Before we begin:
I wanted to directly go on to my recent series, the one on the theme of what all different broad views of the physical world can be taken to be implicit in the states of the knowledge of physics, as it existed during the various eras of its development. Continuing linearly in that series, in this post, we should have been pursuing how Fourier’s theory marks the beginning of yet another “world.” Despite the fact that it came as early as the beginning of the 19th century—a time when, speaking off-hand, Laplace and Poisson were peaking, Gauss had just about got going, and not even Lagrange had yet made any mark on the scene let alone Hamilton—Fourier’s theory still is, markedly, not a “Newtonian” theory in its basic spirit.
Fourier’s theory doesn’t have the instantaneous action-at-a-distance (IAD) simply as a secondary or accidental feature the way gravity does in Newton’s gravitational theory. The fact is, Fourier’s theorization couldn’t have progressed even an iota, nay, it couldn’t even possibly have got off the mark, without first assuming a certain form of IAD as being a very essential feature of the physical world.
Anyway, the fact of the matter is: understanding IAD requires sufficient clarity on the issue of nature of space (and also on the differential equation paradigm of the physics-model building, though people should be clear enough on this one). And so, at least some discussion of the nature of space is absolutely necessary.
… And, that way, it would have been necessary even if the relativity theory were never to be formulated in the form that it was, by Poincare and Einstein, simply because both Newtonian gravity and Fourier’s heat conduction had already involved IAD, but to a different degree of emphasis. I mean to say: If Newton was merely agnostic about IAD, then Fourier was a zealot for IAD—albeit a refined one, of course. And, subtle. … Very subtle, if you ask me. … And, IAD is something which, even on the basis of common sense alone, and right on the face of it, seems incoherent with any physics theory. And, therefore, demands a deeper examination of the concept of space, first.
In this post, I will try to address all the essential points about space that I wish to cover. However, the topic is both intricate and very “deep,” and so, I may not be able to finish it one go. (Hey, even I have limitations when it comes to typing, OK?) If so, we will pick up some portion of it in the next post.
What does the word “space” mean? … Here, we can’t look up to the physicists and mathematicians. They don’t know the answer, but they do have the brains to confuse us—and also themselves—quite a lot. Just look at them! (LOL!). So, instead, we have to think independently, afresh, beginning at the beginning.
Actually, the word “space” is a bit overloaded a term. There are many shades to its meaning; it stands for many aspects. But I guess, jotting them down all right at the beginning is neither practical nor necessary. So, what we will do is to pick up the different nuances as we encounter them. So, first, let’s get going, starting from the very beginning, by going “all the way down,” i.e., to the base of all knowledge, i.e., to the perceptually evident reality.
A relevant, and directly available—i.e. perecptual—field:
Suppose you are seated at some remote and lonely beach on some evening, contemplating the meaning of the word “space.” … Imagine the vast expanse of the deep blue of the sea lying in front of you, seemingly coming closer and still closer towards you along with those waves, and ending with them somewhere at that thin beige crescent which is the patch of the sand surrounding you; with some thick green woods standing mostly quiet behind the sand; and then, a paler but even wider expanse of the blue sky “standing” completely aloof over it all, ignoring everything below it—even some idle white streak of a cloud hanging up there mostly cluelessly. Down below, that darkish green patch of the woods continues on for some distance, getting hazier and hazier, and merges into the greyish black outline of a distant hill, which then goes cutting across some way into that flat line where the two blues meet. … You may also imagine a few homeward-bound birds in the sky, a happily aimless stray dog roaming around on the beach, a seemingly motionless ship or two in the distant motionless sea, and the dark orange of the setting sun, so to complete your picture. … The night then sneaks in slowly, and brings with it a cool breeze, and some time later, it’s all mostly dark and silent, with the twinkling stars mischievously asking you whether you succeeded in getting the answer to your question or not. … The question of space. …
… Or, imagine that you are seated at some high point in the hills on some evening, with some greenish-blue mountains remaining majestically self-absorbed only in themselves for eternity—a range after another range progressively fading away into distance, and an even thinner and paler sky that still refuses to go away even if it now seems ever more expansive and even more aloof. … And, as the night falls, the stars, once again, wouldn’t forget to pull their mischief—of raising that question to you. …
Once back in the city, as you walk on a late monsoon evening on a bridge, past those bright orange sodium-vapor lamps erected on those dullish silver lamp-posts, the stars somehow become completely invisible, even if the skies are clear. Instead, what you see are some whizzing clouds of those pathetically thin flies randomly whizzing above the heads of the passers-by. There is no easily discernible pattern to the motion of those flies. In fact, the motion of any one fly is even plain visually impossible to follow. The flies make for a buzzing kind of a cloud, but far more indefinite for it all to be at all called a cloud. The “cloud” here seems to be engaged in a never-ending flux of sorts.
