Islands of Stability Health
A life, a blood-sugar system, a population against a virus: which states last, what it takes to test them, and what keeps them.
Physiology has its own word for an island of stability: homeostasis, the body holding its temperature, its blood sugar and its blood pressure within narrow bounds against everything that pushes them. This page takes three cases with public data: how the chance of dying changes over a life, how medicine tests blood sugar by pushing it, and how a population keeps measles out. It describes populations and models, and it gives no medical advice.
On this page: A life is not memoryless · Watching and pushing · An island paid for by every birth cohort · Warnings before a seizure? · The propositions
A life is not memoryless
If a human life were an island in the sense of proposition 3, the chance of dying in the coming year would be the same at every age. It is not, and the way it is not is instructive.
In 2022 a newborn's chance of dying before its first birthday was 0.56 percent. The chance fell to its lowest, 0.010 percent, at age 10, about 56 times lower. From 30 to 90 it rises along a nearly straight line on this scale, doubling every 9.3 years (the line accounts for 98.5 percent of the variation in the logarithm), and at 99 it is 33 percent a year.
The curve is a bathtub. On its left, the chance of dying falls through childhood: the frailest die first, and the rest grow sturdier as they grow. On its right it rises at a steady pace, doubling again and again: the body wears. Neither side is memoryless, and version 0.2 of the theory names both: differences in depth, which make a group's hazard fall, and exhaustion, which makes it rise on schedule. A life is not an island of given depth under a steady disturbance, so proposition 3's condition is not met here, as with the stars that leave the main sequence when their fuel runs out. The steady doubling has a name, Gompertz's law, from 1825. The flattening some demographers see at the very oldest ages is still argued over, partly as frailty again.
Watching and pushing
Proposition 2 says that looking stable is not evidence. Only recovery from a push is. Medicine has long worked this way in at least one place. Fasting blood sugar is a resting measure: how the system looks when left alone. The glucose tolerance test is a push: the patient drinks 75 grams of glucose, and the test measures how far the level has come back down two hours later. That is a measured recovery from a perturbation, which is exactly how the proposition says an island is established.
1,670 adults aged 20 and over in the survey's glucose-challenge subsample had both results, drank the whole drink and had the second blood draw 105 to 135 minutes after it. Among those whose fasting blood sugar was normal, 7.1 percent (95 percent interval 4.7 to 9.5) had a raised or diabetic-range result after the drink. Of those whose result after the drink was in the diabetic range, 52 percent (95 percent interval 43 to 60) had fasting blood sugar below the diabetic cut-off of 126 mg/dL: by the resting test alone, they would not have counted as diabetic.
The push finds what watching misses. Fasting glucose and longer-term averages remain the everyday tests because they are simpler: the push costs two hours and a sweet drink. That trade, between what a push costs and what it reveals, is the one proposition 2 asks every field to make knowingly.
An island paid for by every birth cohort
Herd immunity is an island a population holds: measles cannot spread when too few people can catch it. It is held by a throughput. Every year a new cohort is born susceptible and has to be vaccinated for the island to hold. That is proposition 4's case exactly: stability bought by continuous spending, decaying when the spending stops, with the fragility in the stabilizer, the vaccination program itself.
From 1950 to 1962, before the vaccine, the United States recorded an average of 525,730 measles cases a year and 475 deaths. From 2001 to 2018 the median was 79 cases a year, and the most 667, in 2014. In 2019 there were 1,274, and in 2025 2,289.
How long can an island like this last once coverage falls? The model below answers with version 0.2's runway: the gap between the share of people who can catch measles and the share at which it can spread, divided by the rate at which unvaccinated newborns fill that gap. It is known from coverage alone, before any outbreak.
With each case infecting 15 others in a population where everyone could catch it, measles can spread once more than 6.7 percent can catch it, so the island needs at least 93 percent of each cohort vaccinated. In the model, starting from 5 percent able to catch it: at 95 percent coverage the threshold is never crossed. At 90 percent the runway is 30 years, at 70 percent (coverage found in some communities) 5 years, and with no vaccination at all 1.3 years.
The runway is long, so the erosion is silent. For years after coverage falls nothing happens, and the island looks as safe as ever, which is proposition 2 again. When the outbreak comes it runs through the gap in the program, not through any change in the virus. Real populations are not well mixed: communities with low coverage have much shorter runways than the national average suggests, and that is where outbreaks start.
The runway test, country by country
Proposition 4 says an island held by a flow drains when the flow falls short. A test deposited before it ran asked whether, across every country with the records, an outbreak-free spell is more likely to end when more children have been born unvaccinated since it began. If depth were a stock, set when the spell began, that inflow would not matter.
