I continue with the meaning of the concept of space in this post.
0.0 What we saw last time:
In the last post in this series, we saw that all physical objects have the characteristics of extension and location. We began with the perceptually evident reality; then considered only the motionless aspect of the world; and then saw how extension and location are ostensively defined in reference to the objects in that motionless world. We thus did make a lot of progress.
And, even though I am not fully satisfied with my formulations in that post (and for that matter, even would like to rethink even some of my asserted positions), I would like to leave these matters aside for some time. But let me jot down just one issue about which I am not fully satisfied, by way of an example.
0.1. Boundary as an advanced concept:
While isolating the concept of extension, while writing my post, I seemed to have ended up over-emphasizing the use of “beginning” and “end.” The way I wrote it, it seems as if, hierarchically speaking, the concept of “boundary” could at least easily vie for the same hierarchical level as that of extension, if not being even more basic to it. The way I wrote it, the concept of extension seems to require a reference to be made to an object’s boundaries.
But, this is not the position I actually had in mind. It was pretty clear to me that while extensions and locations do exist in the concretely real physical reality, boundaries don’t.
Boundaries are mental objects (“imaginary” ones), and their hierarchical position is therefore at some higher, more abstract, level. A boundary does not exist in the physical world; it is not grasped perceptually. You do not rest at the boundary of a wall (or the backside of your chair); you rest against the wall (or the backside). It, therefore, should be possible to write about this issue in a way that de-emphasizes the references to “beginnings” and “ends.”
… Thus, I seem to have ended up writing what in fact is not my actual position. … While writing on intricate and deep matters completely independently, such things do happen.
Another thing. I am not sure if the English word “location” is the right one to use for the characteristic I have explained in my last post. … I have been confused about the choice of a suitable word to use here, for a long time by now.
0.2. A bit about the terminology I use, and something about the personal background in which it grew:
When I thought about these things seriously for the first time, which was some time in the early 1990s while I was a student at UAB, some of my thinking was actually done in Marathi.
… The way those times turned out for me, I was being in a sustained background state of completely unexpected personal losses (heaped on me by others), was in a foreign country, and overall, also was quite isolated (there was no Internet back then; air-mail would take one week, one way), and so, those unexpected losses were beyond my capacity to bear.
One day, in one of my several (but only partly successful) attempts to snap out of it, by engaging my mind into something new, I had thought of trying my hand at translating some essential philosophical terms into Marathi. It was this attempt which first had, unwittingly, jolted me for a while into an even deeper sense of isolation (and an attendant sharpening of the sense of sorrow), but, immediately later on, the touch with the mother-tongue, even if in this way, also had this magical effect of bringing clarity to the deepest of my thinking on many issues.
It was magical because, you see, in those times, in my attempts to try and keep up with the world, I would always try to think seamlessly only in English, so as to improve on my command over it—a process which I had consciously tried to imbibe for quite some time by then. (In a way, I was trying to keep up with my English medium-educated friends—as well as foes. I was the only Indian student at UAB who was neither Brahmin nor English medium-educated nor someone who had visited a foreign country before—and, of course, I had no relatives or family friends anywhere abroad, let alone in the USA.) But such attempts of mine, I then realized, were in some ways doing more harm to me than good. Thinking in Marathi brought a certain clarity to my thoughts much more quickly and far more easily.
In particular, about certain deeper concepts, esp. the first-level, ostensively defined concepts, it brought about an incomparable kind of clarity. And it’s thus that my thoughts on these matters were first done using certain Marathi terms (and possibly their Sanskrit bases) like “ThikaaN,” “jaagaa,” “sthaL,” “sthir,” and why, even the simple “ithe” vs. “tithe” distinction, etc.
In my informal (though computer-typed) notes in English on this topic (some of which I still keep, though I never consult them in my later writings), I had used the word “spot,” for what I now have called “location.”
[BTW, another personal aside. Speaking of those times, I didn’t even know touch-typing back then, but following the tip of a Chinese graduate assistant working in the Computer Center at UAB—foreign students typically had no computers at home back then—I kept up the practise of keeping both my wrists on the computer table all the time, and that’s how, slowly, I had also mostly picked up touch-typing—I mean, without using any typing tutor software or so (though I did use one later on, while being a student at C-DAC).]
