Books I've read

Reality Is Not What It Seems by Carlo Rovelli

Date read: 2024-04-18. How strongly I recommend it: 9/10

Go to the Amazon page for details and reviews.

A good overview of how core ideas of reality have developed over time, from Democritus' atomic model to quantum gravity. It's eye-opening to learn what we perceive is just a fraction of reality (reality is not what it seems), which sparked my curiosity to study further. What also interested me is the thought process behind each breakthrough, especially Einstein — how they tackled problems and what made them different. Highly recommended if you are interested in all this.

My Notes


We are all in the depth of the cave, chained by our ignorance, by our prejudices, and our weak senses reveal to us only shadows. If we try to see further, we are confused: we are unaccustomed. (see: Plato's Allegory of the Cave)

The incompleteness and the uncertainty of our knowledge, suspended over the abyss of the immensity of what we don’t know, does not render life meaningless: it makes it interesting and precious.

Chapter 1: Grains

The Milesians understand that by using observation and reason, rather than searching for answer in fantasy, ancient, myths, or religion, it is possible to repeatedly correct our world view, and to discover new aspects of reality which are hidden to the common view.

Criticism and the freedom to build on ideas without being afraid to discard or criticize the is key to the development of philosophical and scientific thinking.

Democritus's system: the entire universe is made of boundless space in which the innumerable atoms run. Space has no boundary. Atoms have no quality at all, apart from their shape. Atoms are indivisible (atomos = in-divisible) and everything is made of them. They move freely in space, colliding one with another, they hook on to and push and pull each other. When atoms aggregate, the only thing that matters is their shape, their arrangement, and the order in which they combine. Just as by combining the letters of the alphabet in different ways we may obtain comedies or tragedies.

Imagine that matter is infinitely divisible. Suppose you break up a piece of matter ad infinitum. What would be left? Could small particles of extended dimensions remain? No! because you can continue breaking it down. Therefore, only points without extension would remain. But now, let's try to reassemble the piece of matter starting from these points. Since the points have no extension, no matter how many points you put together, you will never obtain something with extended dimensions. So the conclusion would be that matter is made up of a finite number of discrete pieces which are indivisible, each having a finite size: the atoms.

Similar argument on infinite divisibility: Achilles and the Tortoise (Zeno's Paradoxes).

At the beginning of 1900s, the concept of atoms was largely philosophical and many did not consider atomic hypothesis to be credible.

Einstein's proof of the atomic hypothesis: if we observe attentively very small particles, such as a speck of dust or a grain of pollen, suspended in still air or in a liquid, we see them tremble and dance (See: Brownian motion) as if the small particles is receiving blows randomly from each side of it.

With a little mathematics, it is possible to work back from the amount of movement of the granule, to the dimensions of the molecules (which Einstein does this at the age of 25!)

Lucretius's text (On the nature of things), forgotten for centuries, was rediscovered in January 1417 by Poggio Bracciolini.

The Catholic Church attempted to prohibit Lucretius's work, but it was too late. An entire vision of the world, which had been swept away by medieval Christian fundamentalism, was re-emerging. It was not merely a luminous and serene meditation on the beauty of the world. It was an articulate and complex structure of thinking about reality, a new mode of thinking, radically different from the mindset that had dominated the Middle Ages for centuries.

Chapter 2: The Classics

Aristotle coined the term physics (physis = nature) around 350 B.C.

Aristotle's view of physics divides the universe into the heavens and Earth. Every substance has a "natural place" in a hierarchy: earth at the bottom, then water, air, and fire at higher levels. Objects like stones naturally move downward to their proper level, while air bubbles and fire move upward to their respective natural places.

It's not wrong physics, it's an approximation. The physics of Newton, too, is an approximation of general relativity. And probably everything that we know today as well is an approximation of something else which we don't know yet. The reality has no resolution limit.

The key development of science is Plato: use mathematics as a language to understand and describe the world (See: Almagest of Ptolemy). He carved on the door of his school the phase “Let no one enter here who is ignorant of geometry.”

