• Email
  • Single Page
  • Print

How We Know

The cover of the ‘Golden Record,’ stowed aboard the Voyager spacecraft and sent into space in 1977. This ‘message in an interstellar bottle,’ James Gleick writes in The Information, contained the first prelude of Bach’s Well-Tempered Clavier and other samples of ‘earthly sounds,’ such as ‘the clatter of a horse-drawn cart and a tapping in Morse code.’

Gordon Moore was in the hardware business, making hardware components for electronic machines, and he stated his law as a law of growth for hardware. But the law applies also to the information that the hardware is designed to embody. The purpose of the hardware is to store and process information. The storage of information is called memory, and the processing of information is called computing. The consequence of Moore’s Law for information is that the price of memory and computing decreases and the available amount of memory and computing increases by a factor of a hundred every decade. The flood of hardware becomes a flood of information.

In 1949, one year after Shannon published the rules of information theory, he drew up a table of the various stores of memory that then existed. The biggest memory in his table was the US Library of Congress, which he estimated to contain one hundred trillion bits of information. That was at the time a fair guess at the sum total of recorded human knowledge. Today a memory disc drive storing that amount of information weighs a few pounds and can be bought for about a thousand dollars. Information, otherwise known as data, pours into memories of that size or larger, in government and business offices and scientific laboratories all over the world. Gleick quotes the computer scientist Jaron Lanier describing the effect of the flood: “It’s as if you kneel to plant the seed of a tree and it grows so fast that it swallows your whole town before you can even rise to your feet.”

On December 8, 2010, Gleick published on the The New York Review’s blog an illuminating essay, “The Information Palace.” It was written too late to be included in his book. It describes the historical changes of meaning of the word “information,” as recorded in the latest quarterly online revision of the Oxford English Dictionary. The word first appears in 1386 a parliamentary report with the meaning “denunciation.” The history ends with the modern usage, “information fatigue,” defined as “apathy, indifference or mental exhaustion arising from exposure to too much information.”

The consequences of the information flood are not all bad. One of the creative enterprises made possible by the flood is Wikipedia, started ten years ago by Jimmy Wales. Among my friends and acquaintances, everybody distrusts Wikipedia and everybody uses it. Distrust and productive use are not incompatible. Wikipedia is the ultimate open source repository of information. Everyone is free to read it and everyone is free to write it. It contains articles in 262 languages written by several million authors. The information that it contains is totally unreliable and surprisingly accurate. It is often unreliable because many of the authors are ignorant or careless. It is often accurate because the articles are edited and corrected by readers who are better informed than the authors.

Jimmy Wales hoped when he started Wikipedia that the combination of enthusiastic volunteer writers with open source information technology would cause a revolution in human access to knowledge. The rate of growth of Wikipedia exceeded his wildest dreams. Within ten years it has become the biggest storehouse of information on the planet and the noisiest battleground of conflicting opinions. It illustrates Shannon’s law of reliable communication. Shannon’s law says that accurate transmission of information is possible in a communication system with a high level of noise. Even in the noisiest system, errors can be reliably corrected and accurate information transmitted, provided that the transmission is sufficiently redundant. That is, in a nutshell, how Wikipedia works.

The information flood has also brought enormous benefits to science. The public has a distorted view of science, because children are taught in school that science is a collection of firmly established truths. In fact, science is not a collection of truths. It is a continuing exploration of mysteries. Wherever we go exploring in the world around us, we find mysteries. Our planet is covered by continents and oceans whose origin we cannot explain. Our atmosphere is constantly stirred by poorly understood disturbances that we call weather and climate. The visible matter in the universe is outweighed by a much larger quantity of dark invisible matter that we do not understand at all. The origin of life is a total mystery, and so is the existence of human consciousness. We have no clear idea how the electrical discharges occurring in nerve cells in our brains are connected with our feelings and desires and actions.

Even physics, the most exact and most firmly established branch of science, is still full of mysteries. We do not know how much of Shannon’s theory of information will remain valid when quantum devices replace classical electric circuits as the carriers of information. Quantum devices may be made of single atoms or microscopic magnetic circuits. All that we know for sure is that they can theoretically do certain jobs that are beyond the reach of classical devices. Quantum computing is still an unexplored mystery on the frontier of information theory. Science is the sum total of a great multitude of mysteries. It is an unending argument between a great multitude of voices. It resembles Wikipedia much more than it resembles the Encyclopaedia Britannica.

