"All Possible Dimensions"

HG Wells' Time Traveller argues that:

bodies extend through four dimensions (an instantaneous cube is impossible);

time is the fourth dimension;

only our dimensionless, immaterial minds move along that dimension;

but his Time Machine can accelerate along that dimension (here he contradicts himself).

I have argued against the Time Traveller's account here.

An instructor at the Time Patrol Academy informs recruits that:

travel into the past "'...requires infinitely discontinuous functions for its mathematical description...[and]...involves infinite-valued relationships in a continuum of 4N dimensions, where N is the total number of particles in the universe.'"
-Poul Anderson, "Time Patrol" IN Anderson, Time Patrol (Riverdale, NY, 2006), pp. 1-53 AT p. 9.

Anderson updates the sf rationale for time travel! And there is a big difference between four and 4N dimensions!

Despite his limitation to only four dimensions, the Time Traveller worries that, if his vehicle occupies the same space as another object, then the resultant explosion will:

"...blow myself and my apparatus out of all possible dimensions - into the Unknown."
-HG Wells, The Time Machine (London, 1973), Chapter 4, p. 26.

Surely an explosion would merely destroy the Machine? But I am interested in his references to "all possible dimensions" and to an "Unknown" beyond them. These imply other story possibilities. When the Doctor's vehicle occupied the same space as another time machine, both exploded but then reappeared on a blank TV screen where the time travellers met Chronos, the god of time. The Doctor, like several of Poul Anderson's characters, is a successor of Wells' Time Traveller.

Dimensions

The Old Phoenix multiverse has at least five dimensions because each universe has three spatial dimensions and one temporal dimension and the universes coexist along a fifth dimension.

The Time Patrol universe also has at least five dimensions because it has a second temporal dimension. We are told that it has 4N dimensions and that N is how many particles there are. In that case, the Old Phoenix multiverse and the Time Patrol universe can coexist in different parts of the 4N-dimensioned megamultiverse. It might be possible to travel between the Time Patrol and Old Phoenix realms along a sixth dimension.

However, we saw that three other universes have only four dimensions each. This implies that they exist outside the 4N-dimensioned framework and that there would be no way to enter them from outside unless someone can imagine a different means of transport? Like magic?

The Fourth Dimension In Wells, Heinlein And Anderson

The fourth dimension may be time or an extra spatial dimension.

Time
See 4D + OBE.

References to "world lines" in Poul Anderson's Time Patrol series also imply four-dimensional space-time. In fact, "Time Patrol" states that pastward travel requires not just four but 4N dimensions! The Time Patrol's mutable timeline requires at least a second temporal dimension for that timeline to mutate along whereas the immutable timelines of The Corridors Of Time and There Will Be Time could each fit into a simple four-dimensional continuum as far as I can see.

An Extra Spatial Dimension
Does this exist in any of Poul Anderson's works? I have not read all of his short stories. He refers to four-dimensional chess but this is conceptual, not physical. In any case, it refers, as far as we can see, only to the pieces aging or maturing with time which takes us back to time and not even necessarily to time travel.

I tend to assume that the universes in a multiverse, e.g., in Anderson's Old Phoenix sequence, are located along another dimension although this is not the only possible rationale for a multiverse because, in DC Comics' pre-Crisis multiverse, the many universes occupied the same three-dimensional space by vibrating at different rates. However, Anderson's Valeria Matuchek says:

"'You can picture the cosmoses as lying parallel to each other, like the leaves in a book. That isn't strictly true, either; they occupy the same space-time, being separated by a set of dimensions -'"
-Poul Anderson, A Midsummer Tempest (London, 1975), xii, p. 101.

Earlier, she had referred to "'...parallel universes and all that jazz...'" (xii, p. 99)

Two parallel straight lines are separated by a second spatial dimension. Two or more parallel space-time continua must be separated by a fifth, "inter-cosmic," dimension? Valeria says that the cosmoses are separated by "'...a set of dimensions...,'" which seems unnecessarily complicated. Nevertheless, pages of a closed book are parallel to each other and cosmoses separated by (at least) one dimension are parallel to each other so the "...leaves in a book..." analogy works for me.