The world of Newtonian mechanics: A world made of vast, undifferentiated space where particles run forever and act upon each other through forces as time passes.

The world of Newton is the world of Democritus, rendered mathematical.

Almost all phenomena we see are governed by a single force, other than gravity: electromagnetism. It's the forced which holds together the matter that forms solid bodies; holds together atoms in molecules, and electrons in atoms.

Michael Faraday tries to understand the force which acts between charged and magnetic things. But in close contact with these objects, he is led to an intuition that will become the basis of modern physics: we must not think of forces acting directly between distant objects. We must instead think that there exists an entity diffused throughout space, which is modified by electric and magnetic bodies and which, in turn, acts upon (pushes and pulls) the bodies. This entity is today called the field.

The Maxwell's equations is the mathematical version of the Faraday lines. He computes the speed at which the undulations of Faraday's lines move and the result turns out to be the same as for light!

What is color? Put simply, it is the frequency (the speed of oscillation) of the electromagnetic wave that light is.

Maxwell recognizes that the equations foresee that Faraday's lines can also vibrate at much lower frequencies. Therefore there must be other waves which nobody had yet seen, produced by the movement of electrical charges, which in turn move electrical charges. A few years later, Guglielmo Marconi builds the first radio.

All modern communications technology is an application of Maxwell's predictions; the Maxwell equations are the basis for all calculations made by telecommunications engineers.

Chapter 3: Albert

The deepening of our understanding of the world is based on two theories: general relativity and quantum mechanics. Both demand a daring re-evaluation of our conventional ideas about the world: space and time in relativity; matter and energy in quantum theory.

3.1 The extended present

You don't get to new places by following established tracks.

At his early youth, he would read Euclid's Elements and Kant's Critique of Pure Reason instead of attending to what he was being taught at school.

Einstein's annus mirabilis (1905) papers.

Maxwell's equations state that the velocity of light is constant, regardless of the observer's motion, a concept that is incompatible with Newtonian physics, which posits that velocity is a relative measure.

Einstein asked himself whether there was a way of rendering Newton's and Galileo's core discoveries and Maxwell's theory consistent: Special Relativity Theory.

As space and time fuse together in a single concept of spacetime, so the electric field and the magnetic fields fuse together in the same way, merging into a single entity which today we call the electromagnetic field.

Another implication of the theory is the concept of energy and mass become combined in the same way as time and space. Before 1905, two general principles appeared certain: conservation of mass, and conservation of energy. But Einstein realizes that energy and mass are two facets of the same entity. One maybe transformed into another. What is conserved is the sum of mass and energy, not each separately.

Our intuitive idea of the present - the ensemble of all events happening now in the universe - is an effect of our blindness: our inability to recognize small temporal intervals. It is an illegitimate extrapolation from our parochial experience.

The present is like the flatness of the Earth: an illusion. We imagined a flat Earth because of the limitation of our senses, because we cannot see much beyond our own noses.

3.2 The most beautiful of theories

“Spacetime tells matter how to move; matter tells spacetime how to curve.” - John Archibald Wheeler

Newton himself had suspected that there was something missing, something that could transmit the force between the two; 200 years later, Faraday had found the solution, not for the force of gravity but for the electric and magnetic forces: the field.

Einstein look into the gravitational field and search for what kind of maths could describe it. In 1915, he published the “General Theory of Relativity.”

Instead of simply inventing the mathematical form of the gravitation field. Einstein fishes out the other unresolved question in the furthest depths of Newton's theory and combines the two questions: How can we describe the gravitational field? What is Newton's space? (What if Newton's space was nothing more than the gravitation field?)

The world is not made up of space + particles + electromagnetic field + gravitational field. The world is made up of particles + fields, and nothing else.

The spacetime is curved.

Einstein's only problem was to find the equations to make it concrete. How to describe this bending of spacetime? And here Einstein is lucky: the problem had already been solved by the mathematicians.