Anyway, coming back to this word “location,” well, some other word like “place” perhaps could be more suitable for it. Perhaps. However, I have resisted using it here, because “place” appears in Aristotle’s writings (which I have not yet read even by now), and I am not sure if people would not get confused about the meaning I have in mind vs. the one that Aristotle had indicated. It seems to me that using “location” here would minimize any possible confusions.
But, anyway, let us completely ignore the merely terminological issues for the time being, and instead focus on the actual, live, thought-process which precedes those terms. And, thus, let’s first go further, first finish this series on space, and then, surely, I will come back and revise this whole series again, ironing out the wrinkles in the expressions, as well as probably also revising my intellectual positions. Indeed, I am thinking of dumping a “scientific” version of this series even at arXiv! … So, there.
1. The minimum perceptual field involves two objects:
A certain issue which I had relegated to the miscellaneous notes section in my last post, I now realize, assumes a much greater importance. This issue concerns the “what-if” scenario put forth by Ayn Rand. As she indicated, there is no perception at all so long as there is nothing in the universe except for only a vast expanse of a uniform pale blue. But introduce just a single speck of dust (or a sizeable circular blob of a uniform dark blue) against that background, and suddenly, you would begin seeing—i.e. perceiving.
The point which I now want to emphasize is this. What you then begin to perceive isn’t just the dark blue blob but also the pale blue background. In particular, strictly speaking, what you actually perceive isn’t a single object; it’s two objects, simultaneously—even though, habitually, when asked to conceptually identify, most of us would not identify the pale blue background as an object in its own right. Yet, our perceptual field does actually contain both of them as two separate objects.
A part of your perception (of that what-if scenario) is the fact that you can see that the dark blue is what the pale blue isn’t, and also, exactly symmetrically, the pale blue is what the dark blue isn’t. For instance, the circle is where the background isn’t, and the background is where the circle isn’t. (The idea of “where” refers to both location and extension. More on that, later.)
Now, take the last sentence, drop the particular measurements (e.g. those pertaining to the locations and extensions) so as to isolate the more basic, existence, issue: The dark blue is—and, the pale blue is. Both are. In particular, the pale blue, too, exists.
2. Why people have wrong intuitions about the minimum perceptual field, about aether, etc.
Realize that Ayn Rand’s minimum perceptual field is only an artificial scenario. We consider this highly isolated scenario only in order to help our thought processes.
In actual reality, we never see only two objects of uniform colours (i.e., objects so uniform that various parts within an object, too, are perceptually completely indistinguishable). We always come across real objects, in fact very many of them, all at the same time. They are of various shapes, shades, brightnesses, smells, hot-/cool-ness, textures, tastes, heavy-/light-ness, etc. And, they also differ in their responses to our attempts at handling or manipulating them. Or, plain, in what they do to us. And, therefore, we also tend to focus more on their anticipated potential to do something to us. The teleological end of cognition is to live your life.
When it comes to dealing with all the varied objects of the real world, we make many, many other observations as well, some of them quite crucial to survival (or at least in avoiding pain and enjoying pleasure). We bring to bear the sum-totality of all such observations as a background context in our adult perceptions. Our experience leads us to (correctly) believe that it is usually the foreground object which is the most interesting one because it does so many more important things to us—things which require our attention with so much greater urgency—as compared to any background objects. A hidden thorn (or a needle) gives us an unexpected kind of a pain precisely because it was not in the foreground. When we are hungry and mother brings us some food, the sweets are, say, interesting; the plate isn’t. The sky—the background of all backgrounds—never ever seems to do anything to us (or to any thing, for that matter); the lightening in the clouds and the rains sure do.
… Now, what happens is that we bring these cognitive habits to bear even onto that “what-if” scenario. And it is these habits which might make us believe, but wrongly so, that there would be perception of just one object—that of the dark blue. Yet, the fact is, the pale blue also begins to get perceived at the same time as the dark blue does. One essence of perception—if it may be described this way—is that one (perceived) object is what the other (perceived) object isn’t, and vice versa. As such, the background object also is actually perceived as a separate object in its own right.
If the background object is the “empty space,” we typically don’t identify it as an object, mainly because it seemingly does not offer any resistance to its own displacement—you can always pick a ball and keep it at a place where there is nothing but “empty space,” and thereby displace the “empty space” which had existed earlier there. We don’t notice any such resistance, not in our day-to-day experience anyway; it doesn’t do us something dramatic the way a wall, a thorn, a body of water, or even plain wind does. But therefore to ascribe pure nothingness to that “empty space” is wrong. This is a subtle point to which we will return later.
