# Three to One > Gregor Mendel chose seven pea traits that come in exactly two forms, grew about 28,000 plants over eight years, and counted every one. The ratio he found — three to one — is the proof that inheritance comes in discrete pieces, and it went unread for thirty-four years. Run his crosses, see why sample size matters, and watch blending inheritance destroy variation. Episode 05 of the Great Scientists series. Interactive film: https://www.planetpast.com/stories/scientist-mendel/ Publisher: PlanetPast (https://www.planetpast.com/) · Published 2026-10-13 · Biology, Math, History ## Prologue ### Three to one *A garden, a ratio, thirty-four years of silence* He did not discover genes. He discovered that inheritance can be counted. Everyone before Mendel looked at a hybrid and saw a mixture. Cross a tall plant with a short one and you expect something in between. Mendel did something nobody had bothered with. He picked traits that come in exactly two versions, bred thousands of plants, and counted every single one. One number kept coming back. Three to one. That number is the proof that inheritance is made of discrete pieces that do not blend — and nobody read it for thirty-four years. ![Two hundred and fifty square metres, eight years, twenty-eight thousand plants.](https://www.planetpast.com/stories/scientist-mendel/img/c00.jpg) - **28,000**: plants grown - **7**: traits, each with two forms - **3 : 1**: the number that kept returning > My time will come. (Attributed to Mendel, late in life) Prologue · Why he matters #### Three to one Mendel’s contribution was not a new organism or a new instrument. It was **counting**: choosing traits with exactly two forms, growing thousands of plants, and recording the proportions. - **Born**: Silesia, 1822 20 July, to a farming family - **Died**: Brno, 1884 6 January, known as an abbot - **Experiments**: 1856–1863 about 28,000 plants How to use: pick a chapter below or press ← → to change step · ▶ plays the step · drag to rotate · three steps have buttons you can press. Sources: [Wikipedia: Gregor Mendel](https://en.wikipedia.org/wiki/Gregor_Mendel); [Wikipedia: Experiments on Plant Hybridization (1866)](https://en.wikipedia.org/wiki/Experiments_on_Plant_Hybridization) ## Chapter I · The blending problem ### The paint-pot theory *Chapter I · Before* If inheritance mixes like paint, variation dies. The default picture of inheritance was paint. Red and white parents make pink children, and pink crossed with pink makes pink forever. It matches a lot of what you see. Children are often somewhere between their parents in height and colouring. But it has a fatal consequence. If every generation averages, then every generation halves the variation, and after a few dozen generations everyone is identical. Darwin’s theory needs the opposite: a steady supply of differences for selection to work on. Blending inheritance would have strangled it. - Offspring look like a mixture of their parents - So inheritance must be a blending of fluids - But then every generation is more average - And variation would vanish in a few generations - **½**: of the variation lost every generation, if blending were true ![Plant breeders had crossed species for a century without counting the offspring.](https://www.planetpast.com/stories/scientist-mendel/img/c01.jpg) Chapter I · Step 1 #### The paint-pot theory If inheritance **blends**, each generation loses about half its variation — and after a few dozen generations there is nothing left for selection to act on. The standard theory of heredity was incompatible with Darwin’s theory of evolution. Press the buttons in the scene to switch between blending and particulate inheritance, and watch what happens to the spread. Sources: [Wikipedia: blending inheritance](https://en.wikipedia.org/wiki/Blending_inheritance); [Wikipedia: Charles Darwin](https://en.wikipedia.org/wiki/Charles_Darwin) ### A physicist in a monastery *Chapter I · The man* He failed the biology exam. Twice. Mendel was a farmer’s son with no money. He entered the abbey at Brno in 1843 largely because it would pay for him to study. The abbot sent him to Vienna, where he spent two years learning physics — including under Christian Doppler — and mathematics and statistics. He twice failed the examination that would have let him teach biology formally. He went back to Brno as a substitute teacher and started planting peas. That training is the whole point. A biologist of the period