Carl Friedrich Gauss had written maths to describe curved surfaces, such as the surfaces of hills. Then he asked a talented student to generalize this math to curved spaces in N-dimensions. The student, Bernhard Riemann, produced a ponderous doctoral thesis of the kind that seems completely useless (See: Riemann curvature).

Mercury follows the trajectory predicted by Einstein, not the one predicted by Newton.

But it is not only space that curves: time does, too. Place a watch on the floor and another on a table: the one on the floor registers less passing of time than the one on the table.

The theory predicts that space ripples like the surface of the sea: the Gravitational Waves (See: Binary stars).

This rich and complex range of phenomena — bending of rays of light, modification of Newton's force, slowing down of clocks, black holes, gravitational waves, expansion of the universe, the Big Bang — follow from understanding that space is not a dull, fixed container but possesses its own dynamic, its own ‘physics’, just like the matter and the other fields it contains.

3.3 Mathematics or physics?

Einstein was no great mathematician. He struggled with maths. During the last year in which he was completing the construction of his theory, Einstein found himself competing with David Hilbert, one of the greatest mathematicians of all time. Hilbert grasped the idea and tried to overtake Einstein and be the first to write the correct equations of the new theory Einstein was slowly building. But at the end, Einstein found the right one. He had won the race.

“Every boy in the streets of Göttingen understands more about four-dimensional geometry than Einstein. Yet, it was Einstein who completed the task.” — David Hilbert.

Why? Because Einstein had a capacity to imagine how the world might be constructed, to ‘see’ it in his mind. The equations, for him, came afterwards; they were the language with which to make concrete his visions of reality.

3.4 The Cosmos

For thousands of years, men has asked themselves whether the universe was infinite, or had a limit.

Einstein finds a third way: the universe can be finite and at the same time have no boundary. Just as the surface of the Earth.

A 3-sphere: If I leave in a spacecraft and journey always in the same direction, I fly around the universe and eventually end up back on Earth.

However incredible it might seem, the same idea had already been conceived by another genius, from an entirely different cultural universe: Dante Alighieri, Italy's greatest poet.

How is it possible that Dante had an idea that sounds so modern? One possibility is due to the fact that Dante was writing well before Newton convinced everyone that the infinite space of the cosmos was the flat one of Euclidian geometry. Dante was free of the restraints upon our intuition we have as a result of our Newtonian schooling.

This example demonstrates how great science and great poetry are both visionary, and may even arrive at the same intuitions. Our culture is foolish to keep science and poetry separated: they are two tools to open our eyes to the complexity and beauty of the world.

Dante's 3-sphere is only an intuition within a dream. Einstein's 3-sphere has mathematical form and follows from the theory's equations. The effect of each is different. Dante moves us deeply, touching the sources of our emotions. Einstein opens a road towards the unsolved mysteries of our universe.

Chapter 4: Quanta

4.1 Albert again

For Max Planck, taking energy in finite-size packets was only a strange trick which happened to work for the calculation — that is, to reproduce laboratory measurements — but for utterly unclear reasons. Five years later it is Albert Einstein who comes to understand that Planck's packets of energy (the photons) are in fact real. This is the subject (the photoelectric effect) of the third of the three articles sent to the Annalen der Physik in 1905. And this is the true date of birth of quantum theory.

It is easy to understand things once someone has thought them through. The difficulty lies in thinking them through in the first place.

4.2 Niels, Werner and Paul

Colour is the speed at which Faraday's lines vibrate, and this is determined by the vibrations of the electric charges. Therefore, studying spectra, we can understand how electrons move around nuclei.

But then why does the light emitted by an atom not contain all colours, rather than just a few particular ones? Bohr finds a tentative solution. He realized that everything could be explained if the energy of electrons in atoms could only assume certain ‘quantized’ values.

Bohr makes the hypothesis that electrons can exist only at certain ‘special’ distances from the nucleus, the scale of which is determined by Planck's constant h. And that electrons can ‘leap’ between one orbit with the permitted energy to another (the ‘quantum leaps’).

