The slow diffusion is thought to be due to manufacturers' reluctance to abandon their accumulated expertise with old technologies, which were embodied in the design of existing plants.
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Motivated by these hypotheses, we build a quantitative model of technology diffusion which we use to study this transition to a new economy. We show that it implies both slow diffusion and a delay in growth similar to that in the data. Development of the American Economy. Economic Fluctuations and Growth. International Finance and Macroeconomics. International Trade and Investment. Productivity, Innovation, and Entrepreneurship. The Science of Science Funding Initiative. Problems abounded: mechanical, electrical, financial. The traditional view was to build the cable, wind it on lots of big coils, put the transmitting apparatus at one end, the receiving apparatus at the other end and send signals along the whole length of the cable.
If the rate of transmission of the signals is fast enough, the cable is OK, if the rate of transmission is not high enough then the cable must be modified.
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Surely, by experimentation alone one would eventually arrive at the correct design. This is how it used to be but in that specific case this was not a possibility. The cable had to be built before it could be measured. Each experiment would have cost close to hundred thousand pounds.
Whitehouse, the man in charge of the electrical problems had an ingenious idea. There were many cables in existence. He connected them together achieving a very long cable although still far from the length required for the Atlantic cable. He was happy that on the basis of these experiments he would be able to design the transatlantic cable. He was one of the Directors of the Atlantic Telegraph Company.
One might be permitted to think that he was elected on the grounds of his superior knowledge of things electrical. However, this assumption would not be borne out by the facts. He was elected by the Scottish shareholders as an eminent man who would be able to represent their interests on the Board. Did the Board of Directors want to involve Thomson in the electrical problems of the cable? As it happened Thomson followed the progress of both attempts in and , sailing with the Agamemnon, but not in an official capacity.
In the words of S.
So what did Thomson do next? He took ink to paper and filled the paper with equations. It was high mathematics. Apart from half-a-dozen kindred souls nobody would have understood them in Britain. He set up what we would nowadays call a mathematical model. A model is a simplified version of the real thing. You need some skill to realise what matters and what does not. Thomson needed to take into account the diameters of the wires, the kind of insulation used, the thickness of the insulation, the distance between the two wires in the cable.
Then he sat down and solved the problem of pulse propagation, how it deteriorates as it moves along the cable, how the retardation the time needed to wait before the next pulse could be sent depends on the properties of the cable. He could not entertain any hope that his calculations will be understood, so he just offered them a law that came out of the calculations and was simple enough for the layman to understand. It became known as the law of squares. It meant that the retardation increased with the square of the length of the cable.
If a certain cable with a given length would cause a retardation of one hundredth of a second then a cable ten times as long would give a retardation hundred times as large, i. Whitehouse had little faith in the calculations of an academic. Whitehouse felt that he should not go too far in his criticism.
He approved the final design. The cable was built and laid.
The fourth attempt succeeded. It was a momentous time in history although most history books keep silent about the event. For the first time ever, sophisticated mathematics entered the realm of industrial design. Victory was not immediate.
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Two decades later when the same problem arose with telephone lines, the initial reaction of experts was once more that higher mathematics was irrelevant in solving the problem. After that, the scribbling of mathematicians became respectable. All major projects, industrial or otherwise, needed the assistance or possibly the lead of mathematicians. An example when a mathematician was in charge of a major project, was the breaking of Enigma, the secret German code, in the second world war.
I have said that we are still in the midst of the Second Industrial Revolution. Mathematicians are Kings. Technological advance is faster than ever. The Third Industrial Revolution is coming. Couple of decades? Three decades?
Second Industrial Revolution: The Technological Revolution - Richmondvale Blog
That will be a new age signifying the end of work. It will enable mankind to devote more time to realising their innermost desire: to kill their fellow human beings. What's this for? Already have an account with TheArticle? Sign in here.
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