Article 4.
Memory Principle
Abstract
The spatial representation of information on digital media (Spatial Paradigm) has one fundamental contradiction: the information in our memory is not data, but experience. Experience has a nature of time, not space, and therefore requires a model for reflecting information in time.
This contradiction leads to a crisis similar to the crisis of the mechanistic scientific paradigm of the early 20th century. Big Data, Smart Sensors and Neural Networks are milestones comparable to the Michelson–Morley experiment and the discovery of X-rays and radioactivity, which in their time led to the creation of the Special and General Theory of Relativity on the one hand and Quantum Mechanics on the other.
If we consider this contradiction as limitations of spatial models, then it is in Physics that we should look for a new model of information representation in time.
Geometric Models of Space: Euclidean, Elliptical, Hyperbolic.
Preprint
In Progress
Models of Space
Physics has gone from the model of space without time (Aristotle's Physics), through the model of space where time is absolute and isotropic (Classical Mechanics) to the model of space where time is relative and forms a single fabric with space (General Relativity). And, to date, Physics raises questions about the fundamentality of space itself.
However, among these and other models, for some reason there is no stand-alone geometrical model of time, without space (Fig.1).
(a) Euclidean Space
(b) Spacetime
(c) Time?
Fig.1. Some Geometrical Models in Physics
The reason seems simple or even superficial: Physics has always tended towards geometry as the most obvious way of conceptualization [1]. There are plenty of examples of geometrization: from the atomists who invented the very concept of space [2], to variants of String Theory [3]. But another thing is important here: no matter how sophisticated the mathematical basis of geometry is, and no matter what perfect models of space it describes, the idea that space is a fundamental level of physical reality remains unchanged:
…the world is ordered and space is a convenient notion for describing that order.
Musser, 2015, pp.171-172
Perhaps the absence of a geometric model of time can be explained as a historically rooted view of the applicability of geometry only to space or spacetime. And hence, it is commitment to the established views that prevents us from thinking about geometrization of time itself, without space.
Nonlocality
The fundamentality of the space is shaken due to difficulties in explaining nonlocality [4], which implies instantaneous communication between any distant points, as if there were no space between them.
The paradox itself has been present in physics for more than a century and has many interpretations, among which it is logical to look for those that explain the problem through time. But, for some reason, the problem of out-of-space communications excludes time from consideration by definition: if space is not fundamental, then time is even more so.
If you agree that the fundamental level of physics is not local, everything is natural, because these two particles which are far apart from each other explore the same fundamental nonlocal level. For them, time and space don’t matter.
Heller & Musser, 2015, p.168
However, it is the interpretation of nonlocality through time, that could fit well as a missing model (see Section 10). The closest example, outside of physics, is biological memory, which apparently possesses nonlocality properties [5].
If we mentally observe memory, the information* in it is not stored in spatial hierarchies, as on digital media, and is available instantly and often for no reason [7].
*The term “information” in colloquial speech is currently predominantly used as an abstract mass-noun used to denote any amount of data, code or text that is stored, sent, received or manipulated in any medium [6].
The retrospective of thought is not traceable through any spatial structures. Rather, it is a network in which the principle of locality is violated: from one of its elements to another can be moved in one step [8]. In other words, if memory contains any structure, it is by nature time rather than space.
But, at the same time, we cannot completely exclude locality from memory:
The world we experience possesses all the qualities of locality. We have a strong sense of place and of the relations among places. … And yet quantum mechanics and other branches of physics now suggest that, at a deeper level, there may be no such thing as place and no such thing as distance.
Musser, 2015, p.168
Thus, we can assume that biological memory has the properties of locality and nonlocality at the same time. This makes memory a suitable basis for geometric formalization, but not of time as such, but only of our perception of time:
However much we strive to exclude from the description of the World patterns, that are consciously or unconsciously built on empirical knowledge, this is likely to be impossible with respect to time. At best, we can identify the properties of time perception rather than time as such.
This approach, in principle, raises the question: how many theories, not only in science but in general, can be reduced to the perceptual properties of our memory residing in physical reality? As Niels Bohr said, that we cannot describe the World without including in our description the fact that we are describing it [9].
Arguably, any empirical or theoretical description of reality is determined only by the nature of biological memory (Fig.2):
• Observe — "external" sensorics;
• Recognize — "internal" sensorics;
• Memorize — experience.