The number N appears three times:

there are 4N dimensions in the Time Patrol universe;
the number of universes in the Old Phoenix sequence is either infinite or N factorial;
in the Technic History, Starkadian mathematicians think that factorial N is the largest number. (See also here.)

I was going to mention Wells and Heinlein but they can wait for another post.

Quantum Time

Quantum Mechanics
What is it?
Can subatomic indeterminacy coexist with macrocosmic determinism? (I think so: see here.)

Dimensions
How many are there?
Is time a fourth dimension?

How do quanta and dimensions interact?
(i) In Poul Anderson's Time Patrol series, time travel requires 4N dimensions and causality violation is described as quantum indeterminacy on the macroscopic level. Thus, time travel links multiple dimensions to macroscopic indeterminacy.

(ii) "The attempts thus far to reconcile the quantum microcosm with the classic macrocosm have led to such mind-wrenching extravagances as string theory, notions that require extra dimensions, ranging between ten and twenty-six, before the mathematics will make sense."
-Alan Moore, Jerusalem (London, 2016), pp. 781-782.

Thus, string theory synthesis of quantum mechanics with classical physics requires additional dimensions - although not as many as 4N of them!

Three Kinds Of Dimensions

For convenience, let us describe Poul Anderson's The Corridors Of Time and There Will Be Time as his two Time novels. Let us also consider his Time Patrol series and his Old Phoenix sequence. This totals seven novels, one omnibus collection and two further short stories.

In all of these works, there are, of course, three spatial dimensions. In the two Time novels, there is a single temporal dimension. No surprises there. So far, that accords with our experience. In the Time Patrol series, we are told that theoretically there are 4N dimensions but we need only consider three spatial dimensions and two temporal dimensions. The Old Phoenix multiverse has three spatial dimensions, one temporal dimension and one other dimension. We must call this fifth dimension something so perhaps "inter-cosmic" will suffice.

The two Time novels are set in different universes which, however, have the same four-dimensional framework. Thus, we are considering only three frameworks. Let us imagine that each framework is represented diagramatically on a different page.

The Time Novels
A single horizontal straight line.
An arrow pointing from left to right at the foot of the page.
The straight line is a single timeline.
The arrow indicates that "past" is left and "future" is right.
Each point on the straight line represents a moment which is "present" to any conscious being living in that moment.
The three spatial dimensions are not represented.
Most personal world-lines merely extend from an earlier to a later moment.
The description of a time traveler is more complicated and different in each of the two novels.
However, from our perspective looking down on the page, each time traveler exists statically on different sections of the straight line.

To be continued.

Records Of What Did Not Happen

This post should be called "Records Of What Did Not Happen In The Current Timeline." Each timeline has three spatial dimensions and one temporal dimension. Several of these four-dimensional continua succeed each other along a second temporal dimension.

Some Danellian records state that Charles Whitcomb remained a bachelor and eventually "...was killed on active duty with the Patrol." (Time Patrol, p. 52)

However, in the current timeline, Whitcomb:

retired from the Patrol after a single mission;
married Mary Nelson;
lived with her in Victorian London, starting in 1850;
sometimes thought wistfully about what he had been in the Patrol;
but decided that his wife and children had been worth that sacrifice.

The Whitcombs serve high tea before a cannel fire when visited by Manse Everard. Thus, Charlie retains an indirect contact with the Patrol although his bachelor life and eventual death on active service did not happen in this timeline.

When Everard and Van Sarawak are in the Carthaginian timeline, it is their lives and history that "did not happen." Everard remembers, among other things, his parents, visiting the Whitcombs and:

"...the austere cantos of Dante and the ringing thunder of Shakespeare; the glory which was York Minster and the Golden Gate Bridge -" (p. 184)

York Minster gets a consistently good press in Anderson's works. Later along Everard's world-line, when the Danellian history has been restored:

"Light streamed through the Golden Gate." (p. 746)

When Wanda Tamberly has come dangerously close to breaking the Patrol's Prime Directive, she is shown records of "'...time gone awry...'" (The Shield Of Time, p. 253) which teach her a necessary lesson.

In my opinion, this terminology of successive timelines makes sense of most of what is said about variable reality in the Time Patrol series although it is not the terminology used by the Patrol itself. I would love to learn Temporal and discuss the matter with Patrol agents on their own terms.

