All scientific inquiry involves some kind of uncertainty, but the uncertainties in cosmology are particularly daunting. As well as being complex and difficult to describe, the systems cosmologists investigate are almost by definition out of reach. In these conditions of uncertainty, how confident can we be in the models we’ve built? How can we come to know how galaxies form, how the universe began or how much dark matter it contains?

In The Random Universe: How Models and Probability Help us Make Sense of the Cosmos, cosmologist and astrophysicist Andrew Jaffe offers a masterful and refreshing take on these questions. As the director of the Centre for Inference and Cosmology at Imperial College London, UK, and a past co-investigator on ESA’s Planck satellite that provided us with so much new information about the cosmos, Jaffe is well-equipped to walk readers through the tools that allow us to learn about the world despite its uncertainties. Anchoring his insights in beautifully narrated episodes from the history of physics, astrophysics and cosmology, he sheds light on how our theories of the universe evolved into our current best cosmological model – which nonetheless still has limitations.

Jaffe is particularly good at recounting how we refined, revised and even replaced some of our assumptions in light of incoming evidence such as the first measurements of stellar distance; the discovery of galaxies beyond our own; and precise measurements of cosmological parameters. Throughout this journey, he engages thoughtfully with a rich philosophical tradition that runs from David Hume in the 18th century through Willard Van Orman Quine, Imre Lakatos and Paul Feyerabend in the 20th.

Bayes’ theorem is important because it tells us how to update our degree of belief in light of new evidence

The book’s main protagonist, though, is the mathematician Thomas Bayes. For Jaffe, Bayesian probability is key to dealing with uncertainty, and even to solving Hume’s notorious problem of induction: how do we justify inferences from a finite set of observations to generalizations that go beyond them? Bayes’ theorem is important, Jaffe argues, because it tells us how to update our degree of belief in light of new evidence. It shows us why and how, even in an uncertain world, “the more observations we make, the surer we become”.

Of course, before we can use probability to deal with uncertainty, we first need a model. As Jaffe puts it, “Absent a model, I can’t assign a probability, and absent a probability, I can’t quantify my uncertainty about the world.” So, what exactly is a model? I found Jaffe’s answer to be one of the most captivating elements of the book. As the title of a subsection of chapter five puts it, “a model is a story about the world”. Without models, Jaffe tells us, our world would be an unexplained series of unrelated events. Models are also what allow us to take a finite set of data and use it to create something new. Without this leap, Jaffe suggests, we cannot learn anything about the world, because “you can’t make sense of an experimental result unless you have some model to interpret it”.

Of course, if the way we interpret data depends on our model, then different people may well obtain different interpretations depending on which model and which prior probability they choose. This charge of subjectivity is a longstanding accusation against Bayesians, but Jaffe offers at least a partial solution: “If you and I agree on the model, we should assign the same probability.” This, Jaffe argues, is where objectivity emerges, writing that “we come to the same conclusions if we start from the same premises”.

Models allow us to understand the world by bridging subjectivity with objectivity, and the personal with the collective

Many contemporary philosophers are at odds with the idealized view of science as an objective and linear enterprise that produces theories from a God’s-eye view. Instead, they strive to portray it as something that is social and human, but reliable nonetheless. Jaffe’s own views seem to align with this endeavour; as he puts it, “the scientific coupling of models and observations is a living, breathing, subjective endeavour, simultaneously collective and personal”. Through their interplay with data, he argues, models allow us to understand the world by bridging subjectivity with objectivity, and the personal with the collective.

Not everyone will agree with Jaffe that Bayesian probability offers a solution to Hume’s problem of induction. Personally, I (or perhaps the hardcore rationalist in me) was not convinced. Nevertheless, I found the book’s thesis – that uncertainty is not a hindrance to knowledge, but an opportunity to learn (and learn more) about the world – simultaneously liberating, humbling and empowering. I recommend The Random Universe to scientists, philosophers and anyone interested in better understanding the role of probability in science; the philosophical problems with how we handle uncertainty; and how our standard cosmological model came to be. I also hope it will encourage more collaborations between philosophers and scientists. There are many questions we can explore further if we work together.