Fig.2. Self-organizing Cycle
The very fact that the totality of our sense experiences is such that by means of thinking ... (it) can be put in order, this fact is one which leaves us in awe, but which we shall never understand. One may say "the eternal mystery of the world is its comprehensibility.
Einstein, 1936, p.351
From this point of view, Einstein's statement [10] is not so much a rhetorical question as a statement of fact: it is not surprising that observable patterns are ordered by biological memory as recognizable and understandable (simply because, for it, there can be no others but these). This view can be summarized as Memory Principle, by analogy with Anthropic Principle [11].
Memory Principle prioritizes the creation of a model of human memory that by definition will contain observable patterns, but will also allow us to explain why these patterns are the way they are when we observe them. But this Principle must take into account its limitation: to understand and formalize memory we use only a small part of it, self-defined as Consciousness.
Geometric Model of Memory
The properties of time perception, which have already been used in time measurement tools for more than 500 years, were described in the "Image of Time". And the model of time geometry itself — Temporal Geometry and Temporal Space (Fig.3), were described in the "Temporal Geometry".
Fig.3. Compactified Space on the Time Axis.
The main idea of these two works in a nutshell: in order to geometrize time, it is necessary to "take space out of brackets". This idea is based on the hypothesis of applicability of geometry to time as such.
If we interpret the found solutions through Memory Principle, then Temporal Space can be considered as a geometrical model of memory.
First of all, let us fix that the essence of memory is the past with access to the present. Consequently, the geometric model of memory is a model of the past, and the Compactification Method is an access mechanism.
If we define time through a synchronization tact, then with an increment of Planck time, the current moment of space is compactified into a point that becomes the past. In Temporal Space, the connectivity of such points is given by (Fig.4):
• Temporal Axis (t);
• Dimensionality of Recognition
(t1, t2).
Fig.4. Temporal Axis & Dimensionality of Recognition.
The Temporal Axis can be imagined as a string or thread on which fluctuations or knots are formed (Fig.5). The representation of the Temporal Axis depends on the Dimensionality of Recognition, i.e. on the ability of the Observer to "unfold" such a dimensionality, within which the information: will be recognized as events-processes, or will not be recognized at all.
(a) "Knot"
(b) "Fluctuation"
Fig.5. Temporal Axis Representations.
The Observer can:
• Move between points within the same dimension;
• Move between dimensions.
In both cases, these are movements in time, which have at least 2 properties:
• Movement between points (of compactified space) is only possible in time;
• To move to a point, it must be contained in memory, i.e., it must constitute experience.
Space of the Past
Movements in time raise the question of representing space beyond the current moment: does space exist in the past as space exists in the present? A good illustration is the statement of Dr. Julian Jaynes [12]:
It is like asking a flashlight in a dark room to search around for something that does not have any light shining upon it. The flashlight, since there is light in whatever direction it turns, would have to conclude that there is light everywhere.
Jaynes, 1976, p.23
Technically, time travel is impossible, but if we assume the opposite, a paradox similar to the flashlight paradox will arise. If an Observer manages to make a journey into the past, wouldn't his presence in the space of the past make such a space present? This seems like an "infinite loop": any attempt to get into the space of the past will make that space present. Such a “loop” can be viewed from different Observer's perspectives:
• Observer in space:
▪ Space is illusory (4.1);
▪ Space is only accessible in the present (4.2).
• Observer outside of space.
4.1 Observer: Space does not exist
One explanation of the "flashlight paradox" does not require the existence of space ("room") and can be considered within the Simulation Hypothesis [13].
A virtual Universe in which only memory and the current moment of time exist is defined by universal time and a clock generator with a frequency of one Planck time. This definition makes the geometric model of memory similar to a simulation:
Perhaps space is a compacted point on the Temporal Axis, in which all the diversity of our observations is given by the infinite number of configurations and dimensions of the Temporal Axis passing through the single point of the current moment (Fig.6).
Fig.6. Configuration via Point on the Axis.
However, Temporal Space differs from Simulation Hypothesis in two fundamental ways:
• Space compactified at a point is a geometric abstraction and does not essentially affect the nature of space:
o If space is fundamental, then according to Tyron and Vilenkin's theory:
"The Universe began as a quantum fluctuation, a disturbance of Nothing, a quantum leap. ... Seen from without, there is zilch, nothing. Seen from within, there is everything we know. The whole Universe." [14].
