I derived at a theory a while ago that consciousness (if it experiences the dimensions we inexorably observe), then perhaps this could be describable under vector calculus and used as a model to describe reality alongside the relativistic model of spacetime. It turned out a few months later that i was not the first to propose the idea, as Arthur Eddington was the one who initially created what was called ''a spacetime theory.''
Indeed, Arthur Eddington was not the only one to consider this, as you will soon see. This post is an overview of a complete work i have finished, but i wondered what the general audience thought of it.
(Here is a quick summery)
So what is my theory?
My theory has a mix of principles it abides, just like any good theory of physics; but the underlying hypothesis is that the ‘’world’’ we see has itself a description which is analogous to the freedom of a spacetime metric. I decided my theory independently two years before the writing of this book. I soon found on my investigation the idea of treating the mind with some kind of dimensional freedom as we treat space and time physically as vectors on a continuum:
“ The general theory of relativity brought with it a decisive change in this point of view [the 3D world]. Space-time and matter were found to be interdependent, and there was no longer any question which one of the two is more fundamental. Space-time was also found to have its own inherent degrees of freedom, associated with perturbations of the metric-gravitational waves.
...
Is it possible that consciousness, like space-time, has its own intrinsic degrees of freedom, and that neglecting these will lead to a description of the universe that is fundamentally incomplete? ”
—Andrei Linde
(And now here is to the work i want to show)
Sequential Monotonic Convergence and Interleaver Relations
In part one, I explained:
Another explanation why the human perception may seem so free from the chains of quantum supremacy is perhaps the idea of having its own degrees of freedom (or dimensions) are in fact unique yet analogous to those that exist outside the human mind. These include the idea’s that we certainly ‘’see’’ a three-dimensional world which may be uniquely different yet essential in the formation of a linear external world.
Brings me now to explain that whilst the space dimensions seem analogous to the external space dimensions, the time dimension seems to be the one vector dimension taking totally different forms: Time as a Minkowski Geometry shows in Relativity is but yet another dimension of space, and imaginary dimension. If we are to take this seriously, then one might find it interesting that the physical world seems quite intact, whilst some perception of time does not.
Time according to the observer is linear in nature; it does not engulf a wide spectrum that we call past and future; in fact, without the observer, the distinction of past and future would not even exist (4). So one could say, a consequence of having perception, is to have only a present time, and no knowledge of the boundary existing beyond the record of our memories.
It seems important to note though, that strangely enough, wishes seem to beyond the observer; the choice or mindless ponderings to act (5). So while choice remains as a probability in the future, the ability to have memory of the subject remains to us as being beyond us in time. This brings about another concept I will use in physics, and this is ‘’linear knowledge’’ which will be discussed in part 7.
Concerning the mind and the law of cause and effect (which are closely related and may even be equivalent), I set two postulates. The first refers to exactly the linear nature of observations and events. The second refer to the necessity of having observations to define linear actions in spacetime.
1) For a natural set of observed sequences, they need to unravel in a uniform distribution
2) For a natural set of external events, linearity is not conserved unless some linear representation has made a resolution along its path. This reduces events from being ‘’everywhere’’ to just ‘’one place’’.
The linear direction of consciousness was something I contemplated two years ago, but did not have enough insight into physics to develop a demanding theory relative to its origin. But mathematical formulation by idea always eludes me.
Mathematical descriptions of trivial form concerning this abstract theory requires abstract terms, and sometimes basic abstractive acceptance, where ignorance could be related. In the end, a true spacetime theory of everything cannot satisfy a single equation.
But, there is some math which can help us understand the theory even if it cannot understand it fully. In the following, $$A$$ is equivalent to the ‘’focal points’’ of Dr Wolfs theory, which ascend in time $$n+1$$.
