Most strategy tools are built on clean lines and rigid boxes (e.g., OKRs, SWOT, five-forces diagrams). But the real world bends, warps, and shifts in unpredictable ways. What if our strategies need to stretch just as flexibly? AI will tell us all pretty quickly.
That’s where topology, a branch of mathematics that studies shapes and surfaces, offers a useful metaphor. Topology doesn’t care about exact dimensions. It cares about relationships, holes, connections, and continuity. That’s like good strategy.
Below are four powerful topological ideas that can help you think differently and more effectively about your strategy.
1. The Donut and the Coffee Cup: Structure Over Surface
In topology, a donut and a coffee cup are considered the same. Not because they look alike, but because they share a core structural feature: each has one hole.
You can stretch a donut into a coffee cup (handle becomes hole) without tearing or gluing. That makes them topologically equivalent.
Strategic lesson: Two companies may look wildly different (one sells furniture, one flies planes) but share the same underlying model. For example:
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IKEA and Southwest Airlines both focus on operational simplicity, limited choices, and high asset utilization.
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Their forms differ, but the structure (the “hole” in their model) is the same.
Ask yourself: “Am I copying what a company looks like, or learning from what holds it together?”
2. The Rubber Sheet: Strategy Must Stretch
Topology assumes shapes can be stretched or bent as long as they’re not torn. That’s a perfect metaphor for strategy in uncertain environments.
Rigid strategies break under pressure. Flexible strategies bend and recover. This is especially true when:
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A new technology displaces your product
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A partner shifts allegiance
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Talent markets tighten or policies shift
Strategic lesson:
If your core model can’t be stretched to meet the moment, it will snap. But if your strategy is topologically sound, defined by relationships and loops, not just form, it can adapt without losing coherence.
3. The Möbius Strip: Blurred Boundaries, New Risks
A Möbius strip is a surface with only one side. Run your finger along it, and you’ll find no clear inside or outside. It’s paradoxical and very real.
Modern business ecosystems often feel like Möbius strips:
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Platforms like Amazon or Apple intentionally blur the lines between customer and competitor.
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Internal teams and external partners co-develop offerings.
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AI systems are both tools and agents.
Strategic lesson:
The old boundaries between “us” and “them” may no longer apply. When roles blur, risks multiply. Your strategy must anticipate what happens when edges disappear.
Ask yourself: “What if the boundary I rely on today between vendor and rival, or employee and algorithm, vanishes tomorrow?”
4. Disconnected Spaces: When Strategy Falls Apart
In topology, a space is connected if it’s “in one piece.” Once a space breaks apart, it’s no longer unified.
Same with strategy.
Many companies build strategies in silos:
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A marketing strategy that doesn’t match product capabilities
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A digital transformation with no tie to customer behavior
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A growth goal with no operational support
Strategic lesson:
Disconnected strategies might look impressive on slides but fall apart in practice. To succeed, your “where to play,” “how to win,” capabilities, and metrics all need to be tightly connected.
Ask yourself: “Can I draw a clean line from my choices to my actions to my outcomes?”
Closing Thought: Strategic Topology > Strategic Planning
Strategy isn’t about the shape of your plan. It’s about the structure of your thinking:
- Is it coherent under pressure?
- Does it hold together as the world changes?
- Can it bend, shift, and adapt—without tearing?
You don’t need to understand topology to build great strategy. But it helps to think like a topologist. Form is fleeting. Structure endures.
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