The space of such a Universe does not prevent to describe "from outside" as a point.
o If space is non-fundamental (illusory), we have even more freedom to interpret one abstraction through another.
• The virtuality of space represented by a point does not mean that the Temporal Space in which it is located is also a simulation.
Proof of the Simulation Hypothesis has not yet been found (e.g. [15]), but at the same time, the Simulation Hypothesis does not generally contradict the Memory Principle. The difference lies in the virtual nature of our memory, the model of which must be recreated.
In the end, virtual or fundamental space does not change the essence of the question: why is space only available to us in the present moment?
4.2 Observer: Space exists only in the Present
The fact that we do not have access to space beyond the present moment is rather not a matter of the fundamentality of space, but is evidence of the Observer's own limited perception of time.
If for the Observer space exists only in the present, then access to it is determined by the throughput of sensorics — the maximum amount of information passing through per unit of time. The Observer's sensorics can be roughly divided into "external" and "internal" (Fig.7):
• “External” sensorics
— the scale of interaction with space, or the scale of space for interaction;
• “Internal” sensorics
— the scale of space recognition
(or the scale of formalization within the boundaries of Consciousness).
Fig.7. External Sensorics = Internal Sensorics.
In fact, sensorics has no subdivision [16] which means that the throughputs of the "external" and "internal" sensorics must be equal. Consciousness is conventionally included in the "internal" sensorics, where its throughput is always strictly less than either of them (at least in the case of human Consciousness).
If we consider Physics, by artificially increasing the throughput of "external" sensorics, we are able to manipulate the scale of observation of space:
• Splitting space into ever smaller fragments — Micro-physics (Quantum Mechanics);
• Looking into the farthest reaches of space — Marco-physics (Gravitational Physics).
But it is the throughput of Consciousness that allows us to think in the categories of Quantum Mechanics and Theory of Relativity. This also means that no matter how advanced an artificial "external" sensorics may be (LHC, JWST), they will still be "plugged in" and equated to the limited throughput of Consciousness.
Local Domain of Past Space
Conscious and unconscious "relocation" in memory between points of compactified space means that some point becomes available to Consciousness as a speculative local domain (or Consciousness finds itself in some local domain). The qualitative definition of Consciousness is both:
• Duration of retention from compactification
("paradox of temporal awareness" [17]);
• Scale of the local domain [18].
Together, they generalize Consciousness as a non-persistent (temporary, periodic) local domain "inside" non-local memory. A good illustration of the given generalization is the expression “to see the big picture” — the bigger the picture we are able to hold, the greater the interconnectedness we see.
The locality of Consciousness allows to unfold and hold no more than one compactified point at a time and obviously there are also periods of time when there is no local domain at all:
We are thus conscious less of the time than we think, because we cannot be conscious of when we are not conscious.
Jaynes, 1976, p.24
The non-persistent and limited locality of Consciousness determines the necessity to create permanent and stable external media. Such media, being physical objects, are “protected” from compactification into a point by being together with us in the present space.
Being external, they inevitably lead to the emergence of an interface, which affects the throughput capacity of transferring experience to an external media. However, the limitations of the interface are essentially linguistic rather than technical, i.e., they are a consequence of the limitations of natural language itself, which in one way or another underlies any formalization.
Fig.8. Consciousness and External Media.
From this perspective, all external media (from pictography, speech, writing, print and data) can be seen as a global medium, constantly expanding and withholding from compactification. Access to such a cumulative medium implies the ability to move to points beyond personal experience. But the throughput of such access is determined by natural language, which is the product of conscious formalization, and thus is by nature spatial.
External media are determined by space (Spatial Paradigm), we can say, determined by the very act of placing in the "outside". Consequently, it is possible to consider space itself as a whole, as a global “external” medium of information. This requires expanding the meaning of "external": from that which is in space to that which is space itself.
Universe–Observer
The concept of space as an "external" medium of information requires two definitions:
• Observable Universe — global external medium of information;
• Observer — a medium of information with sensorics that allow it to gather experience.