So obviously, $$n$$ is the initial time or start of supposed observation.
$$\partial A^{n+1}$$ implies that there is some change in time $$n+1$$ from the past n. Now consider the system under a change in time, and this would be:
$$\partial A^{n+1}-A^n=\partial A^n$$
The next assumption supposes what we really want:
$$\frac{\partial A^n}{\partial t}=k$$
The $$k$$ here represents some variable related to the change in probability over some increasing time. If we use the dot product we could assume the first geometric model of this theory.Whilst the dimensional freedom we assume for the mind (which is nothing but the dimensions we come to observe) is imaginary in every sense, it can be represented as three dimensions to keep true the experience we come to know as the world everyday:
$$a=<a_1,a_2,a_3>$$
Where $$a$$ represents the $$R^3$$ dimensions of space. In the following equation by deduction of logic, then $$a*$$ must represent the space dimensions we observe, which may not be the same thing as $$R^3$$ dimensions, so we can represent them as being individual and unique:
$$a*=<a_1*,a_2*,a_3*>$$
So in my model of reference theory, they refer to each other’s existence, and merge into one real entity, or value mathematically-speaking;
Since taking the dot product with $$a$$ would yield the square of the vector $$\sqrt{a•a}=|a|$$ then the comprising of $$\sqrt{a• a*}$$ will yield some absolute third value:
$$\sqrt{a• a*}=|b|$$
The third value is the mathematical relationship i derive for explaining some abstract model of the observed and the observer in relationship with two vector representatives.
So the mere act of observation ‘’glues’’ the observer and the observed together. Geometrically-speaking, the collapse is attained from precise representations of reality created in the neurological network of the mind; this information is processed upon interaction of both fields $$a$$ and $$a*$$. One could even say that without $$a*$$, $$a$$ then remains undefined, and brings an importance to the observer, an idea in physics as old as physics is.
One might even now take the cross product and analyse one of the vectors as being the human mind; the cross product only works for (which is a three dimensional space). It can be argued that the mind is zero-dimensional – (but treating the observational three dimensions we experience – whether existing in the vacuum as a real thing or not, has its benefits for a geometric theory of consciousness.) Another problem, is the idea of treating distance in the vector mind-model as being a real physical entity, whilst can treat it as such. So typically we should know that a physical real distance given as:
$$D(P_1,P_2)= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$
Since the observer however measures distance being taken, then it can be said the real physical distance is only defined through a measuring observer; in fact, special relativity which deals with this is defined by most as being an observer-dependant theory of relativity.
Going back to the sequence mathematics, one can evaluate the sequence $$\partial A^{n+1}-A^n$$ as a linear flow, and I want to represent one sequence with the vector mind-model and the vector analysis of the three dimensions ‘’out there’’. Traditionally, to merge two sequences together, we use a interleave sequences. Interleave sequences are good theory for this model, because both the ‘’internal’’ and ‘’external’’ worlds are described as having the same limit in the sequence.
Defining a Directionality
Since $$a*$$ required $$a$$ and vice versa in the geometric vector analysis are represented as ‘’linear’’ together, then individually the sequences we describe them with could be represented mathematically as being increasing $$a_n<a^{n+1}$$ or decreasing $$a_n>a^{n+2}$$, which indicated that they could be monotonic, (whatever that means according to the fundamentals of the theory). It may mean nothing. After all, we are working with undefined concepts without $$a$$ acting on $$a*$$; for us to make such a directional distinction, we would require the proof;
$$a_n=\frac{n}{n+1}=f(n)<f(n+1)=\frac{n+1}{n+1+1}=a^{n+1}$$
So
$$a_n<a^{n+1}$$
Which is a neat proof for it ascending in the positive direction, which is essential for observer-observed synchronicity; so we can finally say the sequence is moving as thus,
$${a1,a2… … … … a_n,a_n+1}$$
For two representative realities (the one we experience and the one objectively ‘’out there’’ defined from the vector algebra I initiated for it, could then be used.
If the choice to evaluate $$\Delta t$$ in too large a steps, it would result in an answer that oscillates. This is analogous to the function of consciousness, which happens on frames very small when compared to time. So the choice of evaluating $$A$$ is very essential. Taking very small steps, we can create an ordered state of events in time.
We certainly don’t exhibit an oscillation in space coupled with time (10). An oscillation indicates varied coordinates over the dimensions, which sporadically change from one state to another. One that does couple in synchronism is the description of a linear directionality, where events occur under cause and effect create with it some order in a preferred direction.
