''What We Cannot Know: Explorations at the Edge of Knowledge'' is a 2016

popular science Popular science (also called pop-science or popsci) is an interpretation of science intended for a general audience. While science journalism focuses on recent scientific developments, popular science is more broad ranging. It may be written ...

book by the British mathematician

Marcus du Sautoy Marcus Peter Francis du Sautoy (; born 26 August 1965) is a British mathematician, Simonyi Professor for the Public Understanding of Science at the University of Oxford, Fellow of New College, Oxford and author of popular mathematics and popula ...

. He poses questions from science and mathematics and attempts to identify whether they are known, currently unknown or may be impossible to ever know.

Background

The author, British mathematician

, succeeded

Richard Dawkins Richard Dawkins (born 26 March 1941) is a British evolutionary biology, evolutionary biologist, zoologist, science communicator and author. He is an Oxford fellow, emeritus fellow of New College, Oxford, and was Simonyi Professor for the Publ ...

Simonyi Professor for the Public Understanding of Science The Simonyi Professorship for the Public Understanding of Science is a chair at the University of Oxford. The chair was established in 1995 for the ethologist Richard Dawkins by an endowment from Charles Simonyi. The aim of the Professorship is ...

. His contributions to

science communication Science communication encompasses a wide range of activities that connect science and society. Common goals of science communication include informing non-experts about scientific findings, raising the Public awareness of science, public awar ...

include television documentaries and a co-hosting role on '' Dara Ó Briain: School of Hard Sums''. Du Sautoy said that the book took three years to write. He was inspired to explore unknowns in science by considering provable unknowns in mathematics: for instance, Gödel's first incompleteness theorem states that in any (sufficiently sophisticated) logical system, there are true statements about positive whole numbers that cannot be proven true. In analogy, du Sautoy says that there are unknown questions around

consciousness Consciousness, at its simplest, is awareness of a state or object, either internal to oneself or in one's external environment. However, its nature has led to millennia of analyses, explanations, and debate among philosophers, scientists, an ...

because every person is limited to their own consciousness (like a

formal system A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in ma ...

is limited to its

axioms An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or f ...

). Another mathematical analogy du Sautoy made is that

Euclid's theorem Euclid's theorem is a fundamental statement in number theory that asserts that there are Infinite set, infinitely many prime number, prime numbers. It was first proven by Euclid in his work ''Euclid's Elements, Elements''. There are several proof ...

—that there are infinitely many

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

s—is a finite proof of a fact about

infinity Infinity is something which is boundless, endless, or larger than any natural number. It is denoted by \infty, called the infinity symbol. From the time of the Ancient Greek mathematics, ancient Greeks, the Infinity (philosophy), philosophic ...

. Du Sautoy imagines that, in physics, some proof of infinitude of the

universe The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...

could be similarly possible. The book was published on 19 May 2016.

Synopsis

Du Sautoy identifies seven "edges" of human knowledge, through consideration of physical objects. For instance, he questions whether it is possible to know what side a

die Die, as a verb, refers to death, the cessation of life. Die may also refer to: Games * Die, singular of dice, small throwable objects used for producing random numbers Manufacturing * Die (integrated circuit), a rectangular piece of a semicondu ...

will land on prior to rolling, using

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

and

chaos theory Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sens ...

in his analysis. He explores philosophical and scientific concepts of

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

and

. Other topics include

evolutionary biology Evolutionary biology is the subfield of biology that studies the evolutionary processes such as natural selection, common descent, and speciation that produced the diversity of life on Earth. In the 1930s, the discipline of evolutionary biolo ...

and

particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...

. As well as unknown questions, he illustrates known facts from

quantum physics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

and

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

. Du Sautoy connects the unknowns of human knowledge to

God In monotheistic belief systems, God is usually viewed as the supreme being, creator, and principal object of faith. In polytheistic belief systems, a god is "a spirit or being believed to have created, or for controlling some part of the un ...

, recalling that a radio interviewer defined God to him as "something which transcends human understanding". He ultimately rejects belief in a deity himself. He illustrates topics with examples from his own life, such as his practice of the trumpet and cello.

Reception

In ''

Undark Magazine ''Undark Magazine'' is a nonprofit online publication exploring science as a "frequently wondrous, sometimes contentious, and occasionally troubling byproduct of human culture." The name Undark is a deliberate reference to a radium-based luminous ...

'',

science communicator Science communication encompasses a wide range of activities that connect science and society. Common goals of science communication include informing non-experts about scientific findings, raising the public awareness of and interest in sci ...

John Durant praised that du Sautoy's book is "honestly self-deprecating" and that he manages to be "amiable and entertaining" without exaggerating scientific fact. Similarly, Nicola Davis of ''

The Guardian ''The Guardian'' is a British daily newspaper. It was founded in Manchester in 1821 as ''The Manchester Guardian'' and changed its name in 1959, followed by a move to London. Along with its sister paper, ''The Guardian Weekly'', ''The Guardi ...

'' praised that du Sautoy "exposes with humility his own confusions, apprehensions and concerns", but criticised that he "somewhat limply concludes" that what humans cannot know may remain unknown. In contrast, a writer for ''

The Economist ''The Economist'' is a British newspaper published weekly in printed magazine format and daily on Electronic publishing, digital platforms. It publishes stories on topics that include economics, business, geopolitics, technology and culture. M ...

'' found the conclusion to be "optimistic" and saw the book as "fascinating". Barbara Kiser reviewed the book for ''

Nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

'' as a "finely synthesized study" in which du Sautoy takes readers on a "dazzling journey". Rob Kingston recommended it as a science book of 2016 for ''

The Times ''The Times'' is a British Newspaper#Daily, daily Newspaper#National, national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its modern name on 1 January 1788. ''The Times'' and its si ...

''. The

University of Limerick University of Limerick (UL) () is a Public university, public research university institution in Limerick, Republic of Ireland, Ireland. Founded in 1972, as the National Institute for Higher Education, Limerick, it became a university in Septemb ...

's Centre for Teaching and Learning listed it as one of seven books that they encouraged students to read in 2020.

References

{{reflist 2016 non-fiction books Books about philosophy of mathematics Epistemology books Popular science books