Consider thus two points of view:
• Medium, "inside" of which is the Observer;
• Observer who is "inside" the Medium;
Due to the vastness of space, the Observer "inside" the Medium observes distant events of the past as his present.
For the Medium "inside" of which the Observer is located, his observation looks like this:
• An Observer perceives the past in his present;
• The past as radiation in the present coming from a distant (from the Observer) source;
• And the source itself in the present, which may no longer be emitting anything for billions of years.
We know that the limitation of the speed of light makes our observation of space an observation of the past [19] and therefore the observed space must be compacted to a point, but we observe it uncompactified. The reason is our way of observing information:
Information is uncertain* until observed;
*In the following sense: "until the moment that we have received all possible information and the amount of uncertainty is zero".
At the moment of observation, the information is sensed by the "external" sensorics, and is recognized by the "internal" sensorics as uncompactified;
And immediately after is compactified into a point, which now constitutes part of the Observer's experience.
Observing the Universe can be thought of as traveling through time to some point in the past. In the case of memory, for this to happen, the point must already be contained in experience. But we are traveling to a point in the past that is not yet contained in experience, which leaves one option — the point is stored on an external medium.
Transitions in time to a point in the past, which is not yet contained in experience, allow us to consider space itself as an external medium of information. But from our point of view, the external medium of information is an attribute of limited Consciousness. Does this mean that space as a whole is the external medium of some limited Consciousness?
• If yes, then space contains domains that do not constitute the experience of such Consciousness. Since we consider space as a whole, it means that there are completely isolated domains in space. Continuing the analogy with human Consciousness:
o If such domains constituted part of the experience and then compactified into points that are no longer present in the experience, then they can be considered conditionally "forgotten";
o If such domains never contained in the experience, then they were originally contained in another external medium.
Fig.9. Black Hole Singularity as Compactified Point.
• If there are no isolated domains in space, then every point in space must be contained in experience, which makes space not an external medium but Consciousness, i.e. a local domain "inside" non-local memory.
We know that such a domain (i.e., all of space) expands at an accelerating rate [20], but it does not (or we cannot observe it) relocate itself between points of compactified space, as it consciously or unconsciously happens within our memory. A possible explanation is that such a Consciousness is simply in consciousness all the time, and, its throughput is equal to the whole space (Fig.10). It is all the time in the present, in consciousness.
Fig.10. Throughput of the Universe*.
*A graphical representation of the expansion of the Universe from the Big Bang to the present day.
Now let's go back and generalize the concept of "space as an "external" medium of information" within the framework of the Memory Principle:
• The observable Universe is a local domain of Consciousness within the nonlocal memory of the Universe;
• Nonlocal memory of the Universe — Temporal Space.
Another interesting parallel: the fundamental limitation of the speed of light and the limitation of the throughput of human Consciousness.
Universe's own Clock
The local domain in the memory of the Universe constitutes the entire observable space, and, cannot be "somewhere" because there is no concept of "where" outside of space. Only time remains, which in the geometrical model of memory is defined as Temporal Space.
Being in the Temporal Space, a local domain observes itself by its own clock. This is a consequence of considering space as a whole, where nothing will remain but its own clock. This is exactly what the Space Compactification Method returns: a point of compactified space and time (Fig.11).
Fig.11. Compacticifation Method.
Such a point, which is nowhere, can only be surrounded by simultaneous time; or it is in simultaneity. Otherwise, non-simultaneity requires spacing, which would result in a discontinuity of the point or a multiplicity of points.
The concept of simultaneity can be grasped through comparison with instantaneity:
• Simultaneity absorbs into itself the whole space in all its states;
• Instantaneity can contain only one state of space.
Simultaneity means that all the past is present in the present moment. If so, then space's own clock counts down the duration of simultaneity. In this case we could say that 13.813±0.038 billion years [21] is not an age, but the duration of simultaneity of the Universe in Temporal Space.
Measuring the Duration of Simultaneity
Here arises the question of the role which is played by our measuring methods, for we not only regulate time by means of clocks; these clocks in turn regulate our time. ... The supposition remains that time equals time.
Jünger, 1946
Cyclic time forms the basis of the Mechanical Measurement of Time, thanks to which the exact natural sciences became possible at all [22].
But the question still remains whether there are any uniform repetitions at all, whether in all nature there could be found two events which are exactly alike and different only in the moment of their occurrence.