A trainer at the Time Patrol Academy states that travel to the past:

"'...involves the concept of infinite-valued relationships in a continuum of 4N dimensions, where N is the total number of particles in the universe.'" (Time Patrol, p. 9)

I think that time travel in an immutable timeline requires no extra dimensions and that time travel in a mutable timeline requires only one extra dimension. However, I am a philosopher, not a physicist. 4N is an enormous number. I think that it assumes a finite universe? Otherwise, N would equal infinity and 4N would also equal infinity? However, even if 4N is finite, it is a large enough number to incorporate not only the many successive timelines of the Time Patrol universe but also, in some other part of the multi-dimensional framework, the many coexisting timelines that have access to the Old Phoenix Inn.

N And Lincoln

The Wardens and Rangers and later "time wardens" of Poul Anderson's The Corridors Of Time inhabit a single immutable timeline.

The mutant time travellers of Anderson's There Will Be Time inhabit a different single immutable timeline.

His Time Patrollers believe that they inhabit a single mutable timeline although it is impossible to formulate a coherent account of all the events that are described as occurring in the Time Patrol series.

The patrons of Anderson's Old Phoenix inhabit multiple timelines.

An immense dimensional framework would be necessary to incorporate such diverse scenarios into a single multiverse.

However, we find similar theoretical language and practical examples in the Time Patrol universe and in the Old Phoenix multiverse.

According to a Time Patrol instructor, both instantaneous transportation and travel into the past require infinitely discontinuous functions for their mathematical description and also involve:

"'...the concept of infinitely-valued relationships in a continuum of 4N dimensions, where N is the total number of particles in the universe.'"

-Poul Anderson, "Time Patrol" IN Anderson, Time Patrol (Riverdale, NY, December 2010), pp. 1-53 AT 2, p. 9.

According to Valeria Matuchek:

"'Nobody's proved, in my world, whether there's an infinity of [universes], or whether the number's finite but enormous - N factorial, to be exact, where N is the total number of matter and energy particles that exist....'"

-Poul Anderson, A Midsummer Tempest (London, 1975), xii, p. 101.

OK. "N" means the same in both cases but, in the first case, there is a single continuum with 4N dimensions whereas, in the second case, there are possibly N factorial continua!

Secondly, there is a common practical example.

As far as the Time Patrol is concerned:

"'...suppose I went back and prevented Booth from killing Lincoln. Unless I took very elaborate precautions, it would probably happen that someone else did the shooting and Booth got blamed anyway.'"

-"Time Patrol," 2, p. 15.

And for Valeria:

"'...suppose I happened to meet Abe Lincoln here...given a lot of time together, I probably couldn't resist warning him against Ford's Theater. Lord knows what that might do to his world. Make a new continuum? I'm not sure if that's possible.'"

-A Midsummer Tempest, xi, pp. 93-94.

The host of the Old Phoenix performs the same function as the Time Patrol by preventing conversations that would result in an Abraham Lincoln that was going to be assassinated by Booth not being assassinated by Booth.

And the scenarios have similarities because they have a common creator.

(Lastly, Sheila and I now live on Lincoln Rd, Lancaster.)

A Vaster Scenario

We tried to fit the Time Machine, the Time Patrol and a version of Doctor Who into a single scenario. See here. Let's extend the scenario further. The Time Patrol universe has either a single mutable timeline or several successive timelines - although these are two ways to say the same thing. See here. This is possible because this fictional universe has more than four dimensions, thus at least two temporal dimensions. Theoretically, it has 4N dimensions.

(We could say either that the contents of three dimensional space change, are mutable, or that a succession of 3D spaces with slightly different contents exist along a fourth dimension. These also would be two ways to say the same thing.)

Anderson's The Corridors Of Time, There Will Be Time and The Dancer From Atlantis are each set in a different universe. However, each of these universes has:

only four dimensions;
therefore, only one temporal dimension;
therefore, only a single immutable timeline.

The Old Phoenix multiverse has many parallel timelines. Thus the Anderson multiverse contains at least:

one universe with a single mutable timeline/many successive timelines;
three universes, each with a single immutable timeline;
one multiverse with many parallel timelines.

