Descriptive statistics
Counting, medians, robust trends and uncertainty intervals that summarise what was recorded. These are the only calculations that describe health records, and they never diagnose or predict.
Interactive explainers
The science of EndoAI, explained honestly.
Beautiful maths is easy to misuse. Each explainer below says what an idea means, lets you play with it, shows where it appears in EndoAI, and is clear about what it cannot do.
Three kinds of maths on this site.
Geometry and physics for layout
Growth curves, golden-angle spirals, orbits and spring forces arrange pictures in a calm, readable way. They are not models of the body or of health.
Ideas worth understanding
Neural networks and wave interference are explained with abstract examples. EndoAI does not use them to assess anyone, and does not use quantum computing.
Mathematics · visual metaphor
Bounded exponential growth
Some quantities rise quickly at first and then level off. The curve b(N) = 1 − e−λN does exactly that: every new record adds a little, the total never exceeds 1, and it never goes down.
Where it appears
EndoAI’s Living Garden module, in development, uses this curve (λ = 0.085) to grow a decorative flower from the total number of records.
What it is not
A bigger flower is not better health, and missing a day never removes a petal. There are no streaks to lose. The garden only reflects how many records exist.
Mathematics · visual metaphor
The golden angle
Turn by the same angle after placing each point, and step a little further out. With most angles the points form spokes and gaps. With the golden angle, about 137.508°, they pack evenly, as seeds do in a sunflower head.
The positions follow Vogel’s model: point i sits at radius c√i and angle i × 137.508°.
Where it appears
The Living Garden arranges its petals this way, and this website’s hero arranges its glowing points the same way.
What it is not
Nature uses this pattern because it packs well. It carries no health meaning here: it simply keeps a picture tidy.
Physics and numerical methods · visual metaphor
Orbits and numerical iteration
Planets move faster near the Sun and slower far away. Kepler’s equation, M = E − e sin E, links time to position on an ellipse, but it cannot be solved with simple algebra. Newton–Raphson iteration guesses, measures the error and corrects, usually reaching machine precision in a handful of steps.
Where it appears
EndoAI’s Health Orbit, in development, uses this to pace a marker around a decorative ellipse. The time for one orbit is your own recorded cycle length. Until a cycle length is recorded, it asks you to set one up.
What it is not
The orbit does not identify cycle phases, ovulation or your next period. Cycles vary: this demonstration only ever uses the length you set, and the module is built around the length you record.
Physics · visual metaphor
Springs, repulsion and damping
Imagine every point pushing the others away, like charges (Coulomb’s law), while springs pull connected points together (Hooke’s law). Friction, or damping, drains energy each step, so the picture settles into a calm arrangement.
Where it appears
EndoAI’s Body Constellation, in development, uses this to lay out body regions that were recorded on the same days. Here the points are synthetic symptom categories from the Pattern Universe’s example timeline A.
What it is not
A short line means two entries were often recorded together. It does not mean one caused the other, and the physics does not model anything happening in the body.
Statistics · describes records
Robust trends: Theil–Sen
An ordinary best-fit line can be dragged off course by one unusual value. The Theil–Sen estimator instead takes the median of the slopes between every pair of points, so a few unusual values barely move it.
Where it appears
EndoAI’s Insights describe trends in your own records. The Pattern Discovery Lab, in development, uses Theil–Sen with an interval to show how certain a trend is. The Pattern Universe uses it on synthetic data.
What it is not
A trend describes past records. It does not prove that a condition is progressing or that a treatment is working, and a few weeks of records are not a medically validated baseline.
Probability · describes records
Bayesian intervals
If fatigue was recorded on 3 of 4 days, is it really “75% of days”? With so little data, the honest answer is a range. Bayesian probability starts with a gentle assumption (here, every frequency equally plausible) and updates it with the records, giving a credible interval.
Where it appears
The Pattern Discovery Lab, in development, reports how often things were recorded with Beta credible intervals, and the Pattern Universe does the same on synthetic data.
What it is not
An interval describes the uncertainty in a recorded frequency. It is not a risk score and not the probability of having any condition.
Computational intelligence
AI and machine learning, plainly
Computational intelligence is a broad name for methods that let computers find structure in data, from simple rules to learned models.
What EndoAI actually uses
- Rule-based insights that describe trends, flares and patterns in your own records.
- Descriptive statistics such as counts, medians and intervals.
- AI-supported summaries: if you choose, a third-party large language model drafts plain-language summaries of the records you include, processed through EndoAI’s servers as the Privacy Policy explains. Summaries are educational discussion points, not a medical assessment.
EndoAI does not use a model that detects, diagnoses or predicts endometriosis.
How machine learning works, in general
- Inputs are measurements; outputs are predictions or categories.
- A model learns from training data. If that data is incomplete, biased or wrongly labelled, the model learns those flaws.
- Missing data is rarely random: people record more on bad days, or stop when they feel well.
- Uncertainty matters: a confident-looking output can still be wrong.
- A pattern a model finds is an association, not proof of a cause, and not a clinical judgement.
Deep learning · education only
Watch a tiny neural network learn
This network has two inputs (the x and y position of an abstract point), two hidden layers of six and four neurons, and one output: how confident it is that a point belongs to the gold class. Training nudges every connection to reduce its mistakes, a process called backpropagation.
Try adding label noise: when some training examples are wrongly labelled, the network learns a messier boundary. That is why the quality of training data matters so much.
What it is not
The points are abstract shapes, not health data. EndoAI does not deploy a neural network that detects or predicts endometriosis.
Physics · education and art only
Waves, interference and amplitudes
When two waves overlap they add. Where crests meet crests they reinforce; where crests meet troughs they cancel. Physicists describe each wave with a complex amplitude A eiθ, and the brightness is the squared size of their sum, |ψ₁ + ψ₂|². The same arithmetic underlies the famous double-slit experiment in quantum physics.
Educational only. EndoAI does not use quantum computing. Quantum physics does not explain, detect or predict endometriosis or its symptoms. This simulation is here because the mathematics is beautiful and inspired the site’s visual style.
In development
Five scientifically inspired modules.
These modules exist in EndoAI’s codebase and are going through release verification. They are not yet confirmed in the current App Store and Google Play versions, so the pictures here are website illustrations, not app screenshots.
Living Garden
A record-keeping garden that grows with bounded exponential growth and golden-angle petals.
No streaks, no wilting, no loss for missed days.
See the maths →Health Orbit
An orbital view of recorded cycle history, paced by Kepler’s equation.
Built around your recorded cycle length, with a setup prompt until one exists. No ovulation day or period prediction.
See the maths →Body Constellation
A force-directed picture of body regions recorded on the same days.
Connections show co-occurrence, never causation.
See the physics →Pattern Discovery Lab
Descriptive statistics with robust trends and Bayesian credible intervals.
Small samples are labelled as such. No baselines, diagnoses or predictions.
See the statistics →Doctor Prep Quest
Optional milestones for genuine preparation: reviewing records, adding questions, gathering documents.
Never locks features, never invents progress, never rewards symptoms.
Preparing for appointments →The website’s demonstrations re-implement the same published formulas in the browser for teaching. They run on synthetic data and are separate from the app.