As a somewhat interesting aside, I will now merely assert, without explaining, the fact that even if you have a complete darkness in place of that pale blue background, what you would perceive still would be two objects. The bright (“visible”) object, and the absolutely dark (“invisible”) object.
…Incidentally, this is another interesting issue that I am now leaving as an exercise for you. The first one was (see my last post): even if you don’t see the outer boundary of the pale blue, how come it is still perceived at all; why the “indefinite” extension (or location) of the background does not stop us from perceiving it; why this nature of the background object does not stump us from visualizing it (unlike either an object of no extension or one of infinite extension).
In a way, the fact that there are two objects even in the simplest possible perception, is something that we have already used, while discussing the characteristics of extension and location. Epistemologically, we had noted, a grasp of any characteristic requires at least two objects possessing the same characteristics but in different measures.
… Now, in the what-if scenario, the characteristic perhaps easiest to grasp, in fact, could very well be the colour! It’s just that since we here are concerned with the spatial matters that we have highlighted the characteristics of extension and location.
As far as the spatial characteristics go, I assert (without separate proof), that extension and location are the simplest possible spatial characteristics. In the simplest scenario (the dark blue over the pale blue), they correspond with certain differences in which you use your mental focus. Extension corresponds to what you grasp when your mental focus moves away from the inner parts of the object in question to its outer parts and continues on to the next object (extension). Location corresponds to the characteristics that you grasp in the reverse—when your mental focus moves from the next object, and towards the inner parts of the object in question. I consider these to be the simplest possible, perceptual-level, activities, and so, further assert that there are no other spatial characteristics at their hierarchical level.
The concept of space is deep. But it is not as deep as Einstein (and the relativity theorists) asserted it to be. Contraries to the concept of space are easily possible (e.g. colour is a contrary to extension and location, and therefore, to every possible conception of space).
And, BTW, while at it, let’s note just in the passing that the spatial characteristics are perceived right in the motionless world. In contrast, what the relativity theorists did, was to posit time at par with space. That is plain impossible. You actually define space only in the motionless world.
3. Towards measuring extensions:
While discussing the concept of extension, I had asked you to ignore the questions of the how, and the how much, of the extensions of objects, but instead, to focus on the existence-related fact that each object has [some, finite] extension. Though we did not discuss this idea in detail for the concept of location, the same consideration, of course, holds also for the concept of location: each object has [some, finite] location. The specific measures of those finite extensions/locations are dropped while forming their concepts; concepts are formed via a process of measurement-omission.
I am not sure, but anyway guess, that now might be a good time to begin focusing on the issue of measurements of extensions and locations. But let’s not therefore dive directly into an inventory of the specific methods of measurements. Instead, let’s continue keeping our focus primarily on the referents in the concrete world, at least initially.
First, take a moment to fully recall the kind of perceptual field we had considered in the last post, viz., that of the motionless world at the beach, or a similar one at the mountain top. (To remind: by the term “motionless world,” we mean: the motionless aspects of the real, motion-having world which is perceptually evident.)
Now, though it is time to begin examining the issue of measuring extensions and locations of the concretely real physical objects, it still is not time to bring out your foot-rules and compasses. Not yet. … Many aspects of measuring extensions and locations precede these!
Indeed, the next simplest concept, I think, is that of shape, which primarily arises in the context of measuring extensions, and not locations.
[Here, I am skipping over other possible simple spatial concepts such as the specifically relational ones, e.g., “is next to/is on the upside of/is on the downside of” or “is a neighbour of,” etc.]
Just one more important note, before we go to “shape.”
For convenience, our further discussion in this post will assume that measuring extensions or locations requires at least two foreground kind of objects present in a single perceptual field. (I mean to say: as apart from that ever-present background object.)
One important reason I kept postponing posting of this post right on the 5th of October (by which time its first draft was anyway ready) was to see if I could present this issue of the background object in simple enough and clear enough a form. But I could not. I then decided to cut it out, and first to make a simpler presentation by assuming that both of the two minimum necessary objects are only of the foreground kind.
Actually, most of the following discussion does apply also to the contexts wherein only one foreground and one background object exists. However, I believe that it is an advanced issue, not a primary one. For a primary, simpler, discussion, it should be enough to refer to only the foreground objects.
