User talk:Zoetrope/Archive1

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Hi . Nice of you to join us. If you'd like to know a bit more about the site please have a look at our RationalWiki:Newcomers' guide.--Bob^{Not Jim} 09:15, 11 July 2009 (UTC)

WIGO

You doubtless thought that you had a reason for removing a WIGO entry, but we don't do it. That's what the votes are for. ^{This message brought to you by: respond}_and honey 13:26, 11 July 2009 (UTC)

Delete me?

What do you mean? And why? tmtoulouse 06:23, 12 July 2009 (UTC)

Indeed, my curiousity has been piqued. Ace McWickedⁱ⁹ 06:45, 12 July 2009 (UTC)

Quercus

Is a very nice genus. ħuman 03:05, 27 September 2009 (UTC)

wat 09:18, 27 September 2009 (UTC)

Andy and the unique square root

The WIGO might have to be phrased better, but you should check out the diff in it:

Andy: You're the person who claimed it was wrong that complex analysis assumes a unique, algebraically manipulable square root of negative 1, which was silly.

To put this into perspective, check Patrick's posts on cp:Talk:Elementary proof:

Patrick: The notion that complex analysis depends on a purported uniqueness of the square root of -1 needs to be put to rest. There is no assumption that the square root of -1 has to be unique. And a good thing, too, because it isn't unique.

So why does Andy disagree?

Andy: Complex analysis does rely on an assumption that there is a unique, algebraically manipulable square root of negative one. It's a unique pair, obviously

(He also says a shorter version of this in the WIGO'd diff, but this was clearer IMHO)

So Andy's basic issue (in my eyes) seems to be that he doesn't understand that he alone uses "unique" in a different way than the others. While most people would say that there is no unique square root of 4, Andy would say that yes, there is a unique square root of 4 - a unique pair. And if you skip to the top of the Elementary Proof talk page, you will see that this isn't something new - Andy debated this with his brother more than two years ago already.

There also is a section called "Complex analysis" on Conservapedia Talk:What is going on at CP? where people discussed this further. --Sid 12:05, 27 September 2009 (UTC)

Here's my best guess at what's going on in Andy's "mind". Though it seems to have changed a tiny bit recently. He believes that complex numbers depend on -1 having a "unique" square root. I believe he doesn't mean unique in the sense that there is actually only one of them, but unique in the sense that one of them is "right" and the other is "wrong". The "right" one is what we call "i", and the "wrong" one isn't. If we can't tell which one is "right", the complex numbers can't be defined properly. Yes, I know, it's bullshit. Now he can sort of argue that there's a precedent for this. There are two square roots of 4, and one of them, +2, is clearly the "right" one, while -2 is the "wrong" one. The choice of the positive square root as the principle square root is accepted practice in calculus etc, when dealing with real numbers. But it has no analogue for complex numbers. (Which is the "right" square root of 6+7i?)

So Andy's real problem is that he thinks complex numbers depend on this choice being made before the imaginary unit can be defined. If we don't know which one is "right", the whole edifice comes crashing down. So he believes that the whole edifice has crashed down, from which he goes off on elementary proofs, and Erdos, and Atle-Selberg, etc.

The fact is, and Patrick was apparently trying to say this, is that "i" is chosen a priori, as a completely formal concept, not as the ("right") square root of -1. The concept of -1 having a square root doesn't even make sense until the complex numbers have been constructed. When Andy said "I'd like to see a proof of a unique square root of -1", he meant, first of all, that "unique" means "there is a special 'right' one", and, secondly, that he knows this isn't the case, so complex numbers don't work.

Now Andy seems to have softened his stance with the comment "It's a unique pair, obviously". Of course, if you consider just the pair, without regard for which one is "right", you could consider that pair to be unique. But that's about as useful as saying that there is a unique set of 44 (so far) Presidents of the United States. None of them is the "unique President", but collectively the set is unique. I guess. Whatever.

But just before "It's a unique pair, obviously", he says "Complex analysis does rely on an assumption that there is a unique, algebraically manipulable square root of negative one." So he still really doesn't get it. At all.

Gauss 01:48, 28 September 2009 (UTC)

I think that part of the problem is not just this "unique pair" nonsense, but that he thinks constructing the complex numbers involves some "assumption" like a new axiom, rather than just a definition. What if someone were to define the complex numbers as 2x2 matrices ( a b \\ -b a ) with the usual operations, instead of adjoining "i"? He can't call anything an assumption, like the existence of a unique pair of square roots of -1. It just turns out that there happen to be exactly two such matrices that square to ( -1 0 \\ 0 -1 ). It's just a definition of a set (in fact, a field, and we can even toss in a norm) -- no "assumptions" for him to latch onto. We could even prove Cauchy's theorem and all the rest by doing a find/replace in a usual proof, I don't know where he'd object. Heck, we could even give an Andy-style "elementary proof" of the Prime Number Theorem by using 2x2 matrices instead of complex numbers, thereby avoiding the extra assumption inherent in complex analysis!!! --Lesjohn 04:55, 28 September 2009 (UTC)

Guys, guys, ssshh. I don't care this much.