Information is non-physical: The rules connecting representation and meaning do not obey the laws of physics

1. Introduction

Living in the information age, people receive and send all kinds of information every day. Ironically, although numerous papers on information research have been published, the nature of information has always been a controversial topic in the science and technology community.

Since 1991, Landauer [1–4] has claimed that information is physical in a series of papers with titles such as ‘Information is physical’, ‘The physical nature of information’, ‘Information is a physical entity’ and ‘Information is inevitably physical’. Since then, the idea of information as a physical component of the universe has been widely adopted in the scientific community, and many scientists regard ‘information is physical’ as a dictum. They stressed that all information processes, namely, the generation, encoding, transmission, decoding and interpretation of information, belong to natural processes with thermodynamic costs, in which entropy increases due to the dispersion of energy [5–8]. However, many others reject these ideas and believe that information and matter are different. Wiener [9], recognised as the founder of cybernetics, pointed out that information is information, not matter or energy. Hayles [10] claimed that information and materiality are conceptually distinct and that information is in some sense more essential, more important, and more fundamental than materiality. Some scientists and philosophers emphasise that abstract objects such as knowledge, which must be composed of presumably abstract information, are as real as physical entities [11].

The title of this article, Information is non-physical: The rules connecting representation and meaning do not obey the laws of physics, apparently challenges Landauer’s assertion that information is physical. In this article, I propose the definition of non-physical entity:

An entity is non-physical if and only if it does not obey the laws of physics.

I will show that this definition clearly distinguishes non-physical entities from the physical world. I will explain that information consists of physical representation, abstract meaning and rules that connect representation to meaning. Most importantly, I will demonstrate that the rules that interpret the physical representation of information to its abstract meaning do not obey the laws of physics, so information is non-physical.

2. The representation of information is physical

Landauer’s [2] main argument for claiming that information is physical is that, as he wrote,

Information is not a disembodied abstract entity; it is always tied to a physical representation. It is represented by engraving on a stone tablet, a spin, a charge, a hole in a punched card, a mark on paper, or some other equivalent. This ties the handling of information to all the possibilities and restrictions of our real physical world, its laws of physics and its storehouse of available parts.

Landauer [3] expressed the same view in his other papers: ‘Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe ... information is inevitably inscribed in a physical medium’ and ‘Information is inevitably tied to a physical representation, and therefore to all the possibilities and restrictions allowed by our real physical universe’ [4].

Indeed, information is always embodied in physical representation. Living in the information age, people watch messages sent by friends on the screens of computers, cell phones and iPads, students learn knowledge from textbooks, and professionals share their data and research progress on the global network. All information is displayed on books, electronic devices or other media. No information can exist without a physical representation. It is the observed fact that information ‘is represented by engraving on a stone tablet, a spin, a charge, a hole in a punched card, a mark on paper, or some other equivalent’. In the 21st century, more and more information people receive – documents, photos, graphics and videos – is displayed on the screens of various electronic devices.

As Landauer pointed out, information is always tied to physical representation, which leads to that the processes of information are related ‘to all the possibilities and restrictions of our real physical world, its laws of physics and its storehouse of available parts’. For example, in 1961, Landauer [12] stated that erasure of one bit of information increases the entropy of at least k_b ln2 and generates the heat of at least k_bT ln2, where k_b is Boltzmann’s constant, which is later called Landauer’s principle. Landauer’s principle sets the fundamental thermodynamic constraints for information processing, which affects various branches of computer science and engineering. Recently, experiments have tested and verified Landauer’s principle for classical systems [13–15] and for quantum systems [16]. Because information has physical representation, the second law of thermodynamics governs all information processing, in which entropy increases by the dispersion of energy, and the laws of physics dictate what computers, the physical systems for processing information, can and cannot do. Lloyd [17] explored that the speed at which a physical device can process information is limited by its energy, the amount of information it can process is limited by the number of degrees of freedom it possesses, and, in particular, the physical limits of computation are determined by the speed of light, Planck’s constant in quantum mechanics and the gravitational constant.