Electrons don't always exist. They exist when they interact. They materialize in a place when they collide with something else. The quantum leaps from one orbit to another constitute their way of being real: an electron is a combination of leaps from one interaction to another.

In the end, it is another 25 years old who picks up the work initiated by Heisenberg, takes the new theory in his hands and constructs its entire forma and mathematical scaffolding: Paul Dirac.

We don't know with certainty where the electron will appear, but we can compute the probability that it will appear here or there. Chance operates at the atomic level.

4.3 Fields and particles are the same thing

After completing the general formulation of quantum mechanics, Dirac realizes that the theory can be directly applied to fields such as electromagnetic ones, and can be made consistent with special relativity. In doing this, Dirac discovers a profound simplification of our description of nature: the convergence between the notion of particles used by Newton and the notion of fields introduced by Faraday.

The general form of quantum theory compatible with special relativity is thus called quantum field theory. Particles are quanta of field, just as photons are quanta of light.

The world is not made up of fields and particles but of a single type of entity: the quantum field.

4.4 Quanta 1: Information is finite

Quantum mechanics has revealed three aspects of the nature of things: granularity, indeterminacy, and the relational structure of the world.

The first meaning of quantum mechanics is the existence of a limit to the information that can exist within a system: a limit to the number of distinguishable states in which a system can be. This limitation upon infinity is the first central aspect of the theory. Planck's constant h measures the elementary scale of this granularity.

4.5 Quanta 2: Indeterminacy

Quantum mechanics introduces an elementary indeterminacy to the heart of the world. The future is genuinely unpredictable.

The more we look at the detail of the world, the less constant it is. The world is not made up of tiny pebbles. It is a world of vibrations, a continuous fluctuation, a microscopic swarming of fleeting micro-events.

Democritus assumed (just like Newton) that the movement of atoms was rigorously determined by their collisions. But his successor, Epicurus, corrects the determinism of the master and introduces into the notion of indeterminacy.

How do we compute the probability that an electron in A position will reappear in final position B? In the 1950s, Richard Feynman found a method of making this calculation: consider all possible trajectories from A to B. Each trajectory determines a number. The probability is obtained from the sum of all these numbers (See: Feynman's sum over paths or Feynman's integral)

4.6 Quanta 3: Reality is relational

Speed is not a property of an object on its own: it is the property of the motion of an object with respect to another object. Einstein extended the notion of relativity to time. Quantum mechanics extends this relativity in a radical way: all variable aspects of an object exist only in relation to other objects.

The world of quantum mechanics is not a world of objects: it is a world of events. The events of nature are always interactions. All events of a system occur in relation to another system.

4.7 But do we really understand?

The obscurity of the theory is not the fault of quantum mechanics but, rather, is due to the limited capacity or our imagination. When we try to ‘see’ the quantum world, we are rather like moles used to living underground to whom someone is trying to describe the Himalayas. Or like the men imprisoned at the back of Plato's cave.

Chapter 5: Spacetime is Quantum

Between the two theories (general relativity and quantum mechanics). They cannot both be true, at least not in their present forms, because they appear to contradict each other. In general relativity, the world is a curved spacetime where everything is continuous; in the quantum mechanics, the world is a flat one where discrete quanta of energy leap and interact.

We do not know how time and space behave at very small scale. Quantum mechanics cannot deal with the curvature of spacetime, and general relativity cannot account for quanta. This is the problem of quantum gravity.

It isn't the first time that physics has found itself faced with two highly successful but apparently contradictory theories: Newton discovered universal gravity by combining Galileo's physics of how things move on Earth with Kepler's physics. Maxwell and Faraday found the equations of electromagnetism by bringing together what was know about electricity and what was known about magnetism. Einstein found special relativity in order to resolve the conflict between Newton's mechanics and Maxwell's electromagnetism — and then general relativity in order to resolve the resulting conflict between Newton's mechanics and his own special relativity.

