It's all really very simple. The concept of "you" or "me" is just that - an abstract concept. This concept only makes sense when certain conditions hold.

Umm, do you have a proof of that?

After the betrayal that was "Lost", I'm no longer watching anything by J. J. Abrams. Apparently the latest model of attracting viewers is to keep throwing mysteries and questions on them, without any plan to ever answer them. This is not something I am interested in.

Compare "Lost" to "Babylon 5".

I don't think it's as clear cut as that. If I sell you a painting I made, would you not agree that I still have the right to say that I painted it? Would you say that you have the right to erase my signature, draw your own and tell everyone you painted it?

No, you can't use that energy to move forward. The experiment boils down to two mediums moving relative to each other (we can choose to tie the coordinate system to the ground, to the wind, or at any constant speed). If you are stationary relative to one of the mediums, you can only use the other medium to change your velocity. You can only use it to change your velocity in the direction of the movement of that medium.

Imagine two opposing winds with between them, moving at the speed of wind1 (in its direction). Can you use wind2 to propel yourself in the direction of wind2?

As the grand-grand-parent says, however, it is very much possible to achieve the feat in the article by storing energy during the acceleration phase (you would end up accelerating slower than you would otherwise) and then once you reach wind speed, use that energy to move faster. Once that energy runs out, however, you will slow down to wind speed.

The string "SC2" is forever and ever reserved as an identifier for the best quest ever made, and a definite contender for the best game ever -- Star Control 2.

I'm probably too late to get modded up, but since none of the existing responses gave the exactly correct explanation, I'll have to post rather than moderated.

sqrt(1) is 1. It's not -1. By definition.

A list of transformations of an equality like the one given in the grandparent's "proof" is shorthand for a list of "implies" statements. For example, a proof like this:

2x-4=0
2x=4
x=2

is actually shorthand for:

A. 2x-4=0 (assumption).
B. 2x-4=0 implies 2x=4 (by rules of arithmetic).
C. 2x=4 implies x=2 (by rules of arithmetic).
D. 2x-4=0 implies x=2 (from B and C, as implication is transitive).
E. x=2 (from A and D, by Modus Ponens).

When you rewrite the shorthand proof in the grandparent post in full form, the mistake becomes (more) obvious: a^2=b^2 does not imply that a=b. But this has nothing to do with the sqrt function, it is because of the square function; because it is not an injective (one-to-one) function.

To illustrate by taking it to an extreme - instead of f(x)=x^2, let's take a different non-injective function: f(x)=0. Would you have any trouble realizing that f(a)=f(b) does not imply a=b?

As an amusing curiosity, one way to define |x| (the absolute value of x) is sqrt(x^2). |x|, as you may guess, is also a non-injective function.

Uhh, what?

An algorithm that runs in n*log(n) is slower than n.

Also, big-O is the wrong thing to use here - you want little-o (or little-omega). An algorithm being O(f(n)) only means that the algorithm runs in (asymptotically) less than or same number of of steps as f(n). An algorithm that runs in k*log(n)+p steps is in O(n^2) and in O(n) and in O(log(n)). To show that an algorithm A (that runs in f(n) steps) is faster than algorithm B (that runs in g(n) steps) you need to show that g(n) is in w(f(n)) ('w' is little-omega), or conversely that f(n) is in o(g(n)) ('o' is little-o).

I hate the use of the equals sign with the asymptotical growth notations, because it is extremely confusing to people who forget that O(f(n)) is a set, as are o(f(n)), w(f(n) and Omega(f(n)). If you use '=', you get confusing things like n=O(n^2) and n^2=O(n^2), so one might deduce that n=n^2. So let's everyone agree to use \in instead of '=' from now on. OK?

Big-O Notation

As an avid EVE player and an experienced software developer, I can confidently tell you that from the perspective of software design and development EVE is a pile of steaming crap. Every new release breaks existing features and known bugs last for years. Much of the code, the developers themselves have admitted, can't be touched anymore because nobody understands how it works. Instead of fixing bugs, they write new features which are released unfinished and then promptly forgotten when the next expansion is due.

What keeps EVE afloat and myself playing the game is that the concept itself is amazing. The day I managed to load Elite on my Sinclair, I knew that the the same game, with added massively multiplayer gameplay over the network would be awesome.

Who in their right mind would compare codec quality by encoding screenshots in a lossy image format??? To add insult to injury, the GIF image files in the article have a .jpg extension.

This article, and the person who wrote it, are worse than useless.