Ha! If that’s actually what I said, then clearly, I said what I wanted to say wrong. However, if that’s actually what you think I said, you misunderstood me.
I think I’ve mentioned, to you or to someone, or maybe I was just talking to myself, that one of the biggest challenges in trying to talk some things through is coming to an agreement on taxonomy. If you want to say cosmos = universe = world, fine, I can live with that However, In that case, I can only handle one: one cosmos/one universe/one world. Anything smaller is a subset of “The One”; and, IMO, there are subsets of subsets and subsets of subsets of subsets, all the way down to indivisible things that have mass and move through “The One”.
AND, because we’ve agreed–if, indeed, we do agree–that “the One Cosmos”, “the One Universe”, “the One World” are synonyms, I am not saying that an infinite number of universes exist NOR would I be silly enough to suggest that there’s a possibility for there to be an infinite number of them.
On the other hand, if you’re willing, I prefer: One cosmos, and a subset of many universes in the one cosmos, and subsets of many things in each of the universes.
Your call, if you want to make it. If you don’t, then I call the latter option: One cosmos and, potentially (i.e. possibly), an infinite number of universes. Why infinite? Because my Absolute Space is really, REALLY, R-E-A-L-L-Y big and can hold an infinite number of universes, but it’s only big enough to hold one cosmos.
As far as what logic requires and what the objective evidence supports I certainly agree with you. But when you factor in what this God belief is supposed to accomplish and what positive roles it can play in human life, then the role God plays in the origin of the universe and ourselves does make a difference.
On the other side of this, it has recently been claimed by some that our ultimate destiny and nature of our existence after death is irrelevant also. But again it depends on what this God belief is supposed to accomplish. Long term planning and living life in the context of long term objectives is a very important part of our humanity. And thus both origins and destiny has a profound impact on how we live our lives and the value we see in it. This is not to say these are the same for everyone to be sure. It is quite true that while theists see more meaning in a life which is in the context of a continuation, atheists often see more meaning in a life which has an end.
Some people who talk about the One would question the objective reality of other things. I’m just not sure if you are that kind of thinker, and sometimes I suspect people don’t understand what it is they are really describing.
I certainly ain’t one of them kind of guys. In fact, I think, quite the opposite. For example: I can say, and have said, that I am confident that I live, move, and have my existence on an objectively real planet, and I am absolutely, 100% certain of at least two things: that (a) my wife and (b) my dog, both of whom are laying down near me, are my wife and my dog and not yours or anybody else’s nor are they figments of my imagination. Moreover, I am not so egocentric that I believe the world around me will cease to exist when I die.
As for many of the things that I have mentioned in private messages to you and in this thread, my understanding could always be honed to become sharper, but currently I’m of the opinion that my understanding is sufficient here and now.
So I’ll take that as a no regarding the relativity of quantity.
As far as the private messages, besides the wall of text that I didn’t bother to read, I felt like the conversation was left hanging on whether a person (as in a disembodied observer, if I wasn’t clear about it) can measure a purely empty space.
A brief comment: IMO, neither claim is unfalsifiable nor provable, empirically, i.e. by experiment. That does not, however, preclude my ability to reject both claims.
In my OP, I introduced “the problem ofThe Now” briefly.
Note that Einstein was the first, on record, to raise it. Then he discussed it with Rudolf Carnap, according to Carnap’s 1963 account. Fifty years later, the theoretical physicist, Lee Smolin, recapituated and restated the problem, once in his book, “Time Reborn”, and again in a public lecture, Lee Smolin Public Lecture: Time Reborn.
Key point: I didn’t cause or create, nor was I the first to identify “the problem”.
In my second post in this thread, I described what I believe is “the source” of ‘the problem’ and I proposed a solution to ‘the problem’: restoration of three Absolutes: Space, Time, and Simultaneity.
My response, in my Post #4, to Mark’s first comment quoted above was: “My impression from Smolin’s comments (in his book and his Public Lecture) is that the lack of a athematical/physics model bothered Einstein (and Carnap ?), and now bothers Smolin enough to bring it up in writing and lecture. While the rest of us get by well enough without a model.”
My response to Mark’s question, quoted above, was terse, tongue-in-cheek, non-informative, and potentially appearing flippant or dismissive. Perhaps I should have said: “I’ll try to show you.”
Then, eventually, in my Post #21, I presented a brief essay by a now-deceased acquaintance
which discusses the concepts of Discreteness and Continuity.
Continuing from there, I now offer a standard mathematical definition of a metric space.
Let X = {x, y, z} and let d be the distance function or metric on X . If
d is a non-negative real number;
d(x, y) = 0 if and only if x = y;
d(x,y) = d(y,x); and
d(x,y) ≤ d(x,z) + d(y,z)
then (X, d) is a metric space.
