Chiara Marletto,The Science of Can and Can’t: A Physicist’s Journey Through the Land of Counterfactuals,Viking,New York,2021

Science and engineering: the usual understanding. In a nutshell, the main objective of science is to predict what will happen in the future, and the objective of engineering is to describe how to make this future as beneficial to us as possible –be it by manipulating natural processes or by designing machines and devices that will help. From this viewpoint, both science and engineering are important for humanity: engineering is more useful short-term, but science is also useful: while engineers design devices based on known physical laws, scientists analyze nature and come up with new laws, many of which will be used by engineers of the future.

But there is a serious problem. The goal of physics is to predict future events. In pre-quantum physics, the belief was that if we know the initial conditions of a system, then we can predict its state for years and even centuries ahead –just like Newton’s theory predicted the motion of the planets, solar eclipses, etc. With quantum physics, the paradigm changed: in quantum physics, we cannot predict the results of future measurements, but what we can, in principle, predict, is probabilities of different measurement results.

And here lies a problem. If the initial state of the Universe uniquely determined its future state, as the physical theories claim, and we can predict the future –be it the events or the probabilities of different outcomes –then how can we change this future? So, according to physics, what we call engineering is simply not possible.

But we know that we can change the future: we can invent many useful machines and devices and make life better, or we can start a war, ruin the environment, or otherwise make the future worse.

The problem is not just between physics and engineering, it is within physics as well. Indeed, how do we find physical laws? First, we try to find some formulas that fits all the observations, but the real test is when we make an experiment.

Let us take a naive example –there are many such examples in statistics textbooks. The number of papers published in the world grows exponentially, and the amount of uranium in a given sample decays exponentially. So, based on the observations, there is a clear power dependence between the number of papers published in a year and the amount of uranium left in a sample at the end of this year. This formula fits all the observations –but it does not mean that we have discovered a new physical law, and a simple experiment shows that. A physical law would mean that if we change one of the variables, another one will change. However, if one year, the world publishes fewer papers that usual, it will not affect the amount of uranium in the sample.

To distinguish between statistical correlation and causal relations –which physical laws are supposed to be –we need to perform an active experiment. This is what Galileo did when he dropped different objects from the Leaning Tower of Pisa, this is what Newton did when he passed the Solar light through a prism, etc. This is all part of Physics 101, but to perform an experiment we need to be able to change the state –which intuitively makes sense, but which contradicts the main idea of physics as a way to predict the future state of the world.

Many physical concepts from high school are actually based on what can and what cannot happen. For example, what is energy –one of the most fundamental concepts of physics? It is usually defined as the ability of perform some work: in other words, having energy means that we can perform some work –not that we are predicted to do something. But what does it mean that we can if everything is pre-determined –either deterministically or probabilistically?

How Einstein tried to resolve this paradox. Einstein, with his deeply philosophical mind, could not avoid this problem. But he was so much convinced by the triumphs of physical theories, that his solution was to ignore common sense completely and to conclude that there is no free will. This was not just an opinion that he expressed in his article: this was a guiding principle that he followed in his life. For example, while he did not know how to swim, to the horror of his friend, he liked to sail a yacht on his own. To calm them down, he explained that since everything is pre-determined, no matter what he does will not change his fate –if he is pre-determined to drown, he will drown no matter what, and if we is pre-determined to come back safe, he will come back safe.

This solution may have worked for Einstein, but for most of us, this idea is too far from our common sense, from our experience. We need a more onvincing solution.

So what can we do? Since physics itself has fundamental methodological problems in it, it is necessary to change physics. This is exactly what the author of this book has been proposing –and this is what the book is about. According to the author, the goal of physics is not to predict the future state of the world, but to predict what can and what cannot happen in the world. What exactly will happen, which possible future state of the world will be implemented, depends on us.

Terminological comment. In logic, there is a notion of counterfactuals: statements that describe what would have happened if the past was different, if things went contrary to what, in fact, happened. Example: If I did not go to the movies that night, I would not have met my current wife, and we would not have had our beautiful kids. Usually, this term is used to describe would could have happened. The author extends this term –and uses it also to describe what can and cannot happen. This is why she calls her approach counterfactual.

How can we develop this new approach to physics? On the philosophical level, the idea that we have free will, that future is not pre-determined but depends on our actions, this idea has been formulated millennia ago –it fits much better with our understanding of the world, with our ethics, with our experience of changing the events. However, so far, no one knows how to transform this natural philosophical idea into a productive physical theory.