Landauer’s reason is correct. In our spacetime, there is no disembodied information, or in other words, information always needs matter to carry it. This is a fact without exception. As Landauer pointed out, information is not a disembodied abstract entity. His mistake is that because information is not a disembodied abstract entity, he inferred that information is physical. The negative statement that information is not a disembodied abstract entity may lead to two possible positive inferences. A possible positive inference is Landauer’s conclusion that information is a physical entity. The second possible positive inference is that information is an abstract entity embodied in a physical representation. What is the abstract entity? The meaning of information. We will see that the second inference is correct.

Some scientists have further clarified that information is physical by connecting information with physics more fundamentally. Bawden and Robinson [18] suggested that the physical nature of information can be understood from three main perspectives: the relation between information and physical entropy, the strongly informational nature of the quantum view of nature and the possibility of recasting the laws of physics in informational terms. These scientists directly connect information to the physical world. Vedral [7], for example, claimed that the states of physical systems should be thought of as catalogues of information. Recently, Vopson [19] used Shannon’s information theory to estimate that ~6 × 10⁸⁰ bits of information are encoded in all the matter particles of the observable universe by deriving a detailed formula to estimate the total number of particles in the observable universe and by determining that each particle in the observable universe contains an average of 1.509 bits of information. The word information has been used so widely that people may use the same word information, but, in fact, they are talking about different things. For these scientists, information is directly related to the states of physical systems or the observable physical quantities. The word information used in that way is not the information discussed in this article: meaningful information.

3. The meaning of information is abstract

Claude Shannon was the first scientist to study information systematically. In his seminal paper published in 1948, Shannon defined information as a measure of the reduction in uncertainty (i.e. mathematical entropy). According to Shannon’s [20] definition, the amount of information is inversely proportional to the probability of information occurrence. Shannon’s theory is a mathematical model developed to solve the fundamental engineering problem of communication: reproduce the message selected at the sender side as precisely as possible at the receiver side for any possible sequences of symbols rather than some special sequences of symbols. He wrote,

The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is, they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages. The system must be designed to operate for each possible selection, not just the one that will actually be chosen since this is unknown at the time of design.

Therefore, any possibly selected sequence of symbols, whether it is meaningful or not, is Shannon’s information. In English, the sequence yes is information in common sense because it is meaningful. However, in Shannon’s theory, all six sequences composed of the same three English letters y/e/s – yes, yse, eys, esy, sye and sey– are Shannon’s information. For communication engineers, information is just a sequence of symbols or a sequence of bits (0s and 1s) in electronic devices, which must be accurately transmitted. Because the semantic aspects of communication have nothing to do with the engineering problem, these semantic aspects of communication are not included in Shannon’s theory. Shannon’s theory is usually known as information theory. As Floridi [21] commented, calling Shannon’s theory information theory, an appealing but unfortunate label, causes endless misunderstandings. Shannon’s theory is better called by Shannon himself the mathematical theory of communication.

Scientists like Landauer apply the second law of thermodynamics to analyse information processing, which some of them call the thermodynamic theory of communication. They use the concept of information defined by Shannon, but emphasise the physical representation of information. Similar to the mathematical theory of communication, because the semantic aspects of communication are irrelevant to the changes of heat and entropy in information processing, these semantic aspects of communication are also not included in thermodynamic theory of communication. Whatever the meaning of a bit of information, Landauer’s principle is the same, that erasing that bit of information increases entropy by at least k_b ln2 and generates heat at least k_bT ln2. For these scientists, information is just a sequence of electronic signals, representing 0s and 1s in electronic devices, so information is indeed nothing but physical. Understanding and controlling the heat generated by information processing in electronic devices are very important for the proper operation of electronic devices. Sometimes, when my laptop gets hot, it is hard for me to open videos on YouTube or some websites; in this case, I must turn off the computer, improve the ventilation conditions to cool it, and then turn on the computer again. Scientists engaged in the field of thermodynamic analysis of information processing can completely ignore the semantic aspects of information, but they cannot deny them, because the significance of their work is to improve the operation of electronic devices in order to process meaningful information more efficiently and accurately.

