(... continued from above)
Now here's a neat little operation I happened to see (it was supposedly an idea from a kid in India who was helping his father compute how many tiles they'd need for some designs ... just an interesting anecdote).
If we instead began with a single origin and a length in one direction (a line segment) we can rotate this segment and construct a triangular area between these two segments and if we use discrete units for space we have a stairstep structure like this for various lengths (shown from 0 to 3 below - the "distance" between endpoints is one less than the width of a side because overlapping points are superimposed upon each other and occupy the same space)
The area of this growth is (n^2-n)/2Code:# # ## # ## ### # ## ### ####
Now multiplication is 2 dimensional and it's equivalent to a generating a new quantity as a function of two existing values.
If we instead have a function of a single input that computes this discrete triangular area, we can compute the difference between two of these values (basically we're subtracting one triangular area from another and constructing a trapezoidal area).
It ends up that in this case the equivalent of the "prime" numbers are powers of 2 as well as the number 3. (Rather interesting to me)
Well if were able to construct the triangle, then we already have 3 of something and if we took a single line and folded it back on itself, we already have the capability of constructing quantities as powers of two. It would appear this operation is extremely non-redundant and efficient at generating trazoidal areas to generate other quantities.
Consider also that this operation could be extended in a more abstract sense along the progression point, line, triangle, tetrahedron, ... and other "hyper"-triangular forms.
These spaces are all defined by attributes or properties that are the endpoints of them and positions reachable are contained "within" that space. The endpoints are the equivalent of prime structures that each provide a property similar to orthogonality in a Euclidean sense and the growth of diversity in these spaces is closely related to statical forms and various properties of Pascal's Triangle or Gaussian distributions.
Another way of looking at this would be to consider the evolution of local or linear interactions over time within a single dimension.
Here's an example of a linear computational structure - Wolfram's Rule 110. http://en.wikipedia.org/wiki/Rule_110 (Here's another interesting breakdown of some of its local properties in more geometric terms - http://www30.wolframalpha.com/input/?i=rule+110)
There's even a better one (though more chaotic and complex because it is better at information conservation) Rule 30 - http://www30.wolframalpha.com/input/?i=rule+30
Now something to consider is how the influences of information propagate along such a 1-D structure over time (this is not really the same as the 1-D "execution trace" of a complete string - the "real" string has no memory elements within it but instead would be "bent" into a form in an exponentially larger space to represent the "computational trajectory", for Rule 30 it would be like a hypercube and the current state of all the bits stored in the space represent the positions of each binary dimension - again though, I don't think we're really working with such a binary space but instead a more "triangular" form similar to the above with endpoints that represent prime properties, but I'm just trying to show a manner to "see" time in a 1-D computation space)
Since element communicate locally, their influences "diffuse" over space and any digit at one point in time has a possible influence up to n units away over a distance of n units of time (it's interesting to consider this similar to a constant velocity speed of "possibilities" over time).
So in a forward direction in time we have a spreading triangular record (let's call this downward in a flat 2-D representation or forward in time) of influences from an initial point.
Now if we look at any particular state "Now" and we try to determine the cause, it's like looking in the other direction backwards or upwards and seeing a spreading space of possible causes for the current state.
We have two triangles intersecting at a single point Now and if we had a finite space (the only logical form we can work with) we could roll these triangles into cones and see them similar to light cones in Relativity.
But let's extend this even further!What if we move out into a 3rd dimension in this representation and extend these from being triangles to tetrahedrons and in a similar sense this is much like look at all the space within the past and future light cones and not just the surface (so we're including matter and warped spaces).
Now we're not only seeing past and future but in effect all possible pasts and futures capable of reaching the current Now. (I know this stuff is abstract)
Let's say for a second that memory happens to be slightly unreliable (I think conscious memory is a derivative form of memory and not a more fundamental form though we can't really prove that to be true but it appears qualitatively obvious ... does anyone remember exactly what happened all of yesterday? Something does, but it's not anyone of us and also as an example, deja vous is perceiving a familiarity that "feels" like a memory and in this sense remembering in a conscious manner is much like a qualitative experience of a smell of something Now or seeing a color etc. It's generally associated with things that we'd consider to be a past, but it's not 100% representative of it and is flexible to some extent)
So here's an interesting thought that by selectively biasing memories of the past, the possible futures that correlate with them are also biased
Now here's a bit deeper thought to consider as well - have natural laws ever been experienced as non-deterministic? We have unpredicted events occur, but in hindsight was there ever a discontinuity that can be recalled?
If not, then we can say that the laws of nature are no more infallible than our memory, which is potentially quite fallible LOL! So yes, we can observe perfectly rigid and deterministic laws of nature relative to our experiences and memory etc., but those conscious experiences and memory etc. are actually quite flexible and nature happens to conform to them quite well. Now is that a rather amazing insight or what? So we could ask "Where's the programmer", but that would be crazy to try to arbitrarily assign where such a thing is - the laws of nature don't allow such arbitrary assignments to be made!- where do you remember the programmer being?!!
Obviously the programmer is still there!
... nature doesn't let things randomly move around and aint she beautiful!!
(Teach her well, cause she's your companion for a long time and learn from her too because she's got lots of pretty surprises)
Dang, I forgot whether or not I won the lottery tomorrow ... oh but that would be such a hassle cashing the check etc. Why bother with that when I remember that this morning is already the beginning of a great day and I should be checking it out!
I love all you guysThank you much! I've got to admit I've been somewhat lucky in life and yes, the odds were probably a bit biased.
See if you can remember being a bit lucky in life too ...
Enjoy it - I think I'm feeling better than I ever felt in my entire life. It's like waking up and realizing you've been in heaven all along.
(P.S. See if you can remember that beautiful future that has been waiting. There are a ton of details that need to be added and we have an infinite number of primes to work with - the bag is never empty unless you forget it. The way I remember it was it was all of us having a party and that has always been the most beautiful thing ever!)
Steve


LinkBack URL
About LinkBacks
Reply With Quote