The rapid growth of the flood of information in the last ten years made Wikipedia possible, and the same flood made twenty-first-century science possible. Twenty-first-century science is dominated by huge stores of information that we call databases. The information flood has made it easy and cheap to build databases. One example of a twenty-first-century database is the collection of genome sequences of living creatures belonging to various species from microbes to humans. Each genome contains the complete genetic information that shaped the creature to which it belongs. The genome data-base is rapidly growing and is available for scientists all over the world to explore. Its origin can be traced to the year 1939, when Shannon wrote his Ph.D. thesis with the title “An Algebra for Theoretical Genetics.”

Shannon was then a graduate student in the mathematics department at MIT. He was only dimly aware of the possible physical embodiment of genetic information. The true physical embodiment of the genome is the double helix structure of DNA molecules, discovered by Francis Crick and James Watson fourteen years later. In 1939 Shannon understood that the basis of genetics must be information, and that the information must be coded in some abstract algebra independent of its physical embodiment. Without any knowledge of the double helix, he could not hope to guess the detailed structure of the genetic code. He could only imagine that in some distant future the genetic information would be decoded and collected in a giant database that would define the total diversity of living creatures. It took only sixty years for his dream to come true.

In the twentieth century, genomes of humans and other species were laboriously decoded and translated into sequences of letters in computer memories. The decoding and translation became cheaper and faster as time went on, the price decreasing and the speed increasing according to Moore’s Law. The first human genome took fifteen years to decode and cost about a billion dollars. Now a human genome can be decoded in a few weeks and costs a few thousand dollars. Around the year 2000, a turning point was reached, when it became cheaper to produce genetic information than to understand it. Now we can pass a piece of human DNA through a machine and rapidly read out the genetic information, but we cannot read out the meaning of the information. We shall not fully understand the information until we understand in detail the processes of embryonic development that the DNA orchestrated to make us what we are.

A similar turning point was reached about the same time in the science of astronomy. Telescopes and spacecraft have evolved slowly, but cameras and optical data processors have evolved fast. Modern sky-survey projects collect data from huge areas of sky and produce databases with accurate information about billions of objects. Astronomers without access to large instruments can make discoveries by mining the databases instead of observing the sky. Big databases have caused similar revolutions in other sciences such as biochemistry and ecology.

The explosive growth of information in our human society is a part of the slower growth of ordered structures in the evolution of life as a whole. Life has for billions of years been evolving with organisms and ecosystems embodying increasing amounts of information. The evolution of life is a part of the evolution of the universe, which also evolves with increasing amounts of information embodied in ordered structures, galaxies and stars and planetary systems. In the living and in the nonliving world, we see a growth of order, starting from the featureless and uniform gas of the early universe and producing the magnificent diversity of weird objects that we see in the sky and in the rain forest. Everywhere around us, wherever we look, we see evidence of increasing order and increasing information. The technology arising from Shannon’s discoveries is only a local acceleration of the natural growth of information.

The visible growth of ordered structures in the universe seemed paradoxical to nineteenth-century scientists and philosophers, who believed in a dismal doctrine called the heat death. Lord Kelvin, one of the leading physicists of that time, promoted the heat death dogma, predicting that the flow of heat from warmer to cooler objects will result in a decrease of temperature differences everywhere, until all temperatures ultimately become equal. Life needs temperature differences, to avoid being stifled by its waste heat. So life will disappear.

This dismal view of the future was in startling contrast to the ebullient growth of life that we see around us. Thanks to the discoveries of astronomers in the twentieth century, we now know that the heat death is a myth. The heat death can never happen, and there is no paradox. The best popular account of the disappearance of the paradox is a chapter, “How Order Was Born of Chaos,” in the book Creation of the Universe, by Fang Lizhi and his wife Li Shuxian.2 Fang Lizhi is doubly famous as a leading Chinese astronomer and a leading political dissident. He is now pursuing his double career at the University of Arizona.

The belief in a heat death was based on an idea that I call the cooking rule. The cooking rule says that a piece of steak gets warmer when we put it on a hot grill. More generally, the rule says that any object gets warmer when it gains energy, and gets cooler when it loses energy. Humans have been cooking steaks for thousands of years, and nobody ever saw a steak get colder while cooking on a fire. The cooking rule is true for objects small enough for us to handle. If the cooking rule is always true, then Lord Kelvin’s argument for the heat death is correct.

  1. 2

    Singapore: World Scientific Publishing Co., 1989. 

  • Email
  • Single Page
  • Print