what I'm thinking is that in addition to a binary tree of replication there must be a trinary tree also. These two would be sufficient to recreate the infinite order sieve of Diophantus for the entire universe of ordinary matter. Nonetheless, an opposing directional sieve of Diophantus would completely recreate the entire anti-universe. These two universes are not allowed to come in contact since their interaction would become pure energy. In a state of solely pure energy, time cannot exist.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
Well, it is hard to reply because what I keep re-enforceing seems to be over looked.. Simply every level or scale for t would be infintesimal. That is small or big the minimum and max do not exsist. I think you want to find a bottom for t but its scale is all set in relation. As you were saying if you had two values for t half of one could be used to divide it even more. This idea is infintesimal but conceveable by matter of relation.
I was going to metion this as well. I think I left it out for simplistic reasons. Basical because you could devide this relational as well. I was headed in that direction and though there must be a better way of discribeing the matrix. but I think thats just it... You have to discribe it asThere are two "numbering systems" you could have for these a(t), b(t), ... values (we could rewrite these as a(p,t) and then let p be an enumeration of a,b,c,...) and this would appear to describe the process of a compression of a dimension.
a(p,t)
b(p,t)
c(p,t)
In that abc are segments of a spacial level. You could then discribe them as..
x(p,t)
y(p,t)
z(p,t)
As they come in sequance and an upper and lower boundry could be denoted as -1 to t at any given point. normal echanges in the matrix would be done with all three but any value can be zero and discribed as a gravimetric or temporal wave. If in consideration to 'c' the speed of light it would have to be denoted across all three as a singular value, that is the matrix would have to be calculated first and [xyz (+,-,/,*) c].. I have mentioned before that 'c' maybe denoted across any one but must be devided first and considared the max for 'c' as the lower end could also be zero depending on the varitalbes in any calculation.
So you could do it like this...
x(p,t)(c/3)
y(p,t)(c/3)
z(p,t)(c/3)
Only if every thing in that frame of referance were equal on the p plain. If any x, y or z's p is off the calculation would be incorrect.( in addition) It could be calculated you would just have to add to the c for the p plain, that is if it was off.. let say
x(p*(c/3),t)(c/3)
y(p*(c/3),t)(c/3)
z(p*(c/3),t)(c/3)
Yes, that's similar to my comment regarding a factorially growing space, though there's another way of generating different prime ratios and some correlations with Pascal's Trangle (always a fun one).Originally Posted by AntonioLao
For example, if we have the first two binary splits construct 4 elements as two left/right pairs, if the center elements were equal in quantity, they could be compressed (via. the sorting mechanism) into a single representation and this would give us a space with 3 elements, instead of 4 (one of these would be a superposition of 2 objects of indentical quantity in the uncompressed/unsorted representation).
For example, if at every binary split we recursively incremented the elements laying on the right hand side by 1, this would lead to a growth like this:
0
0,1
{0,1},{1,2}
{{0,1},{1,2}},{{1,2},{2,3}}
{{{0,1},{1,2}},{{1,2},{2,3}},{{1,2},{2,3}},{{2,3}, {3,4}}}
...
If we listed the "densities" (# of occurances) of these for each quantity at different layers, it grows according to Pascal's Triangle:
And so there is a mechanism to indirectly generate other primes. (Here are also a few links showing correlations between Pascal's Triangle and atomic structure http://www.mi.sanu.ac.rs/vismath/weise1/index.html, http://www.atomgeometry.com/default.html and http://milan.milanovic.org/math/engl...om/proton.html)Code:012345 ------- 1 11 121 1331 14641 ...
An interesting consideration regarding symmetry though - imagine that there existed two classes A and B of objects of equal distribution in the environment and we had no direct manner to communicate, except in terms of quantities. If we tried to describe either A or B in terms of their quantities, the other person could assume we were referring to either one and there could be an inversion in perception.
