Formal sciences use formal systems to generate knowledge, including mathematics, logic, statistics, information theory, and theoretical computer science. They lack empirical basis but are important for quantitative science. They have a long history, with math texts emerging in Mesopotamia in 1800 BC and logic developing in China and Greece. Information theory, theoretical computer science, and modern statistics date back to the mid-20th century. Soft sciences have become more quantitative, and theoretical physics heavily relies on mathematics.
A ‘formal science’ is an area of study that uses formal systems to generate knowledge. Mathematics is the prototypical example. Others include logic, statistics, information theory, and theoretical computer science. While it has sometimes been questioned whether these are truly “science” or not – considering the lack of real-world experiments – these disciplines often still get lumped together in science. Despite their lack of an empirical basis, the formal sciences are generally regarded as extremely important, and indeed, all quantitative science depends on them. It is an ongoing debate whether or not formal sciences are true sciences.
Math texts emerge in ancient history around 1800 BC, in Mesopotamia, the location of Babylon, the largest city on Earth at the time. The original purpose was to quantify commodities, such as slaves or grain. Around 600 BC in China and 400 BC in Greece was the initial development of logic, the explicit analysis of methods of reasoning. In Greece were the great ancient Greek philosophers such as Pythagoras, Socrates and Aristotle, whose insights and beliefs about logic and science dominated the Western world well into the modern era, up to 17th century luminaries such as Pierre de Fermat, Blaise Pascal and Christiaan Huygens initiated the development of mathematics in its modern form.
Information theory, theoretical computer science, and modern (Bayesian) statistics date back to Claude Shannon and Jon von Neumann in the mid-20th century. Alan Turing also made important contributions. Computer theory, radio signals, and antenna design all hinge on the milestones achieved by these thinkers. These areas are all important parts of the formal sciences.
After many decades of confusion in experimental methods and analyses, recently the “soft sciences” (social sciences, political sciences, etc.) have become more quantitative, heralding a fundamental change in the way things are done. Psychology has become more experimental, and many of these findings are sweeping away the traditional wisdom of older thinkers like Freud. Experimental psychology often falls under the banner of “cognitive psychology.”
Theoretical physics seems to be heavily dependent on mathematical developments to make progress. Theoretical physics often uses the most advanced mathematics available of the day and describes its results and predictions in these terms.
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