A modern fable
This is a story about the worlds greatest failure. The story is true, the people in it are real, just some of the facts may not be right. If you are someone who thinks that facts are more important than the story then by all means write your own version.
Once upon a time (as all good stories should begin) There were some people called mathematicians who were attempting to solve some particularly difficult problems. These problems were far more difficult than the numeracy problems you may get at school such as what is 7 x 9 or 169 x 27. In fact they were so difficult, mathematician's would find them very hard to describe even to other mathematician's.
One day two mathematicians called Alfred Whitehead and Bertrand Russell decided that one of the reasons that the problems were so difficult was that no one really understood why mathematics worked at all. They often did things like this because as well as being very good at numbers, they were both something we call philosophers. Now philosophers are people who spend all their time thinking about things most people just take for granted. For example, a philosopher will spend days thinking about whether you are sharing your room with a Rhinoceros, while most other people would just assume you were not due to the lack of things like Rhinoceros poo and the fact that Rhinoceros's are pretty poor at hide and seek. Anyway for these men it was not enough that the answer to 1+1 was 2, they wanted to know why it was not 3, 4 or even rhinoceros's. In fact next time your maths teacher gives you a sum, you can try asking them why it has to be that answer and not something else. If they are a pretty cool maths teacher, they may thank you for asking such an intriguing question, but most likely they will just get annoyed(teachers generally prefer to ask questions, not answer them ).
It is also worth saying a little about the man called Bertrand Russell. You probably haven't heard much about him at school, but once he was one of the most famous men in the world. One of the reasons he was so famous is that he was pretty good at everything. He must of been terrible to be at school with. For example, just imagine getting 9/10 in your Maths test and feeling pretty good about yourself, until you find Bertrand had 10/10 not only in Maths but English, History Science, etc. In fact the only subject he doesn't seemed to been very good at was sport, but that was probably only because he didn't have any time to do it. In fact as well as being good at mathematics he also won the Nobel prize for his writing, which is the best award any writer or scientist can get. You would also of thought that spending loads of time thinking and writing and not playing sport would mean he didn't have any girlfriends, but in fact he seemed pretty good at having girlfriends too.
Anyway Bertrand and Alfred decided to try and answer why 1+1 equals 2 by creating from Mathematics from scratch. They hoped that once the 1+1=2 problem had been solved, they could then solve more difficult problems (such as 7x9 and 169 x 27). So they wrote a book called the Principia Mathematica, which is a very grand title for a book. However this is not a book you are likely to find in the library (unless your library is very big and/or very weird). In fact even if you did get it, it wouldn't be a very good read. Most of it is written in something called symbolic logic which is very strange and not really understood by many people. (In fact if you ever meet a mathematician, ask them what they think of Principia Mathematica. They will probably tell you how important it is, but then ask them if they have ever read it, and they will almost certainly say no [or lie]).
Writing this book turned out to be a big job. In fact it took over 17 years and eventually it had to be written down in 3 books. The amazing thing is they only managed to show that 1+1=2 by the middle of book 2 (it is not known whether they also found the presence of any rhinoceros's in the book).
Unfortunately at the same time there was a man called Kurt Godel who was also thinking about things and had an idea that he called his Incompleteness theory. His idea was that it doesn't matter how clever we are or how hard we try, some problems can just never be solved. Now this was a big problem for Bertrand and Alfred, because Kurt's idea showed that they could never solve all maths problems, which after 17 years of work must have been very disappointing to Bertrand and Alfred. (Kurt Godel unfortunately came to a rather sticky end when he was convinced everyone was trying to poison him and refused to eat anything. He then starved himself to death. This can happen when people spend a lot of time thinking about really deep questions rather than what is next for dinner.)
However our story is not finished. Often when mathematicians come up with ideas, they describe them in really complicated ways that make it difficult for other people to understand them. Other mathematicians sometimes think of easier ways to describe them. Such a thing happened in this case. A man called Alan Turing thought he had much neater way to better describe Godel's theory.
His idea was to design an imaginary problem solving machine. This machine has a tape with an instruction on it, which could move backward and forward. Each time it read a new symbol it would cause the machine to do something and remember the result. This way the machine could be made to do mathematical problems. So if our tape has the values '1','+','1' then our machine would load each symbol in and do something with them. For example when it found the '+' symbol it would know it had to add the previous symbol to the next symbol on the tape.
You may recognise this imaginary machine as a computer, but this was a long time before computers actually existed. This was just an idea in Alan Turing's head. Turing could see that such a machine could do any type of mathematical puzzle, but for some problems it was difficult to work out when the machine had got to the answer and could be stopped. For example you could asked the machine to find all the numbers that could be divided exactly by 7. Now it's possible that if we carried on long enough you would find all the numbers in the universe that could be divided exactly by 7, but how will you know that if you do not keep on going you will not find another one? Well Alan showed his imaginary machine had the same problem and therefore some sums could never be solved so proving Kurt Godel's idea was correct (but in way that is easier to explain).
However the idea of a universal calculating machine was so good that people actually made them. In fact every computer, calculator, and mobile phone uses the same idea as Alan Turing's.
So that is the story about the world's greatest failure. However the word 'greatest' here does not mean in this case the worst failure. This time it is used to describe the most successful failure. If Alfred and Bertrand had not started writing their Principia Mathematica, Kurt Godel may not of had his big idea and Alan Turing may not of invented his universal machine. If that had happened then we would not have computers. Can you imagine a world today without computers? No mobile phones, no X Box! It would be a very different place wouldn't it.
