5D Library

Preface: Curves, Switches and Doses

5D Library › Ageing Kinetics, the mTOR-AMPK Autophagy Switch and Hormesis · 中文

Preface: Curves, Switches and Doses

Note

Health and medical notice: please read this first. This book discusses biomathematical models of ageing and the epidemiology of exercise, and uses simple programs to illustrate the arguments. It is not medical advice and cannot be used to diagnose or treat any disease; it is not medical advice on any anti-ageing drug (for example rapamycin, metformin or NAD+ precursors), on supplements or on extreme fasting, and it gives no doses of any drug or supplement. Where these drugs and substances are mentioned, it is only to show the distance between animal research and human evidence; rapamycin and metformin are prescription drugs with well-known adverse effects and contraindications, and no one should take them on their own initiative for “anti-ageing”.

Before starting any new exercise programme, have your cardiovascular risk screened (following the American College of Sports Medicine’s preparticipation health screening; see Chapter 8). In the following situations, consult a doctor first and do not start or increase exercise, treadmill grade or fasting intervals on your own: known heart, cerebrovascular or peripheral vascular disease; high blood pressure (especially if uncontrolled); diabetes or other metabolic disease; kidney disease; pregnancy or the period after childbirth; recent surgery, acute illness or fever; chest pain or tightness, unexplained breathlessness, dizziness or fainting, or palpitations during exercise; joint or tendon injuries that limit walking. Wherever eating intervals are concerned, the contraindications of Books 5 and 17 of this series also apply: people with type 1 diabetes, people taking insulin, sulphonylureas or SGLT2 inhibitors, pregnant and breastfeeding women, minors, and people with a history of eating disorders or who are underweight should not lengthen their eating intervals on their own. The book does not recommend lengthening eating intervals or fasting; wherever its examples and records involve an overnight fast, 16 hours is the ceiling (a limit not to be exceeded, not a target to reach), and it sets no weight target.

If chest pain, chest tightness, unusual breathlessness, dizziness, an irregular heartbeat or anything else abnormal occurs during exercise, stop at once and seek medical care. Extrapolating results from animals and cells to humans carries great uncertainty, and the book says so wherever it happens.

Almost every population life table shows the same shape: after adulthood, the death rate rises roughly exponentially with age, doubling every few years. This curve is the oldest and most robust quantitative description of ageing. Meanwhile, over the past twenty years, words such as “autophagy”, “hormesis”, “mitochondrial low-dose stress” and “Zone 2” have passed from the laboratory into popular health talk, often combined into a tidy story: eating too often locks cells into a building state, moderate hunger and exercise stress switch on repair, and so the mortality curve can be pushed back.

Every part of this story has a real research background, but most of the links between the parts are inference rather than evidence. This book tries to take those links apart one by one: which are published observations, which are consequences of mathematical models, and which are only hypotheses, the author’s or popular ones.

What the book covers

The book discusses ageing, stress and fitness at six levels, each with programs that can be run: the mortality curve (the Gompertz–Makeham law, reliability theory and the compression of morbidity, Chapter 1); the nutrient-sensing switch (mTORC1, AMPK and ULK1, Chapter 2); hormesis and mitochondrial low-dose stress (Chapter 3); proteostasis and the critical clearance rate (Chapter 4); the epidemiology of cardiorespiratory fitness and its biases (Chapter 5); and training models, polarised training and Zone 2 (Chapter 6). Chapter 7 reads these studies beside the Lüshi chunqiu chapter “Fulfilling One’s Years”, the Sanguo zhi biography of Hua Tuo and the Suwen chapters “Treatise on the Heavenly Truth of High Antiquity” and “Treatise on the Vital Qi Communicating with Heaven”, and reviews the poisoning caused by ancient mineral elixirs, arguing that classical guiding exercises, dietary restraint and daily routines summarise experience of the rhythms of life and are neither molecular mechanisms nor clinical evidence. Chapter 8 offers a “four-step physiological resilience and recovery checklist” and a pre-registered randomised controlled trial.

Relation to earlier books in the series

Book 5 (fasting, ketones and attention) and Book 17 (ketone metabolism and intermittent fasting) of this series already covered Ohsumi’s autophagy research, why mouse fasting times cannot be converted into human hours, why an autophagy marker is not flux, NAD+ and sirtuins, and classical texts such as the Suwen’s “Great Treatise on the Five Regular Policies” and the Lingshu’s “Ordinary People Cut Off from Grain”. This book keeps their medical rules and conclusions and only cross-refers to them; Book 17’s AMPK–mTORC1 hysteresis program is not repeated, and Chapter 2 here asks instead how two inputs converge on ULK1 and how the switch relates to damage. Chapter 5 cites Book 22 on twin studies and genetic confounding.

