As I shall explain in this book, some of these things, such as information, heat, and work, already have some explanation in physics, but it is insufficient: it is only approximate, unlike more fundamental theories of physics, such as quantum theory and general relativity. Some others, such as knowledge creation, have no explanation yet. All these entities must be understood, without approxima­tions, for science to make new progress in all sorts of fields -- from physics to biology, computer science, and even arti­ficial intelligence. Counterfactuals are essential to understand them all."

In certain areas, it is no longer the case. The assumption that all fundamental explanations in science must be expressed only in terms of what happens, with little or no refer­ence to counterfactuals, is now getting in the way of progress. For counterfactuals are essential to a number of things that are cur­rently explained only vaguely in science, or not explained at all. Counterfactuals are central to an exact, unified theory of heat, work, and information (both classical and quantum); to explain mat­ters such as the appearance of design in living things; and to a sci­entific explanation.

However, by thinking hard enough, we can come up with more and better ways of performing a pos­sible transformation -- for instance, that of constructing a steam engine -- which can then improve over time. "In the prevailing scientific worldview, counterfactual proper­ties of physical systems are unfairly regarded as second-class citi­zens, or even excluded altogether. Why? It is because of a deep misconception, which, paradoxically, originated within my own field, theoretical physics.

A pioneer in the field, Chiara Marletto explores the extraordinary promise that this revolutionary approach holds for confronting existing technological challenges, from delivering next-generation processors to designing AI. But by contemplating the possible as well as the actual, Marletto goes deeper still, showing how counterfactuals can break down barriers to knowledge and form a more complete, abundant and rewarding picture of the universe itself.

"If you could soar high in the sky, as red kites often do in search of prey, and look down at the domain of all things known and yet to be known, you would see something very curious: a vast class of things that science has so far almost entirely neglected. These things are central to our understanding of physical reality, both at the everyday level and at the level of the most fundamental phenomena in physics -- yet they have traditionally been regarded as impossible to incorporate into fundamental scientific explana­tions.

Things that have not happened -- but could happen -- are the things that constitute the world of counterfactuals, a neglected area of scientific theory. A luminous guide to how the radical new science of counterfactuals can reveal the full scope of our universe. There is a vast class of properties, which science has so far neglected, that relate not only to what is true the actual but to what could be true: the counterfactual. This is the science of can and can't.

The world of Counterfactuals

The computer may never be so programmed; but the fact that it could is an essential fact about it, without which it would not qualify as a computer. The counterfactuals that matter to science and physics, so far neglected, are facts about what could or could not be made to happen to physical systems; what is possible or impossible. They are fundamental, they express essential features of the laws of physics -- the rules that govern every system in the universe. For instance, a counterfactual property imposed by the laws of physics is that it is impossible to build a perpetual motion machine.

"Another significant counterfactual property of physical sys­tems, central to thermodynamics, is that a steam engine is possible. A steam engine is a device that transforms energy of one sort into energy of a different sort, and it can perform useful tasks, such as moving a piston, without ever violating that principle of conserva­tion of energy. Actual steam engines (those that have been built so far) are factual properties of our universe. The possibility of build­ing a steam engine, which existed long before the first one was actually built, is a counterfactual.

The misconception is that once you have specified everything that exists in the physical world and what happens to it, then you have explained every­thing that can be explained. Does that sound indisputable? For it is easy to get drawn into this way of thinking with­out ever realising that one has swallowed a number of substantive assumptions that are unwarranted. You can't explain what a computer is solely by specifying the computation it is actually per­forming at a given time; you need to explain what the possible com­putations it could perform are, if it were programmed in possible ways.

The box may be never found; and laden with significance. It would signify, for instance, that a civilization visited the planet, and much about its degree of sophistication. To further grasp the importance of counterfactual properties, and their difference from actual properties, imagine a computer programmed to produce on its display a string of zeroes. That is a factual property of the computer, to do with its actual state -- with what is. The fact that it could be reprogrammed to output other strings is a counterfactual property of the computer.

They are facts not about what is -- the 'actual' -- but about what could or could not be. In order to distinguish them from the ac­tual, they are called counterfactuals. Suppose that some future space mission visited a remote planet in another solar system left a stainless-steel box containing among other things the critical edition of, say, William Blake's poems. That the poetry book is subsequently sit­ting somewhere on that planet is a factual property of it. That the words in it could be read is a counterfactual property, which is true regardless of whether those words will ever be read.

A perpetual motion machine is not simply an object that moves forever once set into motion: it must also gener­ate some useful sort of motion. If this device could exist, it would produce energy out of no energy. It could be harnessed to make your car run forever without using fuel of any sort. Any sequence of transformations turning something without energy into something with energy, without depleting any energy supply, is impos­sible in our universe: it could not be made to happen, because of a fundamental law that physicists call the principle of conservation of energy.

The fundamental types of counterfactuals that occur in physics are of two kinds: one is the impossibility of performing a transformation (building a perpetual motion machine); the other is the possibility of performing a transformation (building a steam engine). Both are cardinal properties of the laws of phys­ics; and, among other things, they have crucial implications for our endeavours: no matter how hard we try, or how ingeniously we think, we cannot bring about transformations that the laws of physics declare to be impossible -- for example, creating a per­petual motion machine.

More generally, you can't explain the presence of a lifeboat aboard a pirate ship only in terms of an actual shipwreck. Everyone knows that the lifeboat is there because of a shipwreck that could happen (a counterfactual explanation). And that would still be the reason even if the ship never did sink! Despite regarding counterfactuals as not fundamental, science has been making rapid, relentless progress, for example, by devel­oping new powerful theories of fundamental physics, such as quantum theory and Einstein's general relativity; and novel expla­nations in biology.

A luminous guide to how the radical new science of counterfactuals can reveal the full scope of our universe There is a vast class of properties, which science has so far neglected, that relate not only to what is true - the actual - but to what could be true: the counterfactual. This is the science of can and can't. A pioneer in the field, Chiara Marletto explores the extraordinary promise that this revolutionary approach holds for confronting existing technological challenges, from delivering next-generation processors to designing AI. But by contemplating the possible as well as the actual, Marletto goes deeper still, showing how counterfactuals can break down barriers to knowledge and form a more complete, abundant and rewarding picture of the universe itself.

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A luminous guide to how the radical new science of counterfactuals can reveal the full scope of our universe There is a vast class of properties, which science has so far neglected, that relate not only to what is true - the actual - but to what could be true: the counterfactual. This is the science of can and can't. A pioneer in the field, Chiara Marletto explores the extraordinary promise that this revolutionary approach holds for confronting existing technological challenges, from delivering next-generation processors to designing AI. But by contemplating the possible as well as the actual, Marletto goes deeper still, showing how counterfactuals can break down barriers to knowledge and form a more complete, abundant and rewarding picture of the universe itself.

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4. Albert Einstein called German mathematician Emmy Noether a creative mathematical genius.