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Comment Re:Mistake in Summary (Score 1) 318

You can solve TSP for 1 million cities if you're willing to wait a few billion years

No you can't. You can't solve TSP for 1 million cities before the expected heat death of the universe.

Umm, do you have a proof of that?

Comment Re:That's Not What The Article Says (Score 1) 775

I recently gave up trying to explain to some mentally challenged person here on Slashdot the very simple concept of property ownership and how once somebody sells you something they literally have no rights over it. Morally, ethically, etc... no rights.

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?

Comment Re:store and release energy? (Score 1) 315

Assume that, to begin with, the car is moving at wind speed. The wheels are spinning (because the car is moving) and you can use that energy (i.e. brake the car) to push the propeller

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.

Comment Re:I went one further (Score 2, Informative) 1260

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:


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.

Comment Re:Ugh. (Score 1) 187

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

Comment Re:Common sense prevails (Score 1) 195

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.

Comment Re:This is not your father's Thinkpad Lenevo! (Score 1) 806

They would do better to remove the CAPS LOCK key, which is more bulky and - as far as I know - useful only to morons who don't know how to keep from SHOUTING on the internet.

I can't believe this is being repeated on slashdot of all places. Does nobody capitalize their constants anymore?? P.S. The otherwise lovely new Apple USB keyboard drives me insane when I use it to write code because of this feature (which I can't find how to disable).

Comment Re:Ridiculous (Score 1) 752

"What about the environmental impact of the extra time required to write the same functionality in C++?"

Should be about equal to the environment impact of maintaining the PHP language itself; in fact, it is likely to be less than that, since there would be no need to maintain the actual interpreter, but only duplicate some functionality. This is really a one-off, and the libraries could be reused by thousands of enterprises.

You're making a strange argument. Why does maintaining the C++ language have less of an environmental impact than that of maintaining the PHP language?

Bugs and security breaches do not cause any more CO2 emission than bug-free code, so I do not really see your point in bringing them up.

So having a person wake up and drive to work to fix something in the middle of the night doesn't cause any pollution? And that's just a very minor issue (and minor impact). Serious bugs and security breaches can create a lot of extra work with a lot of environmental impact.

P.S. Due to the laws of thermodynamics, work is always (thermal) pollution :-)

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