The Science of Can and Can't: a Physicist's Journey Through the Land of Counterfactuals
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
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
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
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
The counterfactuals that matter to science and physics, and that have so far been neglected, are facts about what could or could not be made to happen to physical systems; about what is possible or impossible. They are fundamental because they express essential features of the laws of physics —the rules that govern every system in the universe.
Knowledge in this sense does not have to be known by anyone: the moth does not know its wings are black. ‘Knowledge’ merely denotes a particular kind of information, which has the capacity to perpetuate itself and stay embodied in physical systems—in this case by encoding some facts about the environment.
A physical theory, therefore, is not just the set of its formulae, such as E = mc2, nor is it just the collection of its testable predictions; it is a conjectured explanation, which includes, for example, the informal descriptions of what E, m, and c are in that formula, and why they are related in that way.
Paul Davies’s The Goldilocks Enigma
The computer performed a computation to find the factors of, say, the number 15, and the ‘on’ transistor is part of the encoding of the output (3 and 5). A reductionist would discard the latter explanation as ‘less fundamental’ (because, after all, “factoring a number is nothing but electric currents in the computer”). Reductionism ultimately denies that the computational description is necessary, though some reductionists may accept that it is helpful as a manner of discourse. But this is, of course, nonsense. Both explanations are essential to understand what is happening; they refer to different, autonomous levels of explanation, which do not implicate one another. By ignoring one of them, one misses something crucial about reality.
Levels of explanation work together like layers in a cake. It is impossible to get the cake’s full flavour by ignoring the top layers and just sticking to the base. In this book you will be able to grasp the flavour of the full cake, by being introduced to counterfactuals
The appearance of design is about what a particular aggregate of atoms can do when provided with appropriate inputs; resilience is the capability of a system to preserve itself. Information, which is about the possibility of copying certain patterns, is another counterfactual concept that is central to our technology
Knowledge, too, which is crucial to understanding phenomena like artificial intelligence, is defined by a counterfactual property: it is information that can keep itself in existence.
teachers forget to tell you what the best bits are; sometimes they focus on the wrong things. Some teachers are all absorbed by box-ticking: do this, do that; make sure the syllabus is covered; follow the government’s directives; blah, blah, blah. So they forget to tell you that there’s glittering stuff and where to find it and how to see
Teachers forget to tell you what the best bits are; sometimes they focus on the wrong things. Some teachers are all absorbed by box-ticking: do this, do that; make sure the syllabus is covered; follow the government’s directives; blah, blah, blah. So they forget to tell you that there’s glittering stuff and where to find it and how to see it.
Teachers are all absorbed by box-ticking: do this, do that; make sure the syllabus is covered; follow the government’s directives; blah, blah, blah. So they forget to tell you that there’s glittering stuff and where to find it and how to see it
The dynamical laws really don’t tell you the whole story; one, because they may not be the ultimate dynamical laws
All you need is a third computer that, when given in input the numbers x and y and the command ‘Add’, sends them to the adder; whereas when it receives x and y and the command ‘Multiply’, sends those two inputs to the multiplier. Together, these three entities form a more general computer that can perform both addition and multiplication. Proceeding in this fashion, nothing stops you from imagining a computer that has all the physically possible computations in its repertoire. It is a universal computer: it can be programmed to perform any calculation that is physically allowed by certain physical laws. It so happens that the laws of physics of our universe do not forbid a universal computer. Computers such as our laptops and personal computers are universal in this sense
A universe where the interoperability property is violated would not have universal computers. This fact is a demonstration of how far-reaching the consequences of the interoperability of information can be.
antum Information Where I explain how systems capable of carrying quantum information are information media with two additional counterfactual properties: the impossibility of performing certain copylike transformations and reversibility; where you encounter the universal quantum computer—a universal computer that harnesses the full power of quantum theory
A universal quantum computer is a universal computer (i.e., a computer that is capable of performing every computation that is allowed by given laws of physics.
Bohr complementarity displayed by quantum systems: the fact that different properties of quantum systems (such as energy and position, or P and PS) cannot be simultaneously measured to arbitrarily high accuracy.
For instance, the velocity and the position of an electron around the nucleus of an atom are both observables, but they cannot be simultaneously measured to the same accuracy. When the velocity of the electron can be measured accurately, its position cannot be. In the early days of quantum theory, this fact gained the name ‘Heisenberg uncertainty principle’. Later, it became known as a special case of the ‘no-cloning’ theorem for general quantum observables.
A quantum information medium is a system with the following counterfactual properties: 1. It has at least two information variables (such as P and PS) that are impossible to copy simultaneously to arbitrarily high accuracy (non-copiability of information variables). 2. It must be possible to reverse all the transformations involving these variables (reversibility)
Well, quantum theory tells us that it is like that. In other words, it tells us that locally inaccessible information is possible, and how to create it—it involves a quantum phenomenon called ‘entanglement’. And that is all a consequence of constraints about what cannot happen in physical systems—in this case the impossibility of copying.
