Looking at the world through mathematics
Our aim is a domain-independent system. I believe in mathematics and in the data itself. A domain is a class that people have defined, but data and mathematics are like DNA and RNA: they always move together. The foundation of this system has to be built this way.
A domain is a label
Banking, retail, livestock, rail and healthcare are names people gave to parts of the economy. They are useful for talking. They are not where meaning lives. A bank counting activated cards and a shop counting completed checkouts compute the same thing: how many of those who started went on to finish.
Software that is built industry by industry needs a new model for every sector, and still misses everything between them. Software that is built on the shape of data recognises the same structure wherever it appears.
Data has a shape
Every dataset is made of a few kinds of things: events, amounts, entities, moments and categories. In 1946 the psychologist S. S. Stevens showed that the type of a measurement decides which mathematics is meaningful on it: you can count a category but not average it, and you can average temperatures in Celsius but cannot call 20 degrees twice as warm as 10. XENTHK reads that shape first. What can be computed follows from it.
One form, many names
The same mathematics appears under different names in every industry. XENTHK computes the form and lets each owner keep their own name for it.
| Form | Shape of the data | Names people use |
|---|---|---|
| Rate | Two counts over the same units | Click-through rate, card activation rate, churn rate, first-pass yield |
| Per unit | An amount and a count | Average order value, cost per hire, revenue per visit, feed cost per animal |
| Share | A part and its whole | Market share, traffic by source, energy mix, sales by channel |
| Change | Two periods or two groups | Month-over-month growth, net new customers, incremental sales |
| Time to event | Two moments of the same unit | Time to first purchase, time to hire, mean time to repair |
The proof is in our own table
- KPIs in the table
- 1,712
- mathematical forms
- 23
- KPIs that are one rate
- 378
- formulas proved on worked examples
- 1,291
- analytical methods computed on your computer
- 79
XENTHK's KPI table holds 1,712 KPIs gathered across dozens of industries. Written down as formulas, 1,688 of them fall into just 23 mathematical forms. One form, the rate, covers 378 of them. 1,606 can be computed directly from the data's own fields, and 1,291 formulas are checked by reproducing their worked examples exactly.
An old idea, made practical
The thought that mathematics is the language beneath the world is older than any industry. XENTHK stands in a long line.
- Pythagoreans, as reported by Aristotle in the Metaphysics Held that the principles of mathematics are the principles of all things.
- Galileo Galilei, The Assayer, 1623 Wrote that the book of the universe is written in the language of mathematics, and cannot be read by anyone who does not learn that language.
- Francis Crick, “On Protein Synthesis”, 1958 Set out how information flows from DNA through RNA into living structure. Data carries the information; mathematics gives it form. Neither works without the other.
- Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, 1960 Asked why mathematics developed for its own sake keeps describing the physical world so well.
- John Tukey, “The Future of Data Analysis”, 1962 Argued that an approximate answer to the right question is worth far more than an exact answer to the wrong one.
- Richard Hamming, Numerical Methods for Scientists and Engineers, 1962 “The purpose of computing is insight, not numbers.”
What this means when you ask a question
- Any dataset, from any industry, is read by the same rules: by its shape, not by a template.
- Every number in an answer comes from a computation on your data, on your computer.
- Every claim stays inside its evidence: an association is not called a cause, a proxy is not called the real thing.
- Your name for a measure stays yours. The mathematics underneath is shared.
Sources
- Aristotle, Metaphysics, Book I, ch. 5 (on the Pythagoreans).
- G. Galilei, Il Saggiatore (The Assayer), Rome, 1623.
- S. S. Stevens, “On the Theory of Scales of Measurement”, Science 103 (1946): 677–680.
- F. H. C. Crick, “On Protein Synthesis”, Symposia of the Society for Experimental Biology 12 (1958): 138–163.
- E. P. Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, Communications on Pure and Applied Mathematics 13 (1960): 1–14.
- J. W. Tukey, “The Future of Data Analysis”, The Annals of Mathematical Statistics 33 (1962): 1–67.
- R. W. Hamming, Numerical Methods for Scientists and Engineers, McGraw-Hill, 1962.
- XENTHK KPI table, version in use on 6 October 2026: 1,712 KPIs; 1,606 directly computable; 1,291 parity examples.