1. Evolution proceeds by natural selection
Natural selection is one of the greatest ideas of science, for it is so simple to express but has consequences of boundless complexity. That organisms accumulate changes as they adapt to their environment is so simple to express, but it results in the biosphere. Theodosius Dobzhansky is credited with the penetrating remark that nothing can be understood in biology except in the light of evolution, and Darwin identified the mechanism. Of course, there are puzzles, but in such an all-pervasive theory of the natural world that is no more than one should expect. One of the great puzzles is the origin of sex, for the complexity of the mechanism required to achieve the doubtful procedure of mingling one's genes with those of a stranger suggests that there must be a mighty pay-off. And if you are seeking the joy not of sex but of abstraction, then you can rarify the principle of natural selection down from species (whatever that is), to individuals, down past genes, and arrive at deep understanding by regarding evolution as the propagation of pure information.
2. Inheritance is encoded in DNA
Not so much an idea, but one of the great rationalisations of all time. The great goal of understanding is the mechanism of achieving the kind of immortality offered by reproduction. It is not we who are extended into eternity but that extraordinary molecule, DNA, several metres of which are coiled into every cell of our body. The cracking of the genetic code is almost as great an achievement as the disentangling of the double-helical structure, and now we can read our composition as a general can read an order of battle. The social consequences, too, are incalculable, for they span from saving and capturing the born to modifying the unborn.
3. Energy is conserved
Everyone uses it, everyone thinks they know what it is, but few can say what it really is. Poets sang of it: Sir Phillip Sidney praised the energy of another's writing but failed to recognise it as an aspect of the musket ball that later killed him. Newton knew nothing of energy, for his focus was force, but the greater abstraction of energy took hold in the middle of the 19th century and is the cement of causality down to today. That it is conserved, that it can be neither created nor destroyed, but merely transformed from one form to another or shipped from place to place, has deep implications about the symmetries of space and time. The Victorian physicists who established the concept unwittingly were discovering the shape of time.
4. All change is consequence of the tendency of energy and matter to disperse
No other law of science has given such powerful wings to humanity's aspirations as the second law of thermodynamics. For me, this is the paramount law of nature, for it embodies the explanation of why anything happens: why gases expand, why hot things cool, why proteins are built, and why opinions are formed. It is the origin of understanding the deep structure of change, and showing how a slide into universal corruption can have exquisite local consequences. It is the spring of all change, of evil, good, and daily life. Evolution is driven by the second law, as are all the events that surround us. But, like all great ideas, the idea at the kernel of the law is extraordinarily simple. This exquisite law reveals the potency of simplicity, yet it came from the contemplation of a steaming, leaking, creaking, wheezing, hulking steam engine. Such is the reach of careful thought.
5. Matter is atomic
A chemist's knife cuts into matter only so far, to the point that the particles of matter, though still cuttable, are survivors in reactions and retain the personalities that render them as recognisable elements. Yet the elements are not a random patchwork of unrelated entities: they form families and show a periodicity of properties that recur like the notes of a musical scale. The periodic table is a summary of these relationships and is, in fact, a manifestation of a deep symmetry of nature. This table was once just an empirical compilation: we now know, though, that a few simple ideas account for the structures of atoms, and that when those ideas are pursued, we see the structure of the table, chemistry's most enduring contribution to our understanding of matter and the magic that chemists can do with it.
6. Symmetry limits, guides, and drives
We saw that the conservation of energy is a manifestation of the shape of time. That is the tip of the iceberg of symmetry, for as we pursue beauty quantitatively we discover that other conservation laws reveal the shape of space. As we leave behind the imaginable symmetries of space and time and enter the internal world of particles we discover symmetries that are no longer tangible but, suitably interpreted, result in the forces of the world. Not only that, but as we pick apart atoms into ever more fundamental particles, so we discover that they are manifestations of symmetry. The very stuff of spacetime becomes comprehensible if we let slip our grip on convention and think about the symmetry of spacetimes of large numbers of dimensions, some of which were caught napping when the universe formed and forever remain unfurled. Quantitative beauty, broken a little by reality, lies at the heart of matter.
7. Waves behave like particles and particles behave like waves
No other theory of matter and radiation has ever proved as accurate in its predictions as quantum theory, in which particles and waves blend together and energy can be transferred only in packets. The trouble with the theory, though, is that no one understands it. However, by listening to what it says, and not trying to force on to its interpretation our classically conditioned expectations, we can see that quantum theory presents an awesomely simple picture of the world. That does not mean that there are no problems: some have tried to cobble together a pseudo-classical version, in which there are agents at work that lie beyond the reach of the theory; others have shown that what were once philosophical speculations can be resolved by that most potent tool, experiment. Quantum theory is extraordinary in its ability to reach successfully wherever it stretches, and totally transforms our vision of the world.
8. The universe is expanding
Nowhere else in science is grandeur more coupled with humility than in the realisation that the universe is expanding. The grandeur stems from the ability of our seemingly puny brains to discover that the universe appears to have had a beginning; the humility from the realisation of our own insignificance in the order of things, perhaps to the point not merely of being inhabitants of a planet near an insignificant star at an insignificant position in an insignificant galaxy, but perhaps even to being inhabitants of an insignificant universe among an infinity of others. But our brains can reach back and unearth the events that took place as the universe came into being - when in conventional human terms events took place in the twinkling of an eye, but when viewed properly were astonishingly slow. And the applecart is upset here too, when we realise that the inception of the universe was more a burst of spaghetti than an explosion of semolina.
9. Spacetime is curved by matter
Einstein's extraordinary contribution to human understanding boils down to exposing the power of geometry. By simple reflections on some crucial experiments we are led to fuse space with time and to think in terms of their union, spacetime. We can understand the origin of the best known equation in science, E = mc2, in terms of the geometry of spacetime. Thus we begin to see that the tides are nothing more than the sweep of geometry over the surface of the Earth: Canute could not keep geometry at bay. The grasp of matter on geometry allows us to peer into the future and comprehend that we have the amazing luck to be alive between two episodes of absolute bleakness - first when there was absolutely nothing, and then when there will be only dead flat spacetime. The theory is incomplete, for quantum theory, although flirting with gravity, has not yet married it; but we can begin to discern the extraordinary depth of understanding that will emerge once that marriage has been achieved.
10. If arithmetic is consistent, then it is incomplete
The most remarkable feature of the universe is that one product of the human mind, mathematics, appears to be the perfect language for elucidating and comprehending it. Einstein wondered at the fact that the most incomprehensible thing about the universe is that it is comprehensible. But what is mathematics, and does it fizzle out when pressed too far? Is mathematics the epitome of abstraction, or is it a tool for mining spacetime for what already exists? If mathematics does fizzle out, then this queen of languages cannot perhaps embrace all the questions we want to ask. Gödel's theorem does indeed circumscribe its potency, so this most abstract of all the sciences - if it is a science - might be limited in what it can reveal about the structure of any formalised system of knowledge.
· Peter Atkins's book, Galileo's Finger: the ten great ideas of science, is published on March 13 by Oxford University Press. Buy Galileo's Finger at Amazon.co.uk