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Not a number: The choice is between the calculator and the personal computer

The choice is between the calculator and the personal computer: Whoever has to plug numbers certainly expects a precise and above all reliable result. But how, when and from whom did computers actually learn how to correctly and logically string together numbers? William Kahan, guest speaker at the first Heidelberg Laureate Forum (HLF), is one pathfinder who taught the computer how to count.

Roughly thirty years ago, computers were still heavy and bulky. It was hardly imaginable back then that in just a few decades the large gray cabinets full of electric circuits and equipped with cathode ray tube monitors would become one of the most important technical ¡V and above all user-friendly ¡V everyday objects.

The computer is omnipresent in many daily situations; indeed we can hardly imagine life without it. This is particularly the case in the workplace where computers are used everywhere you look. They are used to design cars and bridges; they enable the global trade of stocks 24 hours a day; they are an important assistant in laboratories and they can be used to make telephone calls and take pictures. How did the computer become the leading machine in our lives? It did so because it is able to complete the most complex of calculations.

The high productivity of computers is due to the fact that they can calculate numbers with a complicate string of digits, such as the mathematical constant ¡§ƒà¡¨ (Pi), very quickly and with utmost precision. William Kahan, one of the pioneers of computer research, taught computers how to calculate numbers such as Pi. During the first Heidelberg Laureate Forum, the emeritus professor for computer sciences and mathematics, who teaches numerical analysis at the renowned University of California at Berkeley, will give a talk on the possibilities of error diagnosis in computer systems. 200 young researchers from all over the world will be in attendance to listen to William Kahan, and they will also have the chance to meet him personally during the week-long event.

The computer scientist, who after retiring from active teaching duties usually spends one or two days a week at the university, developed applicable standards that are still used today in every processor and thus can be found in any household worldwide. One example of such a standard is IEEE 754, which directs the computer to display ¡§Not a Number - NaN¡¨ as soon as the result of an arithmetic operation can no longer be defined. This happens, for example, if a number is divided by zero because a decimal point has been rounded incorrectly.

Rounding in and of itself is certainly a bit tricky. As we learned in school, rounding fractional digits too early can quickly lead to an incorrect result. While this might be tolerable for individual calculations, for more complex computing, such as weather forecasting, imprecision can lead to greater problems. Mathematicians call this error propagation, or in other words, the error reproduces itself. William Kahan developed a universally applicable standard that taught a computer how to round the fractional digits of a number the best possible way, thereby laying the foundation for the computer¡¦s ability to complete the most complex of calculations.

The Association of Computing Machinery (ACM) in the United States conferred the Turing Award on William Kahan in 1989 for his groundbreaking work on the standardization of computing operations. Today, during the first Heidelberg Laureate Forum, Kahan will speak on how error propagation can be dealt with in long computing operations. While such a phenomenon can still be justified slightly when it comes to weather forecasts, it cannot be tolerated in calculations for the aerospace industry: such things are a matter of life and death.

The Heidelberg Laureate Forum (HLF) was started by the Klaus Tschira Foundation (KTS), which promotes natural sciences, mathematics and computer sciences, and the Heidelberg Institute for Theoretical Studies (HITS). The Forum is being organized by the Heidelberg Laureate Forum Foundation in cooperation with the Association for Computing Machinery (ACM) of the International Mathematical Union (IMU) and the Norwegian Academy of Science and Letters.
To the editors:
With this press release, we would like to extend an invitation to attend the Forum as well as to report on the event. Thank you.
You will find an additional blog entry on William Kahan on our blog:

For a photo of William Kahan, please contact:

Press inquiries:
Sabine Kluge
Heidelberg Laureate Forum Foundation
Schloss-Wolfsbrunnenweg 33, 69118 Heidelberg
Telephone: 06221-533 385
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Sabine Kluge | idw
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