Hi newbie,
Hi RMT, the tshirt arrived today. It's awsome hehe!
/ttiforum/images/graemlins/smile.gif Feel free to market them, but just remember who gets a cut of the action for coming up with the equation!
I know someone who might like one of these handsome pieces of apparal for Xmas! /ttiforum/images/graemlins/yum.gif
I had been hung up on the concept of s. I get that now. Sort of... I still don't know what it's trying to represent but I understand it's a 1 dimensional unit length. It's not a constant is it?
Whether or not it is a constant depends on what aspect of the relationship between information and matter you are analyzing. Certainly there are some cases where my equation can be applied where the length "S" could be a constant... One good example that should stick out like a sore thumb is the very concept of Planck length!!!
http://www.physlink.com/Education/AskExperts/ae281.cfm
Now isn't that just an interesting coincidence? /ttiforum/images/graemlins/ooo.gif
However, there are other cases where I believe my equation is useful for predicting variable types of spatial boundaries, and how they relate to mass and total information. For example, I have a theory that my equation could describe the characteristic length associated with the boundary of any given galaxy. The solution for "S" in this case would depend upon how much total information the galaxy contains per unit Matter (IOW, solve the equation for "S" as a function of I/m... actually the cube root of I/m).
For m, I understand it as a 3x3 matix but again I don't know what each vector would represent. (snip)
So if that matrix is mass in 3 dimensions, I don't understand how to visualize that at all. Does each line in the matrix mean something specific about the mass
First of all, I made an error in my above explanation. The "m" in my equation is actually a 3x3x3 matrix. There is an extra dimension in it. If you've been reading my math posts where I am sharing more of the foundation for this theory with jmpet, you might be able to get a better idea of where this 3x3x3 matrix of Matter comes from. But let me try to tie some thoughts together for you:
1) Recall from earlier in this thread, that I believe in Newton's "F=ma", the "m" is MASS, which we tend to treat as a scalar quantity (i.e. not a vector, which has both magnitude and orientation). It is my belief that if we actually treat the thing we call "Mass" as a full 3-vector (I can show how mass does have both magnitude and orientation characteristics associated with it), that we will come to a greater understanding of the full tensor form of Newton's "F=ma", which will lead us to revelations with regard to "anti-gravity" technology (i.e. how to generate forces that oppose gravity).
2) It is also my belief that the "m" in Einstein's E=mc^2 (which is also treated as a scalar) is actually what I call Matter (Mass/Time). Since I believe Mass should be treated as a 3-vector, and since I also believe the measurement we call Time is a 3-vector, then the blending of these two 3-vectors would result in a rank 2 tensor (to clarify: A scalar is a rank 0 tensor, a vector is a rank 1 tensor, and the multiplication or division of two vectors yields a rank 2 tensor). So I believe that the differential definition of Matter that I provide in the other thread results in Matter being a rank 2 tensor. So if Mass is a vector, it has one subscripting index that can take on one of three values (i,j,k). Then Matter is a rank 2 tensor, which means it is described with two subscripting indices, and each of these indices can take on either the values of (i,j,k). This would also result in Matter being a 3x3 matrix, where Mass is just a 3-vector.
3) Following the same pattern established in (1) and (2) when we move up to my equation, this would make the "m" in my equation a rank 3 tensor (3 subscripting indices). And each of these 3 subscripts can take on the three values of (i,j,k). That is how you get the 3x3x3 nature of the "m" tensor in my equation I = ms^3. I just don't know what to call this parameter yet. I mean, MASS defines the 3-vector quantity, MATTER defines the rank 2 tensor, but I don't know what to call the rank 3 tensor "m" in my equation...any ideas?
I hope this helped out a bit in your understanding. If not, try to follow the math I lay out in the other thread, as it might answer some of your questions. Or you might have more specific questions in that discussion that I might be able to answer.
Basically I think I'm at the point know if you gave me all the numbers, I could punch it into the calculator. Well, the matrix math I'd have to go to wikipedia to refresh but I could do it. I have no idea how to use any mathlab type software.
eg: (all units are SI)
m =
[ 2, 1, 2],
[-1,-2,-1],
[ 2, 1, 2]
I = m * 2 ^ 3
I just picked some random numbers but is that what it would look like with some values filled out?
As noted above, the "m" tensor (rank 3) in my equation would actually be represented by a 3x3x3 matrix (a cube, rather than a square). So your matrix above would need to be expanded to include two more layers that look just like the one you exhibited. Furthermore, I don't think it would be correct to depict "s^3" as just a single, scalar constant being raised to the 3rd power. Remember, "s" is length, and that makes "s^3" (3-D Space) a 3-vector. And since a 3-vector is represented in matrix maths as a column matrix, then the actual structure of my equation would show itself as being a 3x3x3 matrix multipled by a column matrix (vector). Thus, a bit more than what you have above... but you are on the right track.
As to plugging numbers in, I don't think we are "there" yet. I don't think you would learn anything substantial by doing this. I'd suggest you continue to work on understanding how F=ma progresses to E=mc^2 and then how that progresses to I=ms^3. Then, when the time is right, and we have enough understanding about these equations under our belt, doing examples with "real" values for the numbers will be more useful and will tell us a great deal more than just using "random numbers" in the matrices now.
How far away do you think I am from performing a dimensional analysis hehe?
A dimensional analysis, especially with these 3 simplfied equations, is an easy thing to do. All we need to do is express all the values on the right hand sides of these equations in their most basic dimensions.
Force=ma ---> [Mass]*[Space]/[Time]^2
Energy=mc^2 --> [Mass]*[Space]^2/[Time]^2
Information=ms^3 --> [Mass]*[Space]^3
That's all there is to a dimensional analysis.
To what does the analysis being devoid of time, hint?
Well, what it tells me is that "Information" is a measurement of our physical universe that exists
OUTSIDE of the dimension of Time. IOW, the total amount of information in our universe never changes with Time. There are many other different ways to express what this equation and its independence with Time might be telling us:
1) Total information content of our universe never varys with Time.
2) Information is expressed as Mass (Objects) existing in 3-D Space.
3) For a constant amount of Mass, if the characteristic Spatial length (s) is varied, the amount of information increases with the third power of that Spatial length. (i.e. a much greater number of different points of view from which one can observe the Mass).
4) For a constant characteristic Spatial length (s), if the amount of Mass is increased, the amount of information increases linearly with that Mass.
But I believe there are much more interesting things that we can learn from the fractal embedded relationship between the Force, Energy, and Information equations. Prior to the advent of Einstein, Newtonian physics associated with Force and Acceleration were the focus of our scientific understanding of our universe. Once Einstein came along, he showed us how it is not "all about Force", but rather that there is a higher-dimensional metric called Energy which dictates what is possible with respect to Forces, Moments, Accelerations, and physics in general. In essence, Einstein told us that "Energy subsumes Newton's ideas of physical Force". I also believe that Einstein is the one who moved us from a static concept of "Mass" to a more dynamic concept of "Matter" and how it relates to a special velocity barrier we call the speed of light.
I am just wishing to take this fractal progression from Force to Energy and extend it outward by one more fractal layer. What I am trying to say is that understanding our universe is not just "all about Energy", but rather there is a higher-dimensional metric called Information which dictates what is possible with respect to Energy and physical manifestations in our universe of physics. That is why it is my claim that...
"Information subsumes Einstein's ideas of physical Energy" - Ray Hudson (10/29/2005) /ttiforum/images/graemlins/smile.gif
RMT