5 ms·
I think they intended to say quadratic. For N classical objects interacting, each of them can interact with each of the N-1 others, hence O(N^2). The GP is sa
by shwaj 3y ago
I think they intended to say quadratic. For N classical objects interacting, each of them can interact with each of the N-1 others, hence O(N^2). The GP is saying that the quantum interactions don’t follow this rule, hence “not merely O(28^2)”, but in fact much bigger.
- btilly 3y agoNo, they meant exponential because that is what they heard. That is correct, it is exponential. They were just apparently confused about what exponential means.
- shwaj 3y agoNot to make a big thing about it, but you’re wrong. Try read it again, slowly. Edit: hint: focus on “if that’s true” and “merely”.
- db48x 3y agoI disagree too. He asks “If it is truly exponential, why is it not just 28^2× (aka 784×) harder than hydrogen?”. The answer is that he misunderstood exponential growth, and thus it is at least 19342813113834066795298816× harder than hydrogen.
- rich_sasha 3y agoYou misunderstood English. I'm saying simulating 28 quantum particles is not merely O(28^2) harder than one. Because it is exponential...
- shwaj 3y agoHe is not asking anything. He is making a statement. When someone says “that’s why A, and also why B”, they’re making a statement, not asking a question just because the word “why” appears. The lack of a question mark is also a clue.
- btilly 3y agoSorry, but you're wrong. And this isn't simply a question of reading slowly. Read it again, armed with the following fact. What they claim to have been told is correct. It is exponentially hard in N. Your theory is that they meant to say quadratic. This requires: 1. They heard exponential and understood it to be quadratic. 2. While writing down what they heard, they accidentally wrote exponential instead of quadratic. 3. While explaining their question, they failed to catch the second error. Now consider my theory. That they are confused about the difference between exponential and quadratic. This requires: 1. Like many people I've met, that they are confused about the difference between exponential and quadratic. 2. They made no other mistakes. They remembered what they were told correctly. They repeated it correctly. And then asked a reasonable question based on their understanding. In general a whole chain of coincidental errors is far less likely than a single error. Doubly so when it is a single error that is somewhat common. Most people will run across exponential vs quadratic in high school, forget it, then never use that information again. There's an exponent, it's exponential, right? Therefore I think it is far more likely that they misunderstood the term, rather than that they understood the term and then made a whole series of other mistakes to produce the statement that we saw.
- rich_sasha 3y agoErm, what? If it was classical mechanical 28 "balls" with pairwise interactions, complexity would be "merely O(28^2)". But it is not, which is what I said. I mean, there is some irony in accusing people of not understanding the most basic of mathematical terms, while not understanding (repeated!) explanations of the comment.
- ftxbro 3y agoThis is an internet comment section, if you are talking about things being exponentially hard and part of your comment is asking "why this is not merely O(28^2) harder (or do you need the electrons too?)" then of course people are going to think you don't understand what exponential means.
- rich_sasha 3y ago