Considering the two sequences under interleave-mathematics, you can take two real values and make them converge and create a third number, where $$(0,1)$$x$$(0,1)=(0,1)$$.
For some set S let us assume $${a_1}$$ and $${a_2}$$, the two sequences converge if:
$$b(i)=$$
$$a_k{i=2k}$$even
$$a*_k{i=2k+1}$$uneven
Which is the normal derived function of two real values on interleave mathematical analysis. You may have noticed I used $$a*$$ and $$a$$ to denote the two sequences, which are of course, the same notation I used to describe the two worlds of the internal and external vectors.
One may point out quite rightly enough, that $$a*$$ in the theory does not represent the real sequence of $$a$$, because one does not refer to a real physical reality, so one cannot normally use the interleave sequence above. Instead, we need to incorporate one (being $$a*$$) as an imaginary or complex sequence. So we would require one sequence moving in the opposite direction… So the end result is the same, for both the negative direction and positive directional sequences to converge. Whilst having one sequence moving in the opposite direction seems counterintuitive, it is simply one way to express one sequence as an imaginary sequence, where the two sequences will converge to produce a real positive answer.
In the end of the day, I certainly don’t not proclaim that the math shown in this chapter described reality, but only could represent it in an abstract form for us to deal with the complexities of the subjects we work with in physics. In other words, the human mind when interacting with the world at large cannot be simply due to some hidden function of converging sequences, but mathematically-speaking, it does work well with describing how it could all work, and even help conceptually.
The Mind has a set of dimensions it observes, whilst these dimensions may not be the real world, they are certainly somehow entangled into the evolution of the world and systems both macroscopic and microscopic. The quantum zeno-effect is proof alone that the linear evolution of systems are perturbed by the mere act of observation, so our mindless ponderings and mere observation can and do effect the world. Somehow our mind, whether real or not in the sense of existing in some point of space, does overlap the possibilities of the real world, and hence a working model of how this can be achieved is required: (Concerning the observer’s measurement) it’s like having two myriad sheets that once in a while merge upon some fundamental collapse, and the description of the collapse requires the observer and hence, both sheets. If we take one of the sheets away, we have an incomplete description of reality.
Indeed, Arthur Eddington was not the only one to consider this, as you will soon see. This post is an overview of a complete work i have finished, but i wondered what the general audience thought of it.
(Here is a quick summery)
So what is my theory?
My theory has a mix of principles it abides, just like any good theory of physics; but the underlying hypothesis is that the ‘’world’’ we see has itself a description which is analogous to the freedom of a spacetime metric. I decided my theory independently two years before the writing of this book. I soon found on my investigation the idea of treating the mind with some kind of dimensional freedom as we treat space and time physically as vectors on a continuum:
“ The general theory of relativity brought with it a decisive change in this point of view [the 3D world]. Space-time and matter were found to be interdependent, and there was no longer any question which one of the two is more fundamental. Space-time was also found to have its own inherent degrees of freedom, associated with perturbations of the metric-gravitational waves.
...
Is it possible that consciousness, like space-time, has its own intrinsic degrees of freedom, and that neglecting these will lead to a description of the universe that is fundamentally incomplete? ”
—Andrei Linde
(And now here is to the work i want to show)
Sequential Monotonic Convergence and Interleaver Relations
In part one, I explained:
Another explanation why the human perception may seem so free from the chains of quantum supremacy is perhaps the idea of having its own degrees of freedom (or dimensions) are in fact unique yet analogous to those that exist outside the human mind. These include the idea’s that we certainly ‘’see’’ a three-dimensional world which may be uniquely different yet essential in the formation of a linear external world.
Brings me now to explain that whilst the space dimensions seem analogous to the external space dimensions, the time dimension seems to be the one vector dimension taking totally different forms: Time as a Minkowski Geometry shows in Relativity is but yet another dimension of space, and imaginary dimension. If we are to take this seriously, then one might find it interesting that the physical world seems quite intact, whilst some perception of time does not.