Jünger, 1946
The Compactification Method does not answer Jünger's question, but proceeds from the fact that if events took place, they took place in space. Then, if we compactify the whole space into a point the "repetition of these events" will form a cycle.
In Temporal Geometry, time is measured by linked Unit Cycles. The act of time measurement implies the presence of an Observer, who can register the very event of time measurement (i.e. his own presence) only by possessing his own time dimension — Forming Circle (t2). That is why the presence of an Observer requires the presence of at least two dimensions of time (Fig.12).
Fig.12. Dimensionality of Recognition.
Presumably this is what Jünger meant here:
... becomes clear that the measuring of time and its particles by means of timepieces that record the mechanical flow of time does not exist for its own sake. Rather, it is tied closely to the second measuring process whereby our timepieces regulate our time.
Jünger, 1946
Given that one of the Observers is "inside" the Medium, which is also an Observer it follows that in the case of two dimensions of time one of them is inside the compactified point and the second one is outside it:
• Observer in Temporal Space — observes the Signature of the process, but not the process itself;
• Observer in Space — observes the process, but has no knowledge of the Process Signature.
The Signature resides in time and has only one point of intersection with space. An Observer "inside" the Medium cannot say anything about the duration of a process until its Signature intersects with space again, i.e. materializes as an Event (Fig.13). We can measure the time intervals between such events, but we cannot say with certainty that their Signatures are the same.
Fig.13. Signature & Event.
This formulation seems to be similar to Alan Turing's Halting Problem: the time of a program's computation cannot be established except by means of that computation [23]. Only, with respect to time: the measurement of time cannot be established except by the measurement itself.
The Universe-Observer (Medium containing Observer) observes both space (from inside the compactified point) and time (from outside the point). Perhaps it is such an Observer who is responsible for synchronization of both cycles: one cycle in space equals one cycle in time. Thus, we are left with a choice: to assume that one cycle in space always equals one cycle in time, or to admit and try to explain that time may not be self-similar in structure.
Apart from the relations between things, must not there also be relations between times which are distinguished not only quantitatively by measurement, but qualitatively, according to their structure?
Jünger, 1946
In the General Theory of Relativity, space-time is not assumed to be flat, but capable of dynamically changing its curvature. It can be hypothesized that Temporal Space may also be curved through the effect of Time Distortion — a psychological term meaning a change in the perception of time in which time can feel stretched or compressed, regardless of its objective duration [24]. Only in the case of the Universe-Observer can we not say with certainty whether there is any objective duration, or only the subjective perception of such an Observer.
This brings us to the question of the source of the experience of the Universe, which is viewed from the perspective of sensorics as "external" and "internal".
Source of the Universe's Experience
The conditional subdivision of sensorics into "external" and "internal" raises the question of determining the source of the Universe-Observer's Experience:
• The Universe is in Temporal Space
— its "external" sensorics interacts with time, which is the source of its experience (as for us the source of experience is space);
• Temporal Space is part of the Universe:
o Observer who is a source of experience for itself outside of any external influence;
o Observer whose "external" sensorics interacts with something "outside" of space and time.
If we exclude the question: how can anything inherently become part of the experience of the Observer placed in itself, without an "external" sensorics? And we do not go "beyond space and time", then the Universe-Observer has an "external" sensorics placed in time and observes itself through time.
For the Observer "inside" the Medium — we know nothing about time when we are not in Consciousness. For the Universe-Observer — it knows nothing about space if it is not in time.
Now let's go back to the beginning and complete the Observer—Medium system (Fig.14):
• Observer in space-time
(inside the compactified point):
o "External" sensorics — space;
o "Internal" sensorics — time.
• Observer in time-space
(outside the compactified point):
o "External" sensorics — time;
o "Internal" sensorics — space.
Fig.14. Sensorics of Observers.
The condition of equality of "internal" and "external" sensorics allows us to conclude that the throughput of the observed Universe must be equal to the whole space. The Universe-Observer, observing from the Temporal Space, sees the whole space in simultaneity. We are inside a compacted point of space and observe its various states united by the Temporal Axis of 13.8 billion years.
