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Lecture 8

Lecture 8.docx

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Dan Dolderman

Lecture 8Participation perspectivescalenon linearitymotivationslocal multiplicityuncertainty vs local expertise Complex SystemsYou cannot know everything bc there are so many factors there is irreducible uncertainty We cannot do a perfect analysis of s system Reductionist thinking hits a wall especially when you think of non linearity Prediction and control is doomed can try to improve prediction but it is never going to be perfect and it is never going to be close Trying to Predict Weather LorenzCreate a set of equations that represents the variables acting on weather patterns wind humidity temp moon currents etcGet a way of predicting what the weather will doThere will be error but it is a linear approximationImagine the y axis represents weather states o There are more dimensions than this 2 dimensional space but basic logic is same o Historical graph with diff levels representing diff weather stateso With a lot of refining he comes up with a modelo Should be able to extrapolate and predict backward and forward o Info from today tells you what is going to happen tomorrow the output of one day is then entered as the input for the day afteran iterative modeling processo We usually deal with ymxb equations which are simple dependent variablethe slope times x plus an intercept Eg get y2x5put same input in always get the same output If weather is a deterministic system then if you put info in from one day you will get info about the next day if the same variables occur months later the next day should be the same as the day that came after it in the first instanceLorenz had to restart but he started later in history and he already knew all the variables ran the program to determine rest of the days o But got a different line than the first timemathematically impossible o Computer has an internal memory and carries more decimal places than he has on his readout which he had input into the computer With such a small error would expect missing these few decimals shouldnt matterIf just a tiny decimal off model gives completely different story after a few predictions Cant predict the weather unless it is tomorrow cannot predict months down lineThis is an interdependent system very small errors at time one can become big errors at time 2This let to the butterfly effect o Cant track all the variables tiny dynamics of a butterfly flapping its wings start changing the local conditions which changes something else etcWe cannot predict stuff we have irreducible uncertainty Eg a non linear stereo turn nob and never know if volume will go up or down o Imagine each turn of the notch took 500 years Kay ReadingLake Erie died many decades agoIt is a shallow lake ecosystem that can organize itself in one of 2 ways Decades ago there were many happy fish and plants
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