Information must be represented by a physical medium. When Landauer wrote down his assertion that ‘Information is physical’, this sentence is printed on paper or displayed on screen, which is made of matter: ink, paper, pixel and screen. These material components obey the laws of physics: the changes of heat and entropy for producing this sentence obey thermodynamics, the microstructures of these materials are described by the Schrödinger equation of quantum mechanics, the flow of electronic signals representing this sentence in electronic devices is determined by the circuits based on semiconductor physics, and if this message is transmitted wirelessly through electromagnetic wave, the propagation of electromagnetic wave representing this sentence is governed by the Maxwell equation of electromagnetic field. So far, Landauer’s assertion that ‘Information is physical’ is correct, or more accurately, the representation of information is physical. The question is what did Landauer want to convey to readers through his assertion that ‘Information is physical?’ He wanted to spread his ideas, the meaning of the sentence that ‘Information is physical’. Does the ink that prints the sentence on paper, or the pixels that display the sentence on the screen represent the meaning of the sentence? Absolutely not. What is displayed on paper or screen is the sentence, not the meaning of the sentence. The meaning of this sentence is not attached to the sentence. If the meaning of the sentence is attached to the sentence, anyone, even a dog or camera can understand the meaning of the sentence. The sentence itself has no meaning. Sentences written in English are meaningless to people who do not understand English. Only those who can read English can understand the meaning of this sentence with his or her English knowledge.

In Philosophy of Information and Information Science, the nature of information has been profoundly discussed. Among the many definitions of information proposed, the most influential definitions are Marcia Bates’ [22] definition that information is some pattern of organisation of matter and energy given meaning by a living being, and Floridi’s [21] ‘general definition of information’ that information is syntactically well-formed and meaningful data. Both definitions hold that meaning is an essential part of information.

In daily use, the word information means ‘on/about someone/something’ or ‘facts or details that tell you something about a situation, person, event, etc.’, that is, in common sense, information is always meaningful. Nowadays, in the information age, people buy computers, cell phones, iPads, subscribe to Internet services, spend time reading articles, watching TV, checking email, sending messages, writing blogs and so on to receive information from others and send their own information to others. All information received and sent are meaningful, or ‘on/about someone/something’. We receive information because it has the meaning we want to know, and we send information because it has the meaning we want to convey to others. If the information received is meaningless, we will think there must be something wrong. Information always has meaning, and the word information used by ordinary people often refers directly to its meaning. Human-generated information is based on language. The basic element of language is words, and words are connected to each other to form sentences. A word is expressed by a sequence of ordered symbols of the language. These symbols themselves are abstract and meaningless. Each word has its meaning, that is, the correspondence of the word to a conceptual or physical object, which is given by the vocabulary of the language. The inter-relationship between words in a sentence is determined by grammar and sometimes context. Meaning in language can be semantics and/or pragmatics. Semantics is the meaning given by grammar and vocabulary. It does not account for any implied meaning of a sentence in the context. Pragmatic meaning looks at the same words and grammar used semantically, except in the context, covering the relationships between words, people and contexts. Therefore, the meaning of information is determined by vocabulary, grammar and, in some cases, context. Information must be represented by a physical medium, and, at the same time, information always has meaning, which is abstract.

As Bates pointed out, it is living beings that assign meaning to representation of information. Therefore, meaning exists in the mind of living beings, not in the external physical world. This is why the meaning of information is abstract. When William Shakespeare wrote his script Hamlet, he had the story of Prince Hamlet in his mind. The story was presented in some kind of mental state in his brain and nervous system, which is a special sort of physical state. The book Hamlet is the representation of the story. This book does not directly attach the story, but it contains the story. The story was ‘encoded’ into the book by Shakespeare according to English vocabulary and grammar. In order to understand the story, the reader needs to use the same rules, English vocabulary and grammar, to ‘decode’ the text of the book. After reading, the story is recorded in her or his mind. Meaning is abstract, because it always exists in the mind of living beings.

The meaning of information is determined by vocabulary, grammar and, in some cases, context, that is, information obeys the special rules but not the laws of physics. That is why I assert that information is non-physical. Here, I propose my definition of non-physical entity: an entity is non-physical if and only if it does not obey the laws of physics.