4. Shape as a measure of extension:
One of the simplest possible way to measure the extension of an object is not its “size,” but something simpler to it: the shape with which that object remains extended.
The concept of shape is formed by perceiving (at least) two foreground objects of differing shapes.
Here, suppose you do not agree to the above statement. Suppose, you say that you can take just one (foreground) object, and deform it so as to change its shape. This way, you say, you could make do with just one foreground object, and still would be able to perceive different shapes, and therefore, would be able to get to the concept of shape.
However, realize that here you still are implicitly having two referent objects also in this case: the one currently in front of you (with the current shape), and another one in your memory (with the previous shape). A deformation is a kind of a change, and it involves some motion. And so, forming the concept of shape with just one object requires both motion and memory.
On the other hand, if we can in principle form some concept also in a changeless world, then that’s what we should be aiming for, because, this way, it would be defined in a simpler and more fundamental a manner.
Introducing the idea of “motion” right at this place in the hierarchy means wondering about many more relatively much more complex issues, e.g.: (a) either the agent (i.e. another object) that brings about the change (i.e. the motion), or at least the relatively higher-level consideration of the cause of the change—what part of the identity of that one object makes it act in such a way as to effect the observed change; (b) the nature of the change, e.g., whether it is sudden or continuous, whether it is a completed process or an ongoing one, etc.; (c) the metaphysical status of memory and its validation, etc. All these are more complex, more advanced considerations. And, in any case, you still end up referring, at least implicitly (via memory), to two referents. So, instead, let’s stick with the bare minimum referents, and say that the concept of shape can be grasped by looking at two objects of differing shape, right in a changeless, motionless world.
An obvious point here is that shape, too, is grasped perceptually. The way I currently think about it, it’s a part of the concept of extension. Objects exist as extended with their characteristic shapes.
Actually, shape and size are two characteristics with which an object may be taken as extended. However, before we can know how to measure the size of an object, we must know how to measure its shape.
The shapes may be irregular (which would be the case for most natural objects) or regular (which would be the case for most man-made objects). Thus, objects may be seen to exist as extended with more regular shapes like rectangles (windows), spheres (balls), circles (plates), or more irregular ones like ovals (mother’s face), sticks, strings, this animal vs. that animal, or toys replicating various shapes, etc.
The process of classifying objects according to their shapes, too, is a process of measurement, even though it does not involve our usual numbers. It’s a kind of measurement that does not even permit a linear kind of ordering within the different shapes. For instance, you could say that some kind of a linear order exists between: ball, egg, and apple. Also, between: ball, egg, and, say, dumb-bells. But can you place apple and dumb-bells in a linear order? (If you say apple is more primitive, let me ask you: why is a a sharp and inwardly curving surface necessarily more primitive than a smooth and outwardly curving one?)
So, there are measurements here—the same characteristic of extension exists with different measures when it comes to different objects—even if the measures are not even necessarily rank-able, leave alone expressible as multiples of each other or so. You can only say in a broad sense that, as far as shapes go, the measures of the shape of a sphere and an egg are, in some way, closer to each other than they are with the measures of the shapes of the four-legged animals. But beyond that, it all is mostly direct enumeration of your narrower classifications of shapes.
An important way to measure shapes also is via reference to their topology; however, it’s not a topic of sufficient fundamental importance in physics, and so, we will leave it at that. [The non-importance of topology to fundamental physics precisely was the reason I didn’t go over the relations like “is next to,” “is upwards of” or “is connected to,” in detail. The CS folks have been going abuzz with these concepts, but that does not alter their factual nature and make them of any greater fundamental importance in physics—regardless of what the modern physicists, e.g., the “connected worm-hole” types, think. Come to think of it, networks and topology are of considerable interest in engineering (e.g., networks of fluid pipes, electrical power networks, telephone networks, work-flow networks, the networks of meshes in computational science and engineering, etc.). But they are not of any consequence in the fundamental physics theories—at least those (among the valid ones) built till date.]
Measurements of extensions of objects is easy, and sometimes even at all possible, when their shapes are similar—i.e. when the measurements of their shapes fall close enough to each other that thinking of them as being essentially constant, is possible.
In short-and-sweet terms: you can measure the size of an object when the shape is held constant.