Time according to the observer is linear in nature; it does not engulf a wide spectrum that we call past and future; in fact, without the observer, the distinction of past and future would not even exist (4). So one could say, a consequence of having perception, is to have only a present time, and no knowledge of the boundary existing beyond the record of our memories.
It seems important to note though, that strangely enough, wishes seem to beyond the observer; the choice or mindless ponderings to act (5). So while choice remains as a probability in the future, the ability to have memory of the subject remains to us as being beyond us in time. This brings about another concept I will use in physics, and this is ‘’linear knowledge’’ which will be discussed in part 7.
Concerning the mind and the law of cause and effect (which are closely related and may even be equivalent), I set two postulates. The first refers to exactly the linear nature of observations and events. The second refer to the necessity of having observations to define linear actions in spacetime.
1) For a natural set of observed sequences, they need to unravel in a uniform distribution
2) For a natural set of external events, linearity is not conserved unless some linear representation has made a resolution along its path. This reduces events from being ‘’everywhere’’ to just ‘’one place’’.
The linear direction of consciousness was something I contemplated two years ago, but did not have enough insight into physics to develop a demanding theory relative to its origin. But mathematical formulation by idea always eludes me.
Mathematical descriptions of trivial form concerning this abstract theory requires abstract terms, and sometimes basic abstractive acceptance, where ignorance could be related. In the end, a true spacetime theory of everything cannot satisfy a single equation.
But, there is some math which can help us understand the theory even if it cannot understand it fully. In the following, $$A$$ is equivalent to the ‘’focal points’’ of Dr Wolfs theory, which ascend in time $$n+1$$.
So obviously, $$n$$ is the initial time or start of supposed observation.
$$\partial A^{n+1}$$ implies that there is some change in time $$n+1$$ from the past n. Now consider the system under a change in time, and this would be:
$$\partial A^{n+1}-A^n=\partial A^n$$
The next assumption supposes what we really want:
$$\frac{\partial A^n}{\partial t}=k$$
The $$k$$ here represents some variable related to the change in probability over some increasing time. If we use the dot product we could assume the first geometric model of this theory.Whilst the dimensional freedom we assume for the mind (which is nothing but the dimensions we come to observe) is imaginary in every sense, it can be represented as three dimensions to keep true the experience we come to know as the world everyday:
$$a=<a_1,a_2,a_3>$$
Where $$a$$ represents the $$R^3$$ dimensions of space. In the following equation by deduction of logic, then $$a*$$ must represent the space dimensions we observe, which may not be the same thing as $$R^3$$ dimensions, so we can represent them as being individual and unique:
$$a*=<a_1*,a_2*,a_3*>$$
So in my model of reference theory, they refer to each other’s existence, and merge into one real entity, or value mathematically-speaking;
Since taking the dot product with $$a$$ would yield the square of the vector $$\sqrt{a•a}=|a|$$ then the comprising of $$\sqrt{a• a*}$$ will yield some absolute third value:
$$\sqrt{a• a*}=|b|$$
The third value is the mathematical relationship i derive for explaining some abstract model of the observed and the observer in relationship with two vector representatives.
So the mere act of observation ‘’glues’’ the observer and the observed together. Geometrically-speaking, the collapse is attained from precise representations of reality created in the neurological network of the mind; this information is processed upon interaction of both fields $$a$$ and $$a*$$. One could even say that without $$a*$$, $$a$$ then remains undefined, and brings an importance to the observer, an idea in physics as old as physics is.
One might even now take the cross product and analyse one of the vectors as being the human mind; the cross product only works for (which is a three dimensional space). It can be argued that the mind is zero-dimensional – (but treating the observational three dimensions we experience – whether existing in the vacuum as a real thing or not, has its benefits for a geometric theory of consciousness.) Another problem, is the idea of treating distance in the vector mind-model as being a real physical entity, whilst can treat it as such. So typically we should know that a physical real distance given as:
$$D(P_1,P_2)= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$
Since the observer however measures distance being taken, then it can be said the real physical distance is only defined through a measuring observer; in fact, special relativity which deals with this is defined by most as being an observer-dependant theory of relativity.
