Basic UnderstandingPosted: June 23, 2008
I am not an expert on the subject … but these days, i am reading a book titled Shadows of the Mind by Sir Roger Penrose. I have written about some of the things i am thinking from this book, here. Now, at the cost of repeating myself, i am not an expert, so this post is only about what my understanding on the subject till now is.
First thing i have understood … that Mathematics and English dont go together. I am sure a lot of less than average IQ folks like me would have found the book more wonderful if we didnt have to take the double whammy of maths and language, simultaneously.
Second, there is an interesting outcome Sir Roger comes to …
Human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth.
Two things … either these algorithms are not sound, or they are not known to us to be sound, which means that we do not know that these algorithms are sound (there is no chink in their armoury). Either way, there is a mathematical certainty that mathematicians are using something other than pure “logic” at arriving at an understanding of the mathematical world. In other words, either way, the object either knows the algorithm is mathematically unsound, or doesnt know that it is sound, and still uses it.
Interesting … This implies that the science that we know today to be totally “rational” may not be completely so, at least not the science as we know it today.
More on this as i get to understand more …