Computing in the past

Before the large computers - meaning before 1960 - there was only the human brain, pen, paper and some multiplication devices available to perform complicated numerical calculations. People still managed to make rather complicated calculations, it just took them much longer than it does to make the same calculations today.

From observations of the planet orbits of Jupiter, Saturn and Uranus John Couch Adams was in 1843 able to predict the location of an, at that time, unknown planet in the solar system - Neptun. Neptune was not found until 1846 after Urbain Jean Joseph Le Verriere independently of the earlier, unpublished, calculations came to the same result.
In fact, Neptune was already seen by Galileo in 1612-13. It appears as a star on two of his drawings of Jupiter.
After the second world war, the interest in rockets grew enormously, and reliable trajectories for missiles were required. To solve this requires many reputations of the same type of calculations, perfect for doing on a computer. They did not have a computer, instead they used many people, each of them just doing one particular operation and then handing the result on to the next one ... a human computer.

The technical evolution has also had impact on the way that you are being taught. It was not until the mid 70th that the pocket calculator became cheap enough to be introduced in secondary schools. In fact Klaus belongs to the first generation in Denmark that were allowed to use a pocket calculator in written mathematics examinations in secondary school. The calculators were trivial and could only do sums, subtractions, multiplications and divisions. We had to use special tables to find the result of the logarithm, sine and cosine of a number.

Before the pocket calculator the schools used special sliderules for multiplication and division using the concept of logarithms.

Since the beginning of computers their speed has doubled each 1 year and 10 months. This increase has been achieved by increasing the speed at which the CPU operates, the clock speed, by shrinking the physical size of the chip and make increasingly more complicated CPUs that are now able to perform more then one operation at a time. A problem that the computer industry will face in the near future is that the physical process used for making chip determines the minimum size of the CPU and we are getting close to the present limit. Continued increase of the CPU speed of a single cpu therefore requires new manufacturing techniques. The trend today is therefore not only to continue developing faster and more efficient CPUS, but to put more of them together in a way that they can work together on solving the same problem.

Therefore, what is difficult to do today in terms of computing resources, will be easier to do in a few years time!

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