Going back to the sequence mathematics, one can evaluate the sequence $$\partial A^{n+1}-A^n$$ as a linear flow, and I want to represent one sequence with the vector mind-model and the vector analysis of the three dimensions ‘’out there’’. Traditionally, to merge two sequences together, we use a interleave sequences. Interleave sequences are good theory for this model, because both the ‘’internal’’ and ‘’external’’ worlds are described as having the same limit in the sequence.
Defining a Directionality
Since $$a*$$ required $$a$$ and vice versa in the geometric vector analysis are represented as ‘’linear’’ together, then individually the sequences we describe them with could be represented mathematically as being increasing $$a_n<a^{n+1}$$ or decreasing $$a_n>a^{n+2}$$, which indicated that they could be monotonic, (whatever that means according to the fundamentals of the theory). It may mean nothing. After all, we are working with undefined concepts without $$a$$ acting on $$a*$$; for us to make such a directional distinction, we would require the proof;
$$a_n=\frac{n}{n+1}=f(n)<f(n+1)=\frac{n+1}{n+1+1}=a^{n+1}$$
So
$$a_n<a^{n+1}$$
Which is a neat proof for it ascending in the positive direction, which is essential for observer-observed synchronicity; so we can finally say the sequence is moving as thus,
$${a1,a2… … … … a_n,a_n+1}$$
For two representative realities (the one we experience and the one objectively ‘’out there’’ defined from the vector algebra I initiated for it, could then be used.
If the choice to evaluate $$\Delta t$$ in too large a steps, it would result in an answer that oscillates. This is analogous to the function of consciousness, which happens on frames very small when compared to time. So the choice of evaluating $$A$$ is very essential. Taking very small steps, we can create an ordered state of events in time.
We certainly don’t exhibit an oscillation in space coupled with time (10). An oscillation indicates varied coordinates over the dimensions, which sporadically change from one state to another. One that does couple in synchronism is the description of a linear directionality, where events occur under cause and effect create with it some order in a preferred direction.
Considering the two sequences under interleave-mathematics, you can take two real values and make them converge and create a third number, where $$(0,1)$$x$$(0,1)=(0,1)$$.
For some set S let us assume $${a_1}$$ and $${a_2}$$, the two sequences converge if:
$$b(i)=$$
$$a_k{i=2k}$$even
$$a*_k{i=2k+1}$$uneven
Which is the normal derived function of two real values on interleave mathematical analysis. You may have noticed I used $$a*$$ and $$a$$ to denote the two sequences, which are of course, the same notation I used to describe the two worlds of the internal and external vectors.
One may point out quite rightly enough, that $$a*$$ in the theory does not represent the real sequence of $$a$$, because one does not refer to a real physical reality, so one cannot normally use the interleave sequence above. Instead, we need to incorporate one (being $$a*$$) as an imaginary or complex sequence. So we would require one sequence moving in the opposite direction… So the end result is the same, for both the negative direction and positive directional sequences to converge. Whilst having one sequence moving in the opposite direction seems counterintuitive, it is simply one way to express one sequence as an imaginary sequence, where the two sequences will converge to produce a real positive answer.
In the end of the day, I certainly don’t not proclaim that the math shown in this chapter described reality, but only could represent it in an abstract form for us to deal with the complexities of the subjects we work with in physics. In other words, the human mind when interacting with the world at large cannot be simply due to some hidden function of converging sequences, but mathematically-speaking, it does work well with describing how it could all work, and even help conceptually.
The Mind has a set of dimensions it observes, whilst these dimensions may not be the real world, they are certainly somehow entangled into the evolution of the world and systems both macroscopic and microscopic. The quantum zeno-effect is proof alone that the linear evolution of systems are perturbed by the mere act of observation, so our mindless ponderings and mere observation can and do effect the world. Somehow our mind, whether real or not in the sense of existing in some point of space, does overlap the possibilities of the real world, and hence a working model of how this can be achieved is required: (Concerning the observer’s measurement) it’s like having two myriad sheets that once in a while merge upon some fundamental collapse, and the description of the collapse requires the observer and hence, both sheets. If we take one of the sheets away, we have an incomplete description of reality.
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