Health, Formally Defined · A guided reading
Understanding
Health.
I want to invite you into a question that seems familiar until we try to answer it precisely: what does it mean for something to be healthy?
Together, we'll move from everyday examples to the underlying mathematics, and eventually to the difficult work of measurement. I'll explain each idea as we reach it. You don't need a background in formal mathematics to begin.
The approach
We'll build the idea before we ask the mathematics to carry it.
At the center of the research is a way of thinking about health that includes both the organization present now and its capacity to continue under specified conditions.
The mathematics gives that idea a precise form. The empirical work asks which parts of it can actually be observed, reconstructed, calibrated, and tested. I want to make both parts accessible without blurring what has been proved and what still needs evidence.
The reading room
Follow the ideas, one lesson at a time.
A growing library. Each lesson stands on its own and leads into the next.
Lesson 1 · Paper I · Start here
What does it actually mean for something to be healthy?
Two forests. One apparently thriving, another visibly damaged. A simple distinction between how a system looks today and what it can still do tomorrow leads us to the central equation.
Lesson 2 · Paper I · Continue reading
What is a viable continuation?
Begin with a stressed forest and follow the possibilities. Learn why a future may be lawful without being viable, and why the capacity we observe can be simpler than the histories behind it.
Lesson 3 · Paper I · Continue reading
Can two systems have different capacities but still be equally healthy?
Four capacity sets, two health requirements, and a way to group the information each question can see. Explore what changes when I introduce a new requirement.
Lesson 4 · Paper I · Complete the foundation
Why having the capacity to survive is not the same as being robust
A successful pathway is only part of a system's story. Explore why robustness and prospective Health can require information that success-only or present-only observations do not retain.
Lesson 5 · Paper II · A new context
How can the same system be healthy in one context and unhealthy in another?
Two ways a health judgment can change: the capacity available to a system and the requirements licensed to evaluate it.
Lesson 6 · Paper II · Transport and information
How can we carry information about health from one context to another?
Follow a forest state related to two different targets, see why the full target capacity may be indeterminate, and learn when the health-visible answer can still be carried across contexts.
What are we trying to describe?
Familiar examples make the difference between present condition and future capacity visible.
What follows from the definition?
We build the meaning of viability, requirements, scenarios, observation, and representation with care.
What would measurement require?
We bring the formal claims into conversation with data, uncertainty, calibration, and the scope of scientific conclusions.
For readers who want the complete work
The source papers are always close by.
The five published preprints in Health, Formally Defined remain available with their full mathematics, precise claims, limits, and downloadable PDFs.