This is a guest post by Elliott Baxby, a maths undergraduate student who wants to share an appreciation of geometrical proofs.
I remember the days well when I first learnt about loci and constructions – what a wonderful thing. Granted, I love doing them now; to be able to appreciate how Euclid developed his incredible proofs on geometry.
We asked guest author Elliott Baxby to take a look at Andrew Pontzen’s latest book, The Universe in a Box: A New Cosmic History.
Ever since I became interested in mathematics, I have always wanted to learn more about science. I love mathematics, and I can easily spend most of the day reading about it and solving complex equations. The maths books I’m familiar with take the reader up a ladder – they can build foundations of knowledge in one chapter and apply that knowledge to the next. Science books that I have picked up before always seem to do the opposite – after reading the first page, I am always left confused and demotivated to carry on.
The Universe In a Box by Andrew Pontzen breaks this theme. The book takes us on a journey through how scientists’ knowledge of the cosmos has developed over the years, with a strong theme around how simulations have helped shape this progress. The chapters offer detailed explanations of key aspects, theories and phenomena of astrophysics.
I particularly liked the chapters on dark matter and dark energy, as these ideas are ultimately fascinating. Dark matter, which we haven’t been able to see, shows evidence of its functionality within the cosmos and the creation of galaxies; the book also considers the notion that dark energy will eventually tear our universe apart and lead it to its end.
Black holes are also well explained – they have always been something of interest to me, and learning more about them has only made me love them more. A massive source of energy that can suck everything in its path – the power they posses is truly scary. Even more so knowing that every large galaxy has a super massive black hole at its centre… including our own. The chapter goes on to explore how simulations can escape singularities by joining black holes up using wormholes. This scientific thinking and how these tricks can be applied to simulations, like using sub-grid rules, is inspired.
The final chapter is unnerving but interesting. Pontzen talks us through this idea of the ‘simulation hypothesis’. The hypothesis that we actually are living in a simulation created by higher beings or creatures. The argument for this is quite something, and to truly get a sense of the argument, one has to keep an open mind. However, such absurdities have been seen before – the idea of the known universe would not long ago have been considered as blasphemy. Still, I’m not sure I can get behind this idea of simulated reality. The idea of parallel universes was also explored in this book, and is another one I find interesting – perhaps these two ideas could go hand in hand.
Overall, this book was an engaging, informative and a thought provocative read. There were some chapters that I did not enjoy as much, including the chapter on Quantum Mechanics and Cosmic Origins. The chapter was really well explained and very interesting, but there were moments that I had to reread or search up meanings. This was also a theme through other parts of the book – this is not down to the lack of clarity in Pontzen’s explanations, but rather a limitation in my own scientific knowledge.
This book is a must-have for anyone who wants to learn more about the cosmos and its origins, and historical context about the advancement of science and scientific theories. The writing style is accessible and easy to digest. High-school students and above should be able to enjoy this book.
To conclude, this was a pleasant surprise compared to other science books I have read. I look forward to further publications by Andrew Pontzen.
We asked guest author Elliott Baxby to take a look at John Allen Paulos’ latest book, Who’s Counting.
Mathematics is an increasingly complex subject, and we are often taught it in an abstract manner. John Allen Paulos delves into the hidden mathematics within everyday life, and illustrates how it permeates everything from politics to pop culture – for example, how game show hosts use mathematics for puzzles like the classic Monty Hall problem.
The book is a collection of essays from Paulos’ ABC News column together with some original new content written for the book, on a huge range of topics from card shuffling and the butterfly effect to error correcting codes and COVID, and even the Bible code. As it’s a collection of separate columns, it doesn’t always flow fluently – I did find myself losing focus on some of the topics covered, particularly ones that didn’t interest me as much. This was mainly down to the content though – the writing style is extremely accessible and at times witty.
The book included some interesting puzzles and questions, which were challenging and engaging, and included solutions to each problem – very helpful for a Saturday night maths challenge! I even showed some to my friends, who at times were truly puzzled. I loved the idea of puzzles being a means of sneaking cleverly designed mathematical problems onto TV game shows. It goes to show maths is everywhere!
I enjoyed the sections on probability and logic as these are topics I’m particularly interested in. One chapter also explored the constant $e$, where it came from and where else it pops up – a very interesting read. It does deserve more attention, as π seems to be the main mathematical constant you hear about, and I appreciated seeing $e$ being explored in more depth.
This book would suit anyone who seeks to see a different side of mathematics – which we aren’t often taught in school – and how it manifests itself in politics and the world around us. That said, it would be better for someone with an A-level mathematics background, as some of the topics could be challenging for a less experienced reader.
It’s mostly enjoyable and has a good depth of knowledge, including questions to test your mind. While I didn’t find all of it completely engaging, there are definitely some points made in the book that I’ll refer back to in the future!