The Universe-Observer remembers itself for all time, from its beginning (or from the moment we perceive as its beginning), otherwise we would not be able to see the past of the Universe. The Universe continues to gain new experiences expanding and accelerating. But at the same time, it gradually forgets itself, losing its interconnection by moving beyond Event Horizon (at least from our point of view: if we, as a part of the whole, lose touch with the other parts, to what extent does the whole remain a unity?).
An Observer in space-time, the larger scale of space he observes (artificial "external" sensorics), the more he sees the memory of the "external" Observer. But, access to such memory is limited by the speed of light.
With respect to biological memory, the question of increasing the throughput of Consciousness was addressed in the Consciousness & Memory section. With respect to the Universe-Observer, the same question arises: is it possible to access the memory of the Universe in a different way without the throughput being limited by the speed of light?
According to the Memory Principle, in order to understand how to access the "memory" of the Universe, we must first understand how we ourselves access our memory. The answer to this question seems to lie in the unconscious:
So we arrive at the position that the actual process of thinking, so usually thought to be the very life of consciousness, is not conscious at all and that only its preparation, its materials, and its end result are consciously perceived.
Jaynes, 1976, p.41
Instead of Conclusion
The requirements for Temporal Geometry and Temporal Space need not be as high as for a scientific theory. For the same simple reason that the incompleteness of the Spatial Paradigm does not prevent its wide practical application (digital media). At the same time, Memory Principle is nothing more than an attempt to interpret the results obtained, which should in no way affect the results themselves. This is nothing more than a side discussion.
Nevertheless, Temporal Geometry reveals some parallels with existing physical theories:
• Wave–particle duality as an Event-Process (Fig.15).
A particle is compared to an event, and a wave to a process. Observation of an event or process depends on the Dimensionality of Recognition, i.e. on the Observer;
Fig.15. Wave–particle* & Event-process.
*Travelling waves of a free particle on the left; Event & Process on the right.
• Quantum entanglement.
Birth of entangled particles occurs simultaneously, which in Temporal Geometry literally means being within the same Signature (Fig.16). Communication between particles is instantaneous because time is the same for them: entangled particles have one clock for two;
Fig.16. Single Time for Entangled Particles.
• Carriers of Information in Temporal Space — Signatures and Tapes are visually similar to Strings and Membranes from many variants of String Theory (Fig.17), with the difference that they require not additional spatial dimensions, but additional temporal ones.
Fig.17. Calabi–Yau* Manifold & Temporal Tape.
*2D slice of a 6D Calabi–Yau quintic manifold on the left.
Having some parallels with physics looks very interesting, but claims nothing more than geometric intuition.
If Memory Principle is ever developed to the level of a scientific theory, it does not at all have the ultimate goal of proving that the Observable Universe is Consciousness. Unlike the closely related (in terms of meaning) Anthropic Principle, which claims that the fine-tuning of the Universe has to eventually lead to the emergence of intelligent life in it.
The Memory Principle states: what we perceive can be interpreted in no other way than through the properties of our perception. The goal of the Principle is to create a model of biological memory that will by definition contain observable patterns, but will also allow us to explain why these patterns are the way they are when observed. This will clarify the boundary between physical reality and the observation of physical reality.
But, from the understanding of the Universe by limited Consciousness, through the analogy with biological memory, it does not follow at all that the Universe, represented as Consciousness, must belong to some god, and we must be in his memory.
There is nothing else, no magic, no special sauce, only neurons and a dance of information.
Hawkins & Blakeslee, 2004, p.31
Even to explain one's own memory through the limited possibilities of Consciousness is a very difficult task. And to claim to comprehend the "intelligence" of the Universe from the position of such Consciousness in space-time of dimension 3+1 is very naive.
As an illustration, we can think of the local domain of our observation as a neuron whose nucleus is the current moment and whose dendritic trees and branches are a map of all other neurons connected in the network of the Universe. Such a map consists of points of compactified space and is analogous to the Holographic Principle [25]. From such an illustration, we can see that on the scale of the Observable Universe, we are about as intelligent as a single neuron can be on the scale of biological memory.
Fig.18. Similarities between Two Systems.
In this sense, the Memory Principle claims as logically valid the visual similarity between the neuron structure of biological memory and the structure of the Universe on a macroscale [28]. But again, it is precisely because what we observe reflects only the properties of our observation.