The same would be true for a uniform 3 way symmetry, but if we had a superposition cause a compression of two of these 3 into an identical appearance, then a 2 to 1 ratio of distributions would appear and a manner to communicate, via. quantity, regarding specific classes of these objects would be possible. Ironically, a symmetry within a limited context can give rise to asymmetry on a larger context (for example, if we had an "infinite" grid of points, all positions appear (locally) identical and motion wouldn't be noticed, whereas if we removed one of these points, then that asymmetry could provide a reference by which motion became visible. If we could not actually remove these points, we could instead have 1 or more of these points appear with a different second quality and that would similarly allow for such a reference - it would be interesting to study how various arrangements of these properties could lead to different spaces of motions - for example, if every 3rd element differed, we'd have a perceptual space of cyclic motion that was 3 units in length, though less regular distributions would give rise to quite complex perceptual spaces of motion - for example, in one dimension if you interleaved 3 different qualities there would be ways to have the motion appear to be on a toroidal surface).
Oops, looks like I'm probably rambling again ...
greenbug (07-24-2010)
Whether or not that's the case, there still needs to be a common unit in order that these all tie together. "Infinitesimal" can still imply a 1 divided by (or as seen in scale relative to) an infinity (and there should exist a largest relevant infinite quantity in this construction, yet it can be effectively be a finite, yet growing in time, quantity).
If we have multiple infinite quantities, with undefined relationships, then there's no structure that holds these together and they exist as incomparable units that can't exist in the same space - even "random" quantities can't truly be random in the context of not being constructed from common units of something else in a space.
There might exist things beyond logic and form, but in terms of a ToE that at least describes a logical mechanism by which everything can be perceived to exist, something has to hold it together.
So there really are no infinitesimals, zeroes or negative numbers except as relative forms of growth. The units are just natural numbers 1,2,3,4... and everything fits on a number line, as a function of a single largest quantity, which could also be seen similar to the smallest quanta of time, which could also be seen similar to fundamental unit of difference or contrast by which things are unique.
The "creative"/energetic component in this is the growth of t, assigned to or accumulated by these. Every observer has a different reference for this growth of t, and so an "objective" version of t would have to be at a lower level, but that's not particularly relevant as one only sees their own version, so in that sense, an objective version of physics would not be something inherently provable or demonstrably true. You can only reliably verify things for yourself. (Which of course, in this case would be for myself - it would be hypocritical of me to claim the same truth for you).
Anyway, you need a common "1" or unit that's shared by everything in experience, otherwise things will fall apart and be unrelated and we could analogize this with a computation of a limit in Calculus. For example if we had to compute:
a=lim(x/y) as x and y -> "infinity"
There is no specific limit, unless x and y are related. If we know that x~=sqrt(y), then we can determine that a approaches 0 or if x=2y, then a remains 2 etc.
Everything has to fundamentally be in terms of natural numbers and these all have to be functions of a common quantity, which I'll simply call, t, but if we're working with a subset of objects in experience, then these are only dependent upon a subset of that quantity and the equivalent space of their interaction could be seen to proceed related to a function of t (all functions of t would need to be smaller than t, for example there would not exist t^2, nor t+1, but instead we could construct these as derived from t:
a(t)=n
b(t)=n^3
And we have a manner in which we can observe a relative ratio of n^2:1 in terms of b(t)/a(t)=n^3/n=n^2
But n is is not in units compatible with t, so we must rescale these in terms of t and we can assign them to cumulatively equal t:
n+n^3=t
Realistically, as t is incremented, a manner of distributing these units between a and b would be necessary and a and b would not always possess a precise square relationship, and to be even more precise we could even be required to have another layer of computation involved to determine the manner of interleaving/assigning units to a and b over time (in this example, the manner in which to determine whether or not a(t)^3 is less than b(t) in order to assign these units of t to either a or b and this, in itself, could require a lower level structure upon which a and b are built, but still there's always a common foundation otherwise a and b are unrelated and incomparable).
I enjoyed seeing your rewrite in terms of x, y and z but it does appear that we need to be clear as to how units of these are related and comparable and the only manner I see this as possible is if every single value in a computation is basically derived from a common number line, otherwise it all falls apart and the stars fly off into nowhere (or at least I don't think there's any logical explanation as to how it all works without that).
greenbug (07-24-2010)
Well you have it mostly right, I mean the more you write about it the more it sounds like your understanding it. Its really close.