Can we construct a conceptual structure compatible with what we have learned about the world with both theories?

5.1 Matvei

The Planck length is an extremely small unit of length that is defined by combining three fundamental physical constants: the speed of light, the gravitational constant, and the reduced Planck constant. The minimum size of a particle before it falls into its own black hole. If we enlarged a walnut shell until it had become as big as the whole observable universe, we would still not see the Planck length.

Matvei, the year after having been the first to understand that our ideas on space and time had to change in a radical way, is arrested by Stalin's police and condemned to death, 18 Feb 1938. He is 30 years old.

5.2 John

Electrons and Photons are quanta in space; quantum gravity is something else: it isn't enough to describe ‘gravitons’ moving in space, it is space itself that has to be quantized.

Space as imagined by John Wheeler: On our scale, immensely larger than the Planck length, space is smooth. If we move down to the Planck scale, it shatters and foams.

Chapter 6: Quanta Of Space

The closed line that appear in the solutions of the Wheeler-DeWitt equation are Faraday lines of the gravitational field. The discrete structure of space (See: Loop theory)

The spectrum of volume is discrete: An atoms of space.

Achilles does not need an infinite number of steps to reach the tortoise because, in a space made of grains of finite size, infinitely small steps do not exist.

The quantum states of space can be visualized using Graph theory (nodes = grain of space, links = adjacent particles). The graphs are characterized by a volume v for every node and a half-integer j for every line. We called this a spin network.

Quantum mechanics is more than granularity. There is also the fact that evolution is probabilistic. And there is the fact that what matters is not how things are, but rather how they interact.

Chapter 7: Time Does Not Exist

Einstein showed that we cannot separate time and space, that we must think of them together as a single whole: spacetime.

The moment we take quantum mechanics into account, we recognize that time, too, must have those aspects of probabilistic indeterminacy, granularity and relationality which are common to all of reality.

7.1 Time is not what we think it is

The closer you get to the Earth, where gravity is more intense, the slower time passes. Every object in the universe has its own time running, at a pace determined by the local gravitational field. (Time as a localized phenomenon)

But even a localized time no longer works when we take the quantum nature of the gravitational field into account. Quantum events are no longer ordered by the passage of time at a Plank scale. Time, in a sense, ceases to exist.

The absence of the variable time does not imply that everything is immobile and change does not happen. It means that change is ubiquitous.

7.2 The candle chandelier and the pulse

Time appears in most equations of classic physics.

When Galileo lived there were no accurate clocks. Galileo himself discovered a key to making precise timepieces: pendulum clock.

How could Galileo know that his own pulse-beats all lasted for the same amount of time? In reality, we never measure time itself; we always measure the physical variables A, B, C... (oscillations, beats, and many other things) and compare one variable with another.

The point is that it is useful to imagine that a variable t exists, even if we cannot measure it directly. From this we can derive how the variables change in relation to each other and compare this prediction with what we observe in the world.

Newton asserts explicitly in his book that we can't ever measure the true time t but, if we assume that it exists, we can set up an effective frameworks to describe nature.

Physics without time (Quantum gravity) is physics in which we speak only of the pulse and the chandelier, without mentioning time. Things change only in relation to one another.

7.3 Spacetime sushi

Someone once claimed that a theory isn't credible if its equations cannot be summarized on a T-shirt.

Space is a spin network whose nodes represent its elementary grains, and whose links describe their proximity relations. Spacetime is generated by processes in which these spin networks transform into one another, and these processes are described by sums over spinfoams. A spinfoam represents a history of spin network, hence a granular spacetime where the nodes of the graph combine and separate. Every cubic centimetre of space, and every second that passed, is the result of this dancing foam of extremely small quanta.

7.4 What is the world made of?

The world is made entirely from quantum fields (Covariant quantum fields).

