That's the latest book i read. It is another one of those 'science explained in layman terms' book.
It talks of why we must not be surprised by occurrences that are counter-intuitive, and in fact expect such results. He uses the theories such as catastrophe theory, chaos theory, etc to elaborate his point.
The interesting part is when he explains the limitations of logic/mathematics. Consider a Universal Truth Machine (UTM), which can print out ALL and only, TRUE statements. Now, consider the statement, "The UTM will not print this statement". What happens now? If the UTM prints this statement, the statement would be false, and UTM cannot print a false statement. So, it cannot be printed. But, if it is not printed, then the statement becomes TRUE, and the UTM does not print it. So, the UTM is not universal. The conclusion is that we cannot prove all statements in a system, by using the system. Hence, we cannot expect to learn everything using rational thought. Interesting...
It talks of why we must not be surprised by occurrences that are counter-intuitive, and in fact expect such results. He uses the theories such as catastrophe theory, chaos theory, etc to elaborate his point.
The interesting part is when he explains the limitations of logic/mathematics. Consider a Universal Truth Machine (UTM), which can print out ALL and only, TRUE statements. Now, consider the statement, "The UTM will not print this statement". What happens now? If the UTM prints this statement, the statement would be false, and UTM cannot print a false statement. So, it cannot be printed. But, if it is not printed, then the statement becomes TRUE, and the UTM does not print it. So, the UTM is not universal. The conclusion is that we cannot prove all statements in a system, by using the system. Hence, we cannot expect to learn everything using rational thought. Interesting...
1 comment:
Hm ,.. nice post ,... if you have some time you can look mine too
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