• 2025 Yale University Press, £25hb, 288pp

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Here’s how the game works:

1. 1. Enter a word guess – in this game the word has six letters.
   2. After submitting your guess, each letter in the guessed word is coloured to provide feedback:
      • Green: The letter is correct and is in the correct position in the target word.
      • Yellow: The letter is correct but is in the wrong position in the target word.
      • Grey: The letter is not in the target word at all.
   3. Using this colour feedback, refine your next guess.
   4. Continue guessing until you correctly identify the hidden word(s) or run out of attempts.

If you want a clue to the answer, read the article here.

Fancy some more? Check out our puzzles page.

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In today’s technologies, mechanical mechanisms generally provide the brawn while electronics supplies the brains. This is partly because it is challenging to write information into mechanical memories without resetting each bit individually. However, that could change as researchers led by Pedro Reis at École Polytechnique Fédérale de Lausanne in Switzerland and Martin van Hecke at AMOLF in the Netherlands have now found a practical means of writing mechanical bits. Their technique, which they describe in Science Advances, uses structures that resemble children’s slap bracelets placed on a rotating turntable. While they acknowledge it is unlikely to replace electronic memories, they argue that it could have specialist applications and might produce insights that translate into electronic innovations.

“The framework we propose could be very useful, for example, in the domain of physical intelligence, where you provide hardware with capabilities that don’t require essentially a brain or an electronic control system to do individual tasks,” Reis says.

Mechanics for memory

Reis and van Hecke’s interest in mechanical memory stems from their research on metamaterials, which are materials that are defined not just by their composition, but also by the structures within them. Mechanical systems offer a tangible means of getting to grips with the complex behaviour of these metamaterials. “Often, all sorts of things that we do rely on nonlinear responses,” van Hecke notes, adding that such responses are much easier to study in mechanical systems than in optical devices.

A metamaterial made up of an array of switchable mechanical elements could function as a form of mechanical memory. However, to be practical, it needs to be possible to flip the states of individual mechanical bits using global controls, as opposed to addressing them individually. Otherwise, writing data will be very fiddly.

A solution emerged from Reis’ interest in rotating platforms, which he describes as “a very versatile way of loading mechanical systems”. While the pair had been friends for more than two decades, they had been working independently until, during a visit, the penny dropped and they realized that placing the metamaterial array on a rotating platform could provide the control they needed.

Because the angular velocity of the platform sends its momentum outwards, each mechanical object experiences a force in the radial direction, known as the centrifugal force. If this angular velocity is not constant, the object will experience an additional force in the orthogonal azimuthal direction, known as the Euler force. “So you have a complex force and bi-directional field that is highly tuneable,” says Reis. “And this tuneability is what we realized is very powerful.”

A rotating array

To construct their array, the researchers used clamped beams with two stable mechanical states – a little like a slap bracelet can be coiled up or flat, except these beams could either curve to the right or to the left. To individually address different beams, they ensured that each beam was unique in its width, the angle it was clamped at, and so on, all of which affect how much force is needed for a beam to ping into the opposite state. By tuning the parameters of each clamped beam and the angular acceleration of the rotating platform, they could engineer the applied force to switch (or not switch) specific beams, thereby writing data into the array purely by rotating the platform.

Doing this accurately requires a level of precision in acceleration control that surpasses what standard lab motors can achieve. However, the researchers say they were able to team up with a local company that had designed high-spec rotating platforms for its high throughput silicon chip production process. By programming platforms with five tailored clamped beams and the right rotation functions, they showed they could write the letters of the alphabet in ASCII script.

“This is a significant advance because it points toward future smart devices and robots that can be reprogrammed remotely without complex wiring or electronics, using only carefully designed motion‑based signals driven by a sole dynamic driving strategy,” explains Damiano Pasini of McGill University, Canada, who studies systems for mechanical computing but was not involved with this work directly.

Reis says he is excited about the scalability of the approach and its potential in high throughput experiments. Meanwhile, van Hecke is looking into how the idea might transfer to other systems, such as applying engineered force functions to crumpling sheets of complex glasses. “It just opens up possibilities for both studies, really fundamental studies of complex systems, but also real applications where you use this dynamic idea,” he tells Physics World.

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