described what offspring looked like. A physicist counts them and looks for a law. ![A farmer’s son who became a friar because the abbey paid for his education.](https://www.planetpast.com/stories/scientist-mendel/img/s2-mendel.jpg) - 1822: Born to a farming family in Silesia - 1843: Enters the abbey at Brno — it pays for study - 1846: Ordained - 1851–53: Physics at Vienna, under Christian Doppler - He failed his teaching examinations twice - He was trained in physics, not biology - Which is why he thought in ratios Chapter I · Step 2 #### A physicist in a monastery Mendel entered the abbey because it funded his education, studied **physics and mathematics at Vienna** under Doppler, and twice failed the teaching examination in natural science. He approached heredity the way a physicist approaches anything: restrict the variables, repeat at scale, count, and look for a ratio. Sources: [Wikipedia: Gregor Mendel](https://en.wikipedia.org/wiki/Gregor_Mendel) ## Chapter II · Counting peas ### Choosing what to count *Chapter II · The design* The genius is in the choice of question. Peas are a good choice. They normally fertilise themselves, so a line stays pure unless you interfere, and you can interfere with tweezers and a brush. Then he did the thing that made it work. He threw away every trait that comes in a range — and kept only the seven that come in exactly two forms. Round or wrinkled. Yellow or green. Purple or white. Tall or short. Nothing in between, so nothing to argue about when you record it. For two years before the real experiment he grew the lines until he was sure each bred true. Then he started crossing, and counting every seed. ![Seven traits, each with exactly two clean forms and no intermediates.](https://www.planetpast.com/stories/scientist-mendel/img/c03.jpg) - Seed shape: round or wrinkled - Seed colour: yellow or green - Flower colour: purple or white - Stem: tall or short - **2**: forms per trait, with nothing in between - **8**: years of sowing, crossing and counting Chapter II · Step 3 #### Choosing what to count Mendel kept only the **seven traits that come in exactly two forms** — round/wrinkled, yellow/green, purple/white, tall/short and three more — and spent two years confirming his lines bred true before starting. Most heredity research of the time used traits that vary continuously, where any result can be read as a blend. Mendel chose the cases where blending would be impossible to miss — and then it never happened. Sources: [Wikipedia: Experiments on Plant Hybridization (1866)](https://en.wikipedia.org/wiki/Experiments_on_Plant_Hybridization); [Wikipedia: Mendelian inheritance](https://en.wikipedia.org/wiki/Mendelian_inheritance) ### One parent wins *Chapter II · The first cross* No blending at all — the other form just disappears. Cross a pure round line with a pure wrinkled line, and look at the seeds. Every one of them is round. Not slightly wrinkled, not intermediate. All round. If inheritance were a blend, this is impossible. Something has not been mixed in; it has been hidden. Mendel called the visible form dominant and the hidden one recessive. Now the obvious question: is the wrinkled form gone, or just out of sight? - **100%**: of the first generation are round - **0**: that are in between - Round × wrinkled gives all round - The wrinkled form has not been destroyed - It is hidden, and comes back next generation ![Each cross recorded separately, seeds counted and stored.](https://www.planetpast.com/stories/scientist-mendel/img/c04.jpg) Chapter II · Step 4 #### One parent wins Pure round crossed with pure wrinkled gives **100% round** offspring, with no intermediates. The wrinkled form is not blended away — it is **hidden**. Sources: [Wikipedia: Mendelian inheritance](https://en.wikipedia.org/wiki/Mendelian_inheritance); [Wikipedia: Experiments on Plant Hybridization (1866)](https://en.wikipedia.org/wiki/Experiments_on_Plant_Hybridization) ## Chapter III · Three to one ### Three to one *Chapter III · 1863* Let the hybrids fertilise themselves and the hidden form comes back. Let those all-round hybrids pollinate themselves, and the wrinkled seeds reappear — in a fixed proportion. Mendel counted five thousand four hundred and seventy-four round and one thousand eight hundred and fifty wrinkled. That is two point nine six to one. The explanation is arithmetic. Each plant carries two copies of the factor and passes one on at random. Four combinations, equally likely, and three of