4. Definition of non-physical entity

When I searched for non-physical entity online, I found that the entry of non-physical entity on Wikipedia explains: ‘In ontology and the philosophy of mind, a non-physical entity is an object that exists outside physical reality. The philosophical schools of idealism and dualism assert that such entities exist, while physicalism asserts that they do not’. The first sentence of the quoted text appears to be the Physicalists’ assertion that a non-physical entity is an object that exists outside physical reality, so it does not exist in our spacetime. The entry of non-physical entity on Wikipedia also mentioned: ‘The dualist school supposes the existence of non-physical entities, the most widely discussed one being the mind’. Further searching for Dualism online, I found that Dualists often use the word non-physical to describe the property of mental phenomena. In philosophy of mind, Dualism is the view that mind and body are in some categorical way separated from each other, and that mental phenomena are, in some respects, non-physical in nature [23–25]. However, I have not found a clear scientific answer to the reason why mind and body are in some categorical way separated from each other and the exact meaning of ‘non-physical in nature’.

So, what is Non-physical? Non-physical should be the opposite conception of Physical. What are the common characteristics of physical substances? All physical substances obey the laws of physics. Therefore, I propose the definition of non-physical entity: an entity is non-physical if and only if it does not obey the laws of physics. The question is whether this definition draws the right line between physical and non-physical entities. Before doing so, it is necessary to explain the possible misunderstanding of the laws of physics, that is, the laws of physics apply only to physical phenomena. In fact, the laws of physics apply to all phenomena in the material world, from as small as elementary particles to as large as galaxies. There is no other fundamental law governing the material world in other disciplines of science. For chemistry, although observations led to many empirical laws, now it is known that chemistry has its foundations in quantum mechanics. The microscopic structures and properties of matter, including all molecular structures and physicochemical properties of molecules, and chemical reactions between molecules can be theoretically obtained by solving the Schrödinger equation of quantum mechanics.

Therefore, the laws of physics govern all phenomena in the material world without exception. All non-physical entities and non-physical processes are related to organisms, so we only need to consider those physical interactions and physical equations suitable for the environmental conditions on the Earth. There are four fundamental forces in the universe: the strong nuclear force, the weak nuclear force, the electromagnetic force and the gravitational force. The strong and weak nuclear forces work at the subatomic particle level, and they can be completely ignored in the study of phenomena on the Earth. Every particle has mass and interacts with other particles through the gravitational force. Because the gravitational force is very weak, when studying the phenomena on the Earth, the gravitational interactions of a given particle with other particles can be ignored, except the gravitational interaction of the given particle with the Earth – the gravity acting on that particle – needs to be considered. For the electromagnetic force, the most important part is the electrostatic force or the Coulomb force, that is, the interaction between charged particles. All particles are composed of atoms, which are composed of positively charged nuclei and negatively charged electrons, so all particles are affected by the Coulomb interaction. The Coulomb interaction is the cause of covalent bonds and non-covalent bonds (ionic bonds, hydrogen bonds, bonds due to Van der Waals forces and indirectly to hydrophobic groups), so it is the cause of material structures. Quantum mechanics describes microscopic particles, and Newtonian mechanics describes macroscopic particles on the Earth. Therefore, all physical entities obey the laws of physics without exception.

In conclusion, the definition of non-physical entity I proposed in this article – an entity is non-physical if and only if it does not obey the laws of physics – does distinguish non-physical entities from physical entities.

5. Information is non-physical: the rules linking representation to meaning do not obey the laws of physics

In order to explain that information is non-physical, we need to analyse the nature of information in detail. In their definitions, Bates [22] defines information as pattern (of organisation of matter and energy) given meaning (by a living being), and Floridi [21] defines information as (syntactically well-formed and) meaningful data. Either pattern or data are the physical representation of information. They all define information in terms of representation + meaning. In their definitions, representation is noun, and meaning is adjective. In the case of the script Hamlet, this is equivalent to considering information to be the script Hamlet, a printed book or a digital file. Therefore, the information defined by both Bates and Floridi is the meaningful representation, encoded by the information sender, rather than the meaning of the representation, decoded by the information receiver. Dinneen and Brauner [26] pointed out that information is abstract and criticised the view of information as a physical object or information-as-thing. But strangely, they viewed that the information defined by Bates or Floridi is consistent with that information is abstract, although in their previous paper, they classified Bates’s conception of information as ‘a variation of the information-as-thing category’ [27]. As mentioned above, both Bates and Floridi defined information as a meaningful representation, that is, a physical object. Bates [22] claimed that ‘All information is natural information, in that it exists in the material world of matter and energy’, and Floridi [21] endorsed the modest thesis of ontological neutrality: no information without data representation, where representation = physical implementation. As Shannon suggested that it is hardly to be expected that a single concept of information would satisfactorily account for the numerous possible applications of this general field [28]. Bates wrote that she defined and developed fundamental forms of information, as well as the term information itself for the purposes of Information Science, and Floridi’s ‘general definition of information’ has become an operational standard, especially in fields such as Information Science, Information (Systems) Management, that treat data, patterns and information as reified entities. For these fields, their definitions of information are excellent practically and theoretically.