It must be difficult, although not perhaps impossible, to enter the immutable timelines.

In my suggested scenario, the Time Lords are the Danellians and the Morlocks-Eloi timeline is a quantum fluctuation within the Time Patrol timeline(s).

Multi-Dimensional Fiction

OK. After literary hereafters and the English Civil War (see here), there is a third common theme: multidimensional fiction. We recently considered several kinds of dimensions in Poul Anderson's works:

the three spatial dimensions;
the single temporal dimension of an immutable timeline;
the two temporal dimensions of a mutable timeline;
the one or more inter-cosmic dimensions of a multiverse.

Question included:

How many of these dimensions can be incorporated into the 4N-dimensional framework of the Time Patrol universe?

Can there be a megamultiverse?

I raise these questions again because I am currently exploring the ten or eleven dimensions of Alan Moore's Jerusalem. See also here.

1995

Poul Anderson's "The Little Monster" was published in 1974 and is set in 1995 by which time there are telecasts from Mars. Since the first Moon landing was in 1969, this was a plausible future.

The young hero's physicist uncle says:

"'Never mind the physics of it...'" (p. 143)

Such an introduction would usually indicate that we are about to read a brief scientific rationale for "...temporal relativistics..." (p. 144) and "'...time projection...'" (ibid.)

All that we get, however, is:

"'Come back when you know tensor calculus, and I'll explain about n-dimensional forces and the warping of world lines.'" (ibid.)

Is that "n" the same as the "N" in "Time Patrol" where a Time Patrol Academy instructor refers to:

"'...the concept of infinite-valued relationships in a continuum of 4N dimensions, where N is the total number of particles in the universe.'"

-Poul Anderson, "Time Patrol" IN Anderson, Time Patrol (Riverdale, NY, 2010), pp. 1-53 AT 2, p. 9.

 

4N is a powerful lot of dimensions but, if there are that many, then there is plenty of room for the mutable timeline, some immutable timelines, the Old Phoenix multiverse and everything else - what I call the megamultiverse.

Lastly, for now (today is Sunday with a walk in the morning and a zoom meeting in the afternoon), there are two kinds of time machine, I suggest: a temporal vehicle carries time travelers whereas a time projector sends them.

In Past Times:

 

"Wildcat" and "The Little Monster" have time projectors;

"The Nest" has a temporal vehicle, the Rover;

"Flight to Forever" has a temporal vehicle called "the time projector."

Concept And Experience

Time travel involves physics, philosophy and fiction. I can only read popular accounts of the physics but am more familiar with the philosophy and the fiction. 

Any time travel narrative has at least two aspects, conceptual and experiential: a conceptual framework, whether explicit or implicit, for time travel and the experiences of the time travellers.

In HG Wells' The Time Machine, the framework is explicit although confused, a detailed discussion of the nature of time. There are two experiential stages. First, the process of time travelling is itself experienced. The Time Traveller perceives everything outside himself and his vehicle as accelerated. Secondly, his experience of several future periods is described, vividly and colourfully.

In Poul Anderson's "Time Patrol," the conceptual framework is provided by some brief instruction in the Time Patrol Academy in the Oligocene. Instead of the Time Traveller's four dimensions, the Time Patrol deals with 4N dimensions.

The experiential aspect is present but different. First, there is no experience of time travelling as such because each temporal transition is subjectively instantaneous. Secondly, although Manse Everard has been shuttled to the Oligocene for training, then back to the twentieth century, the reality of time travel does not strike him until he is travelling through London in a hansom cab in 1894. Thereafter, this and every other historical period is described in detail.

Conceptual Space

In a vast conceptual space, we are able to compare:

turbulent ages, turning points, beginnings and endings in the Danellian and Technic Civilization timelines;

means of time travel in The Time Machine and in several different works by Poul Anderson;

alternative histories as imagined by various authors;

theories of a multiverse;

whether the many multiverses can be incorporated into one megamultiverse.

I used to think that the Time Patrol mutable timeline and the Old Phoenix multiple timelines were incompatible but it is hard to conceive how a system of 4N dimensions can exclude anything.

The Origin Of The Time Patrol

"Time Patrol" presents a few details whereas the much later "Ivory, and Apes, and Peacocks" retreats into generalities.

