Reading JOHN SNOW DEFEATS “KING CHOLERA” John Snow was a famous doctor in London – so expert, indeed, that he attended Queen Victoria as her personal physician. But he became inspired when he
thought about helping ordinary people exposed to cholera. This was the deadly disease of its day. Neither its cause nor its cure was understood. So many thousands of terrified people died every time there was an outbreak. John Snow wanted to face the challenge and solve this problem. He knew that cholera would never be controlled until its cause was found. He became interested in two theories that possibly explained how cholera killed people. The first suggested that cholera multiplied in the air. A cloud of dangerous gas floated around until it found its victims. The second suggested that people absorbed this disease into their bodies with their meals. From the stomach the disease quickly attacked the body and soon the affected person died. John Snow suspected that the second theory was correct but he needed evidence. So when another outbreak hit London in 1854, he was ready to begin his enquiry. As the disease spread quickly through poor neighbourhoods, he began to gather information. In two particular streets, the cholera outbreak was so severe that more than 500 people died in ten days. He was determined to find out why. First he marked on a map the exact places where all the dead people had lived. This gave him a valuable clue about the cause of the disease. Many of the deaths were near the water pump in Broad Street (especially numbers 16, 37, 38 and 40). He also noticed that some houses (such as 20 and 21 Broad Street and 8 and 9 Cambridge Street) had had no deaths. He had not foreseen this, so he made further investigations. He discovered that these people worked in the pub at 7 Cambridge Street. They had been given free beer and so had not drunk the water from the pump. It seemed that the water was to blame. Next, John Snow looked into the source of the water for these two streets. He found that it came from the river polluted by the dirty water from London. He immediately told the astonished people in Broad Street to remove the handle from the pump so that it could not be used. Soon afterwards the disease slowed down. He had shown that cholera was spread by germs and not in a cloud of gas. In another part of London, he found supporting evidence form two other deaths that were linked to the Broad Street outbreak. A woman, who had moved away from Broad Street, liked the water from the pump so much that she had it delivered to her house every day. Both she and her daughter died of cholera after drinking the eater. With this extra evidence John Snow was able to announce with certainty that polluted water carried the virus. To prevent this from happening again, John Snow suggested that the source of all the water supplies be examined. The water companies were instructed not to expose people to polluted water any more. Finally “King Cholera” was defeated.
Using language COPERNICUS’ REVOLUTIONARY THEORY Nicolaus Copernicus was frightened and his mind was confused. Although he had tried to ignore them, all his mathematical calculations led to the same conclusion: that the earth was not the
centre of the solar system. Only if you put the sun there did the movements of the other planets in the sky make sense. Yet he could not tell anyone about his theory as the powerful Christian Church would have punished him for even suggesting such an idea. They believed God had made the world and for that reason the earth was special and must be the centre of the solar system. The problem arose because astronomers had noticed that some planets in the sky seemed to stop, move backward and then go forward in a loop. Others appeared brighter at times and less bright at others. This was very strange if the earth was the centre of the solar system and all planets went round it. Copernicus had thought long and hard about these problems and tried to find an answer. He had collected observations of the stars and used all his mathematical knowledge to explain them. But only his new theory could do that. So between 1510 and 1514 he worked on it, gradually improving his theory until he felt it was complete. In 1514 he showed it privately to his friends. The changes he made to the old theory were revolutionary. He placed a fixed sun at the centre of the solar system with the planets going round it and only the moon still going round the earth. He also suggested that the earth was spinning as it went round the sun and this explained changes in the movement of the planets and in the brightness of the starts. His friends were enthusiastic and encouraged him to publish his ideas, but Copernicus was cautious. He did not want to be attacked by the Christian Church, so he only published it as he lay dying in 1543. Certainly he was right to be cautious. The Christian Church rejected his theory, saying it was against God’s idea and people who supported it would be attacked. Yet Copernicus’ theory is now the basis on which all our ideas of the universe are built. His theory replaced the Christian idea of gravity, which said things fell to earth because God created the earth as the centre of the universe. Copernicus showed this was obviously wrong. Now people can see that there is a direct link between his theory and the work of Isaac Newton, Albert Einstein and Stephen Hawking. Reading task FINDING THE SOLUTION Do you like puzzles? Euler did. Did you solve the one you heard for the listening task? No! Well, don't worry, Euler didn't either! As he loved mathematical puzzles, he wanted to know why this one wouldn't work. So he walked around the town and over the bridges of Konigsberg several times. To his surprise, he found that he could cross six of the bridges without going over any of them twice or going back on himself (see Fig 3), but he couldn't cross all seven. He just had to know why. So he decided to look at the problem another way. He drew himself a picture of the town and the seven bridges like the one above. He marked the land and the bridges. Then he put a dot or point into the centre of each of the areas of land. He joined these points together using curved lines to go over the bridges (see Fig 1). He noticed that some points had three lines going to them (A, B and C) and one had five (D). He wondered if this was important and why the puzzle would not work. As three and five are odd numbers he called them "odd" points. To make the puzzle clearer he took away the bridges to see the pattern more clearly (see Fig 2). He wondered whether the puzzle would work if he took one bridge away (as in Fig 3). This time the diagram was simpler (as in Fig 4). He counted the lines going to points A, B, C and D. This time they were different. Two of them had even numbers of lines (B had two and D had four).
Two and four are both even numbers so Euler called them "even" points. Two points in Fig 4 had an odd number of lines going to them (A and C both had three) and so he called them "odd" points.
Using this new diagram Euler started at point A, went along the straight line to B and then to C. Then he followed the curved line through D and back to A. Finally he followed the other curved line from A back through D to C where he finished the pattern. This time it worked. He had been able to go over the figure visiting each point but not going over any line twice or lifting his pencil from the page. Euler became very excited. Now he knew that the number of odd points was the key to the puzzle. However, you still needed some even points in your figure if you wanted it to work. So Euler looked for a general rule: If a figure has more than two odd points, you cannot go over it without lifting your pencil from the page or going over a line twice. Quickly he went to his textbooks to find some more figures. He looked at the four diagrams shown below and found that when he used his rule, he could tell if he could go over the whole figure without taking his pencil from the paper. He was overjoyed. He did not know it but his little puzzle had started a whole new branch of mathematics called "topology". In his honour this puzzle is called "finding the Euler path".
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