It may appear strange and difficult to think of discrete elementary entities not in space and time, but weaving space and time with their relations. But how strange it must have seemed to listen to Anaximander, when he claimed that beneath our feet there was only the same sky that we can see above our heads? Or to Aristarchus, when he tried to measure the distance from the Earth of the Moon and the Sun, discovering that they are extremely distant, and are therefore not the size of little balls, but gigantic. Or to Hubble, when he realized that the small, diaphanous clouds between stars are vast seas of immensely distant stars...

Chapter 8: Beyond The Big Bang

8.1 The master

In 1927, a young Belgian scientist, a Catholic priest (Lemaitre), studies Einstein's equations and realizes that they predict the universe must expand or contract. He looks for astronomical data and test it (See: The Big Bang).

Even the greatest make mistakes and are prey to preconceived ideas. Einstein was scepical about the expansion of the universe. He had grown up thinking that the universe was fixed. Lemaitre met Einstein and tried to dissuade him. Einstein resisted. Later, Einstein was obliged to recognize that Lemaitre was the one who was actually right.

The same thing happened again. Einstein had introduced the cosmological constant (the small modification of his equations), in the hope of rendering the compatible with a static universe. When he had to acknowledge that the universe is not static, he turned against the constant. Once again Lemaitre tried to persuade him to change his mind, and he was right.

8.2 Quantum Cosmology

If we take quantum mechanics into account (Big Bang Theory), the universe cannot be indefinitely squashed. A quantum repulsion makes it rebound. A contracting universe does not collapse down to a point: it bounces back and begins to expand, as if it were emerging from a cosmic explosion (Big Bounce Theory).

Chapter 9: Empirical Confirmation?

Science works because, after hypotheses and reasoning, after intuitions and visions, after equations and calculations, we can check weather we have done well or not: the theory gives predictions about things we have not yet observed, and we can check whether these are correct, or not.

Science is not about making measurable prediction. Verifiable quantitative predictions are instruments to validate hypotheses. The objective to scientific research is not just to arrive at predictions: it is to understand how the world functions; to construct and develop an image of the world, a conceptual structure to enable us to think about it.

A theory lacking empirical confirmation is a theory which has not yet passed its exams. Exams never end, and a theory is not completely confirmed by one, two or three experiments. But it progressively acquires credibility, stage by stage, as its predictions are revealed to be correct.

The importance of experimental proof, on the other hand, does not mean that, without new experimental data, we cannot make advances. What Copernicus, Newton, Einstein and many others did was to build upon pre-existing theories which synthesized empirical knowledge across vast field of nature, and to find a way of combining and rethinking them to improve the general picture.

We must distinguish between clues and strong evidence. Clues put us on the right path towards a correct theory. Strong evidence is that which subsequently allows to trust whether the theory we have built is a good one or not. Without clues, we search in the wrong directions. Without evidence, a theory is not reliable.

9.1 Signals from nature

Many theoretical physicists are today looking for new theories by picking arbitrary hypotheses. ‘Let us imagine that...’ I don't think that this way of doing science has ever produced good results. Our fantasy is too limited to imagine how the world may be made, unless we search for inspiration in the traces we have at our disposal. The traces that we have - our clues - are either the theories which have been successful, or new experimental data, nothing else. It is in this data and in these theories that we must try to uncover what we have been unable yet to imagine.

Chapter 10: Quantum Black Holes

The black hole at the centre of our own galaxy is currently being studied in detail. It has a mass a million times greater than our Sun.

For a black hole, the past in the outside; the future is the inside. A rocket could stay positioned at a fixed distance from the sphere, which is called the horizon of the black hole. To do so it needs to keep its engines firing intensely, to resist the gravitational pull. If the rocket stays near enough to the horizon for one hour, and then moves away, it would then find that, outside, in the meantime, centuries have passed.

Traveling to the past is difficult, but traveling to the future is easy. Black hole is a shortcut to the distant future.

Early in the 1970s, Stephen Hawking theoretically deduced that black holes are ‘hot’. They behave like hot bodies: they emit heat. In doing so, they lose energy and hence mass (since energy and mass are the same thing), becoming progressively smaller. They ‘evaporate.’