If Y ⸦ X and the metric on Y is d̃ , then ( Y,d̃ ) is a metric subspace .
Next Step: Assume Absolute Space and Absolute Time are each metric spaces.
Absolute Space or simply, Space, is a set. “The elements of Space are points. The points are some distance each from each. Each such distance may be specified as the product of a nonnegative real number and a unit of distance, such as 3 miles or 4,828.032 meters.
Space is not a physical substance and cannot be stretched or compressed, nor does it expand or contract. Physical substances that can be stretched or compressed are not continua and owe their mutability to the fact that they are not continua.
It makes no sense to say of something that it has changed either its size or its shape unless there is some standard all parts of which retain forever the same size and shape with respect to which standard the size and shape of anything else is defined. This something is Space, so it makes no sense to say of Space or of any part of Space that it changes its size or shape.”
Absolute Time or simply, Time, is a set. “The elements of Time are instants. [‘Instant’, in this context, is just the generic name for the elements of time. Thus time is the set of all instants.] The instants are some distance each from each. Each such distance may be specified as the product of a nonnegative real number and a unit of distance, such as .03 days or 2,592 seconds.”
Time is not a physical substance and cannot be stretched or compressed, nor does it flow.
Terry, I’ve got to tell you this sort of logical precision isn’t something I take to naturally or happily. I’m a big fan of plain speech philosophy. But the distinction between now and past/future is entirely because of their relation to a subject. Past and future are never present in the living world. They are constructs of ours we use to sort experience relative to either the current moment or else to a specified moment from a timeline.
But past and future are abstract and hypothetical, not that they’re controversial. They existed already or will eventually but will always only ever exist when they are present in the now. It isn’t now that is the problem, it’s the only real time. Past and future are easier to model because their existence is restricted to our models of time. Our models of our experience are static and explicit, but our lived experience never is.
I guess I’m saying the problem is simply that no model can include the lived world in its entirety because a useful model can only contain a salient subset of it.
Nor I. And there are, among the vast majority of us, folks–very rare individuals who live and breathe logical precision, the Spocks among us. The acquaintance whose words I share in this thread was such a guy, … so astute that he earned the respect of all but the most envious or obtuse, in the forum that I encountered him in. His most impressive characteristic, besides his willingness to talk with anybody about almost anything, was his ability to understand and answer almost anybody’s question regardless how poorly they expressed it.
My favorite quotation of his words are these:
“To say that the evidence is against the universe’s making sense is an absurd statement. If the universe actually does not make sense, then we should just fold our tents and get drunk or something instead of wasting our time trying to explain the universe. The actual situation is that evidence must be interpreted and it is always interpreted either on the basis of some theory or else on the basis of some set of inchoate presumptions. If one starts out with false fundamental notions, then one will also read falsity that is not in the evidence itself into the interpretation of that evidence. If the evidence seems not to make sense, that is your clue that an examination of the assumptions used in interpreting that evidence is in order.”
I concur completely.
“To say that the evidence is against the universe’s making sense is an absurd statement. … The actual situation is that evidence must be interpreted and it is always interpreted either on the basis of some theory or else on the basis of some set of inchoate presumptions. If one starts out with false fundamental notions, then one will also read falsity that is not in the evidence itself into the interpretation of that evidence. If the evidence seems not to make sense, that is your clue that an examination of the assumptions used in interpreting that evidence is in order.”
Abstract? Yes.
Hypothetical? “…evidence must be interpreted and it is always interpreted either on the basis of some theory or else on the basis of some set of inchoate presumptions”
“They existed already or will eventually but will always only ever exist when they are present in the now.” Whose “Now”?
Rationale for Assumptions about Absolute Space and Absolute Time metric spaces.
“We seem, and have so seemed since at least the time of Thales, to inhabit a world that consists of moving objects and to be moving objects ourselves. In order to describe motion at all, one needs two metric spaces. That way, there is a set of times that are at various temporal distances from each other and a set of places that are at various spatial distances from each other. A physical object can then be said to be moving if it is in different places at different times, or if its parts are. We could say that much even without the metrics. With the metrics, we can divide the spatial distance by the temporal distance and assign a speed to the motion. We can also define the other concepts that we need, such as continuous paths, so that we may distinguish motion from popping out of existence at one place and reappearing at some other place and explain why the universe consists of things that, by and large, retain their identities while they move from place to place and are, so far as we can tell, in intermediate places at intermediate times.
"There are a large number of different metric spaces, more than merely infinitely many of them. Some of them have no such property as dimension. Some of them are n-dimensional for various numbers n. The propositions that are consonant with our perceptions are that time is one-dimensional and space is three-dimensional, at least during our history and as far out as we can see.