You can easily say that a football is bigger than a tennis-ball, because both of them have the same, spherical, shape. But, you know, you can always confuse a child by asking him which one is bigger: the football or grandpa’s walking stick. If he says the stick, you show him how the stick is really thinner, and therefore, smaller than the football. If he says the ball, you show him how the stick is indeed longer, and therefore, really bigger than the ball. (A smart kid—and one who is sufficiently honest—will argue back. (… If he were merely an “introvert,” he wouldn’t have got as far as talking this much with you, in the first place!))
You might think that to measure the size of an object, you wouldn’t have to hold its shape as constant. One could just compare the volume of water displaced by a solid object when the it is completely immersed in the water, you might say. But, actually, measuring volume of one thing via displacement of something else, is an advanced consideration. Displacements are possible only in a motion-carrying world.
And, even in a motion-carrying world, before you can say that the volume of a golden crown is equal to the volume of the body of water it displaces, you still first have to define what you mean by “volume of the displaced water,” of course.
To define the meaning of the latter term, you have no other option except going back to the perceptual concretes. You have to realize that “volume,” in the sense of a certain basic “3D-ness” or a basic “solid-ness” means a certain measure of its extension. And, since extension is measured by both shape and size, you have to keep the shape the same, and change the sizes.
That, incidentally, is precisely what you do when you define the volume measures. You have a cylinder of uniform cross-section, and thus, not just the shape but also the cross-section is held constant. It then is a simple matter to be able to measure volume of a given body of water itself, in reference to the remaining aspect of the extension it has within its container, viz., the height it assumes in the measuring cylinder. Yet, notice two things about this scenario: (i) we are measuring volume of water itself, not of another object like a golden crown, and (ii) liquids are not really physical objects in the primary sense of the term, only solids are. Liquids always require containers to hold them, which makes their extension a bit more complicated (than simplified!): the extension now depends on the shape of other objects. Epistemologically, this is a complicating consideration. No matter how you try to circumscribe it, it involves, directly or indirectly, some kind of a motion—and we are trying to avoid that for as long as possible.
BTW, by volume, I also do not mean the triple integral—which, incidentally, is only a technique, not for defining volume, but simply for going from an infinitesimally small volume to a finite volume, according to a highly precise summing-up scheme. But the whole procedure first assumes that the idea of “volume” of an object itself is already known.
And notice, I said: the volume of an object, and even, the volume of a (liquid) object displaced by another (solid) object being measured.
But I didn’t say: volumes occupied by objects in space.
… We still haven’t reached the far more sophisticated concept of space that would allow us a usage like that. We still don’t have a concept of space defined in that sense. Not yet.
All that we have, thus far, are only the concretely perceived objects in a motionless world, including their spatial characteristics, and whatever sense of the term “space” that might be had with just these basic considerations.
But we still are not ready to fill space with objects, or measure volumes via such a procedure. All of that is way high up, hierarchically speaking. We will get there, in due course of time.
For the time being, let’s just note that volume is a tricky concept to deal with, in a motionless world. It involves displacement, and the only way to measure displacement is to make a reference to a cavity-like feature of the measuring device. So, to measure the volume of a solid object X, you have to make reference to the size of the water body Y displaced by it, and the size of Y when placed in a solid container body Z having a peculiar shape—that of a container, i.e., carrying a “solid” or “volumetric” cavity. Two additional objects (Y and Z) are being required, simply for the measurement of a characteristic of a body X! Rather tricky!! And, it involves displacements, too, i.e. motion.
So, let’s leave the discussion of volume in that form.
Can there be any other spatial characteristics or attributes that can be measured in a motionless world? If not, can we think of some other concepts—the simple or basic or primitive concepts—which arise in reference to space, and which can be meaningful also in a motionless world? Can you?
We will come to a few of such concepts in the next post, and it’s only after examining them that we will be finally ready to go into a motion-full world!
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We are, in a way, shaping up the concept of space, though this fact may not be very obvious at this stage. For basic (or foundational) concepts, the time spent in just “clearing up the earth” is as good as, if not better than, directly “putting up the tent,” so to speak. Many issues of physics attributed to space really don’t belong “in” it, and so, even though the present discussion may seem a bit too lackadaisical, it, eventually, would only help. [Rather like a century coming off the bat of… Rahul Dravid.]
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A Song I Like:
(Hindi) “kahin ek maasum, naazuk see laDki…”
Lyrics: Kamal Amarohi (??)/Jan Nisaan Akhtar (??)/Someone else (??)
Singer: Mohammad Rafi