What are the elementary ‘atom’ that vibrate, making a black hole hot? Hawking left this problem unanswered. It is possible to answer using loop theory: the heat is the result of the microscopic vibrations of the individual atoms of space.

Chapter 11: The End Of Infinity

Quantum gravity is the discovery that no infinitely small point exists. There is a lower limit to the divisibility of space. Nothing exists which is smaller than the Planck scale.

Quantum gravity places a limit to infinity and cures the pathological singularities of general relativity.

Putting a limit to infinity is a recurrent theme in modern physics. Special relativity: A maximum velocity exists, Quantum mechanics: A minimum of information exists, Quantum gravity: A minimum length exists.

The existence of these minimum and maximum values for length, velocity and action fixes a natural system of units. We have a natural system of fundamental unities from which the others follow. The unity of time is the time that light takes to cover the Planck length, and so on. The natural unities are commonly used in research on quantum gravity.

What we call infinite often is nothing more than something which we have not yet counted. ‘Infinite’ is the name that we give to what we do no yet know.

Nature appears to be telling us that there is nothing truly infinite. The only truly infinite thing is our ignorance.

Chapter 12: Information

What is information? The scientific notion of information was defined with clarity in 1948, by the American mathematician and engineer Claude Shannon: information is the measure of the number of possible alternatives for something. E.g. six faces die N = 6, date of the year N = 365.

Instead of N, scientist measure information in terms of quality called S, for ‘Shannon information.’ S = log_2{N}. This unit of measurement is called ‘bit.’

Why is the notion of information useful? For a subtle reason: because it measures the ability of one physical system to communicate with another physical system.

The world isn't just a network of colliding atoms: it is also a network of correlations between sets of atoms, a network of real reciprocal information between physical systems.

In order to grasp the basic grammar of the world, we need to merge three basic ingredients, not just two: not just general relativity and quantum mechanics, but also the information theory.

12.1 Thermal time

Time plays no role at the fundamental level of physics. It is not necessary to use the notion of time to describe physics.

There are many everyday notions which no longer have any role in the fundamental equations; for example, the notions of ‘up’ and ‘down’ (the direction towards gravitational pull), or ‘hot’ and ‘cold.’ (the average speed of single constituents)

How can we recover the notions of our everyday experience? How do they emerge, in our specific context?

Something similar must apply to ‘time.’ What does the passage of time mean, if time plays no part in the fundamental description of the world? The answer is simple. The origin of time may be similar to that of heat: it comes from averages of many microscopic variables. The characteristic of time is that it is an irreversible phenomena. Mechanical phenomena - ones that don't involve heat - are reversible. It is always heat and only heat that distinguishes the past from the future.

Thermal time: How heat produces time?

Understanding the world better often entails going against intuition.

Chapter 13: Mystery

The awareness of our ignorance is the heart of scientific thinking. We are not certain of all which we suspect. To learn something, it is necessary to have the courage to accept that what we think we know, including our most rooted convictions, may be wrong, or at least naive: shadows on the walls of Plato's cave.

Science is born from this act of humility: not trusting blindly in our past knowledge and our intuition.

A scientist is someone who lives immersed in the awareness of our deep ignorance, in direct contact with our own innumerable limits, with the limits of our understanding. Scientist is an explorer.

Science is not reliable because it provides certainty. It is reliable because it provides us with the best answers we have at present. And it is reliability that we need, not certainty. The search for knowledge is not nourished by certainty: it is nourished by a radical distrust in certainty.

This means no giving credence to those who say they are in possession of the truth. For this reason, science and religion frequently find themselves on a collision course. Not because science pretends to know ultimate answers but precisely for the opposite reason.

To seek to look further, to go further, seems to me to be one of the splendid things which gives sense to life. The curiosity to learn, to discover, to look over the next hill, the desire to taste the apple: these are the things which make us human.