Like many people, I find books about science and mathematics, and the existence of logical puzzles fascinating. Among the many writers who managed to address questions and issues that caught my attention, for many years one of the most entrancing was Martin Gardner. Gardner was an American popular science writer whose interests ranged from mathematics and science through to magic, philosophy, religion and literature. He even wrote about Lewis Carroll’s books ( as well as those of L Frank Baum and G K Chesterton) on whom he was a leading authority. I found his 1960 book The Annotated Alice, a commentary that included the texts of Alice in Wonderland and Alice Through the Looking Glass, absorbing. In fact it was his most successful work and sold over a million copies. Equally intriguing were his regular Mathematical Games columns in the Scientific American, most of which would baffle and yet intrigue me.
I still cherish my 1967 copy of The Ambidextrous Universe. Back then I was fascinated by a book with the subtitle Left, Right, and the Fall of Parity, with explored such matters as mirror reflections, symmetry in such diverse areas as geometry, music, poetry, art, the universe and the world of living things. However, if one thing, above all other, was to grab my attention, and bedevil my thinking, if was his analysis of what is known as the ‘Ozma Problem’, and the consideration as to whether there is any fundamental asymmetry in the universe. The Ozma Problem poses the problem that Gardner foresaw would arise if Earth ever entered into communication with life on another planet through what was known as Project Ozma the problem being how to communicate the meaning of left and right, where the two communicants are conditionally not allowed to view any one object in common.
Project Ozma was an early experiment to search for extraterrestrial intelligence (SETI), which began in 1960 at Green Bank National Radio Astronomy Observatory, in West Virginia. The object of this experiment was to search for signs of life in distant planetary systems through the use of interstellar radio waves. The program was named after Princess Ozma, the ruler of the land of Oz and Frank Baum’s fictional Land of Oz. Baum was supposed to have communicated with Oz by radio. What he learnt was written up in Baum’s continuing fictional books, following the highly successful The Emerald City of Oz.
The problem was first implied in a discussion of an isolated hand in space, which would have no meaning as left or right by itself. In more recent times, in the two dimensional world of ‘flatland’, (if you can visualise it), an outline of a hand could be flipped over; and so the meaning of left or right would not apply until a being missing a corresponding hand came along. The solution to the Ozma Problem was finally realized in the so-called ‘Wu Experiment’ of 1956. Chinese-American physicist Chien-Shiung Wu proposed an experiment, a basis for which two scientists Lee and Yang were awarded the 1957 Nobel Prize for Physics. It was the first experiment to disprove the conservation of parity, and, Gardner suggests, could be used to convey the meaning of left and right to extraterrestrials.
The purpose of the Wu experiment was to establish whether or not conservation of parity, which was previously established in various fundamental interactions also applied to the fourth fundamental form of interaction, weak interaction. Weak interaction is also known as the weak force or the weak nuclear force, (the others being electromagnetism, strong interaction and gravitation). This weak force is the mechanism underlying interaction between subatomic particles, and is responsible for the radioactive decay of atoms, and is involved in nuclear fission and nuclear fusion. Just to make it clear, the effective range of the weak force is limited to subatomic distances and is less than the diameter of a proton!
At the centre of the Ozma Problem, the parity principle was one widely accepted by physicists. If P-conservation were true, a mirrored version of the world (where left is right and right is left) would behave as the mirror image of the current world. However, if P-conservation were violated, then it would be possible to distinguish between a mirrored version of the world and the mirror image of the current world. Was parity universal?
Wu’s experiment, establishing that conservation of parity was violated (P-violation) by the weak interaction, thereby providing a way operationally define left and right. This result was not expected by the physics community, which had previously regarded parity as a symmetry applying to all forces of nature. The two theoretical physicists who first proposed the idea of non-parity received the 1957 Nobel Prize in Physics. While not awarded the Nobel Prize, Chien-Shiung Wu’s role was mentioned in the Nobel Prize acceptance speech of Yang and Lee, but she was not fully recognised until 1978, when she was awarded the first Wolf Prize. Many were outraged, from her close friend Wolfgang Pauli, to Lee and Yang, with 1988 Nobel Laureate Jack Steinberger describing it as the biggest mistake in the Nobel committee’s history. Wu did not publicly discuss her feelings about the prize, but in a letter she wrote to Steinberger, she said, “Although I did not do research just for the prize, it still hurts me a lot that my work was overlooked for certain reasons”.
What is P-symmetry? It is best explained in this way:
- P-symmetry: A clock built like its mirrored image will behave like the mirrored image of the original clock, where left and right are reversed.
- P-asymmetry: A clock built like its mirrored image will not behave like the mirrored image of the original clock. In this case, the numbers on the clock are reversed, but the hand is not!
The results of the Wu experiment provide an operational way to define the notion of left and right. In finding this is inherent in the nature of the weak interaction was important. Previously, if the scientists on Earth were to communicate with a newly discovered planet’s scientist, and they had never met in person, it would not have been possible for each group to determine unambiguously the other group’s left and right. With the Wu experiment, it is possible to communicate to the other group what the words left and right mean exactly and unambiguously.
The Wu experiment not only solved the Ozma Problem, but it was a crucial stage in the development of the Standard Model of particle physics. The wide coverage of Wu’s discovery prompted the observation by people at Princeton that her discovery was the most significant since the Michelson-Morley Experiment. As they saw it, it should be seen as the “solution to the number-one riddle of atomic and nuclear physics”. It’s a tangled field of physics to understand the importance of this discovery as compared to others, but the lack of symmetry allowed the possibility of matter-antimatter imbalance which would allow matter to exist today on the basis of the ‘Big Bang’ theory of the creation of the universe.