The author is not proposing such a theory, not yet, but she describes a reasonable path, a path based on what was missing at the times of ancient philosophers –and even at the times of the 19 century and early 20 century philosophy classics –the notion of information.

Back to bits. The smallest part of information is one bit, a system which can be in two possible states: 0 and 1, yes and no, on and off. All modern computers and other devices are based on such bit-implementing units. How is this related to physics?

Well, the whole idea that the state can be 0 and can be 1 means that we cannot predict the future state: we can set it up ourselves. Moreover, we can transmit, communicate the information –i.e., we can take the state of one system and use it to make a corresponding change in the state of another system. When I type this text, the signal from my brain is transferred to the computer. Then, when the reader reads it, the same signal goes from the computer to the reader’s brain.

This is not only about computers and people: DNA stores and transmits information about biological creatures, radiowaves carry, to us, information about faraway quasars, etc. This is how the author plans to revise the physics –as a science of storing, transmitting, and transforming information.

But how is all this related to fuzzy? If you look at the advanced physics textbooks, if you look at papers published in physics journals, you will see a lot of formulas, a lot of complicated mathematics, a lot of derivations. After such a look, it is understandable that many people believe that physics is kind of a part of mathematics, that physicists make rigorous conclusions from equations –and their only difference from pure mathematicians is that the physicists’ equations reflect reality.

To a large extent, this is true, but in reality, the logic and reasoning that physicists use is not always the same as in mathematics. First, physicists use –and successfully –approximate reasoning. The success of this reasoning can be illustrated on the example of General Relativity. Many people known that Einstein discovered its equations in 1915. What fewer people know is that David Hilbert, the greatest mathematician of that time, independently came up with the exact same complex set of non-linear differential equations, and submitted his paper only 2 weeks later than Einstein. But –all Hilbert had was a complex system of equations, while Einstein also came up with some approximate solutions –and even proposed experiments that enabled to test its predictions. How? Einstein did not come up with a rigorous way to solve these equations, but he used his physical intuition, he understood which terms can be ignored and which not –and came up with easier-to-solve approximate equations.

This is how physicists think –they use terms like small, negligible –and get their results. How to formalize such physical reasoning is not fully clear, but it is important to notice that they use the same terms whose formalization inspired Zadeh and led to fuzzy logic –so maybe fuzzy logic, as well as other attempts to formalize physicist reasoning, can help to design the new physics.

And there is more. When a mathematician writes an equation and derives the properties of its solution, he/she implicitly assumes that this equation is always true, that its left-hand side is always equal to the right-hand side. This is usually not the case in physics. Yes, there are fundamental equations that many physicists believe to be absolutely true, but most of the time, when physicists analyze an equation, they understand very well that these equations are only true to some extent. Equations of Newton’s mechanics are only true if we can ignore quantum and relativistic effects. Equations of General Relativity are only true if we can ignore quantum effects. This is part of physics mastery –ability to reason with statement which are true only to some extend –and again, this is exactly what many fuzzy techniques try to do.

Finally, in mathematics, if a theory has a contradiction, then this theory is useless –one we have A and “not A”, we can derive everything. Not so in physics. In physics, at the present state of knowledge, there are still many “paradoxes” –when two different reasoning approaches lead to two different results. And still, physicists manage to make good predictions in many cases. This is not just a weird feature of modern physics –such paradoxes appeared all the time, they have been one of the main driving forces of physics. Paradoxes of Aristotle’s physics discovered by Galileo started modern physics, paradoxes of Newtonian physics –e.g., the fact that in the infinite Universe it would as light at night as in daytime –led to relativity theory and quantum physics, etc. Physicists manage to take into account these contradictions, to take into account, e.g., that an elementary particle (like an electron) is to some extent a wave and to some extend not a wave –and again, this is exactly what Zadeh started with, that, e.g., we not have a crisp transition between young and not young.

Another relation to fuzzy is that physicists do not just solve equations, they also provide an intuitive understanding of their solutions –understanding in terms of words from natural language. In our terminology, physicists fuzzify their solutions –and this fuzzification is an important step that helps them separate meaningful solutions from purely mathematical solutions that have no physical sense.

Conclusion. This book describes, in popular terms, an important direction of foundations of physics, direction that intends to make physics in better accordance with our intuitive idea of free will –and with its own practices. Of course, in a short review, it is not possible to describe all the ideas from a 250+ page book. What is important to emphasize is that the author explicitly mentions that to transform the corresponding ideas into a coherent theory, we need not only to analyze physical phenomena –we also need to be able to describe physicist reasoning, and this reasoning seems to be in line with fuzzy ideas. So maybe our ideas and techniques can help.