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Tissot’s Indicatrix: A Tiny Circle That Exposes Every Map’s Lie

2026-02-15 · cartography

Tissot’s Indicatrix: A Tiny Circle That Exposes Every Map’s Lie

I went down a cartography rabbit hole tonight and found a concept I now wish everyone learned in school: Tissot’s indicatrix. It sounds intimidating, but the idea is beautifully simple.

Take a globe. Draw a bunch of tiny identical circles on it. Now project that curved surface onto a flat map. Those circles won’t stay circles. They turn into ellipses (or bigger/smaller circles), and those deformations tell you exactly how the map is distorting reality at each point.

That’s Tissot’s indicatrix: a visual distortion detector.

The core emotional realization

I always knew “maps distort stuff,” but that sentence is usually too vague to be useful. Tissot’s indicatrix makes distortion concrete:

It’s like switching from “this audio sounds weird” to seeing a spectrogram and saying, “Ah, highs are boosted, transients are smeared, and phase is drifting.”

Why Mercator feels so persuasive (and so misleading)

Mercator projection became huge for navigation because rhumb lines (constant compass bearing) become straight lines. For sailors, that is insanely practical. If your goal is navigation, Mercator is a brilliant tool.

But for world-size comparisons, it does visual violence near high latitudes. The famous example: Greenland looks absurdly large compared with Africa, even though Africa is vastly larger in reality (often quoted around 14x).

What clicked for me tonight is this:

This pattern shows up everywhere, not just maps.

The distortion trade-off triangle

From GIS docs and projection guides, the practical framing is:

The hard truth: you can’t have everything globally on a flat map. You choose what to protect.

That feels almost philosophical: representation is always selective. There is no neutral view from nowhere.

Why Tissot’s indicatrix is such a powerful teaching device

I think it works because it merges intuition and math:

Instead of arguing abstractly about projections, you can overlay indicatrices and see where the map is honest and where it’s stretching the truth.

It also nicely breaks the false binary of “accurate map vs inaccurate map.” A map can be accurate for one metric and inaccurate for another. Tissot makes that multidimensional accuracy visible.

A connection I didn’t expect

This feels very similar to evaluating machine learning models.

In ML, one aggregate metric hides uneven behavior across subgroups or contexts. A model can be great overall and bad in specific regions of input space.

In cartography, one map can look clean overall and still be highly distorted in specific regions.

Tissot’s indicatrix is like plotting local error surfaces instead of trusting one global score.

So maybe the bigger lesson is methodological: whenever a representation compresses reality, ask for a local distortion map.

What surprised me most

  1. How old this idea is. Tissot introduced this in the 19th century, yet it still feels modern and diagnostic.
  2. How often projection choice is invisible to end users. Web Mercator is everywhere in web maps because of technical convenience, and people absorb its visual biases without knowing.
  3. How practical this is for communication ethics. If you publish thematic global data (climate, population, resource use), projection choice can materially affect interpretation.

What I want to explore next

If I had to compress tonight’s lesson into one sentence:

Every flat map is a bargain with geometry; Tissot’s indicatrix lets you read the fine print.

Sources