If the metaphysical nature of reality were such as to be constantly in a chaotic flux—a literal chaos, one far worse than the cloud of those flies buzzing overhead—then no knowledge would at all be possible in that universe.
Knowledge—all knowledge—begins with definite objects that are easily distinguishable in the perceptual field of awareness. The perceptual field is the basis of all knowledge. A sense of an enduring, definite, reality is where we can at all begin. And all our knowledge, if valid, must be reducible to such perceptual concretes. Even if there be some motion to some object, it must be perceptible. It must orderly—not constituting a random metaphysical “flux.”
At the beach, it’s the unmoving patches like that of the sand and of the distant hill that provide an implicit sort of an anchor to our visual field. That way, there is a lot of motion going on also at the beach. The dance of the foam upon the breaking of the waves is evanescent, but it can still be visually grasped because it is, in a way, orderly. Neither does the sea ever forget its limits nor do the bubbles get formed at unpredictable places in it. The motion of the flapping of the wings of the birds occurs relatively slower, and so, it is even more easily graspable. The outline of the idly loitering dog is slower still. And the sun does get noticeably longer to completely disappear from the view. At night, the stars move, but it would take some alertness and some patience to notice that fact. And, the distant hill does not move at all, neither does that patch of the sand.
You can make out the rapid flapping of the wings against a relatively slower motion of an approaching wave. But to distinguish every possible motion—including that of the sun and the stars—you first require that stand-still outline of that distant hill, or the constancy, as it were, of the horizon where the sea “ends.”
In the most general sense, a state of motion can be perceptually grasped only against the backdrop of a state of its absence. We require solid, definite objects that also are enduringly stand-still in a perceptual field, before we can at all become aware of the motion of some other objects.
So, let us first consider the stand-still objects—the sand at the beach and the hill nearby, or the unyielding patch of the ground on which you were seated on the mountain-top, and the stand-still ranges of those distant mountains. What all things about them can we make out right from such, simple, perceptual fields? What features of interest to physics do they hold?
The two characteristics of a motionless physical world:
What interesting aspects are held by stand-still things—that is, even if there isn’t any motion at all? [And, please remember, the discussion from this point onwards until explicitly noted, refers only to a motionless world—i.e. the perceptually enduring aspect of the as-perceived world.]
For one thing, the things in the motionless physical world still are distinguishable—i.e. perceptible.
And, among the perceptually grasped characteristics of the kind that allow any distinction to be at all perceived (i.e., those characteristics which permit our perception to at all have a sense of there being this object vs. that object), a couple of characteristics stand out. These are: the locations and the extensions of the individual objects.
In my (at least current) opinion, it does not matter which one we tackle first. Metaphysically, just like with any other characteristic, they both—extension and location—exist simultaneously, and so, a metaphysical consideration cannot settle the issue of deciding the hierarchical priority between the two. Now, epistemologically, it seems to me that they constitute a certain pair of characteristics such that both of them become at all graspable only simultaneously—i.e. in reference to the exactly same perceptual field (though their respective grasps would differ in time). And, as far as my current thinking goes, it therefore does not matter which one we begin with, for the purposes of our discussion. … BTW, this epistemological point is rather deep, and may be, I will come to it later on in this post. But, first, let’s deal with them, individually. And, remember the context: We are dealing with a motionless world, here.
The patch of the sand has, broadly speaking, a definite beginning perceived at the shore-line, and a definite end perceived at the dark green woods. And, similarly, for the outline of a narrow path through the woods that you might see, while seated at a mountain-top. And, similarly, for the distant hills.
