An Idea Worth Chewing On
On mathematicians, rune readers, and the absence of a base case
We consider three distinct organizations of mind — the rune reader, the ink-blot psychologist, and the mathematician — and observe that the third hides its organizational choices behind a claim to certainty. A brief account is given of one mathematician who elected to build a new notation and thereby found himself with no base case.
Mathematics claims to be certain. And certainty hides the organization underneath.
A rune reader, in the organization of mind, is not too different from a quantum physicist. Both inhabit a world where one event is entangled with another, seemingly unrelated event.
Another organization of mind can be seen in the coffee reader and the psychologist using inkblots. Both trust that the mind reveals itself while moving through visual ambiguity.
The mathematical organization is trickier. Mathematics claims to be certain. And certainty hides the organization underneath.
Every family kitchen tells the same magical story: learn mathematics and you'll become smarter.
One mathematician, moving through different mathematical disciplines, noticed something unusual. His organization of thinking remained the same while every discipline spoke a different language of notation.
He happened to teach several mathematical subjects at a university. His students, however, did not encounter one organization. They encountered many languages.
So a question appeared.
How do you transfer an organization of thinking rather than another notation?
His answer was wonderfully simple. Build a new language. Let notation itself become a tool for thought.
Then something unexpected happened.
To build such a language, he had to begin chewing on his own organization of thinking. There was no base case. No notation for the organization that was creating notation.
No wonder he kept chewing for the rest of his life.
Fortunately, chewing leaves traces. Perhaps another mind can follow those footprints.
Not to repeat his journey. To continue it.
- [1]Iverson, K. E. (1962). A Programming Language. Wiley.
- [2]Iverson, K. E. (1980). Notation as a Tool of Thought.
Conflicts of interest · The author declares no competing interests.
Funding · This work received no external funding, only tea.
Cite as · Solstad, K. (2026). An Idea Worth Chewing On. Acta Observationum, I(1), pp. 26–27.