Tok Presentation Script 47205h
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John Albert IDC4UT6-05 Mr. Smith Friday, October 25, 2013 2013-10-25 Theory of Knowledge
Nestor What is it about mathematics that makes it convincing? To what extent is math more reliable than other areas of knowledge? Mathematics is an area of knowledge that is not based on observations of the world. It is axiomatic meaning the system is purely logical. As well, it is independent of subjective experience. The sciences allow theories and ideas to adapt over time with new discoveries that overturn previous beliefs. In Math however it is certain that 1 + 1 = 2. However, it is possible to come to different conclusions using different systems of mathematics. For example in Euclidean math parallel lines do not intersect. However in Non- Euclidean such as elliptical and hyperbolic geometry they do as seen in the picture.
John Case Study Here is a case study concerning mathematical intuition There is a very rare disease in a population. Few people have it and the government has developed a test that is 99% accurate. If a person tests positive what is the probability that he or she has the disease? More than 50% chance or less than 50% chance?
If you state it is more than 50% than your mathematical intuition has failed you.
The answer is LESS THAN 1%!
Assume you have a population of 10 million people. Since the disease is very rare 100 people have it. Out of a hundred cases of disease 1 out of every 100 people will show up negative. 9,999,900 people do not have the disease and 1% will return positive. Thus 99999+99 results would return a positive result. 100099 /10000000 = 0.01 meaning 1%.
Apple misguiding us with axis y=x^2 + 4
x=y^2 + 4 y = x-4 y = plus minus root (x-4)
f inverse 8 = 2 f inverse 8 = -2 f inverse is not equal to x inverse
Links between mathematics and art Golden Ratio 1.618 Shells, Tiger, sunflower, Parthenon http://www.youtube.com/watch?v=jremlZvNDuk
Nestor What is it about mathematics that makes it convincing? To what extent is math more reliable than other areas of knowledge? Mathematics is an area of knowledge that is not based on observations of the world. It is axiomatic meaning the system is purely logical. As well, it is independent of subjective experience. The sciences allow theories and ideas to adapt over time with new discoveries that overturn previous beliefs. In Math however it is certain that 1 + 1 = 2. However, it is possible to come to different conclusions using different systems of mathematics. For example in Euclidean math parallel lines do not intersect. However in Non- Euclidean such as elliptical and hyperbolic geometry they do as seen in the picture.
John Case Study Here is a case study concerning mathematical intuition There is a very rare disease in a population. Few people have it and the government has developed a test that is 99% accurate. If a person tests positive what is the probability that he or she has the disease? More than 50% chance or less than 50% chance?
If you state it is more than 50% than your mathematical intuition has failed you.
The answer is LESS THAN 1%!
Assume you have a population of 10 million people. Since the disease is very rare 100 people have it. Out of a hundred cases of disease 1 out of every 100 people will show up negative. 9,999,900 people do not have the disease and 1% will return positive. Thus 99999+99 results would return a positive result. 100099 /10000000 = 0.01 meaning 1%.
Apple misguiding us with axis y=x^2 + 4
x=y^2 + 4 y = x-4 y = plus minus root (x-4)
f inverse 8 = 2 f inverse 8 = -2 f inverse is not equal to x inverse
Links between mathematics and art Golden Ratio 1.618 Shells, Tiger, sunflower, Parthenon http://www.youtube.com/watch?v=jremlZvNDuk
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