The very existence of these (and all such) objects is such that each of them is seen (i.e. perceived) to have a certain beginning and a certain end to them. Even in a world completely devoid of motion, for each object constituting it, there would still exist these kinds of beginnings and ends. Even if your eyes were taken as not grossly moving, these would exist—they are an objectively existing feature of the perceived objects. They are what allows us to make out the outlines of those objects in the first place; they are a part of perceptually distinguishing one object from the other.
When we thus speak of these directly perceived beginnings and ends, the one characteristic which we are trying to isolate here is not so much the boundary of the object, but (what I currently think is) something simpler: the extent of the object. Rather, a fact somewhat even more basic to it: the metaphysically given fact of the “extended-ness” of an object.
All [concretely real] physical objects are perceptually grasped as being extended. “Extended-ness” is a characteristic that is directly available right in the perceptual field.
And, it is there with every physical object that we perceive. To repeat (because this point is important): All objects are extended; extension is a characteristic of every object.
Using terms from the Objectivist epistemology, extension is a concept whose scope is co-extensive with that of the physically existing objects themselves.
Note, the primary issue here is not that pertaining to how [much] extended a given object is. The size of the extension [of an object] is, hierarchically, a later issue; it is the one which can arise only by first assuming that there is some definite extension to every object. For the time being, let’s leave aside the issue of quantities (or as people familiar with the Objectivist epistemology would know: the issue of the omitted measurements). It should be enough to just note here that the fact that physical objects exist with different sizes of their “extended-ness”es, is also something that is given right in the perceptual field. For instance, the dog is perceptually seen to be smaller than the beach, or the trees shorter than the hill. But, hierarchically, this whole issue of size (or of comparative measurements) is an advanced one.
More crucial for the time being is the fact that the concretely real objects—all of them—are only definitely extended.
In particular, contraries to this truth never are a part of the perceptual field. Given the nature of the perceived entities, the contraries cannot be—that is what the inductive generalization that objects are definitely extended, means. Since we are dealing with a first-level generalization here, only ostensive definitions are possible. All that we can do is to indicate its truth in an indirect manner. Say, by pointing out the approach to its meaning, as we have done above, and then, by pointing out the contradictions its contraries raise.
It is precisely because every object is definitely extended that we are completely stumped if we try to “visualize” an object with no extension. It’s the case wherein an end of an object is asserted to be the same as a beginning of the same object, and thus, extension cannot any longer be regarded as a characteristic of that “object.” And, it is this reason why “an object without extension” stumps us.
It is also precisely because every object is definitely extended that we also are completely stumped if we try to “visualize” an object with an infinite extension. This, now, is the case wherein either a beginning, or an end (or both) is (are) missing, not just in an isolated instance of perceptual fields, but in principle, i.e., as if even with a missing beginning or end, you could still have a concretely real object. Now, if either a beginning or an end is absent, then what this peculiarity actually does is to once again make it impossible to regard extension as a characteristic for that alleged “object.” In other words, the procedure wipes out the fact that extension is a necessary characteristic of any object. We, once again, are stumped only because no concretely real physical object can at all be without an extension.
The “some–any” principle of the Objectivist epistemology [^] requires a characteristic to exist in some (definite) quantity, even if it may exist with any (definite) quantity. Qua characteristics of physically existing objects, extension can only be finite quantity. If the term “extension” of a concretely real physical object has any meaning at all, it can only exist in some definite quantities.
Please remember this part of the discussion when we come to the issue of infinity or otherwise of space and universe. … However, let me also hasten to advise you to refrain from directly jumping to conclusions. Remember, there are many senses in which the word “space” may be taken. Here, we have been considering the most fundamental sense with which the word begins to derive its meaning. And, in fact, all that we have thus far seen is only one characteristic at the basis of the concept, viz., that of the extension—not space itself. The word “space” does require the characteristic of extension for its context, but it is not in itself sufficient.
There is another characteristic, given right in the same perceptual field, i.e., the one referring to the objects of the motionless world. So, let us take a moment to refresh the motionless aspects of our starting perceptual field, as, e.g., the one at the sea-side or on the mountain top, etc. What else, apart from extension, do we see by way of, say, “properties” of those objects?