Know ledge Where I explain that any transformation that occurs reliably requires a generalised catalyst— an entity that is capable of performing the transformation and retains the ability to cause it again; that any catalyst must contain an abstract catalyst, which consists of knowledge (information capable of self-preservation
Most changes, or transformations, that happen reliably around us require something to stay unchanged
Chemical catalysts are entities that make a chemical reaction happen more reliably and faster
shall use ‘catalyst’ to indicate systems that can cause a transformation and retain the property to do so
I shall use ‘catalyst’ to indicate systems that can cause a transformation and retain the property to do so
The recipe for a fully fledged aircraft is what allows the construction of the aircraft to happen reliably, because the final product is checked against the procedure
The recipe for a fully fledged aircraft is what allows the construction of the aircraft to happen reliably, because the final product is checked against the procedure until it meets the criteria set by the quality control of the company.
The laws of physics do not contain any protocol to preserve or create complex entities such as aircrafts, or even wings or things of that type. Leave an aircraft for a while in a desert, without being repaired or checked, and it will soon become unfit to fly. As I said in chapter 1, the only things that the laws of physics preserve directly are elementary components and interactions, and elementary symmetries.
Most transformations that are possible in the physical world must occur via a catalyst that enables them. I have also noted that all catalysts must contain an abstract catalyst, which is itself made of knowledge.
Knowledge is defined entirely via counterfactuals: it is information that is capable of remaining instantiated in physical systems. Unlike most definitions of knowledge, the good thing about this one
capable of remaining instantiated in physical systems
Knowledge is defined entirely via counterfactuals: it is information that is capable of remaining instantiated in physical systems. Unlike most definitions of knowledge, the good thing about this one
Knowledge is defined entirely via counterfactuals: it is information that is capable of remaining instantiated in physical systems. Unlike most definitions of knowledge, the good thing about this one
Knowledge is defined entirely via counterfactuals: it is information that is capable of remaining instantiated in physical systems. Unlike most definitions of knowledge, the good thing about this one
Knowledge is defined entirely via counterfactuals: it is information that is capable of remaining instantiated in physical systems.
rk and Heat Where I discuss the conservation of energy as a counterfactual principle about impossibility; three different kinds of irreversibility in physics—statistical, forgetful, and counterfactual; where I provide a counterfactual second law, based on an exact distinction between work and heat; and where you encounter the universal constructor, a machine that can perform all transformations that are physically possible
The conservation of energy as a counterfactual principle about impossibility; three different kinds of irreversibility in physics—statistical, forgetful, and counterfactual; where I provide a counterfactual second law, based on an exact distinction between work and heat; and where you encounter the universal constructor, a machine that can perform all transformations that are physically possible
The irreversibility requirement of the second law brutally clashes with the laws of motion ruling the elementary constituents of matter. Remember? I said in chapter 4 that the laws of quantum theory are reversible: if they allow for a transformation, the reverse transformation must also be possible. The laws of general relativity (the other most accurate description of physical reality we possess) are reversible, too. If there is a trajectory that takes a system from A to B, there must also be one that takes it from B to A. Microscopic constituents of matter must operate in this reversible manner because they obey these laws of motion. The problem, then, is: How can the second law require that some energy transfers are irreversible and be compatible with the reversibility of the laws of motion
The irreversibility requirement of the second law brutally clashes with the laws of motion ruling the elementary constituents of matter. Remember? I said in chapter 4 that the laws of quantum theory are reversible: if they allow for a transformation, the reverse transformation must also be possible. The laws of general relativity (the other most accurate description of physical reality we possess) are reversible, too. If there is a trajectory that takes a system from A to B, there must also be one that takes it from B to A. Microscopic constituents of matter must operate in this reversible manner because they obey these laws of motion. The problem, then, is: How can the second law require that some energy transfers are irreversible and be compatible with the reversibility of the laws of motion?
Information and knowledge, for example, have been traditionally considered as mere abstractions—as things that do not belong to the physical world. However, by considering the counterfactual properties of physical systems that enable information and knowledge, one refutes this idea: because whether or not a physical system has those properties is set precisely by the laws of physics.
The other fact is that embracing counterfactuals allows one to express exact laws about entities traditionally considered as approximate (because these laws refer directly to the macroscopic world), such as information, energy, heat, and work.
As I have explained time and again, the traditional conception of physics cannot express counterfactual properties. The traditional conception can refer to the state of the switch—either ON or OFF—at any given time, and can predict what the state will be at a later time, and why. However, a statement of this kind does not tell us anything about what transformations are possible or impossible on the switch.
I said that knowledge is a particular type of information, with the counterfactual property of being resilient—it can cause itself to remain instantiated in physical systems. I also explained that we do not know exactly how it is created, but we know that it can arise out of no-knowledge via the process of natural selection, and that another process for creating new knowledge is what happens in the brain when we think.
Creativity is one of the main tools we have to form stuff that can last. If one is interested in making the good outcomes of our civilisation last and improve, then understanding how creativity is nurtured—both at the individual and at the societal level—is essential
“Ah, one more thing”, said Aristotle. “I wish to give you this.” With those words, he handed Alexander a large scroll that he had produced mysteriously from his tunic. “What is it?” the boy asked with surprise, holding the codex in his hands as if it were a sacred token from the gods. “It is a copy of the Iliad by Homer—my annotated copy.” Aristotle smiled. “It is one of the finest pieces of poetry about knowledge, war, and love, and all those things that a future king like you may want to know. Take it, Alexander, it’s yours.