Research Paper On Paradox

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Foreword
How wonderful that we have met with a paradox. Now we have some hope of making progress.
Niels Bohr

Paradoxes have an immense power. They have the power to turn existing rules upside down and make humans overthink what they think they know. A very good example for this is Olbers' paradox which argues that the night sky should be without any dark spots if the universe is infinite. The reason for this is that for every spot you look in the sky after some time should be a source of light. This paradox motivated scientists to make a lot of research in this area and was responsible for a big knowledge gain.
The simple explanation for the paradox is that the universe didn’t exist forever and therefore at certain spots in the sky the light
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Jonas Gloor, my tutor, who helped me whenever I needed it by giving me useful advice and who gave me the opportunity to perform an experiment in the class 2a.
Furthermore, I want to thank Christian Oehrli who also allowed me to make an experiment during his lesson with my own class.
1 What’s “the Braess Paradox”?
Paradox comes from the Greek word paradoxon and is translated to “para”= contradictory and “doxon”=idea. The word paradox is nowadays used for problems that seem to be unsolvable, not logical and counterintuitive. Paradoxes occur in many different areas ranging from normal life with statements like “this sentence is a lie” http://www.wissen.de/wortherkunft/paradox to physical phenomena like the egg cooking paradox which says that you need less water if you cook more eggs in an egg cooker. Many paradoxes can be resolved if analysed in a structured way. In the case of the egg cooker paradox you can find out that if there are more eggs, there is more surface at which the water can condensate and again be evaporated. (Freistetter, 2015)
That’s why Paradoxes are so valuable because they make us wonder and curious how something works and with that force us to investigate a topic and gain new
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Furthermore, all drivers want to get from O to R as fast as possible. Therefore, the driver’s decision for a route was only influenced by the time needed for the route.
Other aspects which could influence the decision making of drivers like habits or the fact that the consumption of fuel varies extremely with the speed and the number of cars which can cause stop and go driving was disregarded.
(Australian Government, 2008)
All of this assumptions were made to make it possible to formulate equations for the problem and analyse it.
In the illustration I made, the road segment PQ is the new route which is added and which makes the flow worse.
Compared to the original assumptions I changed two parts of the road network (visible on next page). First of all, I added to the road segments of OP and QR a fix part α1 because every road has a certain fix part even if it’s very small. Secondly, I changed the variable part of the road PQ from β2 to β3 because there wasn’t any reason why it should have the same congestion coefficient like PR and OQ.

t = time needed on a sub route f = number of cars on a sub
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