Jerry Smith

-- Nick Petreley at the Christian Forums, in: <a href="http://www.christianforums.com/forums/showthread.php?s=&postid=196466#post196466" target="_blank">http://www.christianforums.com/forums/showthread.php?s=&postid=196466#post196466</a>

[ June 03, 2002: Message edited by: Jerry Smith ]</p>

lpetrich

"Negative numbers" were not admitted as legitimate mathematical entities until the 1500's, and "imaginary numbers" until the 1800's.

Even though they are as real as any other mathematical entities.

As to supernatural causation, I wonder if NP is willing to take seriously the hypotheses of religions other than his.

DonaldW112

Jerry,

See my reply to him on that thread. This is a clever use of terms. Imaginary numbers are well founded in math. The imaginary number i is by definition the square root of negative one. The analog is bad since there is nothing imaginary about the square root of negative one except that it can't be plotted on our standard number line (I don't think). But as I recall from high school you can plot it on an imaginary number line.


Donald

liquid

There are 2 ways to answer this. Either way, it's just playing semantics.

Method 1: 'Imaginary' numbers are totally real. They are as concrete as 'Real' numbers, it's just that we can't visualise them in the same manner.

Method 2: No number is real. Our use of 'real' numbers is just as arbitrary as 'imaginary' ones.

Basically, imaginary numbers are just as valid as real numbers - neither set exists any more or less in the actual universe.

NeilUnreal

This is the best way of looking at it. Mathematical systems usually have two aspects: colloquial and formal. IOW, they are useful for something people actually do, but they also have clearly defined properties. The two aspects are isomorphic to some degree, but the mapping is not rigorous. (Hofstadter's "Godel, Escher, Bach" discusses this at length.)

"Negative numbers," for example, can be colloquially represented in the familiar number line format. Another representation is to think of them as "positive numbers" plus an I.O.U. operator. It's like saying: "I came up shy balancing this equation, so I'll stick this I.O.U. in front of the number and keep working anyway." In this colloquialism, the number "i" is a way of working with the square root of this I.O.U. operator.

-Neil

p.s. If I had invented "i," I would have called it "u" for "Unreal"!

Undercurrent

Conway's Surreal numbers would blow his mind.

m.

NialScorva

Imaginary numbers can easily be imagined, you just have to use a two dimensional surface. That's what their often used for, a measure that has two orthogonal components to be measured. You can even use the square root of i to add another dimension.

seebs

He may have an indirect point, much though I hate to agree with him; the stuff categorized as "supernatural", if it exists, may be subject to study - but it may require a substantial rethink before it can be interacted with. Imaginary numbers took a while to be understood, or to produce informative results.

So... it wouldn't be the first time a new category of things was introduced to a field. It does look like it'd be a tough sell, if it could be made at all. I'm not sure how much of that is nonexistance, how much is intractability of the problem, and how much of it is prejudice. Some of each, I think.

seebs

I'd say there's a lot imaginary about it! It's well grounded *now* - when we've done a lot of thinking using that assumption. I can't have i of an object, I can't describe a line i inches long... it has *VERY* weird properties, whereas real numbers at least roughly correlate to the behavior of objects in the real world.

So... That's a pretty good analogy, up to the point where I don't think we have much in the way of nicely reproducible results from the supernatural.

NialScorva

Seebs,

First off, numbers are a description of the world, not an existing thing. A simple '5' doesn't exist either, it's a label we use to describe a certain count of objects that just exist. If you'll note that in your example, you say we can't measure something that's i inches long. It's the "inches" part that important, that's what ties the number to reality. The fact that complex numbers cannot be tied to reality in strictly the same way says nothing about them. It's like saying green doesn't exist because the sky's color can be measured in greeness.

As I said, imaginary numbers can be used to measure all sorts of things. Household electricity has an imaginary component to it (which if you feed a non-zero imaginary current back onto the grid, you can make your meter run backwards and transformers explode). They're one of several ways of describing a 2-dimensional value in a single piece, and length is not a 2 dimensional value.

The supernatural is a completely different situation. Instead of descriptions, we're now talking about existence. The problem is that science is all about giving descriptions to existing things, and the supernatural is practically undescribable by definition. You can't describe a pattern in a unique event, or rather you can describe any number of patterns that are equally (in)valid. Even assuming that the supernatural does exist, it's never going to be useful because it can't be predicted. If it can be described and predicted, then it's natural. Not much else to it, in my view.