"Time Patrol"

19352 AD (the 7841st year of the Morennian Triumph)

the Chorite Heresiarchy breaking up

commercial and genetic rivalry between giant combines

governments pawns in a galactic game

search for a means of instantaneous transportation

the time effect a by-product

infinitely discontinuous mathematical functions

4N dimensions (N = total number of particles in the universe)

the Nine plan to prevent their enemies from being born

the Danellians appear

the Patrol is established

"Ivory..."

long after the twentieth century

the first time machine built

the Danellian supermen arrive

they organize the Patrol

19352 A.D.

After several months of posting about Poul Anderson's Technic History, let us contemplate a crux period in another timeline:

19352 A.D. is the 8841st year of the Morennian Triumph;
the Chorite Heresiarchy is breaking up;
the age is turbulent;
giant combines are commercial and genetic rivals;
governments are pawns in a galactic game;
a search for a means of instantaneous travel generates time travel;
both require infinitely discontinuous functions for their mathematical description;
time travel involves infinite-valued relationships in a continuum of 4N dimensions;
the Nine realize that their newly discovered means of time travel not only has commercial possibilities but also would enable them to prevent the births of their enemies;
the Danellians, mankind's evolutionary successors, arrive from a million years later;
the Nine are neutralized and the Patrol established;
the Patrol operates in earlier periods when the existence of time travel is concealed;
its Academy exists for half a million years in the American West of the Oligocene period before being carefully demolished.

The Technic History presents a linear history whereas the Danellians and Patrol agents perceive their history as a mutable totality.

Mysterious Characters

I have found three more "mysterious characters of literature" (see here):

ERB's John Carter;
Michael Moorcock's Eternal Champion;
Donovan's Universal Soldier.

These are characters who can appear in different times and places and might travel through the megamultiverse.

Holger Danske is Poul Anderson's version of such a character. The speculation about such characters was inspired by Anderson's inter-universal inn, the Old Phoenix, and by the 4N dimensions in his Time Patrol universe.

Any warrior in an old heroic fantasy might be an earlier phase of John Carter.

Ivory, and Apes, and Peacocks

Poul Anderson, Time Patrol (New York, 2006).

"Ivory, and Apes, and Peacocks" was originally published as the first story in a second Time Patrol collection, Time Patrolman, so it had to summarize the Patrol scenario for new readers or to remind old readers:

"When humans built their first time machine...the Danellian supermen had arrived from farther yet, to organize the police force of the temporal lanes." (p. 250)

The very first Patrol story, "Time Patrol," had presented a lot more detail:

the Nine discover time travel - as a by-product of the search for instantaneous transportation - in 19352 AD, the 7841st year of the Morennian Triumph, during the break up of the Chorite Heresiarchy, an age of galactic commercial and genetic rivalry;

like instantaneous transportation, travel into the past "...requires infinitely discontinuous functions for its mathematical description..'." and "'...involves the concept of infinitely valued relationships in a continuum of 4N dimensions, where N is the total number of particles in the universe'" (p. 9);

the Nine would have prevented the births of their enemies "'[b]ut then the Danellians appeared.'" (p. 11)

All this hard sf background material is unnecessary for the historical science fiction of the Time Patrol series and is omitted in later installments.

Incidentally, when a Patrol recruit remarks:

"'...an event cannot both have happened and not happened. That's self-contradictory.'" (p. 9)

- I agree with her. Her instructor's reply:

"'Only if you insist on a logic which is not Aleph-sub-Aleph-valued...'" (p. 10)

- is gobbledygook - unless anyone can tell me what it means?

An event can have happened in an original timeline and not have happened in a divergent timeline. The Time Patrol would have us believe that, in that case, the original timeline simply does not exist. That is a paradoxical proposition but the Patrol is obliged to consider the consequences even of supposedly nonexistent timelines:

"'...that source perhaps does not exist in our yet, our reality.'"
-The Shield Of Time (New York, 1991), p. 135)

Blink Out

"Delenda Est."

This post addresses a by now familiar issue but might possibly express it in a slightly different way.