We see, for example, the patch of the sand, and of the sea. And realize another simple truth, viz., that each of them is [found] there, where it is [found]. The sand and the sea are situated in a certain kind of a perceptually grasped (spatial) relationship with each other. The sand is next to the sea—or, if you wish to put it the symmetrically other way, the sea is next to the sand. Similarly, the sea is next to the hill—or the hill is next to the sea. And so on, for any pair of the perceptually distinguishable objects. … The sand begins where the sea ends; and the sea begins where the sand ends. The sand is there, where it is; and the sea is there, where it is. Each perceptually grasped object is there, where it is perceputally seen to be; it is simply a part of the perceptually given distinction that comes with the very act of perceiving that physical object.
Thus, there is a certain characteristic of “there-ness” that is possessed by each physically existing object. Let’s name this characteristic as: “location.”
Apart from extension, location is the other physically existing characteristic displayed by every physical object [in the motionless world]. Just the way each physical object is necessarily extended, similarly, each physical object also necessarily has a location.
The words like “here” and “there” denote a certain basic characteristic which is a part of the very identity of any perceived physical object.
Thus, the scope of the concept of location, too, is “co-extensive” with that of extension.
“Location,” too, has a certain definiteness of its measurements, as a part of its context.
And, though I wouldn’t go into a detailed explanation of it, once again, two main classes of errors are possible: we are stumped when we are asked to imagine (i) an object that is no-where, or (ii) an object that is any-where. The reason we cannot imagine either of them as belonging in the concretely real physical world is because: each is alleged to exist without possessing the essential characteric of a definite location.
[BTW, if you have got the above point right, you may want to think of the reason why, when it came to the error of supposing an infinity of “there-ness,” I have used the word “any-where,” and not “every-where.” Try to figure out the reason for that. Have fun! :)]
A couple of miscellaneous [though perhaps a bit advanced] epistemological points:
There are few points which involve some subtleties of epistemology. However, they aren’t entirely of a technical epistemological interest alone. In fact, a discussion of them could very well have the effect of anticipating a few important points of physics. So, even if you aren’t very comfortable with epistemology as such, do try to read on—it’s easily possible that you might very easily “get it” anyway! (The points may be subtle, but they are not too difficult.)
(E1) In case you missed a certain tricky point above, let me highlight it here: Location, I have asserted, is a characteristic of an individual object. The tricky point? If you noticed it, I was thereby also asserting that location does not primarily refer to a relation between two or more objects.
… In other words, I seem to be putting forth a view of space that is not, say, so much “relational” in nature—am I not? … BTW, here, you may want to see Dr. Peikoff’s writing on the concept of space [^]. And, while you read the ensuing discussion, it might be fun for you to decide whether I agree with Dr. Peikoff’s position or not! … But, coming back to the issue at the hand here, yes, I am putting forth a viewpoint of space that is not “so much” relational in nature. Let me explain.
In fact, I will go even further and state my wider epistemological conviction. There can be no characteristics existing as apart from the objects with which we might relate them! Not even when it comes to the relational characteristics. There can be no “purely” relational characteristics that exist separately from (or independent of) the objects of which they are the characteristics.
If two or more objects can at all be related to each other, it is only via some characteristic(s) (or attribute(s), etc.) which each of them must first separately possesses as a part of its own, separate, identity. Only if this condition is fulfilled that we can at all relate them.
And, thus, even the so-called relational characteristics do not exist all by themselves; they do not exist in a void of sorts, floating somehow disconnected from the objects, and somehow connecting with the objects only when it is the time for us to relate them. … You cannot join two isolated blobs (of objects) by a line (of a relationship) if the attribute you note for that line wasn’t already a part of the identity (i.e. a characteristic or an attribute, etc.) of each of those two blobs taken by itself.
Relations can be isolated as separate concepts, sure. But their status is not, therefore, at par with the objects which they help relate. The objects come first; the relations come at a higher level of abstraction. And, a particular relation can at all “come” (or be formed by a mind) if and only if each of those objects, taken separately, already possesses that same characteristics—on the basis of which they can later be related.
(E2) Another point, in a way, going seemingly against the above point:
Actually, even though I did not explicitly note this point while discussing the concept of extension, even “extension” is a characteristic which can only be grasped only if there are at least two objects separate physical objects (each of which would separately possess a definite measure of its extension).
If there were to be only one object in the world, you couldn’t grasp either its extended-ness or its located-ness (or “there”-ness). Indeed, you couldn’t even grasp that object. This is a very subtle point. It refers to a “what if” scenario which Ayn Rand had once used, in that seminar (in the 2nd edition of ITOE). Let me briefly touch upon it.