Claims corrected after checking

Several points in the author’s original framework needed correcting or qualifying after checking:

  1. “The death rate doubles about every 8 years” is a typical value, not a constant (Finch and colleagues 1990). It varies with population, period, sex and fitting method: ignoring the Makeham term overstates the MRDT by about 1–2 years. The Gompertz law is most reliable between about 30 and 90, and whether a late-life plateau is real is still disputed (Barbi and colleagues 2018; Newman 2018).
  2. Reliability theory is a qualitative explanation. The Gavrilovs’ 2001 model shows that exhaustion of redundancy can produce an exponential rise and late-life deceleration; the simplest version used here cannot give both a constant 8-year doubling and a plateau within human ages with one parameter set.
  3. The compression of morbidity is a hypothesis. US data for 1998–2006 show slightly fewer expected disease-free years and more years without basic mobility (Crimmins and Beltrán-Sánchez 2011). Under a Gompertz curve with an MRDT of about 8 years, the standard deviation of the age at death is about 14 years; Fries’s roughly 4 years would need an MRDT of about 2 years.
  4. “Eating around the clock locks in the anabolic state so damaged proteins pile up linearly” and “periodic energy troughs switch on autophagic clean-up” are model inferences and hypotheses. Damage piles up linearly only with zero basal clearance; otherwise it tends to a plateau whose height the fasting window changes. Humans have no marker that times autophagic flux (Book 17), and the classical picture of “AMPK activating ULK1” is itself challenged by the cell studies of Park and colleagues (2023).
  5. “Antioxidants block the benefits of exercise” has not been consistently replicated. Ristow and colleagues (2009) studied 39 men for 4 weeks; in the 12-week trials of Yfanti and colleagues (2010, 2011) improvements in maximal oxygen uptake and insulin sensitivity were unaffected; Paulsen and colleagues (2014) found only muscle mitochondrial markers affected. No doses are given.
  6. The definition of hormesis does not include “beneficial” (Calabrese and Baldwin 2002), and low-dose stimulation is usually only 30–60 %; Kendig and colleagues (2010) criticised extensions of the concept.
  7. The hallmarks of ageing grew from nine (2013) to twelve (2023), adding disabled macroautophagy, chronic inflammation and dysbiosis.
  8. The figures of Mandsager and colleagues (2018) must be read as published: 122,007 patients referred for clinically indicated treadmill tests; “low” is the bottom 25 % and “elite” the 97.7th percentile and above; the adjusted 5.04 for low versus elite contrasts extreme groups, and the comparison of like with smoking (1.41) is below versus above average, 1.41. The paper says “comparable to or greater than traditional clinical risk factors” and “no observed upper limit of benefit”.
  9. Going from hazard ratios to “years younger” needs strong assumptions. The hazard ratio of 0.87 per MET (Kodama and colleagues 2009) is roughly 1.6 years on the Gompertz curve only if causal and proportional across ages; the Generation 100 randomised trial (1,567 older adults, 5 years) found no reduction in all-cause mortality from organised training.
  10. “Zone 2 specifically raises mitochondria” lacks human support (Storoschuk and colleagues 2025); polarised training has only a small advantage for maximal oxygen uptake (SMD 0.24) and none for time trials (Oliveira and colleagues 2024).
  11. Classical texts: the received Lüshi chunqiu reads 户枢不蝼, the later proverb 不蠹, and the Sanguo zhi biography of Hua Tuo 户枢不朽. The Suwen line “they ate and drank in measure” was quoted in Book 5, so this book reads the following passage, “People today are not like this”, instead.
  12. The “15 % grade brisk walking” must be individualised. At 3 miles per hour, a 15 % grade costs about 9.5 METs, above the first ventilatory threshold of most sedentary adults; the trial sets grade and speed from each participant’s measured threshold, with 15 % only as an upper limit.

Each chapter states these issues where they arise, and they are collected in the Editorial Notes published with the book.

How to read the boxes

As in the other books of 5D Library, different kinds of statement are marked separately.

Evidence

Evidence boxes report published research findings, with their sources. Animal and cell studies are marked as such, and observational studies are kept apart from randomised controlled trials.

Calculation

Calculation boxes give formulas and short Python programs. Every program runs as printed in a standard Python 3 environment using only the standard library, and its actual output is shown below it. Unless a source is given, the parameters are illustrative; they are not measurements of anyone and cannot be used to predict a particular person’s lifespan, risk or bodily response. The “participants” and data in the book are fictional or generated by the programs.

Hypothesis · not established

Hypothesis boxes contain the author’s ideas, marked “not established”, together with what result would show them to be wrong.

Source text

Source text boxes quote classical texts, with the author’s translation.

Note

Note boxes give reminders and explain choices.

About this edition

This is version 1.0.0, the first complete edition: a preface and eight chapters, in Chinese and English. The book contains 16 Python programs and 4 vector figures. The text, boxes and code were drafted with an AI writing tool from the author’s title, framework and notes; the author is responsible for reviewing and revising them and for checking every source. Corrections, and references the author has missed, are welcome through the 5D Library website.

Disclosure

The author uses the works of 5D Library, including this book, as the methodological basis of his community courses, the 5D Ascension Cards (Dimensional Shift Card Decks) and the Yafu AI knowledge base, and therefore has a commercial interest in the subject of this book. In addition, the author and the group that includes 5D Library operate ketohackers.com and nadplusnadplus.com, popular-science websites about ketogenic eating and NAD+ respectively, and therefore have a direct commercial interest in the subject of this book; the book names no brand or product, recommends no supplement and gives no doses. The book promotes no course, card deck or service; the Chapter 8 trial is designed to be run and analysed by researchers independent of the author’s business and does not recruit from the author’s community, students or customers; all the code and the study protocol are published openly for anyone to check.

Fan, Y. (2026). Ageing Kinetics, the mTOR-AMPK Autophagy Switch and Hormesis: From the Gompertz Mortality Law and Mitohormesis to Cardiorespiratory Fitness Epidemiology, Read Beside Classical Chinese Longevity Philosophy [衰老动力学、mTOR-AMPK自噬开关与毒物兴奋效应的生物数学模型] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23770092 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).