Hans Christian von Baeyer
Information
The new Language of Science
Weidenfeld&Nicholson 2003
pg 18
In-Formation
The roots of the concept
In order to understand information, we must define it; but in order define it, we must first understand it. Where to start?
Defining words from scratch is like pulling yourself up by your own bootstraps. The paradox animates an anecdote related by the nineteenth-century Austrian physicist Ludwig Boltzmann, the first scientist to have an inkling of the potential role of the concept of information in science. In high school, he recalled later in life, he had the naive ambition to discover a philosophy in which every concept was clearly defined as it was introduced. Once, when he heard a philosophical work praised as uncommonly lucid (it may have been by Hume), he immediately asked his older brother to accompany him to the library to fetch it. Unfortunately, the book turned out to be available only in English, which Boltzmann didn't speak. 'No problem,' quipped his brother, who did not share Ludwig's idealism; 'if this book really achieves what you expect of , the language in which it is written doesn't matter because every single word will be clearly defined before it is used.'
To help define 'information', a trip to the library is no more helpful than it was to young Ludwig. The shelves may well bend under the weight of dictionaries that contain the relevant entry and of books with titles that include the word, but none manages to provide a robust, satisfying definition. There is no choice but to roll up our sleeves and start from scratch.
Just like the word "letter", which refers not only to a written message, but also to the alphabetical symbols that compose it, the word 'information' has two different senses. The colloquial usage, as in 'personal information' and 'directory information', refers to the meaning of a message of some sort. The technical sense, on the other hand, emphasizes the symbols used to transmit a message, whether they are letters, numbers or just the computer digits zero and one. In this second sense 'information technology' is that branch of engineering that focuses on storing, transmitting, displaying and processing symbols, irrespective of what they stand for.
Evidently, the two connotations of 'information' are closely intertwined. The meaning of a message arises out of the relationship of the individual symbols that make it up, just as the meaning of a letter emerges from the particular juxtaposition of its letters; but in spite of this obvious connection, the distinction between the colloquial meaning and the technical definition of information is profound.
The literary scholar and the scientist, perennial antagonists of the 'two cultures' debate, tend to come to the task of definition of concepts from opposite directions. Humanists typically start with an intuitive notion, flesh it out in the light of common usage and etymology, and propose a working definition. With the help of specific examples they then polish their draft until they feel that it catches the right sense. That's how dictionaries are made, and thus words gradually acquire fixed meanings. This haphazard process has led to a number of useful colloquial interpretations of the word 'information', but the persistent, nagging question 'What is information?' has not been answered.
Scientists, especially physicists, usually develop new concepts in a more pragmatic way. Since mathematics is the language of physics, and mathematics deals with numbers, an essential ingredient of every physical theory is measurement, the assignment of quantities to qualities. For this reason new terms are frequently introduced by way of recipes for measurement, called 'operational definitions', which require no real understanding of what it is that is being measured. That's how temperature started out, for example, which began its starring role in physics and chemistry around the year 1600 as something no more subtle tban the quantity that is measured by a thermometer - a number read on a scale. As experience accumulated, readings on different types of thermometers were compared, and more was learned about the nature of heat from a variety of experiments, temperature was finally unmasked in the middle of the nineteenth century as a measure of the average speed of molecules. The journey from operational definition to an understanding of the real meaning of the word 'temperature' took a quarter of a millennium.
Information, too, has been defined operationally. Unfortunately this technical, bottom-up definition is very restricted, and hitherto bears little resemblance to any of the common, top-down definitions. Eventually the two definitions of information should converge, but that hasn't happened yet. When it does, we will finally know what information is; until then we have to make do with compromises.
In this chapter I will briefly examine the common, everyday word before turning for the rest of the book to the technical definition. Etymology offers a clue.
'Information', 'deformation', 'conformation', 'transformation', and 'reformation' obviously derive from 'formation', which, in turn, comes from 'form'.
Information is therefore the infusion of form on some previously unformed entity, just as de-, con-, trans-, and re-formation refer to the undoing, copying, changing, and renewing of forms.
Information refers to moulding or shaping a formless heap - imposing a form onto something. So the question of its meaning reverts to the more fundamental one: What is form?
The word 'form' entered Western philosophy as a translation of Plato's word eidos, the root of the words 'idea' and 'ideal'. Plato paints a picture of a world in which every object and attribute is but a pale, imperfect copy of a perfect, abstract ideal, a form, or archetype, which resides somewhere in an imaginary heaven. Thus a horse is but a copy of the form of horseness, the horse of horses, the Urhorse, the ideal horse that has shed all material properties. Similarly, if you are good or beautiful, you are not really good or beautiful in a profonnd, ideal sense, you merely have some characteristics that reflect, in a crude manner accessible to our senses, the forms of goodness and beauty.
As a boy I was intrigued by this untouchable world of essences, and, being more visually than verbally inclined, tried hard to imagine what the essence of horse-ness would look like, or how I would recognize a simpler form, such as that of a pencil. But even though, unlike Boltzmann, I had no older brother to tease me, I grew out of my youthful stage of Platonic idealism, and went on reasoning without forms.