The test ran once, on 30 September 2026, after its rules were deposited as 10.5281/zenodo.23071574. Its bootstrap seed comes from that identifier.
| Test | Bears on | Verdict | What was found |
|---|---|---|---|
| Does an outbreak-free spell end sooner when more children are born unvaccinated? | P4 | unresolved | Across 276 outbreak-free spells in 138 countries, 166 of which ended in an outbreak, each percentage point of the population born unvaccinated since a spell began multiplied its chance of ending by 1.12 (1.02 to 1.27). Survival needed the interval's lower end above 1.10, and a kill its upper end below 1.10. |
Reported without a verdict, as the rules require:
- Counting the children who missed the second dose instead, from 2000 on: 1.05 (0.95 to 1.15), over 209 spells.
- Spells by the decade they began: 1980s 6 (4 ended), 1990s 37 (15 ended), 2000s 92 (65 ended), 2010s 86 (57 ended), 2020s 55 (25 ended).
- The model's runway at each spell's start: 128 spells began with coverage above the level at which the model's threshold is ever crossed, and 67 of those still ended in an outbreak. The other 148 had a median runway of 7.3 years. Spells that ended lasted a median of 3 years at risk.
The interval lies above 1, so the chance of an outbreak did rise with the unvaccinated inflow, in the direction the flow reading predicts. The test could not show an effect as large as the rules asked for, so the verdict is unresolved, as registered. Reported cases depend on surveillance, mass vaccination campaigns are not in routine coverage, and a national average hides the pockets where outbreaks start. All three blur the relation.
Warnings before a seizure?
Proposition 3 also says that some exits are noise-induced, with no warning, which bounds any early-warning instrument's recall below one. Epilepsy is where that has been tested hardest. If a seizure were a tipping point approached slowly, the brain's signals should slow down before it, as the lake's do before it turns. A study of long recordings from 28 people with epilepsy found no such slowing before 105 seizures (Wilkat, Rings and Lehnertz, Chaos, 2019). Forecasting has turned to other signals, such as the daily and multi-day cycles in seizure risk (Baud and colleagues, Nature Communications, 2018). Open recordings of brain activity would allow a frozen test of the same question with the lake's method. It is not drafted.
Cost line and fragility line
Cost line. Homeostasis is paid for in energy, every second. Blood sugar is held by insulin, made and spent after every meal. Herd immunity is held by vaccinating every new birth cohort.
Fragility line. For herd immunity, the runway: how long until the share who can catch measles passes the threshold, at current coverage. For blood sugar, what only the push shows: how fast the level comes back.
How the propositions meet health
| Proposition | In health | Status |
|---|---|---|
| P2 The evidence rule | The glucose tolerance test is a push. In the national survey it found diabetic-range results that fasting glucose missed in about half of the cases. Illustration on real data. The test's use in medicine long predates the proposition. | illustration |
| P3 Exit statistics | The death rate by age is a bathtub: frailty on the left, wear on the right. A life is not an island of given depth under a steady disturbance, so the condition is not met. Seizures came without the slowing that would warn of them in the study cited, consistent with exits that give no warning. | condition not met |
| P4 Cost | Herd immunity is held by vaccinating every birth cohort. In the model, the runway is known from coverage alone, before any outbreak. Illustration, and tested once on real data from countries worldwide: unresolved. The chance of an outbreak rose with the unvaccinated inflow, short of the effect the rules required. | test run: unresolved |
| P1, P5, P6 | Not applied here. | not applied |
Source and method
Death rates: the life table for the total population of the United States, 2022, from the National Center for Health Statistics (Arias and Xu, National Vital Statistics Reports 74, 2025), SHA-256 04e961f8668f1e863ca5bcd53586eec4b65735c89eb1a4301361f71d35a9d0fd, public domain. Glucose: NHANES 2015–2016, files DEMO_I, GLU_I and OGTT_I, from the National Center for Health Statistics, public domain. Measles: reported US cases, 1919 to 2025, and deaths, in Our World in Data's series compiled from CDC and earlier US government sources, SHA-256 6d483e76cc59033b1fa9c74eba9de33e5747b3d336096b078c4c4b27989792d2, CC BY 4.0. All retrieved 2026-09-29. Every file's size and checksum is recorded, and the code refuses any other file.
Method. The Gompertz line is a least-squares fit of the logarithm of the yearly death probability on age, from 30 to 90. Glucose shares are weighted with the challenge subsample's weights, with 95 percent intervals by Taylor linearization over the survey's strata and sampling units. Categories follow the American Diabetes Association (fasting: under 100, 100 to 125, 126 and over, and for two hours: under 140, 140 to 199, 200 and over, in mg/dL). People taking insulin or diabetes pills were not given the challenge. The herd-immunity model is one well-mixed population with births and deaths at a rate of one seventy-fifth a year. All of it is description.