Some of the implications of the “Many Objects” idea…

0. Context and Review:

This post continues from the last one. In the last post, we saw that the same perceptual evidence (involving two moving grey regions) can be conceptually captured using two entirely different, fundamental, physics ideas.

In the first description, the perceived grey regions are treated as physical objects in their own right.

In the second description, the perceived grey regions are treated not as physical objects in their own right, but merely as distinguishable (and therefore different) parts of the singleton object that is the universe (the latter being taken in its entirety).

We will now try to look at some of the implications that the two descriptions naturally lead to.

1. The “Many Objects” Viewpoint Always Implies an In-Principle Empty Background Object:

To repeat, in the first description, the grey regions are treated as objects in their own right. This is the “Many Objects” viewpoint. The universe is fundamentally presumed to contain many objects.

But what if there is one and only one grey block in the perceptual field? Wouldn’t such a universe then contain only that one grey object?

Not quite.

The fact of the matter is, even in this case, there implicitly are two objects in the universe: (i) the grey object and (ii) the background or the white object.

As an aside: Do see here Ayn Rand’s example (in ITOE, 2nd Edition) of how a uniform blue expanse of the sky by itself would not even be perceived as an object, but how, once you introduce a single speck of dust, the perceptual contrast that it introduces would allow perceptions of both the speck and the blue sky to proceed. Of course, this point is of only technical importance. Looking at the real world while following the first description, there are zillions of objects evidently present anyway.

Leaving aside the theoretically extreme case of a single grey region, and thus focusing on the main general ideas: the main trouble following this “Many Objects” description is twofold:

(i) It is hard to come to realize that something exists even in the regions that are “empty space.”

(ii) Methodologically, it is not clear as to precisely how one proceeds from the zillions of concrete objects to the singleton object that is the universe.  Observe that the concrete objects here are physical objects. Hence, one would look for a conceptual common denominator (CCD) that is narrower than just the fact that all these concrete objects do exist. One would look for something more physical by way of the CCD, but it is not clear what it could possibly be.

2. Implications of the “Many Objects” Viewpoint for Causality:

In the first description, there are two blocks and they collide. Let’s try to trace the consequences of such a description for causality:

With the supposition that there are two blocks, one is drawn into a temptation of thinking along the following lines:

the first block pushes on the second block—and the second block pushes on the first.

Following this line of thought, the first block can be taken as being responsible for altering the motion of the second block (and the second, of the first). Therefore, a certain conclusion seems inevitable:

the motion of the first block may be regarded as the cause, and the (change in) the motion of the second block may be regarded as the effect.

In other words, in this line of thought, one entity/object (the first block) supplies, produces or enacts the cause, and another entity/object (the second block) suffers the consequences, the effects. following the considerations of symmetry and thereby abstracting a more general truth (e.g. as captured in Newton’s third law), you could also argue that that it is the second object that is the real cause, and the first object shows only effects. Then, abstracting the truth following the consideration of symmetry, you could say that

the motion (or, broadly, the nature) of each of the two blocks is a cause, and the action it produces on the other block is an effect.

But regardless of the symmetry considerations or the abstractness of the argument that it leads to, note that this entire train of thought still manages to retain a certain basic idea as it is, viz.:

the entity/actions that is the cause is necessarily different from the entity/actions that is the effect.

Such an idea, of ascribing the cause and the effect parts of a single causal event (here, the collision event) to two different object not only can arise in the many objects description, it is the most common and natural way in which the very idea of causality has come to be understood. Examples abound: the swinging bat is a cause; the ball flying away is the effect; the entities to which we ascribe the cause and the effect are entirely different objects. The same paradigm runs throughout much of physics. Also in the humanities. Consider this: “he makes me feel good.”

Every time such a separation of cause and effect occurs, logically speaking, it must first be supposed that many objects exist in the universe.

It is only on the basis of a many objects viewpoint that the objects that act as causes can be metaphysically separated, at least in an event-by-event concrete description, from the objects that suffer the corresponding effects.

3. Implications of the “Many Objects” Viewpoint, and the Idea of the “Empty” Space:

Notice that in the “many objects” description, no causal role is at all played by those parts of the universe that are “empty space.” Consider the description again:

The grey blocks move, come closer together, collide, and fly away in the opposite directions after the collision.