Aristotle had trouble with Plato's forms too. What proof is there, he asked, that these things called 'forms' enjoy a separate existence? Instead of rejecting form altogether, though, he defined it as the sum total of the essential properties of a thing. An essential property of a horse, for example, is quadrupedalism, whereas colour, being variable and consequently accidental, is not part of its form. Two horses share the essence of horse-ness, Aristotle teaches, bot there is no horse-ness without a real horse. In his theory of perception he assigns an important function to form.
Our understanding of the material world, he claims, depends on having forms within our intellects: 'It is not the stone which is present in the soul, but its Form.' And these mental forms he calls ideas, abstractions, or concepts. Whatever traces of the great classical debate about the nature of form remain in our definition of information, they are more indebted to Aristotle than to Plato.
A much more common use of the word 'form' crops up in biology, where the infinity of shapes of living organisms provides us with a spectacle of awesome profligacy. The first modern biologist who tried to tame this profusion realized that the tool he required for the job, namely mathematics, would apply as well to other manifestations of form. In his book On Growth and Form, which appeared 1917 and inspired a small library of studies of symmetries and other patterns in nature, the Scottish naturalist D'Arcy Thompson wrote:
We have learned ... that our own study of organic form ... is but a portion of that wider Science of Form which deals with the forms assumed by matter under all aspects and conditions, and, in a still wider sense, with forms which are theoretically imaginable ... The mathematical definition of a 'form' has a quality of precision which ... is expressed in few words or in still briefer symbols, and these words and symbols are so pregnant with meaning that thought itself is economized; we are brought by means of it in touch with Galileo's aphorism (as old as Plato, as old as Pythagoras, as old perhaps as the wisdom of the Egyptians), that the Book of Nature is written in characters of Geometry.
The recognition that form must ultimately be expressed in mathematical terms carries over into the modern technical definition of information.
Thompson's idea of form could be expressed more clearly by the word 'shape', but it pays to take his advice and cast the net further out. The writer Paul Young, for example, collected eight synonyms for the word 'form' as he tried to pin down the nature of information: arrangement, configuration, order, organization, pattern, shape, structure, and relationship. Searching for the most general concept that can cover all possible applications in mathematics, physics, chemistry, biology and neuroscience, he settled on the term 'relationship' among the parts of a physical system, taking care to interpret the word in the broadest possible way.
D'Arcy Thompson's most famous examples of natural forms are those of the skeletons of marine micro-organisms called radiolaria. Alan Turing, the English genius whose contributions to the science of information ranged from fundamental theorems in logic to the cracking of the German army's Enigma code, worked for years on a mathematical theory of shape, with the goal of describing these exquisite forms. These structures exhibit patterns of such stunning beauty and intricacy that people who encounter them for the first time must be forgiven for doubting their reality. In fact, they resemble nothing so much as a certain kind of Chinese bone carving that tourists can't believe is made in one piece. The simpler examples resemble soccer balls with spikes, while others are graceful polyhedra with curved surfaces bulging outward. All of them astonish by the subtlety of the relationships between their parts.
The word 'shape' seems too paltry to describe such forms; if they had been secretly carved to incorporate coded messages, just imagine how much information they could transmit!
Complexity of form is not the only key to the amount of information a shape can hold. Take a far simpler, non-biological form - a circle, for example. Its essence resides in the relationship of its parts: each point on the periphery has the same distance from the centre. This kind of mathematical characterization, multiplied and complicated a millionfold, is capable of capturing all of nature's fabulous forms, at least approximately. Nevertheless, when we begin to quantify information, we will be surprised to learn that in principle, if not in practice, even an ordinary, unadorned circle can encode an infinite amount of information.
Further, the relationships of the parts of a system don't have to be spatial. Consider two rocks in outer space, and ignore their shapes and appearances. The relationship between them is summarized by the distance between them, and their mutual attraction as described by Newton's law of gravity. Since they move toward each other, the distance between them changes in time, so it would seem that their relationship cannot be expressed in purely spatial terms. Nevertheless, it was to be recast by Einstein in the general theory of relativity in the language of geometry - albeit in a space of four dimensions. So powerful is the human visual apparatus that physicists consistently strive to picture their equations. 'Geometrizing a theory', they call this exercise, and value it highly.
Other non-spatial relationships are logical or causal - A plus B equals C - and are exemplified by neural connections in the brain and electronic pathways in a computer. Both logical and causal relationships, if we adopt Young's definition, are forms.
Temporal relationships such as the pattern of electrical pulses tapped out by a telegrapher, are, of course, paradigmatic of information transmission. The alphabet itself is a more sophisticated method for transmitting messages than this, each character being represented by a single letter; but again, most letters, by themselves, mean nothing in isolation. Literature resides in the pattern, in the way the letters are strung together, in their relationships to each other.
Tonal, temporal and energetic relationships combine in musical forms, spatial and colour relationships in paintings.
