Sorry this post is long, but it's the theory I've been setting up for a couple pages.
Imaginary numbers are real, they just follow different rules, so we put them in a separate category from real real numbers, because we can make rules for them and put them in that neat little heirarchy bob wrote up.
I think this is an interesting read.
I want to talk about the heirarchy of science a bit.
In the Universe, as I see it, scientifically we establish a hierarchy for deducing everything observable in the Real World. You have Observations, what we see on the surface, not very helpful on its own. Below that you have biology explaining what is actually moving things within us, very mechanical and descriptive. Below that you have Chemistry, describes why these interactions happen, what's happening on a smaller level. Below that you have Physics, describing the inner workings of the smallest particles that drive the actions. Then guiding Physics most intimitately you have Mathematics.
So,
Universe
. . . |
The Real World
. . . |
Observations
. . . |
Biology
. . . |
Chemistry
. . . |
Physics
. . . |
Mathematics
And so, Bob and Q you would then agree that beliefs in God fit somewhere in Appearances only. That's why all this biology talk with dinosaurs makes it pretty clear that Cat Fuzz is defending a position he doesn't have any information for. ( No offense Cat, but the simplest answer is usually the right one, and overturning all of science and changing the half life of carbon seems pretty complex to me.)
So, because a belief in god is not substantiated by the rest of the heirarchy it tries to fit into, then it is in effect, wrong. Agree?
So getting back to mathematics, let's see if we can't examine what works at the most basic level and build off that.
Now look at this, talking about direct applications of imaginary numbers to mathematics:
Source
My conjecture is that the hierarchy works a little bit like the math table. Something like this:
Universe
. . . |----------------------|
The Real World . . . The Imaginary World
. . . |
Appearances
. . . |
Biology
. . . |
Chemistry
. . . |
Physics
. . . |
Mathematics
Now read the above quote with a few words switched around:
Here I use the word Universe as the present moment, life and everything effecting it. I also am not saying the Imaginary world is unreal, but that is is like Imaginary numbers, real and useful, but that it does not follow the same set of rules. Science starts with appearances and observations and therefore has no right to establish a hierarchy in the imaginary world. Just like Cat and Christians shouldn't try to validate God in a scientific world.
Imaginary numbers are real, they just follow different rules, so we put them in a separate category from real real numbers, because we can make rules for them and put them in that neat little heirarchy bob wrote up.
I think this is an interesting read.
I want to talk about the heirarchy of science a bit.
In the Universe, as I see it, scientifically we establish a hierarchy for deducing everything observable in the Real World. You have Observations, what we see on the surface, not very helpful on its own. Below that you have biology explaining what is actually moving things within us, very mechanical and descriptive. Below that you have Chemistry, describes why these interactions happen, what's happening on a smaller level. Below that you have Physics, describing the inner workings of the smallest particles that drive the actions. Then guiding Physics most intimitately you have Mathematics.
So,
Universe
. . . |
The Real World
. . . |
Observations
. . . |
Biology
. . . |
Chemistry
. . . |
Physics
. . . |
Mathematics
And so, Bob and Q you would then agree that beliefs in God fit somewhere in Appearances only. That's why all this biology talk with dinosaurs makes it pretty clear that Cat Fuzz is defending a position he doesn't have any information for. ( No offense Cat, but the simplest answer is usually the right one, and overturning all of science and changing the half life of carbon seems pretty complex to me.)
So, because a belief in god is not substantiated by the rest of the heirarchy it tries to fit into, then it is in effect, wrong. Agree?
So getting back to mathematics, let's see if we can't examine what works at the most basic level and build off that.
Now look at this, talking about direct applications of imaginary numbers to mathematics:
website said:Although such direct applications of complex numbers to the real world are few, their indirect applications are many. Many properties related to real numbers only become clear when the real numbers are thought of as sitting inside the complex number system. Therefore, complex numbers aid in the understanding even of things that are described by ordinary, familiar real numbers.
It's like trying to understand a shadow. The shadow lives in a two-dimensional world, so only two-dimensional concepts are directly applicable to it. However, thinking of the three-dimensional object casting the shadow can aid in understanding it, even though three-dimensional concepts don't have any direct application to the two-dimensional world of the shadow. Likewise, complex numbers may not be directly applicable to a real world measurement any more than a three-dimensional object is directly applicable to a 2-dimensional shadow, but they can still help us understand it.
Source
My conjecture is that the hierarchy works a little bit like the math table. Something like this:
Universe
. . . |----------------------|
The Real World . . . The Imaginary World
. . . |
Appearances
. . . |
Biology
. . . |
Chemistry
. . . |
Physics
. . . |
Mathematics
Now read the above quote with a few words switched around:
chrysaor said:Although such direct applications of the whole universe to the real world are few, their imaginary applications are many. Many properties related to the real world only become clear when the real world is thought of as sitting inside the whole universal system. Therefore, the whole universe aids in the understanding even of things that are described by ordinary, familiar real world science.
It's like trying to understand a shadow. The shadow lives in a world of scientific method, so only scientific concepts are directly applicable to it. However, thinking of the (real + imaginary world = universal) object casting the shadow can aid in understanding it, even though universal concepts don't have any direct application to the scientific world of the shadow. Likewise, universal concepts may not be directly applicable to a real world measurement any more than a universal object is directly applicable to a scientific shadow, but they can still help us understand it.
Here I use the word Universe as the present moment, life and everything effecting it. I also am not saying the Imaginary world is unreal, but that is is like Imaginary numbers, real and useful, but that it does not follow the same set of rules. Science starts with appearances and observations and therefore has no right to establish a hierarchy in the imaginary world. Just like Cat and Christians shouldn't try to validate God in a scientific world.