About this blog

This is the blog of Neil Ingram and reflects a variety of my interests over the years. As a biology teacher, university academic, examiner and author.

I have been deeply interested in the use of IT in schools when Windows 3.0 came out in May 1990.

About ten years ago, I was invited to be part of the Hewlett Packard Catalyst initiative and I developed a model about how school pedagogy could work in the Web 3.0 world. Some of this has been published, but quite a lot has not.

The development of Artificial Intelligence systems is generating the same levels of excitement as Windows 3.0. As the CEO of Microsoft said, “It feels like the 1990s again!“.

I have developed an introduction to the thinking:

Pedagogy AI is a roadmap for the pedagogy of a lesson using AI with students.

This is based on the ideas in a series of ten linked posts, called Teaching and learning with AI. Part one is here.

To show you round the rest of the site:

Stories from Nowhere was a lockdown project, trying to use stories to bring important ideas into middle years biology lessons. It is built on observations in a wood and work we were doing on a 16-19 curriculum framework for the Royal Society of Biology

Exploring the epigenetic landscape is a microsite about how genes interact with the environment and uses the ideas of Conrad (Hall) Waddington.

The home page contains a mixture of posts relating a university course I ran on genetics, society and education.

There are also posts on Evolution relate to a book I co-authored for Oxford University Press.

The title “tools for clear thinking” is based on a book by Conrad (Hal) Waddington, whose ideas run through every article on this site. The cover image was designed by Dall-E3, and the prompt included Waddington’s term “epigenetic landscape. I was delighted that its rendering resembled the original conception by the painter John Piper.

How did the ‘Hardy-Weinberg equilibrium’ get its funny name?

Reginald Punnett as a young man

It is February 1908 and Reginald Punnett has just finished giving a lecture to the Royal Society of Medicine in London, when the unthinkable happens. He is ambushed by a question he cannot answer, posed by his enemies. 

By 1908, Mendel’s ‘lost’ paper had been re-discovered for eight years. Punnett’s boss and mentor William Bateson, one of its re-discoverers, was making Cambridge the centre of the new “Mendelian genetics”. This annoyed a rival school of human geneticists based in London, centred around Karl Pearson. They called themselves the “Biometricians”. 

The Biometricians were having an ongoing row with the Mendelians that was bitter and nasty. The row slowed down the acceptance of Darwin’s theory of evolution for many years. 

There is a lot more about this fascinating argument and how it was resolved in chapter four of our book on Evolution published by Oxford University Press. You can find out more about the book here and on this website. 

So, what was this killer question? Udney Yule hated Bateson and any idea of Mendelism, and he set Punnett a trap concerning brachydactyly. This is a medical condition where the fingers and toes are shorter than usual. It is caused by single gene and is a dominant characteristic. 

Why, wondered Yule, innocently, if the condition was dominant, would we not expect to find three times more people with brachydactyly than normal length fingers, assuming random mating for this condition? 

Punnett was stuck for an answer and burbled something about two Aa heterozygotes mating to produce more heterozygotes. This is true, but does not answer the question. 

As luck would have it, the next day Punnett was playing cricket in Cambridge with the mathematician G.H. Hardy. Whilst they were waiting to bat, Punnett grumbled to Hardy about the question. Hardy is said to have scribbled a solution on a postcard, giving it to Punnett, with the comment, “I would have expected you and your colleagues to have known this already.” Hardy eventually published his solution in the journal Science in 1908. 

So, what did Hardy write? Essentially, it was a new way of thinking about genetics. Mendelians studied the inheritance of characteristics in families produced by parents with known genotypes. The Biometricians did much the same with their human family trees. But populations are different: we cannot determine which individuals will breed to form the next generation. 

The approach is to stop thinking about individuals and think about alleles instead. (In 1908, the terms ‘gene’ and ‘allele’ were not used, and Hardy did not use them, but it is easier, here, to use the modern terms.)

For a single gene, with two alleles, A and a, allele A is dominant to allele a. The frequencies of these alleles in a population are not known, so we can call: 

the frequency of A = p

the frequency of a =q


Hardy pointed out that: 


(This is the binomial theory that is today taught in Year 12 mathematics.)

