. The four mechanics are how it is crossed.NP ≈ P + E · Dr. Hafiz Muhammad Ali

The mRNA Stack

The mRNA arc is the clearest case I know, and it is the whole gradient in one story. The end state was always verifiable: either a cell can be reliably instructed to produce a target protein safely, or it cannot. The concept stayed legible for decades while the capability stayed out of reach, because the stack was incomplete.

NPthe frontier

Pcapability

1. 1961
2. 1990
3. 2005
4. 2010s
5. 2020 to 21

1. DecompositionmRNA identified as the carrier
2. Experimentationexpression shown in vivo
3. Decompositionimmune recognition cleared
4. Recombinationlipid delivery matured
5. Institutionalisationapproval and manufacturing scale

1. 29 years
2. 15 years
3. ≈10 years
4. ≈5 years

The ends do not move. The problem does. Every stop is one prerequisite cleared, and the intervals shorten as the stack fills.NP ≈ P + E · Dr. Hafiz Muhammad Ali

Feasibility arrived through a sequence of reductions, each one supplying a missing piece of the stack.

1. 1961, decomposition.

   Messenger RNA is identified as the transient information carrier. The problem moves from unknown to imaginable. Biology turns out to have a software layer.

2. 1990, experimentation.

   Direct injection of RNA is shown to drive protein expression in vivo. Biological execution is possible, though the system is far too unstable for clinical use.

3. 2005, decomposition again.

   Karikó and Weissman isolate the binding constraint and solve only that: modified nucleosides let the mRNA escape innate immune recognition. The dominant blocking variable, toxicity, becomes a manageable parameter.

4. 2010s, recombination.

   Lipid nanoparticle delivery matures, joining nanotechnology to molecular biology so the instructions survive the journey.

5. 2020 to 2021, institutionalisation.

   Emergency authorisation, then full approval, validate the platform at population scale. Standards, manufacturing and regulatory pathways settle.

Read forwards, none of it was obvious. Read backwards, every step is one item cleared from the prerequisite stack, technical or institutional.

E as a Rate

That arc took sixty years and thousands of people. You have quarters, and a team you can name.

Which raises the only question that transfers: if E is a force at the scale of an industry, what is it at the scale of a company?

It is a rate: how fast you move along the gradient. At industry scale, E is a force you can describe but not steer. At yours it is a number you set, and one I have written about separately in the Efficiency Equation.

Two of the four mechanics do most of that work. Decomposition raises what you produce. Institutionalisation lowers the uncertainty you carry, which is why it feels slow and matters more than it looks.

The same logic holds one scale up. Ecosystems do not produce breakthroughs by having better ideas; they lower the cost of the next reduction. Shared facilities turn one-off experiments into standard procedure, common standards make progress comparable, and dense networks move knowledge faster than any single firm can. Credible IP and procurement regimes supply the permission that scale requires, and a tolerance for iteration means a failed experiment does not end a career.

None of that produces insight. All of it raises the rate at which insight becomes capability, which makes your environment a decision rather than a backdrop. Every item on that list is something you can borrow from where you build, or pay to rebuild alone, on the same runway that funds the reduction itself.

If NP ≈ P + E explains why an industry arrives when it does, the Efficiency Equation explains why one company inside it moves faster than the one next door.

A Diagnostic for Frontier Problems

The lens is only worth having if it changes what you do on a Monday. Four questions, in order. Together they locate you on the gradient and name your next reduction.

WORKING TOOL

Where are you on the gradient?

1. What exactly is unsolvable?

   Name the binding constraint, and name it narrowly enough to be wrong. “The market is not ready” is not a constraint. “Cell yield falls below viable threshold above ten litres” is. If your answer would fit any company in your sector, you have not found it yet.

2. What would count as proof?

   Define the smallest demonstration that would convince an informed sceptic the capability is real. If you cannot describe that demonstration, you are not yet working on a verifiable problem, and no amount of building will tell you whether you are close.

3. What single invention closes the current gap?

   Not the whole vision, the next feasible step. If clearing your named constraint requires three simultaneous inventions, you are further from capability than you think, and the honest move is to find the one that unlocks the other two.

4. What already exists that you have not combined?

   List the components in adjacent fields that would be load-bearing if they were connected to yours. Often the missing piece of the stack is not missing, it is unnetworked.

A note on sequence. Founders usually start at the third question. Starting at the first two is what separates a reduction from a guess.

Conclusion

Entrepreneurship moves the feasibility frontier. Unsolvable problems are seldom solved by one heroic leap. They collapse when someone decomposes them into constraints, builds or borrows the missing components, tests against reality until feasibility holds, and hardens what worked into infrastructure.

The wheel reduced a mobility constraint. The engine reduced a power constraint. Each reduction makes the next one cheaper, which is why progress compounds rather than merely accumulates.

We tend to explain entrepreneurship with capital or grit. Both are real, and neither is an explanation. Money bought the 2020 arc its speed and nothing else about it. Capital cannot tell you which constraint is binding, and it cannot buy a reduction whose prerequisites are missing, which is why the same billions spent in 1995 would have bought years of work and no vaccine.

Capital and grit set the pace. Complexity reduction sets the direction.

So the question worth asking about your own work is not how large the vision is. It is which constraint you are clearing, how fast you are clearing it, and what becomes possible for everyone else once you have.

Acknowledgements

My thanks to Naseer Shaikh for introducing me to P versus NP, and for the conversations that followed. The core move here, translating computational complexity into a lens for founders, began in those discussions.