This post describes my internal thoughts. This post is not mathematically strict. The information is scattered and the final model based on these ideas has not been created. Thus, no paper included in the post yet. Don’t read this post until you really want to know what’s in my head all the time.
Denote the length of the infinite line. Starts with thought-provoking, brain evoking, love arousing illicit lie. Does it? From (not by, here) definition of point we know that ie. (Wikipedia)
In geometry, topology, and related branches of mathematics, a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics dealing with set theory, an element is sometimes referred to as a point.
A line consists of infinite number of such have no volume, length etc. But line itself has length. Lets say that line has length 1, including the infinite number of points it consists of. Taking infinity-embracing strategy from Cantor, the idea of countability, transition of one sequence into another, we could conjecture that as there is a bijection between the number of newly introduced “countable points”. This would work with the infinitude of primes and even with the divergence of the sum of prime reciprocals.
Now, imagine a sound that you don’t hear. Here a poem about it. prime_sound
Notice that it works similarly to Zeta, ie. . Combine this with the limit from one of the previous posts.
See that is integer iff P has all prime divisors till , hence analogy to radio (earlier in the post). A resonance is needed for this to be integer.
Combine these with my paper on prime key set problem (nice name for the problem, isn’t it?). Assuming that sum of prime reciprocals would be the equation describing the geometry of the universe, then we’d have our prime key set up and running.
That would totally eliminate time and would show space as interconnected and self-associated. “Time travel” would be allowed through finding a vector of prime numbers that characterize one subspace but are missing in the other one. The tunnel from one subspace to the other one would have to use these prime vectors.
Time would not exist as the amount of primes would define the next step that the subspace takes (transition from one subspace to another) is not understood. The case is that it would be somehow deterministic and measured by the infinitude of primes.
This model can be explained by the following. If you want to hear a voice that you are unable to hear (e.g. certain waves), you need to advance and adjust your capabilities. But then your decisions and situation changes, because you have more variable to take into account as you perceive more.
For the sake of induction, lets assume that there is infinite number of such variables (e.g. primes modelling them, for which we know it’s true) then in order to make highest level decisions (ie decisions that take into account all of the factors) we need to act as a radio adjusted to receive all of the signals.
If we fail to see just part of the orthogonal value of the signal, we will not receive it. As in a normal radio and resonance model.
The big deal about this model is that a subspace adjusts its capabilities and therefore changes itself, and this change is somehow tantamount to what we see as time. Therefore, better understanding of the humanity as groups of people communicating with each other, having parts of information only, could be of great significance.
Take Goedel’s claim on time-lines. Assuming that the given divergent sum of prime reciprocals defines the “space-time”, then time-lines would certain tunnels (lines) between subspaces. The amount of primes used for the time line would define “time”, whereas prime key sets would define subspaces. The transition from one subspace into another would be based on “action”, not on “time”, ie. “time” does not necesserily have to change, which allows Goedel’s claim.
Time or space constraints are suppressing our capability of understanding the underlying mechanisms. Our deduction can at most as good as our axioms and the axiom that there exist 4-dimensional world, with time as a fourth dimension, is naive. More general thinking is needed thus claims from Goedel, ie. Goedel’s metrics and timelike curves.
In terms of philosophy of mathematics: it can be shown that intuitionism is an effect of extreme formalism which came to us as a result of uncertain claims settled as axioms. From Wikipedia, on Goedel metric:
Because of the homogeneity of the spacetime and the mutual twisting of our family of timelike geodesics, it is more or less inevitable that the Gödel spacetime should have closed timelike curves (CTC’s). Indeed, there are CTCs through every event in the Gödel spacetime. This causal anomaly seems to have been regarded as the whole point of the model by Gödel himself, who was apparently striving to prove, and arguably succeeded in proving, that Einstein’s equations of spacetime are not consistent with what we intuitively understand time to be (i.e. that it passes and the past no longer exists, the position philosophers call presentism, whereas Gödel seems to have been arguing for something more like the philosophy of eternalism), much as he, conversely, succeeded with his Incompleteness Theorems in showing that intuitive mathematical concepts could not be completely described by formal mathematical systems of proof.
About Goedel’s work: http://arxiv.org/pdf/gr-qc/0511015v1.pdf
If One claims connection of the prime key set problem model and timelike curves from Goedel, then what does R-sequence represent in the context of light cones?