For the last few weeks, I’ve been stuck on a strange idea. You know that feeling when your brain suddenly decides that normal mathematics is not enough for your dashboards? That maybe, just maybe, the world of digital analytics would be a better place if we stopped pretending that everything fits neatly into integers, floats, and percentages?
So I did what any reasonable analyst would do: I opened a book on surreal numbers.
Yes. Surreal numbers. Those things that include real numbers, infinitesimals, infinite values, and everything in between — a mathematical universe where GA4 sampling looks almost rational.
And the more I read, the more I realized: surreal numbers are not just a mathematical curiosity. They are a surprisingly elegant metaphor — and, in some cases, a practical framework — for thinking about the messy, chaotic, “undefined‑but‑still‑important” parts of digital analytics.
Let me explain.
Why Surreal Numbers Even Make Sense Here
Digital analytics is full of values that are:
- too small to measure precisely
- too large to interpret meaningfully
- undefined, but still operationally important
- dependent on arbitrary thresholds
- or simply “conceptual” rather than numeric
Surreal numbers were literally invented to handle this kind of weirdness. They include:
- infinitesimals — numbers smaller than any positive real number
- infinite values — larger than any real number
- gaps — values that exist between any two numbers, no matter how close
- ordinal‑like structures — useful for ranking things that don’t behave like numbers at all
If that doesn’t sound like digital analytics, I don’t know what does.
Where Surreal Numbers Fit in Digital Analytics
1. Modeling Micro‑Behaviors (Infinitesimals)
Some user actions are so tiny, so subtle, so low‑frequency that they barely register:
- micro‑hovers
- half‑scrolls
- “ghost impressions”
- UI flickers
- 0.0001% conversion paths
In standard analytics, these get rounded to zero. In surreal arithmetic, they become infinitesimals — still non‑zero, still meaningful, still part of the system.
This is a surprisingly powerful mental model for product analytics: “Not everything that rounds to zero is irrelevant.”
2. Handling Outliers (Infinite Values)
Every dataset has that one user who:
- loads 14,000 pages in a day
- triggers 200 events per second
- spends 19 hours in a session
- buys 1,000 units of something by accident
We usually clip these values, cap them, or pretend they don’t exist.
Surreal numbers treat them as legitimate infinite‑like values — not errors, but structural extremes. This allows for:
- more stable clustering
- more robust anomaly detection
- better segmentation of “super‑users”
- cleaner modeling of long‑tail behavior
3. Comparing Things That Shouldn’t Be Compared (Ordinal Surreals)
How do you compare:
- “engagement” vs. “intent”?
- “scroll depth” vs. “session quality”?
- “user frustration” vs. “time on page”?
You don’t. At least not with real numbers.
But surreal numbers allow hierarchical ordering, where values can be:
- incomparable
- partially ordered
- or ordered only within a specific context
This is exactly how analysts actually think — we just pretend otherwise.
4. Modeling Uncertainty (Gaps and Surreal Intervals)
Digital analytics is full of uncertainty:
- sampled data
- modeled conversions
- missing events
- attribution windows
- privacy thresholds
- delayed reporting
Surreal numbers allow intervals with gaps — values that are not single points, but ranges with structural uncertainty built in.
This is a much more honest representation of:
- attribution
- forecasting
- LTV modeling
- cohort decay
- funnel drop‑offs
Instead of pretending we know the exact number, we can model the shape of uncertainty.
5. Rethinking Metrics Entirely
Some metrics simply don’t behave like numbers:
- engagement rate
- session quality
- “stickiness”
- “friction”
- “activation”
We force them into numeric form because dashboards demand it.
Surreal numbers let us build metric systems that behave like ordered structures, not forced decimals. This opens the door to:
- non‑linear scoring
- ordinal‑based KPIs
- multi‑dimensional ranking
- metrics that adapt to context
Imagine a KPI that doesn’t collapse everything into a single number, but instead behaves like a surreal tree of values.
A Small Example: Surreal Funnels
Traditional funnel:
1000 → 400 → 120 → 10
Surreal funnel:
1000 → 400 + ε → 120 + 3ε → 10 + ω
Where:
- ε = infinitesimal micro‑conversions
- ω = infinite‑like “super‑conversions” (e.g., bulk purchases, high‑value actions)
Suddenly, the funnel captures:
- micro‑behaviors
- long‑tail extremes
- structural uncertainty
- non‑linear effects
This is closer to reality than the clean integer version we usually present.
So… Should We Actually Use Surreal Numbers?
Probably not in production. At least not yet.
But as a thinking tool, surreal numbers are incredibly useful:
- they break the illusion of precision
- they expose hidden assumptions
- they force us to acknowledge uncertainty
- they help us model extremes
- they give structure to “unmeasurable” behaviors
Digital analytics is full of things that are almost zero, almost infinite, or not really numbers at all. Surreal numbers give us a language for them.
And sometimes, that’s all we need.
Final Thoughts
Juzef the Koala is still trying to figure out whether he can store an infinitesimal in BigQuery. He probably can’t. But he likes the idea that not everything in analytics must be forced into a float64.
And honestly — so do I.
If you ever feel that your dashboards are too rigid, your metrics too artificial, or your funnels too linear, try thinking about them through the lens of surreal numbers. It won’t fix your data. But it might fix your intuition.