"Of the one-dimensional and three-dimensional metric spaces, some are infinite in length or volume and some are finite. All the infinite ones have finite subspaces of all sizes.
"For the space and time of the actual universe, assuming that such concepts are parts of the correct description of the actual universe, assuming, indeed, that there is an actual universe and that it has a correct description, we can access only a finite region of either. There are a few thousand years of recorded history and a few billion years before that that can plausibly be inferred by indirect reasoning processes using data such as the amounts of radioactive materials and their decay products found in rocks. Collectively, we experience the major portion of the surface of the earth directly but not much else until we went to the moon. We experience a few billion light-years exterior to our living space indirectly, more only so indirectly that very few people understand the indirect evidence of more to be that.
"Still, a theory of physics, assuming that it is to contain a subset that is a theory of kinematics, is constrained on page one to state axioms that specify space and time to be certain metric spaces. These are preferably axioms 1 and 2 since the concepts of kinematics are so basic that any other axioms about the nature of physical objects are likely to establish relationships either of the concepts of space and time to each other or between the concepts of space and time and something else. Axiom 3, for example, might posit the existence of objects that have positions in space that vary from instant to instant. The decision about whether space and time are finite or infinite could conceivably be held in abeyance, but specificity requires that the decision be made at the time that the axioms of kinematics are stated.
"These postulates, whichever postulates they are, are not going to be testable. Nobody can prove that the world was not created six minutes ago containing what appears to be internal evidence that it is older. Nobody can prove that, given any period of duration one hour, there was another period of duration one hour that preceded it. Nobody can prove that there exist points or instants with irrational numbers as their co-ordinates, or that there aren’t. Nobody can prove that the geometry of the real world is Euclidean rather than either hyperbolic or elliptic, provided that its curvature, if not zero, is small enough to be undetectable by human beings.
"If we decide to postulate a time of infinite duration and a space of infinite volume, we are extrapolating from the known to the unknown, or, actually in this case, from the unknown on the small to the unknown on the large, even better, from the unknown at distances intermediate between the small and the large to the unknown on the large. There is always a danger in extrapolation. Following the same principle, nobody in England would have believed that there are elephants or black people in Africa, or that the sun is there in the northern part of the sky.
"Still, the simplest possible proposition consonant with what is known is that space and time have Euclidean metrics and consist of the entirety of, respectively, a one-dimensional Euclidean time and a three-dimensional Euclidean space.
"The decision to prefer or even to consider a non-Euclidean metric would be very strange. No such metric is simpler in structure than the Euclidean metric and there is a total lack of any empirical data or philosophical reasonings whatever that even suggest that a Euclidean metric is in any way unsuitable.
"Granted the Euclidean metric, the decision to speak of a beginning or an end of time or a boundary of space would be completely arbitrary and ad hoc and could be motivated only by some extra-logical and extra-experiential consideration such as an irrational dread of the infinite or a theologically motivated preference for a creation theory.
"There are other reasons for assuming an infinite space and time. One is that if they are finite, we must then make a completely arbitrary decision about how big they are, there being no reason to prefer any size over any other, so long, anyway, as we choose sizes sufficiently large to encompass our visible environment and recorded or reconstructable history. Another is that a beginning or an end to time is incompatible with any conservation law. If physical stuff (matter, energy, momentum, whatever) popped into existence from time to time or vanished from time to time, and in particular if there was more of something at some times and less of it at other times, then it would be possible that there have been or will be times when there was none of it. However, the real world seems to be governed by a set a laws that say that this stuff can be here or there but it can never be nowhere, that you can move it about and concentrate it or rarefy it, but you can’t make any more of it than there already is and you can’t get rid of any of it. You can’t, however, have, say, conservation of momentum unless time goes on forever and has always been doing so. A limit to space is also incompatible with conservation laws. An object moving at some speed in some direction and subject to no external force continues moving at the same speed and in the same direction forever, not just until it arrives at “the edge of space.”
Such arguments, however, prove nothing. It is always possible that quantities that appear to be constant are changing at imperceptible rates. In the end we must merely make such postulates as appear reasonable. We can have some hope that they are false and that evidence from the real world will contradict them so that we may learn something. We have to understand that if this does not happen, that fact does not prove that the postulates are true. We have to understand that there is no way whatever to show that they are true. Indeed, we have to understand that there is no way even to show that they are reasonable. ‘Reasonable’ is a judgment call and doesn’t mean much more than ‘I am interested in exploring the consequences of these propositions’.
"Once we have a theory of kinematics that posits the existence of a space within which physical objects are to move about and a time that passes as they do so, there are a number of subsidiary notions that are part of this picture that we shall want to retain at least until our theory can’t explain something or is actually contradicted by some observation. There are also any number of suggestions that are incompatible with these notions in which we should have no interest. I will deal first with the latter issue.