In addition to physical representation and abstract meaning, information has a third component: rules that link physical representation with abstract meaning. The information defined by Bates or Floridi is broad enough. For the information defined by Bates, what are the rules that link the pattern of organisation of matter and energy with its meaning? For the information defined by Floridi, what are the rules for associating the well-formed data with its meaning? In general, what are the rules that relate the physical representation of information to its abstract meaning? These rules of course depend on what living being perceives what physical representation and gives it meaning. However, it is certain that these rules cannot be the laws of physics, because all quantities appearing in the laws of physics are physical, observable and measurable, and on the other hand, meaning is abstract, unobservable and unmeasurable, so no laws of physics can contain meanings. Furthermore, meaning is not the inherent property of patterns or data, but is given to patterns or data by living beings. This means that different living beings can give different meanings to the same pattern or data, and the same meaning to the different patterns or data. For example, in most countries, nodding the head up and down means ‘yes’ and shaking the head from side to side for ‘no’, but in Bulgaria, an up-and-down head movement is used for ‘no’ and a side-to-side movement for ‘yes’. In human language, people can find much more examples that the different words have the same meaning, for example, Sun is called Soleil in French and Sol in Spanish, and that the same word has different meaning, for example, English word hell means bright in German, gift means poison, English word main means hand in French, sale means dirty. All these examples illustrate that the link of patterns or data with meaning is governed by conventional rules rather than the laws of physics. For human beings, the most common and important information is information based on human language, that is, linguistic information. For linguistic information, the representation is an ordered symbol sequence of language, and the rules to determine the meaning of the ordered symbol sequence are language vocabulary and grammar. The reason for asserting that information is non-physical is that the process transferring the physical representation of information into the abstract meaning follows special rules rather than the laws of physics. This conclusion has ontological significance: information is ontologically different from physical substances. In the inanimate world, the laws of physics govern all physical substances and their processes; while in the living world, in addition to the laws of physics, other rules – language vocabulary and grammar in the case of linguistic information – play a role as well.

All information generated by human beings based on language is non-physical. Here, language represents some kind of formula for expressing or recording information, including human oral and written languages (such as English and Spanish), special notes (such as music score and Braille), codes (such as Moose code and ASCII code), computer language (such as JavaScript and Python), document formats (such as Microsoft Word and PDF) and so on. Human culture based on human language – including literature, education, history, science, philosophy, religion and so on – is also a non-physical entity.

Human life is purposeful and guided by ideas or thoughts. In the history of human civilisation, humans have invented and manufactured countless products, including everything around us, such as buildings, cars, ships, airplanes, computers, televisions, telephones and even as simple as tables and chairs. These inventions first appeared in the human mind, then were shown in the designs or models, and finally became real products. These products – buildings, cars, ships, airplanes, computers, televisions, telephones, tables and chairs – are the materialisation of information.

