scigirl

(scigirl is scared of the math in this thread so she's moving it to science and skepticism)

scigirl

seebs

Heh.

The odd thing is, everyone reading this has probably imagined the five cows, but we don't call *that* an imaginary number.

I hate terms of art.

ohwilleke

Imaginary numbers do corrolate to phenomena in the real world, such as electric circuits.

seebs

In a way different from what you get by just using two arbitrary dimensions with no relationship between them?

Undercurrent

Yes. The meat of complex numbers is not really the structure of the set itself, which is just another isomorphism of R^2, but the multiplcation operation it provides (i.e. (x1,y1)*(x2,y2) := (x1*x2 - y1*y2, x1*y2 + x2*y1) where the "*" on the right represents ordinary real-number multiplcation.)

This operation can be used to describe of a wide variety of functions in the "real world", the most glaring example, in my mind, being the Feynmann rule for compositing probability amplitudes, which underlies quantum mechanics.

Moral: Just because an algebra provides no value to someone who wants to inventory a warehouse or balance a checkbook, doesn't mean it can't describe anything.

NeilUnreal

Any attempt to determine whether or not "numbers exist" requires that you either 1) axiomatically accept their existence in a Platonic sense, or 2) define them such a way that the determination of reality can be made. In either case, it becomes difficult or impossible to say whether one class of numbers exists in a more real way than any other class.

The classical way is to try to reduce them to some sort of essence or "obvious" set of axioms. Unfortunately for Plato, this is usually just a way of either begging the question, or making a functional statement about how much "bang for the buck" a particular set of axioms provides.

-Neil (A Reformed Platonist)

NialScorva

Define exist. I didn't say that "5" isn't a property, rather that "5" doesn't exist in isolation. You say N inches, why not 2.54N centimeters? Did the "reality" of that length change, or did I change the description?

It's not about saying that I have no grounds for "5" to exist. In a sense it does-- within the game of mathematics, and as an arbitrary description of empirical things. I maintain that it doesn't have an isolated existence without a necessarily tied in measure. Numbers are a pure abstract description, they do not take empirical attributes. I can learn "blue" by someone grunting and pointing at objects until I distill the common empirical attribute among them. It can be claimed that "blue" is real based upon it's ability to be assigned empirical properties such as frequency and energy. One learns "5" similarly, but it cannot be described in other empirical terms.


[/quote]
It exists as much as the referents of most personal pronouns do; careful study of bodies has never revealed a "person" anywhere in them, but we all believe in people.
I see numbers as being just as meaningful as the reality they describe; they're just not physical objects.
[/quote]

Meaningful does not imply existence. Numbers are a useful analogy, a description between an world of thought and a world of experience, but they rely on *our* ability to tie those two together with an analogy. Attributes such as identity and measure are the bridge between the two, but are necessarily arbitrary. In short, a rock exists, I can kick it. Blue exists, I can measure it. Numbers do not exist, rather they are a way of describing what exists by how hard I kick it, or what the measure is.

As I've been arguing, since all numbers are merely an analogy to reality rather than reality itself, I have to say that you are mixing two distinct things. The second dimension is a reality that can be measured. Imaginary numbers are a descriptive thing that is used to measure them. As Micheal said, they are useful because multiplicatively they follow the same rules as a vector, and there are nifty trig functions that you can do on them that is easier than dealing with vectors in certain situations. Then again, everything that can be done with imaginary numbers can probably be done with vectors, so it's a matter of which tool we use to describe, and which is the most fit.

Consider that simple natural numbers are the mathematical analogy is the closestly tied to the assumptions we make about reality. We like to see things as wholes, as nice discrete pieces. A donut is a donut is a donut. One "thing" is one "thing". However, as you try to identify things in greater and greater detail, the analogy starts to fail. There are two donuts, but one is glazed and one is jelly-filled. Are they still a both the same "one"? One weighs more than the other, are they the same "one"? One is burnt to a crisp, is it still the same "one"? Set theory addresses some of this, by saying "donut" is a class of objects, laying out the definitions for "one" from the outset. However, it's because of this very need for the definition that we must divorce numbers from strict reality in order to maintain the integrety. The further you move past the most degenerate cases of mathematical description, the more aware of the metaphoric glue that allows us to describe what is real by using the language of mathematics.


True, true. However you have to consider that methodolical naturalism, aka science, assumes that in principle there are two conditions, the natural and the not yet explained by natural means. The supernatural, whether it exists or not, is indistiguishable from not-yet-explained. The reason is not because of a bias against the supernatural, but because the only way to prove that something cannot be described by a set of rules is to know all of the rules, and exhaustively show that no rule can apply. Mathematically (heh, strange turn of events, eh?) it has been shown that we cannot do this.

So, for me at least, it's not a matter of the supernatural not existing, or precluding the existence of it, rather it's that even if the supernatural does exist, it's not a useful tool in describing the universe precisely because of it's necessary randomness.

Starboy

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Saying you will not consider the possibility of supernatural causes in science sounds to me like saying you refuse to deal with imaginary numbers in math simply because they don't exist.
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A more appropriate anology would be "Saying you will not consider the possiblity of supernatural causes in science sounds to me like saying you refuse to deal with division by zero in math simply because it is not allowed."

Veil of Fire

And I thought Ceremonial Magicians used weird words and impossible-to-grasp concepts....