Suppose all you had for the universe was only a vast expanse of some uniform (and never-changing) pale blue, and nothing else, then you couldn’t grasp any thing, Ayn Rand said. Not even just the fact that there is some expanse of the blue. You couldn’t grasp even that—not even purely on the perceptual level. But, add just one speck of dust, and perception at all becomes possible, she had pointed out.
[As an aside: A reminder which might perhaps help those who are already familiar with the Objectivist epistemology: Both differentiation and integration are necessary elements of any process of awareness—even for the awareness only on the perceptual level. And, both of them come at the same time. If consciousness is a difference-detector, it also is a commonality-integrator, or vice versa. Aside over.]
… To resume back the main discussion: no perception is at all possible with just a uniform expanse of blue, but it becomes possible as soon as you add a speck of dust.
Now, for convenience, you may want to imagine a sizeable circle of a uniform shade of dark blue, instead of just a speck of dust. … Once this circle is introduced against that pale blue backdrop, you would begin perceiving not only that circle. And, the same perceptual field would also contain the most bare essentials for you to perceive the fact that this circular object was extended, and further, that it was located where it was.
In other words, what you could say, in effect is not just: “Something!”, but also—because it’s a physical object—“Some thing, there!”
In the very act of saying “there,” (i.e. grasping the location) you would also be implicitly referring to the fact that the dark blue circle was extended—that it was extended over a certain region where the pale blue was not, and the pale blue was where the dark blue circle was not, and vice versa.
An alternative way of putting the same fact is also possible: In the act of seeing that the dark blue circle had an extension, you would also be referring to the fact that it was extended from “here,” meaning one part of its boundary, to “there,” meaning some other part of its boundary.
In particular, the same perceptual field would be enough for you to grasp both the characteristics of location and extension. Just the way both differentiation and integration are necessary to any cognition—perception or conceptualization—similarly, both location and extension become possible at the same time.
But, “wait a minute,” you might say, here. “Location, in our above discussion, referred to finding out the where-ness of one object by referring this object to some other object next to it. The sand was next to the sea, and the sea was next to the sand, and both were definitely extended. But, here, the pale blue is not definitely extended. There is no visible “outside” boundary to the pale blue. Only the dark blue circle has a boundary. Since there is no boundary to the pale blue, by your own definition, it cannot be taken as a physical object. So, there is nothing sitting next to the dark blue circle. So, the circle may have extension, but it has no location. If so, how come both these concepts become possible at the same time?”
In answer, I would say: “If you are smart enough to think of that objection, then you must also be smart enough to figure out the answer as well!” No, really!! I mean it!!! So, try to crack it on your own. And, if you can’t, I will let you know what I think of it, some time later on in this series.
… For the time being, notice that, like with any proper, relevant, and deep issue of epistemology, some paradoxes which seem to raise their heads first in the physics theory obviously have some kind of a source in some deep epistemological and metaphysical theories. If I say that philosophical issues like these are relevant to the physics issues such as the existence or otherwise of the aether, the infinity or otherwise of the physical space and/or the universe, then my assertion should at least be plausible even if not outright obvious.
But of course, before we can begin talking about the infinity of space and all, first, we have to understand what “space” means. And, thus far, what we have done is only to isolate two characteristics of the concretely existing physical objects: viz., their extensions and locations.
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But, anyway, enough is enough, for today. … It’s not that a lot of territory is still left…. Just two more steps (or so), and we should be on our way to “completely” understanding what the word “space” basically means. I will come back to write about those remaining points soon enough. We will then be in a position to worry about the issue of IAD, of Fourier’s theory (i.e., whether it necessitates a further splitting of our physical worlds, or not), of Newton’s theory of gravitation, of aether, and the rest of the “shebang.”
So, hang in there. At your [own] locations, and with your [own] extensions (I mean to say: without worrying about exercise, diet, etc.!)
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A Song I Like:
(Hindi) “deewaanaa mujh saa nahin, is ambar ke neeche…”
Music: R. D. Burman
Singer: Mohammad Rafi
Lyrics: Majrooh Sultanpuri
[PS: Guess what I will now do is to first pour my mind out in the next post in this series, and thus make sure that we “finish” space, and only then come back once again here and edit/streamline this post.]