Manse Everard reflects:

"There were other Patrolmen in the pre-Roman past. They'd return to their respective eras and...see what had happened, and try to correct the trouble. If any of them succeeded, this world would blink out of spacetime, and he would go with it." (5, p. 204)

Some of them will see what has happened. By "world," Everard means not a planet or a universe but a particular course of history. That course of history will not merely "blink out" but will be replaced by another course of history.

First, to "blink out" is to cease to exist. To cease to exist is to have existed, not never to have existed. Indeed, Everard exists when he thinks this and refers to his blinking out as a future possibility. He does not, as elsewhere in the series, claim that it is possible that he has never existed and does not even exist now.

Secondly, if a "world"/course of history blinks out of spacetime, then one state of the four-dimensional spacetime continuum (before the blinking out) is succeeded by another state of the 4D continuum (after the blinking out). "Before" and "after" are temporal terms that obviously do not refer to any successive moments within the 4D continuum itself. To say that one 4D state succeeds another 4D state is to say that these two states are related to each other within a fifth dimension/second temporal dimension. 3D states of the universe succeed each other along the first temporal dimension and 4D states of the continuum succeed each other along the second temporal dimension.

Within the current continuum, it is true to say that Carthage never won the Second Punic War but within the total reality which, we are told, includes not just five but 4N dimensions, it is true to say that there was a history with a Carthaginian victory in the Second Punic War.

Everard and Van Sarawak could have returned Deirdre to live out the rest of her life in her home timeline. 

19352 A.D.: Observations

See 19352 A.D.

The Morennian Triumph and the Chorite Heresiarchy not only are in a different timeline from Technic civilization but also are at a much later date in their timeline.

The fact that the past can be changed means that other timelines, like that of Technic civilization, could be generated.

Also, 4N dimensions, with N as the total number of particles in the universe, give more than enough space for multiple timelines, even including the Old Phoenix multiverse, to coexist in different parts of the multidimensional totality.

However, the Danellians and the Time Patrol exist in a part of the totality that comprises not many coexistent timelines but one mutable timeline.

The Patrol language, Temporal, has tenses both for time travel and for variable reality. Even in English, by applying logic, we can discuss the relationships between timelines whether or not all of those timelines are regarded as existent. Thus, a time traveler with memories of World War II who arrives in 1938 and somehow prevents World War II can be regarded either as a macrocosmic quantum fluctuation or as a traveler from timeline 1 (with a World War II) arriving in timeline 2 (with no World War II). Timeline 1 can either precede "timeline 2" along a second temporal dimension or be regarded as a metaphysical fiction. There is more than one way to save the appearances.

Question

One last question this evening before I return to other reading, then retire to bed (not a new question but a recurrent one):

Do the many parallel timelines of the Old Phoenix multiverse, the single mutable timeline of the Time Patrol universe and the different immutable timelines of The Corridors Of Time, There Will Be Time and other works exist in discrete zones or regions of just one megamultiverse (scroll down) which has 4N dimensions, as mentioned in "Time Patrol," and are there mysterious beings, like maybe obscure deities, who can travel through the megamultiverse, appearing in different times and places, intervening discretely in important events but never staying in one place and always just passing through?

I leave you with that until some time tomorrow.

On The Other Hand... II

I said here that the way to avoid arriving back in an altered timeline is to remain in your present but does someone who merely remains in his present risk being deleted by an earlier causality violation? Well, from the point of view of a time traveler who prevents World War I, he thereby deletes our version of history 1914-2019 etc. However, from our point of view here and now in this version of history, either we exist or we do not exist. Since we currently experience existence, it is not the case that we do not exist. The universe of 4N dimensions mentioned in Time Patrol training is vast enough to incorporate both a time traveler who has prevented us from existing in his timeline and us existing here and now in our timeline.

It makes no sense to say, as Patrol agents sometimes do, that, although I exist here and now, it might nevertheless turn out to be the case that I do not exist here and now. Of course, there can be another "here and now," exactly identical with this one except for my absence from it and that other here and now might exist after this one in the experience of a time traveler who has gone through the process of preventing my parents from meeting. But I exist here and now.

I have made these points before but will re-make them now and again as long as they continue to feel fresh. I am trying to pin down every implication of the Time Patrol series, an impossible task.