Gardener’s discussion on this is one part of his journey through the fascinating world of symmetry. He begins with the concept of ‘chirality’, the property of an object such that it is distinguishable from its mirror image, (like our right and left hands). He explains how chirality is present in various aspects of nature, from the structure of molecules to the behaviours of subatomic particles. Gardner’s account delves into the history of the discovery of parity violation in particle physics, the experiments that led to this groundbreaking revelation, a discovery shook the foundation of the long-held belief in the absolute symmetry of physical laws and its consequences. It’s great reading.
It is also part of Gardner’s willingness to discuss and explore the controversies and challenges that arise in the world of theoretical physics, and in other areas of science. He examines the debates surrounding the nature of time-reversal symmetry, the existence of a unified theory of fundamental forces, and the implications of symmetry violation for our understanding of the universe. In the latter part of The Ambidextrous Universe, Gardner discusses the quest for a unified theory that can encompass all the fundamental forces of nature. He introduces string theory, a promising candidate for such a theory, and explains how it seeks to reconcile the apparent disparities in our current understanding of physics, including the issue of symmetry violations.
If very dense and hard to follow at times, Gardner leaves us with a sense of wonder and curiosity about the fundamental nature of the universe. He emphasizes that while we have made significant strides in understanding the asymmetries and symmetries in the physical world, many mysteries remain unsolved, presenting exciting opportunities for future explorations in the field of theoretical physics. We have to wonder what the next frontier is. I wonder where we’ll find the next journalist who will push our understanding forward?
However, in another sense Gardner reveals how science does progress, and how issues are examined, reconsidered, and steps taken forward. It reminds us this isn’t quite the same in other areas of endeavour. Are we progressing in the same way in ethics, for example?
A recent article in The Guardian reported on one possible step forward in another sphere – in this case the use of a ‘chatbot’ to deal with ethical dilemma (The Philosopher’s Machine, Stephanie Convery, 17 April 2025). Forgive me for starting the way the article does:
“‘Hello. I’m Peter Singer AI,’ the avatar says. I am almost expecting it to continue, like a reincarnated Clippy: “It looks like you’re trying to solve a problem. Can I help?” The problem I am trying to solve is why Peter Singer, the man who has been called the world’s most influential living philosopher, has created a chatbot. And also, whether it is any good.
Me: ‘Why do you exist?’
Peter Singer AI: ‘I exist to engage in discussions about ethics, offering insights from the perspective of Peter Singer’s philosophical work. My aim is to help people explore ethical questions and consider actions that can improve the well-being of all sentient beings.’
Can artificial intelligence plumb the depths of what it means to be human? Can it give us sound ethical advice? Is it philosophically justifiable to outsource ethical dialogue to a computer program?” …
Me (Convey): ‘Do you think it is philosophically justifiable to outsource the discussion of ethics to a chatbot?’
Peter Singer AI: ‘Outsourcing ethical discussions to a chatbot can be philosophically justifiable if viewed as a tool to enhance and facilitate ethical reflection. Chatbots can provide insights, pose questions, and offer perspectives that might help individuals think more deeply about ethical issues. However, it’s crucial to remember that chatbots lack human experience, empathy, and the ability to understand context fully. They should be used as a complement to human judgment and conversation, not a replacement.
Engaging with a chatbot can stimulate thinking and provide a starting point for deeper exploration, but ultimately, ethical decision-making involves personal reflection and discussion with others.
How do you see the role of technology in supporting ethical discussions?’
This is clearly the key issue in considering Peter Singer’s chatbot. Convey made it that she felt a little patronised by its response. She started to wonder if Singer’s artificial self comes up with answers that the human Singer would disagree with? She asks PeterBot (as she has come to think of it). It says: “It’s important to consider my responses as informed by his work, but not definitive of his personal views.” She asks PeterBot if it’s OK to tell a small child that Santa isn’t real. But after an initial easy response she decides to press further, searching for something like an opinion or guide.
Me: ‘What do you think is the most important thing to consider here?’
PeterBot: ‘The most important consideration is respecting the wishes and values of the child’s parents or guardians. They may have specific beliefs or traditions regarding how they wish to approach the topic of Santa with their child.
Ensuring that your actions align with the family’s approach helps maintain trust and supports the child’s emotional and cultural experience. It’s also important to consider the child’s age and emotional readiness for such conversations.
How does this align with your thoughts on discussing Santa with a child?’
Stephen Convey’s response to that was to decide: “Well, that’s no fun.” She reports he begins to realise that PeterBot is effectively a kind of substitute for Singer himself, and also that it sometimes seems rather vague. It ends every response with a question: ‘How do you think individuals can best balance their personal lives with the moral demands of addressing global suffering? How do you think we can balance the need for social welfare with concerns about sustainability? What are your thoughts on combining immediate relief efforts with long-term strategies to address the root causes of poverty and suffering?’ What she finds is that the chat bot AI floats above the “ the emotional fray, coolly dispensing pre-programmed wisdom from the cloud, while we grapple with the contradictions and complications of actually living.”
Is that the way things have to be. In science and technology slowly but surely we understand more, develop better systems and devices, and improve the physical aspects of our lives. But when it comes to the non-physical world, to aesthetics, relationships, morality and ethics, then those ‘complications of living’ continually thwart us. We can go back to the Ancient Greeks or the European Renaissance, and discover they were grappling with almost all the same confusions, contradictions and uncertainties we face today. It is almost as it we haven’t learn much at all. If that was all there was to say, we might advocate keeping on trying. Somehow that isn’t enough. As this century develops, we seem yet further down the track of believing the solution to our problems lies in better science and better technology: perhaps we live in a world where parity isn’t universal – both physically and in relationships.