The further we pursue this string of associations, the more the world appears to be a tangled web of relationships. Relations are the stuff of science. 'The realm of science is not things in themselves, as the dogmatists in thetr simplicity imagine,' wrote the French mathematician Henri Poincare, 'but the relations between things; outside those relations there is no reality knowable.'
The Austrian philosopher Ludwig Wittgenstein pushed the point to its logical conclusion: 'We cannot think of any object apart from the possibility of its connection with other things.' This bothered him terribly, because he shared with the other Ludwig, his countryman Boltzmann, a yearning for a completely defined and consistent philosophical system. In the end he was stymied: it is impossible to define anything without first defining other things.
In human life, Wittgenstein's insight is almost self-evident. From birth we are enmeshed in a web of relationships that defines us and to a large extent determines our destiny. No one has expressed this truth more graphically than the Italian novelist Italo Calvino. His novel Invisible Cities is a haunting fantasy of travels through imaginary cities that symbolize different aspects of the human condition. In Ersilia the townspeople connect each others' houses with colour-coded strings to indicate relationships: '... white or black or grey or black-and-white according to whether they mark a relationship of blood, of trade, authority, agency'. Every relationship is represented, every house festooned with an evergrowing number of strings. Eventually, the tangle becomes so thick that movement becomes impossible, and the residents are forced to leave. The last sentence of the story is a poetic definition of the nature of community: 'Thus, when traveling in the territory of Ersilia, you come upon the ruins of abandoned cities, without the walls which do not last, without the bones of the dead which the wind rolls away: spiderwebs of intricate relationships seeking a form.'
Form, in short, expresses relationships, and this insight carries over into the concept of information. Information, however, is not the same thing as form. The tiles on my bathroom floor display an interesting pattern, which has a form, and might even be called 'a form', yet there is no useful sense in which that pattern could be referred to as information.
Information carries a connotation of activity that is absent from mere form. Cicero used the verb 'inform' to signify giving shape to something, forming an idea, and moulding a person or his mind. Art critics often use the term in sentences like this: 'Picasso's personal experiences in the war inform all his paintings of that period.' Information, then, refers to imposing, detecting or communicating a form. It connotes change. It possesses 'informative power', in the words of science writer Robert Wright. Indeed, when we think about information, we associate it with learning something we didn't know before, with the news (which the French call les informations), with some kind of transfer of knowledge. To be sure, information can be stored in a memory, but that's a temporary arrangement. If it were permanently locked up with no possibility of flowing in or out, it would be useless, and not really information at all.
Information is the transfer of form from one medium to another. In the context of human information-exchange, 'communication' is a more descriptive term than 'transfer', and since form is about relationships, we can tentatively define information as the communication of relationships.
Two final remarks are necessary to round out this definition. The first concerns the way a form is imprinted on a medium of transmission. Translating a pattern in one medium into the same pattern, expressed differently in another medium, is called coding, and the dictionary that accomplishes it is the code. (Contrary to popular usage, a code is usually not secret. Secret codes, the concern of cryptographers, are called ciphers.) By way of example, consider listening to a live piano recital on the radio. The music, whose pattern is stored as notes on paper, or in some mysterious fashion in the player's brain, is translated into physical gestures, and from there into vibrations of the instrument. These, in turn, excite a sequence of pressure waves in the air, which induce vibrations in a distant microphone. That device delivers a coded electrical signal to a transmitter, which causes an oscillating current to slosh back and forth in a transmitting tower. This current is accompanied by electromagnetic radiation in the form of radio waves, electric rain pelting your receiving antenna. Then the transformation is reversed, step by step, until your brain registers the music. The code has changed many times in the intervening process, and none of the individual signals, be they mechanical, acoustical, electrical or nervous, resemble their connterparts in other media. At the same time, the kind of energy that was associated with the signal also changed with each successive encoding of the musical information; but despite this, the pattern, the relationship of the magnitudes and positions in time of the individual signals - in short, the form of the music - has survived intact throughout.
The second explanatory remark will sonnd perverse in view of what has preceded it. Even though information is, as Young put it, a flow of form, through most of this book we will consider information as a static phenomenon. The method of suspending time is trivial: a changing pattern can be recorded as a graph in which time is represented by distance along the horizontal axis. Thus a telegraphic message, which in reality consists of a temporal sequence of dots and dashes produced at one point in space, is most easily thought of as a long tape on which the dots, dashes and pauses are recorded in ink. More dramatically, an entire movie, with its complex sounds and actions, is encoded on a strip of magnetic tape in the form of dots and blanks, ones and zeroes. Thus, no sooner is time introduced as an essential factor in the definition of information than it is yanked off the stage again by a mechanical trick.
In-formation - the infusion of form - the flow of relationships - the communication of messages. The halting explanations by philosophers such as Aristotle, scientists such as D'Arcy Thompson, and writers such as Young and Wright, superimposed on our own preconceptions, help to endow the word 'information' with meaning. No crisp, robust definition emerges, but every gloss brings us closer to an understanding of that elusive concept; and as we turn from the rich, layered humanistic version to the skeletal technical definition, we must keep in mind that in the end the two must be reconciled.
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