them contain at least one copy of the dominant form. This is why he needed thousands of plants. With twenty seeds the ratio is lost in the noise. Set the sample size and run the cross. - **5,474**: round seeds - **1,850**: wrinkled seeds - **2.96 : 1**: the ratio he got - Each parent carries two copies - Each passes on one at random - Four equally likely combinations - Three of them show the dominant form - **20**: plants: the ratio looks like noise - **1,000**: plants: the ratio is obvious Chapter III · Step 5 · **Interactive** #### Three to one Self-pollinate the hybrids and the hidden form returns: Mendel counted **5,474 round to 1,850 wrinkled** — 2.96 to 1. Each parent carries two copies and passes on one at random; three of the four combinations show the dominant form. Press **Grow** with different sample sizes. With 20 plants the ratio is noise; with a thousand it is unmistakable. That is the whole reason for eight years of counting. Sources: [Wikipedia: Experiments on Plant Hybridization (1866)](https://en.wikipedia.org/wiki/Experiments_on_Plant_Hybridization); [Wikipedia: the Punnett square](https://en.wikipedia.org/wiki/Punnett_square) ### The thing Darwin needed *Chapter III · The consequence* Particles keep variation alive. Switch the scene between the two models and watch the spread of a population. Under blending, the distribution narrows every generation until everything is the same. Under particles, the same alleles keep being dealt out, and the spread stays. That is precisely the resource natural selection consumes. Without it, selection runs out of raw material. Mendel and Darwin were alive at the same time and never corresponded. The two halves of modern biology sat in different countries for thirty-four years. - Particles do not dilute - A recessive copy can hide for generations - Then reappear unchanged - So variation is preserved, not averaged away - **0**: variation lost per generation Chapter III · Step 6 · **Interactive** #### The thing Darwin needed Discrete factors are not diluted. A recessive copy can hide for generations and return unchanged, so **variation persists** — which is exactly what natural selection requires and what blending destroys. Switch between **Blending** and **Particles** and run the generations to see the distributions diverge. Sources: [Wikipedia: blending inheritance](https://en.wikipedia.org/wiki/Blending_inheritance); [Wikipedia: Mendelian inheritance](https://en.wikipedia.org/wiki/Mendelian_inheritance) ## Chapter IV · Two traits at once ### Nine, three, three, one *Chapter IV · Two traits* The ratios multiply, because the traits travel separately. Now track two traits at once: shape and colour. Cross round-yellow with wrinkled-green, let the hybrids self, and you get four kinds of seed in the proportions nine, three, three and one. That is just three-to-one multiplied by three-to-one. Which means the two factors are handed down independently — inheriting round does not force you to inherit yellow. He counted three hundred and fifteen, one hundred and eight, one hundred and one, and thirty-two. Run the cross and see the grid fill. - **9 : 3 : 3 : 1**: two traits, four outcomes - **315 : 108 : 101 : 32**: the numbers he actually counted - Shape and colour are inherited independently - Round does not drag yellow along with it - So the ratios multiply: 3:1 times 3:1 - Which gives nine, three, three, one Chapter IV · Step 7 · **Interactive** #### Nine, three, three, one Two traits tracked together give **9:3:3:1** — the product of two independent 3:1 ratios. Mendel counted **315 : 108 : 101 : 32**. The factors are dealt out separately. We now know independence only holds for factors on different chromosomes, or far apart on the same one. Mendel’s seven traits happen to behave independently; he was lucky as well as careful. Sources: [Wikipedia: Mendelian inheritance](https://en.wikipedia.org/wiki/Mendelian_inheritance); [Wikipedia: Experiments on Plant Hybridization (1866)](https://en.wikipedia.org/wiki/Experiments_on_Plant_Hybridization) ## Chapter V · Nobody reads it ### The room said nothing *Chapter V · 1865* He read it twice to a society that did not understand it. In February and March 1865 Mendel read his results to the natural history society of Brünn, in two sittings, to about forty people. The minutes record no questions and no discussion. The paper was printed the next year and the society posted it to more than a hundred libraries. It was cited roughly