Re: Fw: Distance between 2 points
----Original Message Follows----
>well, anything other than 2d or 3d rapidly becomes
>metaphysical or undefined.
Actually, I'd say it becomes 'abstract'. It's just as valid
algebraicly, but doesn't really mean anything to anyone living in 3
dimensions of space. In fact, a lot of the stuff mentioned below
(temperature, electrical charge) doesn't have anything to do with a
location in space at all.
>here's the question that'll stump the big boys:
> define the angle of vector Dt in relationship to
> the angle of vector Dxyz.
It's the same relationship that Dz has to Dxy. Again, we can't really
visualize this, but it makes sense.
>now, there are a few more states of existence that
>a particle may have. (oh,JOY!)
>a particle can have spin (Ds),and that dimension
>exists independently of Dxyz, but is dependent
>upon Dt. so, define Ds as
> delta{time_spin_began..time_spin_ceased,
> speed&direction_of_rotation,
> rotationalacceleration}
I don't think that you'd want to call this a new dimension. Have to
check with my calc books, but I think the best way to talk about this
would be in some sort of a paramaterization. I think that's how it's
usually dealt with.
> 1>a particle can be charged (+/-,amount)
> 2>a particle can be magnetized (amount)
> 3>a particle can be accelerating (+/-,amount)
> 4>a particle can be stable or decaying
>and maybe not last, defnly not least:
> 5>a particle can be emitting (radioactive)
> (typeofemission,amount)
>so now we need definitions of vector angles for 1..5
>as well, for a total of how many dimensions of
>existence for a particle?
>if you can determine the angular definitions for all
>these states, we can include them in the program.
>if you cannot, i suggest we leave it with 2d/3d.
Any time you're talking about an angle, you're dealing with something
that exists in a certain plane (2d). We've already said (I think
someone did), that to represent an angle in 3-space, we need two
figures. Well, for each new dimension, we just add another angle. A
computer can handle 5 dimensions as easily as 2 or 3, even though we
can't (by visualization).
>>However you can easily calculate distance of two
>>points defined in 5 dimensions.
>>And in one, is no problem also. Its just pos (a -b)
>*distance*, yes. *angle*, no.
>for 5d, yes, distance=no prob. *angle*=BIG prob.
All you're doing for distances is breaking down the components in the
proper axes and computing. That's all you need to do for the angles.
>>Could we get angles to work in any number of dimensions.
>>In theory, giving 2 dimensions, you will get {distance,angle}
>>Giving 3 dimensions should give you {distanze,xyangle,zangle}
>>And with 4 dimensions we should get
>> {distanze,xyangle,zangle,more_angles}
>define more_angles, as per above???
Well, I don't know why it might be useful to know the angle between
something's location and its temperature, say, but that's not to say
that it's difficult (or impossible) to calculate.
But I bet if you dug around in some psychology journals, you'd find a
lot of studies that used many dimensions. Stuff like personality tests
and the like. Could be all sorts of metrics where this type of analysis
might make sense.
There's my two cents. :)
______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com
|
Not Categorized, Please Help
|
|