Perhaps what I need to do is rephrase what I'm saying. There is no max or minimum for t its self, when you consider its base. Yet when you consider that t has more then one relation the first two observable relations become its base, or minimum. Which I think you have, for the most part. The maximum from there is how those two instances of t relate by value and relation. As I've said before the normal relation for a single instance 'c' is the instance before 'a' and instance after 'b' so the maximum becomes abc. What those values are for that level of reference constructs the perception of all other instances and values of t off into infinity, for that level of perception. (amusing your observing from that point, as it would change as you change your observable perception by a scale of p to abc as we said. Whos maximum would be the number of relations 3, but unless you knew where you started it could be 3+2 at max or 3-2 at minimum if you were in space this might be narrowed down quite easily but in a single dimension you would need three observable perceptions a(p) b(p+1) c(p-1) to consider you understand where abc is at in level of p)
What you wrote as " n+n^3=t " is actually an instance of energy rather then normal space or time for that instance. Because if in grouping n > abc which if held by ^3 it would be, you would have to consider it as t(p) not just t... as if initial a(t)=n then a(t) = n(p) as n would have to fit into some level considering t at some point. Like you said in order to fit it in, even if it doesn't at what ever level of a your at you must consider that even if its off by 2 such as a(t) b(t) = n(p) then n(p) could never be an equivilent of the next level such as d(t) unless. n(p+1) = d(t)
SteveA (07-24-2010)
Hi again, greenbug. Yes, there's no finite limit for t. It's just the largest natural number that exists at any moment and it acts in place of the single unknown/infinite/variable that's required to describe change in time. (Any number of unknown quantities can be compressed into the influence of a single unknown quantity (that is larger)).
So there should just be one unknown in the universe at any moment and that's the quantity, t.
Realistically, we'd likely work with it in terms of functions that could potentially estimate its state and I cut an attempt at an earilier post short in order to think along those lines a bit. Though t could be a quantity, it would most likely be too large to describe in a conventional manner and this got me thinking in terms of using an alternate model of a linear stack of functions/operations/transformations instead. So we might, for example, find some manner to describe t as t=f(g(h(n))), where n is a number describing many possible points in time.
This then go me thinking that one abstraction layer that may exist, but is not immediately visible would be that these processes/function/operations could be appended to an origin state and not necessarily added to the present state.
Basically, imagine that instead of time progressing over a set of preexisting and likely unquantizable set of objects in the present, for which most all of these are unknowns and unobserved, that instead we have units continually added to an equivalent Big Bang and the present arises from a continual reconstruction of things reflecting those alterations made in the "past". In that case, causation could still flow forward in time, but things viewed as creative and non-deterministic could arise from addition made to the origin instead. (Notice that this would allow for the wave function in quantum mechanics to update effectively instantly)
Basically, if we had a finite (though potentially massive) 1-D structure, then we have two endpoints - things could either move "forward" through time appending to one end, though similarly a change in the present could result from an alteration to an origin.
I need to think about this a bit and read through your comments more closely as well. So I'll keep this post "short" (at least in a relative sense).
Until later,
Steve
greenbug (07-25-2010)
I dont know. I think if you were to extend the matrix out you might run into complications. I'm not all that good with math so it may be posible to explain things with long chains or functions that discribe how that matrix works out. But at least for me its easyer to think of it on each level and how each level effects the next. As there are two sets of rules there once you understand the rules for the level and how they effectively create the rules for the influance of the next level operating on the same set of rules. Then you can see how larger sets might appear but only work for the instance and not the whole underlineing structure. That is where I might cation you as you move on with more complicated sets even if they do function with in sets of primes or other functions.
I have also thought that there might be an underlineing value for t and it might be calculated fairly easy. But its crutial that that number is correct and from a single perspective it might be fleeting so I'd rather think about each perspective first then directly attack t. I'd rather discribe it in terms of intigers rather then absolute numbers only because its more useful to larger sets that way.
Any how like I said I think your on the right track for the most part and if you dont realise some of the constraints now youll run into them eventualy. Most of the time its easyer to understand them when you discover them your self so.
I'm content that at least one person understands this type of perspective.
SteveA (07-25-2010)
It appears that logic does require that linear structure. If we have branches or multiple dimensions, then those represent choices that are not inherent in that logic. We should instead be able to synergistically combine all these as a single object by having it be 1 dimensional (fundamentally just a quantity of time - a number, though of an unknown magnitude) and then all the "choices" can be placed into how its perceived to grow.