Which just goes to show, that when you are doing hard things, starting them is more important than finishing them. Which is why we send space crafts to Pluto or build huge machines to smash atoms into tiny bits. You just never know what important things we will find along the way
Once upon a time (as all good stories should begin) There were some people called mathematicians who were attempting to solve some particularly difficult problems. These problems were far more difficult than the numeracy problems you may get at school such as what is 7 x 9 or 169 x 27. In fact they were so difficult, mathematician's would find them very hard to describe even to other mathematician's.
One day two mathematicians called Alfred Whitehead and Bertrand Russell decided that one of the reasons that the problems were so difficult was that no one really understood why mathematics worked at all. They often did things like this because as well as being very good at numbers, they were both something we call philosophers. Now philosophers are people who spend all their time thinking about things most people just take for granted. For example, a philosopher will spend days thinking about whether you are sharing your room with a Rhinoceros, while most other people would just assume you were not due to the lack of things like Rhinoceros poo and the fact that Rhinoceros's are pretty poor at hide and seek. Anyway for these men it was not enough that the answer to 1+1 was 2, they wanted to know why it was not 3, 4 or even rhinoceros's. In fact next time your maths teacher gives you a sum, you can try asking them why it has to be that answer and not something else. If they are a pretty cool maths teacher, they may thank you for asking such an intriguing question, but most likely they will just get annoyed(teachers generally prefer to ask questions, not answer them ).
It is also worth saying a little about the man called Bertrand Russell. You probably haven't heard much about him at school, but once he was one of the most famous men in the world. One of the reasons he was so famous is that he was pretty good at everything. He must of been terrible to be at school with. For example, just imagine getting 9/10 in your Maths test and feeling pretty good about yourself, until you find Bertrand had 10/10 not only in Maths but English, History Science, etc. In fact the only subject he doesn't seemed to been very good at was sport, but that was probably only because he didn't have any time to do it. In fact as well as being good at mathematics he also won the Nobel prize for his writing, which is the best award any writer or scientist can get. You would also of thought that spending loads of time thinking and writing and not playing sport would mean he didn't have any girlfriends, but in fact he seemed pretty good at having girlfriends too.
Anyway Bertrand and Alfred decided to try and answer why 1+1 equals 2 by creating from Mathematics from scratch. They hoped that once the 1+1=2 problem had been solved, they could then solve more difficult problems (such as 7x9 and 169 x 27). So they wrote a book called the Principia Mathematica, which is a very grand title for a book. However this is not a book you are likely to find in the library (unless your library is very big and/or very weird). In fact even if you did get it, it wouldn't be a very good read. Most of it is written in something called symbolic logic which is very strange and not really understood by many people. (In fact if you ever meet a mathematician, ask them what they think of Principia Mathematica. They will probably tell you how important it is, but then ask them if they have ever read it, and they will almost certainly say no [or lie]).
Writing this book turned out to be a big job. In fact it took over 17 years and eventually it had to be written down in 3 books. The amazing thing is they only managed to show that 1+1=2 by the middle of book 2 (it is not known whether they also found the presence of any rhinoceros's in the book).
Unfortunately at the same time there was a man called Kurt Godel who was also thinking about things and had an idea that he called his Incompleteness theory. His idea was that it doesn't matter how clever we are or how hard we try, some problems can just never be solved. Now this was a big problem for Bertrand and Alfred, because Kurt's idea showed that they could never solve all maths problems, which after 17 years of work must have been very disappointing to Bertrand and Alfred. (Kurt Godel unfortunately came to a rather sticky end when he was convinced everyone was trying to poison him and refused to eat anything. He then starved himself to death. This can happen when people spend a lot of time thinking about really deep questions rather than what is next for dinner.)
However our story is not finished. Often when mathematicians come up with ideas, they describe them in really complicated ways that make it difficult for other people to understand them. Other mathematicians sometimes think of easier ways to describe them. Such a thing happened in this case. A man called Alan Turing thought he had much neater way to better describe Godel's theory.
His idea was to design an imaginary problem solving machine. This machine has a tape with an instruction on it, which could move backward and forward. Each time it read a new symbol it would cause the machine to do something and remember the result. This way the machine could be made to do mathematical problems. So if our tape has the values '1','+','1' then our machine would load each symbol in and do something with them. For example when it found the '+' symbol it would know it had to add the previous symbol to the next symbol on the tape.
You may recognise this imaginary machine as a computer, but this was a long time before computers actually existed. This was just an idea in Alan Turing's head. Turing could see that such a machine could do any type of mathematical puzzle, but for some problems it was difficult to work out when the machine had got to the answer and could be stopped. For example you could asked the machine to find all the numbers that could be divided exactly by 7. Now it's possible that if we carried on long enough you would find all the numbers in the universe that could be divided exactly by 7, but how will you know that if you do not keep on going you will not find another one? Well Alan showed his imaginary machine had the same problem and therefore some sums could never be solved so proving Kurt Godel's idea was correct (but in way that is easier to explain).
However the idea of a universal calculating machine was so good that people actually made them. In fact every computer, calculator, and mobile phone uses the same idea as Alan Turing's.
So that is the story about the world's greatest failure. However the word 'greatest' here does not mean in this case the worst failure. This time it is used to describe the most successful failure. If Alfred and Bertrand had not started writing their Principia Mathematica, Kurt Godel may not of had his big idea and Alan Turing may not of invented his universal machine. If that had happened then we would not have computers. Can you imagine a world today without computers? No mobile phones, no X Box! It would be a very different place wouldn't it.
Which just goes to show, that when you are doing hard things, starting them is more important than finishing them. Which is why we send space crafts to Pluto or build huge machines to smash atoms into tiny bits. You just never know what important things we will find along the way
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