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January 9th, 2017, 09:59 AM  #11  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,049 Thanks: 680 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
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Let's consider some algorithms. You could basically follow these steps to measure the length of the field: 1. Walk forward 1m. 2. Check: are you at the end of the field? 3. If so, print result. If not, go to 1. This algorithm has polynomial complexity, but we have no idea how many steps we are going to take until we actually measure the length. Now, let's say, for the sake of argument, that all football fields were made according to a formula: $\displaystyle f(N) = 100 + 0.0001N$ where N is the capacity of the stadium and f(N) is the length of the football field. We know that Crewe Alexandra has a capacity of 6000. What is the result? The algorithm is as follows: 1. Multiply 0.0001 by N 2. Add 100 to the result 3. print result No matter what stadium you have, this algorithm is always going to give a result that is directly computable; no checks needed. Therefore, the algorithm is a P algorithm. It is always evaluable in 3 steps, making it "easy". Even though the value is constant, we consider this polynomial space, so we just say that the algorithm is evaluable in polynomial time. Quote:
Basically, evaluating a result directly and checking whether some existing result is correct are different things and should be treated differently. In complexity terms, your Hamiltonian path finding is an NPhard problem, where the number of guesses that is typically needed to obtain a correct result skyrockets with the number of entities in your problem. Quote:
 
January 9th, 2017, 11:07 AM  #12  
Newbie Joined: Jan 2017 From: United States Posts: 9 Thanks: 0  Quote:
"This algorithm has polynomial complexity, but we have no idea how many steps we are going to take until we actually measure the length." This is the essence of life. We "think" we know until we "actually" get there and THEN we find the "correct" truth and correlation. From your own problem experiences to the world's problem experiences together as a whole. We are essentially evolving together yet separately by solving more problems because well more people, more problems, more experiences.. etc. This is the ONLY circumstance in which P will = NP. Math, History, Science, and even languages work this way. It's pretty much the essence of how we "learn". Think of "knowing" as like a ladder to climb. If you are missing steps to your ladder it will be much harder to climb. If you blindly mistake that you already know something you will also miss a step completely blind. Always stay humble and be aware so you can climb at a much steadier pace. P doesnt = NP if you give up.  
January 11th, 2017, 01:55 AM  #13  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,049 Thanks: 680 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
I'm really sorry, but I just can't resist... I haven't had my coffee yet and this post was just too funny. Quote:
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1. Pick a thing that looks cool (that you don't know already) 2. Read something about it or listen to someone talking about it 3. Try doing it 4. Can you do it yet? If not, try going back to 2 or 3 5. If so, go back to 1 Actually... that's an NP problem Quote:
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Last edited by Benit13; January 11th, 2017 at 01:56 AM. Reason: added a winky face at the bottom ;)  
January 11th, 2017, 07:35 AM  #14  
Newbie Joined: Jan 2017 From: United States Posts: 9 Thanks: 0  Quote:
You aren't understanding a word I say. I find this normal among the people stuck in the numbers. You are off in this algorithm world where everything is "suppose" to be exact. When things are only "exact" when correct. You are thinking in terms way too complicated. You pick apart my post like I was making different conjectures when actually the whole thing was one point. This may be part of the exact problem we have as a world. People don't look at the world as a "whole". They just pick apart all the problems when in reality there is only "one". Are you a robot? By the way. There is no such thing as algorithms for evolution. "We" are essentially the "algorithms" to evolution. You are not fully grasping the concept of what "learning" is. In this life you either "learn" or you "don't". You may "know" some things but that doesn't mean you've learned squat. Last edited by TwoCoins; January 11th, 2017 at 07:41 AM.  
January 11th, 2017, 08:31 AM  #15  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,049 Thanks: 680 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
I'd wager that the reason that you are finding that it is "normal among the people stuck in the numbers" to disagree with you is because those people are actually equipped with the knowledge to realize that what you are saying is silly or nonsense. Also, something can be both precisely defined and incorrect. Take a look at the meaning of "accuracy" versus "precision" and sources of error. They typically apply to measurements, but those concepts are fairly general. Quote:
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Well, by the way, here's a link to a MATLAB implementation of a genetic algorithm, which is part of their global optimization toolbox: https://uk.mathworks.com/discovery/g...algorithm.html Here's some wikipedia articles about genetic algorithms and their applications, which you might find enlightening. https://en.wikipedia.org/wiki/Genetic_algorithm https://en.wikipedia.org/wiki/Evolutionary_algorithm Numerical methods are my forte. I have helped two Masters students so far with their Masters theses on numerical models Have fun! Last edited by Benit13; January 11th, 2017 at 08:36 AM.  
January 11th, 2017, 09:03 AM  #16  
Newbie Joined: Jan 2017 From: United States Posts: 9 Thanks: 0  Quote:
Yes there is an "exact" of everything "yet" to be found or it has been found. Whether you realize this or not. I didn't actually mean there is no algorithms to evolution. I meant more in the terms of the "bigger picture" as YOU are an "in the works algorithm" yourself solving foreign algorithms outside of your consciousness to in turn hopefully "learn" what your algorithm is. Last edited by TwoCoins; January 11th, 2017 at 09:10 AM.  

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