Realistically what this means is that we'd likely end treating t in terms of sequences of different functions with different characteristics interleaved over t. For example, we could represent 65,536 as (2^(2^(2^2))) and we could then, in a compressed version of time, predictively "lead" time in some subsets of characteristics (for example, if this example described periodically recurring binary properties, then when the presence of this influence was detected we could determine that t was at some multiple of 65,536, and utilize this knowledge regarding when that (sub)state recurred, though t would still be unbounded. There are also functions that can dynamically sweep through time (similar to red-shifting) and ways of nesting these on different scales (fractally recurring properties on different scales, though not necessarily identical as these scales inherit properties from other scales)).
At least that appears to be a way that all these forms can be connected together into a common/objective landscape.
I think this is where those functions of t come in and they have an equivalent of faster or slower forms of growth in some other dimension/property.As there are two sets of rules there once you understand the rules for the level and how they effectively create the rules for the influance of the next level operating on the same set of rules. Then you can see how larger sets might appear but only work for the instance and not the whole underlineing structure. That is where I might cation you as you move on with more complicated sets even if they do function with in sets of primes or other functions.
For example, 2^n grows exponential. If this function is "fit into" a common t, then n grows inversely to this relative to t and n~=log(t). n! (factorial) grows faster would be an even slower growth. A square root of n would have inverse properties and n would appear to accelerate relative to t (and potentially become harder to predict its motion), though we also have scalings of these and period functions (which could appear to construct (potentially divergent) superpositions because multiple solutions could be possible over time).
I think we could only determine a finite component of t as we'd only have finite information, derived from t to work with.I have also thought that there might be an underlineing value for t and it might be calculated fairly easy. But its crutial that that number is correct and from a single perspective it might be fleeting so I'd rather think about each perspective first then directly attack t. I'd rather discribe it in terms of intigers rather then absolute numbers only because its more useful to larger sets that way.
Yes, I enjoyed seeing the exchange and it does appear we have some very similar views, "Greenbug". Thanks,Any how like I said I think your on the right track for the most part and if you dont realise some of the constraints now youll run into them eventualy. Most of the time its easyer to understand them when you discover them your self so.
I'm content that at least one person understands this type of perspective.
Steve
You said it better then I could.Realistically what this means is that we'd likely end treating t in terms of sequences of different functions with different characteristics interleaved over t
No no other dimension or property but those interlining functions have an effect on the whole. Picture a newtons cradle of functions. Once they establish a system, so to speak, they effect it linearly. Be each function some set of three or based on primes, the growth comes in when they interact or exchange vales "a(p,t)" of 't' .. Thats where most of the difference comes from, from there it affects what 'p' the 't' is capable of and becomes part of the function for the current 'p' level that 'a' is on. Now that 'a' is part of a function like I said the depth of each function, and its dependent functions, cant surpass 81 or they brake down into new functions (with conservation), more then likely separating a 'p' somewhere.I think this is where those functions of t come in and they have an equivalent of faster or slower forms of growth in some other dimension/property.
SteveA (07-26-2010)
I was programming my model of a single dimension again, I think I might have mentioned before that using Rate for time is confusing when thinking in terms of how I think the single dimension is formatted..
So in the program I've renamed rate as relational difference. Both space and time fall under the category of relational difference. That and when the relations combine into further dimensions they better fit the descriptions of rate and space. That is to say, the overall relational difference between two points is the rate. A single point compounded or deconstructed may have a neutral relation, in this there is no other point to compare difference and so relationally it is neutral. This can happen when compounded (or grouped) points on either side have a grater relation then one in the center, example..
(0 0 0) (.) (0 0 0)
In this the direction of relation dictates rate and so directional 'time' could be introduced.
<(0 0 0) (.) (0 0 0)>
This creates a true void in a single dimension that can be ignored by the grouped, yet interactions may trigger its relevance. Things like movement or perspective.
I have thought of this before and its relevance to three-dimentonal space where space is ignored by objects. An object’s relational difference is communicated threw objects quicker then threw void spaces, as void spaces can complicate (in reference, curve) relations. Any how I just thought I’d throw that out there..
labelwench (08-04-2010)
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