three times in the following thirty-five years, usually as a note about hybrid peas. The problem was not obscurity. It was that the paper is full of ratios, and the biologists who received it were not in the habit of reading biology as arithmetic. ![He read the paper to the Natural History Society of Brünn in two sittings. There were no questions.](https://www.planetpast.com/stories/scientist-mendel/img/c06.jpg) ![Versuche über Pflanzenhybriden, printed in the society’s proceedings and sent to libraries across Europe.](https://www.planetpast.com/stories/scientist-mendel/img/s8-paper.jpg) - **~40**: people in the room - **~3**: citations in thirty-five years Chapter V · Step 8 #### The room said nothing Read aloud in **1865**, printed in **1866**, distributed to libraries across Europe — and cited about **three times in thirty-five years**. The paper was available and unread. It is a useful warning about how discoveries actually spread. Publishing is not the same as communicating, and a result in an unfamiliar language — here, statistics — can sit in plain sight for a generation. Sources: [Wikipedia: Experiments on Plant Hybridization (1866)](https://en.wikipedia.org/wiki/Experiments_on_Plant_Hybridization); [Wikipedia: Gregor Mendel](https://en.wikipedia.org/wiki/Gregor_Mendel) ### Promoted out of science *Chapter V · After* The abbey made him abbot, and that was the end of the peas. In 1868 the monks elected him abbot. The job came with accounts, buildings and a long fight with the government over monastery taxes. He kept experimenting for a while, and chose hawkweed on the advice of a famous botanist. It was the worst possible choice: hawkweed often makes seeds without fertilisation, so the ratios never appear. The failure seems to have shaken his confidence in the pea results. He died in 1884, locally respected as an abbot and a weather observer, and unknown as a scientist. ![Elected abbot in 1868, he spent his last sixteen years on administration and a tax dispute.](https://www.planetpast.com/stories/scientist-mendel/img/c08.jpg) - Elected abbot in 1868 - Tried the same work on hawkweed and failed - Hawkweed reproduces asexually — the ratios never appear - He died in 1884 as a well-liked abbot Chapter V · Step 9 #### Promoted out of science Elected **abbot in 1868**, Mendel disappeared into administration. His follow-up work on **hawkweed** failed because that plant often reproduces without fertilisation — the ratios cannot appear. He died in **1884** unknown as a scientist. Sources: [Wikipedia: Gregor Mendel](https://en.wikipedia.org/wiki/Gregor_Mendel) ## Chapter VI · 1900 ### Three people find it at once *Chapter VI · 1900* They all did the experiment again before they found the paper. In the spring of 1900 three botanists published hybridisation results within a few months of each other: Hugo de Vries in Amsterdam, Carl Correns in Tübingen and Erich von Tschermak in Vienna. All three had the ratios. All three then went to the literature and found a thirty-four-year-old paper by an unknown abbot that had got there first and explained it better. Within five years the field had a name — genetics — and within ten the units had one too: genes. - 1900: De Vries, Correns and Tschermak publish within months - 1900: All three find Mendel’s paper and cite it - 1905: Bateson coins the word genetics - 1909: Johannsen coins the word gene ![Three botanists, working separately, got the same ratios and then found the paper.](https://www.planetpast.com/stories/scientist-mendel/img/c07.jpg) - **34**: years between publication and rediscovery - **3**: independent rediscoverers Chapter VI · Step 10 #### Three people find it at once In **1900** de Vries, Correns and Tschermak independently reproduced the ratios, then found Mendel’s paper. **Genetics** was named in 1905 and the **gene** in 1909. Sources: [Wikipedia: Hugo de Vries](https://en.wikipedia.org/wiki/Hugo_de_Vries); [Wikipedia: gene](https://en.wikipedia.org/wiki/Gene) ### Data that is too good *Chapter VI · The complication* The laws are right. The numbers are suspiciously tidy. There is an awkward footnote. In 1936 the statistician Ronald Fisher checked Mendel’s published counts and found they fit the predicted ratios more closely than chance allows. Nobody thinks the conclusions are wrong — the laws have been confirmed thousands of times since, in every sexually reproducing organism anyone has tested. The likeliest explanations are mundane: an assistant who knew