Expanding the equation: 


This gives us the frequency of the genotypes: 

AA = p2

Aa= 2pq

Aa= q2

So far, so good. But what about the next generation? Assuming random mating, each A allele is equally likely to combine with allele A or a. So, using Mendel’s method:

AlleleA (p)a (q)
A (p)p2 AApq Aa
a (q)pq Aaqaa

The genotype frequencies in the next generation are the same as the previous generation.

AA = p2

Aa= 2pq

Aa= q2

Because the allele (and their genotype) frequencies stay the same, they are said to be in equilibrium

Yule’s hypothesis was shown to be false, the frequency of brachydactyly in the population will stay the same, given certain assumptions. The frequency will change only if the assumptions are not true. These assumptions are:

  • random mating
  • no mutation
  • no immigration or emigration from the population,
  • large population size (N>10)
  • no selection of phenotypes.

By a cruel twist of fate, one month earlier, in January 1908, Wilheim Weinberg read a paper to a meeting in Stuttgart in Germany, in which he proposed the same equilibrium model. It was obviously an idea waiting to be discovered. History credits both people in the name ‘Hardy-Weinberg equilibrium’. 

Punnett has been criticised for not thinking of the idea for himself, but this is rather unfair. Neither Yule, Bateson or Pearson saw it either, even though it develops directly from Mendel’s paper. At least Punnett recognised the problem and discussed it with Hardy, who was probably the best mathematician in the world. This is what excellent scientists do, they share questions and collaborate on answers. 

Punnett became a professor of genetics and did important work testing the limits of Mendel’s ideas. In doing so, he and his colleagues discovered linkage and the effects of two genes on the same characteristic (epistasis). He was also able to improve the breeding of poultry. He was the author of the world’s best selling genetics textbook and introduced the Punnett square method of displaying crosses to the world. His students remember him as a caring and thoughtful teacher.

The world’s first Punnett Square from 1907

It just shows how useful cricket can be!

I am grateful to A.W. F. Edwards for his 2008 paper (Genetics 179: 1143-1150) for the inspiration for this story. 

Evolution – a primer for 16-19 year olds

Get free tickets here!

The book is beautifully illustrated and engaging. It is are aimed at 16 to 19 year olds who want to learn more and who may be contemplating a biological career.  However, we also have several non-biologist and non-scientific adult friends who have bought and enjoyed Evolution.

The first two chapters explore natural selection and how it leads to evolution, as well as giving insights into those who played key roles in the story of the theory of evolution.  For instance, did you know that there were two ‘parties’ in the early 20th Century who were at loggerheads with each other – the Mendelians and Darwinists?

The next two chapters focus more on types of evidence for evolution, as well as how the theory of evolution is itself evolving.  Learn the latest on the story of how the giraffe got its long neck and how genomics is putting the cat among the pigeons of established consensus.

The final two chapters look at human evolution.  After explaining what palaeontologists look for when they classify hominim fossils, the chapters go on to show how ancient humanity became a patchwork of small, very genetically diverse, groups interbreeding to eventually create Homo sapiens. 

The book contains case studies, with opportunities to see the ‘bigger picture’ and regular stops to ‘pause for thought’. Each chapter ends with a summary, recommendations for further reading as well as broader discussion questions, suitable for individuals or use with classes. There is a useful glossary of technical terms.

You can purchase the book at the following online stores:




WH Smith

Here is a recent review of the book on Amazon:

A recent review of the book on Amazon.
A recent review of the book on Amazon

A 5* review from Kathy Freeston (@KJF239):

The Evolution edition of the new Oxford Biology Primers series was written with the intention to stimulate the curiosity and interest of A level students who may be considering studying life sciences at university.  I found this book has met its objectives well and would recommend it to any student keen to further their knowledge beyond that covered at A level as well as any teacher looking to deepen their own understanding.

The book has six sections covering the birth & death of species, the evidence behind the theories, the changing views on the topic and human evolution.  Alongside the main text each section includes well laid out diagrams and figures, discussion questions and suggestions for further reading.  The discussion questions are designed to make the reader think about the section in more depth rather than the questions found in textbooks which tend to solely test knowledge.

