From: d@d.d   
      
   Hello...   
      
      
   I will add again more logical rigor to my post about about computational   
   complexity:   
      
   As you have just noticed in my previous post (read below), i said the   
   following:   
      
   That time complexities such as n*log(n) and n are fuzzy.   
      
   But we have to be more logical rigor:   
      
   But can we take as enough precision ?   
      
   I think that when we say 2+2=4, it has no missing part   
   of precision, so this fact is enough precision,   
   but if we say a time complexity of n*log(n), there is a missing part   
   of precision, because n*log(n) is dependent on reality that needs   
   in this case more precision about an exact precision about the   
   resistance of the algorithm(read below my analogy with material   
   resistance), so this is why we can affirm that time complexities such as   
   n*log(n) and n  are fuzzy, because there is a missing part of precision,   
   but eventhough there is a missing part of precision, there is enough   
   precision that permits to predict that there resistance in reality are   
   average resistance.   
      
   Read the rest of my previous thoughts to understand:   
      
   I correct again one last typo, here is my final post about computational   
   complexity:   
      
   I continu about computational complexity by being more and more   
   rigorous, read again:   
      
   I said previously(read below) that for example the time complexities   
   such as n*(log(n)) and n are fuzzy, because we can say that n*(log(n) is   
   an average resistance(read below to understand the analogy with material   
   resistance) or we can say that n*log(n) is faster than if it was a   
   quadratic complexity or exponential complexity, but we can not say   
   giving a time complexity of n or n*log(n) how fast it is giving the   
   input of the n of the time complexity, so since it is not exact   
   prediction, so it is fuzzy, but this level of fuzziness, like in the   
   example below of the obese person, permits us to predict important   
   things in the reality, and this level of fuzziness of computational   
   complexity is also science, because it is like probability calculations   
   that permits us to predict, since computational complexity can predict   
   the resistance of the algorithm if it is high or low or average (by   
   analogy with material resistance, read below to understand).   
      
   Read my previous thoughts to understand:   
      
   What is science? and is computational complexity science ?   
      
   You just have seen me talking about computational complexity,   
   but we need to answer the questions of: What is science ?   
   and is computational complexity science ?   
      
   I think that we have to be more smart because there is like   
   higher level abstractions in science, and we can be in those   
   abstractions exact precisions of science, but we can be more fuzzy   
   precisions that are useful and that are also science, to understand me   
   more, let me give you an example:   
      
   If i say that a person is obese, so he has a high risk to get a disease   
   because he is obese.   
      
   Now you are understanding more that with this abstraction we are not   
   exact precision, but we are more fuzzy , but this fuzziness   
   is useful and its level of precision is also useful, but is it   
   science ? i think that this probabilistic calculations are   
   also science that permits us to predict that the obese person   
   has a high risk to get a disease. And this probabilistic calculations   
   are like a higher level abstractions that lack exact precision but   
   they are still useful precisions. This is how look like computational   
   complexity and its higher level abstractions, so you are immediately   
   understanding that a time complexity of O(n*log(n)) or a O(n)   
   is like a average level of resistance(read below to know why i am   
   calling it resistance by analogy with material resistance) when n grows   
   large, and we can immediately notice that an exponential time complexity   
   is a low level resistance when n grows large, and we can immediately   
   notice that a log(n) time complexity is a high level of resistance   
   when n grows large, so those time complexities are like a higher level   
   abstractions that are fuzzy but there fuzziness, like in the example   
   above of the obese person, permits us to predict important things in the   
   reality, and this level of fuzziness of computational complexity is also   
   science, because it is like probability calculations that permits us   
   to predict.   
      
   Read the rest of my previous thoughts to understand better:   
      
   The why of computational complexity..   
      
      
   Here is my previous answer about computational complexity and the rest   
   of my current answer is below:   
      
      
   =====================================================================   
   Horand gassmann wrote:   
      
   "Where your argument becomes impractical is in the statement "n becomes   
   large". This is simply not precise enough for practical use. There is a   
   break-even point, call it n_0, but it cannot be computed from the Big-O   
   alone. And even if you can compute n_0, what if it turns out that the   
   breakeven point is larger than a googolplex? That would be interesting   
   theoretically, but practically --- not so much."   
      
      
   I don't agree, because take a look below at how i computed the binary   
   search time complexity, it is a divide and conquer algorithm, and it is   
   log(n), but we can notice that a log(n) is good when n becomes large, so   
   this information is practical because a log(n) time complexity is   
   excellent in practice when n becomes large, and when you look at an   
   insertion sort you will notice that it is a quadratic time complexity of   
   n^2, here again, you can feel that it is practical because an quadratic   
   time complexity is not so good when n becomes large, so you can say that   
   n^2 is not so good in practice when n becomes large, so   
   as you are noticing having time complexities of log(n) and n^2   
   are useful in practice, and for the rest of the the time complexities   
   you can also benchmark the algorithm in the real world to have an idea   
   at how it is performing.   
   =================================================================   
      
      
      
   I think i am understanding better Lemire and Horand gassmann,   
   they say that if it is not exact needed practical precision, so it is   
   not science or engineering, but i don't agree with this, because   
   science and engineering can be like working with more higher level   
   abstractions that are not exact needed practical precision calculations,   
   but they can still be useful precision in practice, it is like being a   
   fuzzy precision that is useful, this is why i think that probabilistic   
   calculations are also scientific , because  probabilistic calculations   
   are useful in practice because they can give us important informations   
      
   [continued in next message]   
      
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