Well I am trying to understand it better. Instead of explaining it to me better, I get downvoted instead.
Please explain it further and tell me how you can estimate the time when a DDoS attack is being done on the system, or the CPU is overheating, I'd really like to know how you estimate that. Apparently I'm clueless and in need of many clues.
Your comment was not phrased along the lines of "Can anybody please explain this?" It was phrased as though meant to impart wisdom. That's why it got downvoted and why people are correcting you — because you (apparently) meant to ask a question but ended up making a bunch of erroneous claims instead.
Big O notation is an expression of a theoretical concept that applies to the algorithm itself. It is independent of any hardware that might be used to implement an algorithm.
Specifically, asymptotic complexity is an expression of the number of abstract operations or units of memory an algorithm will require. The meaning of "operation" or "unit of memory" depends on the algorithm. In the case of comparison sorting algorithms, for example, the operation in question is the number of comparisons.
Even if the CPU time allotted to a running algorithm changes due to system load or overheating, the algorithm still performs the same number of operations. Actual running time under system load can be calculated, but this is unrelated to big-O notation or complexity.
Regarding your explanation, it is excessively wordy and uses awkward phrasing. Your subsequent complaint about the terminology used in responses to your previous questions about P=NP demonstrates a serious lack of prerequisite knowledge. You learn the definition of "polynomial" in algebra; teaching you algebra is far beyond the scope of a discussion on HN.
As someone who is primarily self taught but also finished most of a college CS education, I can understand your frustration. In order to understand one thing you need to learn three other things, and there's no map that leads you from what you know now to what you want to know. Until someone makes that map, or you know enough to make up that map as you read Wikipedia, you'll have to learn things in the order they're taught in school.
So here's what you should do if you want to understand what people are talking about on HN:
1. (Re)learn basic algebra from start to finish. Use Khan Academy. You absolutely need this to understand what a polynomial is.
2. Accept Wikipedia as a source of information. Use a dictionary and other Wikipedia articles to look up terms you don't understand.
3. Related to #2, try to study cognitive biases, critical thinking, and logical fallacies. Studying these concepts will help your brain process information, such as difficult to understand Wikipedia articles. Check out lesswrong.com.
4. Study basic CS. Look for an Introduction to Computer Science course on Coursera or elsewhere.
5. Study algorithms. Take an algorithms course on Coursera or elsewhere.
I studied computer science at the University of Missouri Rolla. My instructor Dr. Pyron said that this stuff wasn't needed to learn Computer Science and that most of it was hoaky and kind of hinky. But he also told our Freshman class that "Ethics don't matter" as well. So I think I was robbed of that opportunity to learn it. BTW I feel that "Ethics do matter" and told him of my opinion, and he said it wouldn't work in the computer business.
I had a TA for College Algebra who couldn't teach it, and the professor was nowhere to be found. They made Catch-22 Jokes that he was like Major Major you could only see him if he wasn't in his office. It made me feel better but did not help me learn. I was in the Delta Tau Delta fraternity and they helped me out, but claimed the TA had messed up some of the problems that could only be solved with Calculus which I didn't learn yet. To make matters worse I got caught up in the party college thing and underage drinking. I quit eventually. But at least I didn't get forced to meet "Alice" like some unfortunate souls. I still have my Intro to Pascal and Pascal with Data Structures books in my basement, I should re-read them and try stuff with Free Pascal.
In 2005 I had a car accident and almost died, was in a coma, and lost some memories as a result. I may just have to relearn everything all over again. Since I am on disability, free online classes and sources are my only hope. Thanks.
With 25 years of experience in computer industry, you should be explaining us all how we can estimate the time when a DDoS attack is being done:).
Anyways we are talking here about complexity of the algorithm, and not its actual speed or performance which will depend on a lot of factors. But complexity tells for example how many steps it will take for the algorithm to solve the problem. The algorithm can be used by Humans or super computers, so performance can vary from days to microseconds, but complexity will remain same.
I think I covered that in this ebook: http://www.smashwords.com/books/view/314107 :) BTW it is a joke written by MIT's AI SciGen software to show how hard it is to tell if a thesis is serious or a parody written by clever AI software. Even if I mark it as parody and Computer Science Fiction some people are taking it seriously. Even when it says stuff like added 27 25Ghz Intel 386 chips to the network. :) The 386 chip does not run that fast.
OK complexity, then why is polynomial time used to describe it? I know some compilers can optimize machine code better than others, how does that affect the complexity? If the performance can vary from days to microseconds, well that is a very big gap. Video gamers always complain about 'lag', and days well that is one heck of a 'lag'! :)
The point of all this isn't to estimate exactly how fast it will take to do a task. It's to compare how efficient one way is against another.
Newer, faster computer will do them faster. A DDOS or CPU overheating will slow them down. But that's not the point.
Lets try a crap example I just made up. Imagine you want to go with your friends to see a movie. Here's a bad way to organise that. You drive to your first friends house. Ask what they want to see. Then you drive to each of your other friends houses and tell them what friend 1 wants to see. Then you drive to friend 2's house and ask them. And then drive to each of your friends houses (including friend 1) to tell them all what friend 2 has.
Can you see how with a large group of friends, that would be insane? It really doesn't matter if you have a fast or a slow car. It's just crazy.
A better plan would be to drive to each friends house, ask what they want to see and write it down on a piece of paper. Then at the end -- you can drive around again and tell everyone what movie you are all going to see.
If you've got 2 friends -- in the first plan you get to visit 4 houses. And in the second plan you get to visit 4 houses. With 3 friends it's 9 and 6. And then 16 and 8. And 25 and 10. 100 and 20.
Now lets say the person doing plan 1 discovers this amazing thing called the telephone. Plan 2 person is still using a car. Person 1 can do things so much faster. They don't have to leave home and can call in a manner of seconds.
But let's think it through.
4 calls vs driving to 4 people. 25 calls vs driving to 10 people. Still a big win for plan 1 at the moment. But how about 10,000 calls vs 200 car trips? 1,000,000 calls vs 2,000 car trips?