The main text of the book tells a story rather than being a dry regurgitation of facts, and uses a more demanding level of literacy than the average A level textbook.  It allows the reader to take their own knowledge and expand on it by putting ideas into the context of the time in which individual discoveries were made.  The book uses many interesting examples to illustrate the complicated theory of evolution including modern research such as the mosquitoes of the London Underground and the beaks of Great Tits in the UK and The Netherlands.     

Having an accessible, high level modern book on Evolution can only be a good thing to encourage young people into further study of this area of Biology.

Other Twitter responses:

#T03 Beware the “either or” of binary thinking

a baby learning
a baby is learning about her world

Learning to understand the world

From our earliest days, we try to make sense of the world by dividing it up into categories:

me/not me, safe/not safe/, dog/mum

and so on.

These are called “binary” categories, because everything has to fit into one of the two choices.

“Would you like tea or coffee?” forces you to choose one of the categories.

You might prefer milk, but you can’t have it, because it is not available to you.

Binary categories are how we navigate people and things in the real world.

We use categories like:

like/dislike, good/bad,  hungry/not hungry, day/night, presence/absence, ill/well.

Binary thinking is quick and easy.

To survive we need to think quickly and easily about our world. However, binary thinking also oversimplifies the world.

Unless we live on the equator, day/night are not discrete binary categories. Twilight blends day into night; sunrise gradually turns night into day.

The same is true of many other supposedly binary categories.

Type two diabetes can show a range of symptoms, from mild to severe.

So can depression and  conditions like autism, dyslexia and bipolar disorder.

Thinking about spectrums

We are learning to talk about these conditions in terms of spectrums. The analogy comes from the light spectrum:

there is a continuum of wavelengths of light, each associated with a particular colour

The wavelength of light increases continuously from left to right from about 380 to 780 nm.

The colour changes imperceptibly depending on the wavelength.

We can use the spectrum to distinguish obvious landmarks such as red or blue.

Recognising the exact shade of red or blue is much more difficult.

Traditionally, genetics has been built on binary thinking.

Its founding father Gregor Mendel studied differences in pairs of contrasting characters.  Such as tall/short pea plants or round/wrinkled pea seeds.

It is easy to think that everything is like that.

In fact, everything is not like that.

In a population of individuals, most characteristics vary continuously from the minimum to the maximum.

Think of human height,  it is more like a spectrum than a binary category. Individuals can be any height, rather than just being either tall or short.

#T03 We need to be very wary the “either/or” of binary thinking. 

One of the biggest pitfalls of binary thinking,  is the binary category of nature/nuture. This is causing real problems in our contemporary thinking on genetics.

Of this, much more, later.

#T02 Genes are generalists

The Jim twins
The Jim twins – identical, but separated at birth.

The fascination of twins

The 1980s were the golden age for twin studies. Identical twins share the same DNA, because they come from the same single fertilised egg.

Some pairs of twins were (sadly) separated at birth to be adopted into different families. Many did not know they were twins until they were adults.

Separated identical twins are a natural laboratory for studying the effects of genes and the environment on behaviour.

Thomas Bouchard studied such twins in the University of Minnesota. One pair, both called Jim, became international celebrities.

The Jims were remarkably similar, enjoying maths and carpentry at school, but not spelling. They both married  women named Linda and then Betty.

The Jims both had a child called James Allan.

They both worked in the security business, both drove a Chevrolet, and both chain smoked the same cigarettes. Their families took holidays on the same beach in Daytona at the same time of year.

The conclusion drawn was that their genes were somehow producing these behaviours and that there had to be many genes to produce such specific effects.

How many genes are there?

I remember being in seminars where these (and other similar) findings were being shared. This was “cutting-edge” science and we were caught up in the enthusiasm. One (now very) eminent geneticist speculated that there had to be at least 250 000 human genes.

The idea was that one (or more) genes somehow caused each of these characteristics. Jim and Jim were machines built by their genes.

We no longer think like that. The Human Genome Project reported that there were 30 000 genes; now we think it is nearer 20 000. There are fewer genes than there are human proteins, so the old idea that one gene produces one protein is also wrong.

Furthermore, the idea that there are genes “for” choosing a type of car or a wife by her name or a beach to holiday on is also redundant.

Genes shape personality but only in very general ways, probably through their effects on brain development and the actions of  nervous systems.

So, the second tool for clear thinking is:

#T02 “Genes are generalists: they only have an indirect effect on the development of characteristics.”