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Resources:
[1↑] Atiyah, M., Dijkgraaf, R., & Hitchin, N. (2010). Geometry and physics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368(1914), 913–926. [doi]
[2↑] W., T. C. C. (1999). Democritus: Life. In The Atomists, Leucippus and Democritus: Fragments: A text and translation with a commentary (p. 58). essay, Univ. of Toronto Press.
[3↑] Becker, K., Becker, M., & Schwarz, J. H. (2007). 1. Introduction. In String theory and M-theory: A modern introduction (pp. 1–16). essay, Cambridge U.P.
[4↑] Musser, G. (2015). 1. The Many Varieties of Nonlocality. In Spooky Action at a distance: The phenomenon that reimagines space and time-and what it means for black holes, the big bang, and theories of everything (pp. 13–42). essay, Scientific American/Farrar, Straus and Giroux.
[5↑] Stuart, C. I. J. M., Takahashi, Y., & Umezawa, H. (1978). On the stability and non-local properties of memory. Journal of Theoretical Biology, 71(4), 605–618. [doi]
[7↑] Jaynes, J. (2003). The Consciousness of Consciousness. In The origin of consciousness in the breakdown of the bicameral mind (pp. 21–47). essay, Houghton Mifflin.
[8↑] Konopka, T., Markopoulou, F., & Severini, S. (2008). Quantum Graphity: A model of emergent locality. Physical Review D, 77(10). [doi]
[9↑] Petersen, A. (1963). The philosophy of Niels Bohr. Bulletin of the Atomic Scientists, 19(7), 8–14. [doi]
[10↑] Einstein, A. (1936). Physics and reality. Journal of the Franklin Institute, 221(3), 349–382. [doi]
[11↑] Barrow, J. D., & Tipler, F. J. (1986). The anthropic cosmological principle. Clarendon Press.
[12↑] Jaynes, J. (2003). The Consciousness of Consciousness. In The origin of consciousness in the breakdown of the bicameral mind (p. 23). essay, Houghton Mifflin.
[13↑] Bostrom, N. (2003). Are we living in a computer simulation? The Philosophical Quarterly, 53(211), 243–255. [doi]
[14↑] Nørretranders, T. (1999). Inside Nothing. In The user illusion: Cutting consciousness down to size (p. 353). essay, Penguin Books.
[15↑] Campbell, T., Owhadi, H., Sauvageau, J., & Watkinson, D. (2017). On testing the simulation theory. [arXiv] preprint.
[16↑] Shapiro, L., & Spaulding, S. (2021, June 25). Embodied cognition. Stanford Encyclopedia of Philosophy. [link]
[17↑] Dainton, B. (2023, March 17). Temporal consciousness. Stanford Encyclopedia of Philosophy. [link]
[18↑] Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63(2), 81–97. [doi]
[19↑] Yan, I. (2023, June 12). NASA’s Webb proves galaxies transformed the early universe. NASA. [link]
[20↑] Riess, A. G., Anand, G. S., Yuan, W., Casertano, S., Dolphin, A., Macri, L. M., ... & Anderson, R. I. (2023). Crowded No More: The Accuracy of the Hubble Constant Tested with High Resolution Observations of Cepheids by JWST [arXiv] preprint.
[21↑] Aghanim, N., Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., ... & Roudier, G. (2020). Planck 2018 results-VI. Cosmological parameters. Astronomy & Astrophysics, 641, A6. [doi]
[22↑] Jünger, F. G. (1949). The failure of technology perfection without purpose. H. Regnery.
[23↑] Sangalli, A. (1999). APPENDIX 3. The Halting Problem Is Unsolvable. In The Importance of Being Fuzzy: And Other Insights from the Border between Math and Computers (pp. 164-165). Princeton: Princeton University Press. [doi]
[24↑] Tse, P. U., Intriligator, J., Rivest, J., & Cavanagh, P. (2004). Attention and the subjective expansion of Time. Perception & Psychophysics, 66(7), 1171–1189. [doi]
[25↑] Susskind, L. (2008). The World in a Box. In My battle with Stephen Hawking to make the world safe for Quantum Mechanics (p. 410). essay, Little Brown and Company.
Figures:
Figures 5, 6, 12, 13, 15, 16, 17 and 18 were generated using Temporal Geometry Simulation.