"Anyone who thinks that space is a physical object that can itself move or wiggle or be compressed or rarefied or expand or contract is not talking about space at all and has no understanding of what the term ‘space’ means within the context of a theory of kinematics. Anyone who speaks of time as moving or as speeding up or slowing down or of physical objects as moving through time, etc., similarly is using words in funny ways and is not talking about the concepts that go by the names ‘time’ and ‘move’ in a theory of kinematics.
"The notions that physical objects interact with either space or time or that space or time cause or have any effect on the behavior of physical objects or that physical objects cause changes in the structure of space and time or that physical objects are changes in the structure of space and time are the same sort of nonsense.
"So too are notions such as that there exist objects that have momentum but do not have definite positions or that have positions but do not have definite speeds or directions of motion or that a physical object has position and momentum as a single property that looks like either position or momentum depending on what experiment is done on it but does not have both position and momentum at once.
"… In a universe that consists of moving objects:
"1. There must be a space and a time, since otherwise there is no way to have motion, which consists of having different locations in space at different locations in time and, more specifically, in continuous change of location in space with respect to location in time.
"2. Space and time must be metric spaces, since otherwise there are no distances in space and durations in time and hence no way to define motion, as opposed to merely being somewhere at one time and somewhere else at some other time.
"3. Metric spaces are point sets, so space must be a set of points and time must be a set the elements of which, called instants, have the same size and shape as points, that is, the same relationship to distances between instants, or durations of intervals of time, that points have to distances between points, or lengths of intervals of space.
"4. The physical universe, the set theoretical union of the set of moving objects, must be a set of things that occupy singleton point sets at the instants of time, for anything larger would have parts and hence would be a subset rather than an element of the universe.
"5. These atoms must move all at the same constant speed, for otherwise there would be no way to distinguish a co-ordinate system for space from a moving spatial reference frame nor a uniform clock from a non-uniform clock, and no sense to the proposition that any atom even has a speed, much less to the proposition that any atom has a varying speed or that any two atoms have different speeds.
"6. The elements of the physical universe must therefore each be completely surrounded by empty space and isolated from each other, since there is no way for continuous aggregates of atoms to move at variable speeds or with variable directions if their punctiform parts must all have the same constant speed.
"7. The atoms must interact with each other according to some such law as Newton’s law of gravity, since otherwise they would move only in straight lines and retain constant amounts of mass, energy, momentum and angular momentum, which is not the case, for physical objects are observed to move at variable speeds and in variable directions and to exchange energy, momentum and angular momentum with each other.
"8. Since the atoms are separated from each other by positive distances, these interactions must be “action at a distance.” The philosophers to whom this notion is repugnant might as well hate the fact that two plus two is four.”
Final Step: Postulate a single cosmos consisting of Absolute Space, Absolute Time, and Atoms.
Let Κ be the cosmos, i.e.
the set of all dimensionless spatial points in a three-dimensional Absolute Space,
the set of all dimensionless temporal instants in a one-dimensional Absolute Time, and
the set of all dimensionless atoms moving through Absolute Space.
Because all points in Κ are simultaneously—that is, at the same instant—in Κ, that instant of Time isthe Now in Κ.
To seethe Now, let Sxyz be a cubic unit subset of Κ, i.e. Sxyz ⸦ Κ. [Figure 1.]
Figure 1.
Because all points in Sxyz are simultaneously—that is, at the same instant—in Sxyz, that instant of Time is the Now in Sxyz.
Because Sxyz ⸦ Κ, the Now in Sxyz is the Now in Κ.
Instants preceding the Now in Sxyz and in Κ are elements of a subset that we call The Past, regardless when in the cosmos they once were the Now.
Instants subsequent to the Now are elements of a subset that we call The Future, regardless when in the cosmos they will be the Now.
By definition,
The Past precedes the Now and the Now precedes the Future anywhere in the cosmos; and
The Future does not precede the Past or the Now and the Now does not precede the Past anywhere in the cosmos.
Conclusion: The restoration of Absolute Space and Absolute Time restore Absolute Simultaneity in the Now, which ensures cosmic chronological order in a way that Relative Space, Relative Time, and Relative Simultaneity could not, cannot, and will not.
In kinematics, an event is an “idealization” of an actual event, i.e. an occurrence of some kind during an interval of time somewhere. An idealized event takes place at some point in Space, at some instant in Time, and is describable by one temporal and three spatial coordinates, and often represented by a dot, “•”.
Let Ė1 be an idealized event with coordinates {x1, y1, z1, t1} and Ė2 be a second idealized event with coordinates {x2, y2, z2, t2}.