what was expected, or stopping a count once it matched. It is worth keeping because it shows something real. A result can be correct and its data still be handled in ways that would not pass today. - Fisher tested Mendel’s numbers statistically - They fit the expected ratios too well - Chance should have produced more scatter - Most likely explanation: a helpful assistant, or stopping when the numbers looked right - **1936**: Fisher’s analysis - **every**: later repeat confirms the laws Chapter VI · Step 11 #### Data that is too good In **1936** R. A. Fisher showed Mendel’s counts fit the expected ratios **more closely than chance should allow**. The laws are not in doubt — they have been reproduced countless times — but the data handling would not pass a modern review. Sources: [Wikipedia: the Mendelian paradox (Fisher, 1936)](https://en.wikipedia.org/wiki/Gregor_Mendel#Mendelian_paradox) ## Epilogue ### From peas to genomes *Epilogue* Everything downstream is this ratio, scaled up. Mendel never used the word gene and had no idea what his factors were made of. He simply showed that they behave like discrete objects, dealt out at random, two per parent. Within fifteen years those factors were traced to chromosomes. Within fifty, to DNA. Within a hundred, we were reading the whole sequence. And the arithmetic is unchanged. When a genetic counsellor says one in four, that is Mendel’s second generation. The chapter stills in this film are AI-generated; the portrait and the printed paper are real. - Mendel’s factors are genes - Genes sit on chromosomes - Chromosomes are made of DNA - The 3:1 ratio is what two copies and random assortment look like - **1910s**: genes located on chromosomes - **1953**: the structure of DNA - **2003**: the human genome sequenced ![Every genetic test, crop line and inherited-disease risk runs on the arithmetic he found.](https://www.planetpast.com/stories/scientist-mendel/img/c09.jpg) Epilogue · Step 12 #### From peas to genomes Mendel’s “factors” became **genes**, then **chromosomes**, then **DNA**. The arithmetic never changed: when a genetic counsellor says one in four, that is Mendel’s second generation. Sources: [Wikipedia: gene](https://en.wikipedia.org/wiki/Gene); [Wikipedia: the modern synthesis](https://en.wikipedia.org/wiki/Modern_synthesis_(20th_century)); [Wikipedia: Mendelian inheritance](https://en.wikipedia.org/wiki/Mendelian_inheritance) ### The quiet experiment *Epilogue* One garden, eight years, a number. What Mendel did is available to anyone with patience: pick a question that can be counted, strip it down until the answer cannot be argued with, and then repeat it until chance is ruled out. He never knew it worked. He died sixteen years before anyone noticed. The sentence attributed to him late in life — my time will come — may or may not be his. It was accurate either way. Sources are listed below. - 1856: starts the pea experiments - 1865: reads the paper aloud - 1866: published, and ignored - 1884: dies unknown as a scientist - 1900: rediscovered three times over - Choose a question that can be counted - Restrict it until the answer is unambiguous - Repeat it enough times that chance cannot explain it - Publishing is not the same as being heard Epilogue · Step 13 #### The quiet experiment One garden, eight years, 28,000 plants and a number. Mendel died **sixteen years** before anyone understood what he had done. - 1856–63 the pea experiments - 1866 published and ignored - 1900 rediscovered independently three times Chapter stills in this film are AI-generated illustrations. The portrait of Mendel and the page of the 1866 paper are real historical images, credited where they appear. Sources: [Wikipedia: Gregor Mendel](https://en.wikipedia.org/wiki/Gregor_Mendel); [Wikipedia: Experiments on Plant Hybridization (1866)](https://en.wikipedia.org/wiki/Experiments_on_Plant_Hybridization); [Wikipedia: Mendelian inheritance](https://en.wikipedia.org/wiki/Mendelian_inheritance); [Wikipedia: blending inheritance](https://en.wikipedia.org/wiki/Blending_inheritance); [Wikipedia: Hugo de Vries](https://en.wikipedia.org/wiki/Hugo_de_Vries); [Wikipedia: the Mendelian paradox (Fisher, 1936)](https://en.wikipedia.org/wiki/Gregor_Mendel#Mendelian_paradox); [Wikipedia: the Punnett square](https://en.wikipedia.org/wiki/Punnett_square); [Wikipedia: gene](https://en.wikipedia.org/wiki/Gene); [Wikipedia: the modern synthesis](https://en.wikipedia.org/wiki/Modern_synthesis_(20th_century))