If there's one thing that I admire most about the major scientific and mathematical discoveries of the 20th century, it's how humble they are. Compare the last century to say... the Scientific Revolution. Mathematicians and scientists had opened up an entire treasure chest of physical and mathematic laws, and they were certainly convinced that these laws were absolute in their truth. According to the likes of Isaac Newton, Karl Gauss and the other great minds of the classical era, the universe could be entirely described by adhering to a few simple laws and rules. Their acheivements can not be understated and the relevance of their work is just as influential today as it was 100s of years ago. What is remarkable about the 20th century is just how quickly the methods of the times past were abandoned to make way for a new era of uncertainty.
Take mathematics for instance. There was little doubt in the minds of mathematicians in the 19th century that all there was to know about mathematics would be unified under one single infallible system. Of course many to this day still do regard mathematics as being a rigid, indisputible field. The drive to capture math as a whole and then dissect it had reached its peak with mathematicians such as Russell and Whitehead publishing the beast that is Principia Mathematica. It was only shortly after that their dream has crumbled and Kurt Godel, one of the greatest logicians to ever live, illustrated the impossibility of fully comprehending mathematics or logic itself by any finite means.
It was a century that saw Albert Einstein, a man who changed how it is we think of space and time and a man so determined to unify the laws that governed nature, watch as his ideal of a grand unified theory fall before the mysterious and peculiar quantum mechanics.
And finally, it was a century where people convinced that computers could at least in theory be able to mechanically solve any problem, come to terms with the fact that computers are also restricted in their capabilities.
Whereas the classical era was about what human beings could know and come to understand about the universe... the modern era focused on what science and mathematics are unable to teach us about the universe. That math is subject to just as much uncertainty, fuzziness, and imprecision as art. That science is full of incredibly strange and even contradictory natural phenomenon. That computation can never compare itself to the ingenuity held by our imaginations.
Where does that leave us today? Perhaps the greatest marvel to come out of the last 100 years, and also the one least known, is Information Theory. What is so special about Information Theory is how in such a subtle way, it combines all the ideas of computation, science, and mathematics. It is my firm belief that the greatest advancements that await us in this century will be a direct result of the application of Information Theory.
Information theory, spawned by Claude Shannon in 1948, was at the time nothing more than an attempt to transmit signals efficiently over a physical medium, such as a telephone cable. But what makes it so great is that for the first time in human history, someone was able to take such an abstract and formless concept, and quantify it. Information theory is a way to measure, in precise terms, just how much information content there exists in a pattern of symbols.
It's remarkable... for example, one can take a newspaper, a novel, or heck, even take this very blog, and actually quantify into a single number just how much information it contains. Furthermore, by measuring how much information is contained in a pattern, and then measuring how many symbols are being used in a pattern, one can determine how much redundancy there is in the pattern.
The implications of this have been well understood for practical purposes. For example, anytime you listen to an MP3 or watch a movie on your computer, information theory was right at the core of making sure that the sound file or video file contained only as many symbols (binary digits) as is needed to communicate the content of the sounds or images. It's only recently, however, that information theory has begun to play a major role in mathematics, and theoretical science.
Now that scientists and mathematicians have matured to acknowledging that there are limits to what we can know, information theory has played an influential role in quantifying whether the solution to a problem is knowable or not. If one seeks to determine if the solution to a problem can be solved more efficiently, one can simply ask "Is the amount of information contained in this problem less than the amount of information contained in this solution to the problem."
Since information is at the core of every single problem or idea, any single problem or idea can be rephrased so as to analyze its information content. It's because of this, that information theory will prove to be very powerful tool this century. Now that we have a better grasp of what's knowable and what is not, what is needed is a way to understand the very root of knowledge itself and to study it in its most purest of forms: raw information.