Before the invention of the computer, human beings invented a variety of devices, such as radio, typewriter, abacus, manual calculator and electric calculator. These devices are more or less related to information processing. However, since these devices must be operated step by step by humans, their invention did not change the fact that all human information processing was still carried out in the human brain at that time. Great changes have taken place since the invention of the computer. Scientists engaged in the thermodynamic theory of communication emphasise that all information processes – namely, the generation, encoding, transmission, decoding and interpretation of information – belong to the class of natural processes with thermodynamic costs, in which entropy increases with the dispersion of energy [5]. However, this is only one aspect of the information processes: because information always has a physical representation, all information processes are accompanied by changes in energy and entropy. However, those information processes involving the meaning of information, such as encoding, decoding, interpretation, numerical calculation, follow their special rules, rather than the laws of physics. These information processes involving the meaning of information are non-physical information processes. Today, computers and microprocessor-controlled electronic devices have been applied to all corners of people’s life. According to the specified programmes, they can independently perform various information processing, such as scientific numerical computation, engineering design, data processing and communication, document conversion, business management, and even control the room temperature and the vehicle working status for you. Computer-controlled devices, equipped with modern artificial intelligence, can learn by themselves, accumulate experience, collect data, make judgements and take actions. Computers have really become an extension of the human brain.

In addition to human beings, many animals – such as dolphins, bees and elephants – communicate among their members using their own language for the benefit of their populations. The information they exchange with each other is also non-physical.

My conclusion –information is non-physical because the rules connecting the representation of information to its meaning do not follow the laws of physics – applies to all meaningful information, but not to all meaningless information, such as the information mentioned in the final paragraph of section ‘The representation of information is physical’. This information is more fundamentally connected to physics or even directly related to the state of a physical system or observable physical quantities. Krzanowski [29] defined a category of information as a physical object or phenomenon, it can be measured and quantified, it lacks meaning, and it expresses the organisation or form of physical objects. Bates has proposed two definitions of information. The definition of information quoted above is her Information 2. In her basic definition or her Information 1, Bates [22] defines information as the pattern of organisation of matter and energy, which is objectively existing phenomena in the universe without meaning. Bates’s basic definition of information, or her Information 1, is very similar to the information defined by Krzanowski. In their definitions of information, the only thing which may relate to information is ‘the organisation or form of physical objects’ in Krzanowski’s definition or ‘the pattern of organization’ in Bates’s definition, when living beings perceive and give meaning to the organization, form or pattern. In fact, ‘the organization or form of physical objects’ in Krzanowski’s definition and ‘the pattern of organization of matter and energy’ in Bates’s definition are some states, structures and properties of physical substances, which are physical, meaningless and objective. Krzanowski acknowledged that ‘such information is a property of matter and the physical world’. They are phenomena of the physical world, but these scientists and philosophers call them information. The word Information used in this way deviates from the meaning of the word Information in common sense and the explanations of the word Information in dictionaries. The conclusion obtained in this article does not apply to such so-called information.

6. Conclusion

In this article, I define non-physical entities as entities that do not obey the laws of physics. This definition is based on the fact that the laws of physics govern all phenomena in the material world. All matters obey the laws of physics. If an entity does not obey the laws of physics, it cannot have materiality, or in other words, it is non-physical. This definition clearly distinguishes non-physical entities from physical entities, and provides a testable method to judge whether an entity is a physical entity or a non-physical entity.

Information is composed of physical representation, abstract meaning and rules connecting representation to meaning. This understanding of information is consistent with the triadic (three-part) model of semiotics, which consists of: (1) the Representamen, the form, which the sign takes; (2) an Interpretant, the sense, made of the sign and (3) an Object, to which the sign refers [30]. The fact that meaning is abstract, unobservable and unmeasurable leads to that the rules linking representation with meaning cannot be the laws of physics. For information based on human language, representation is an ordered symbol sequence of language, meaning is the information recorded in our brain and nervous system, and rules are language vocabulary and grammar. Because information follows its special rules rather than the laws of physics, information is non-physical. This conclusion that information is non-physical has ontological significance: information is ontologically different from physical substances. In the inanimate world, the laws of physics govern all physical substances and their processes; while in the living world, in addition to the laws of physics, other rules – language vocabulary and grammar in the case of linguistic information – also play a role. This conclusion provides the scientific foundation for (property) dualism.

Information based on human language is non-physical. In addition, human culture based on language – including literature, education, history, science, philosophy, religion and so on – is also a non-physical entity. Francis Bacon wrote in 1597 that ‘Knowledge is power’. Now, we can say that Information is power. Human beings live purposefully, and human activities are guided by information. It is information that has changed the world in which we live and human beings themselves.