Notice how this entire description is anchored only to the grey blocks. Whatever action happens in this universe, it is taken by the grey blocks. The empty white space gets no metaphysical role whatsoever to play.

It is as if any metaphysical locus standi that the empty space region should otherwise have, somehow got completely sucked out of itself, and this locus standi then got transferred, in a way overly concentrated, into the grey regions.

Once this distortion is allowed to be introduced into the overall theoretical scheme, then, logically speaking, it would be simple to propagate the error throughout the theory and its implication. Just apply an epistemologically minor principle like Occam’s Razor, and the metaphysical suggestion that this entire exercise leads to is tantamount to this idea:

why not simply drop the empty space out of any physical consideration? out of all physics theory?

A Side Remark on Occam’s Principle: The first thing to say about Occam’s Principle is that it is not a very fundamental principle. The second thing to say is that it is impossible to state it using any rigorous terms. People have tried doing that for centuries, and yet, not a single soul of them feels very proud when it comes to showing results for his efforts. Just because today’s leading theoretical physics love it, vouch by it, and vigorously promote it, it still does not make Occam’s principle play a greater epistemological role than it actually does. Qua an epistemological principle, it is a very minor principle. The best contribution that it can at all aspire to is: serving as a vague, merely suggestive, guideline. Going by its actual usage in classical physics, it did not even make for a frequently used epistemological norm let alone acted as a principle that would necessarily have to be invoked for achieving logical consistency. And, as a mere guideline, it is also very easily susceptible to misuse. Compare this principle to, e.g., the requirement that the process of concept formation must always show both the essentials: differentiation and integration. Or compare it to the idea that concept-formation involves measurement-omission. Physicists promote Occam’s Principle to the high pedestal, simply because they want to slip in their own bad ideas into physics theory. No, Occam’s Razor does not directly help them. What it actually lets them do, through misapplication, is to push a wedge to dislodge some valid theoretical block from the well-integrated wall that is physics. For instance, if the empty space has no role to play in the physical description of the universe [preparation of misapplication], then, by Occam’s Principle [the wedge], why not take the idea of aether [a valid block] out of  physics theory? [which helps make physics crumble into pieces].

It is in this way that the first description—viz. the “many objects” description—indirectly but inevitably leads to a denial of any physical meaning to the idea of space.

If a fundamental physical concept like space itself is denied any physical roots, then what possibly could one still say about this concept—about its fundamental character or nature? The only plausible answers would be the following:

That space must be (a) a mathematical concept (based on the idea that fundamental ideas had better be physical, mathematical or both), and (b) an arbitrary concept (based on the idea that if there is no hard basis of the physical reality underlying this concept, then it can always be made as soft as desired, i.e. infinitely soft, i.e., arbitrary).

If the second idea (viz., the idea that space is an arbitrary human invention) is accorded the legitimacy of a rigorously established truth, then, in logic, anyone would be free to bend space any which way he liked. So, there would have to be, in logic, a proliferation in spaces. The history of the 19th and 20th centuries is nothing but a practically evident proof of precisely this logic.

Notice further that in following this approach (of the “many objects”), metaphysically speaking, the first casualty is that golden principle taught by Aristotle, viz. the idea that a literal void cannot exist, that the nothing cannot be a part of the existence. (It is known that Aristotle did teach this principle. However, it is not known if he had predecessors, esp. in the more synthetic, Indic, traditions. In any case, the principle itself is truly golden—it saves one from so many epistemological errors.)

Physics is an extraordinarily well-integrated a science. However, this does not mean that it is (or ever has been) perfectly integrated. There are (and always have been) inconsistencies in it.

The way physics got formulated—the classical physics in particular—there always was a streak of thought in it which had always carried the supposition that there existed a literal void in the region of the “gap” between objects. Thus, as far as the working physicist was concerned, a literal void could not exist, it actually did. “Just look at the emptiness of that valley out there,” (said while standing at a mountain top). Or, “look at the bleakness, at the dark emptiness out there between those two shining bright stars!” That was their “evidence.” For many physicists—and philosophers—such could be enough of an evidence to accept the premise of a physically existing emptiness, the literal naught of the philosophers.

Of course, people didn’t always think in such terms—in terms of a literal naught existing as a part of existence.

Until the end of the 19th century, at least some people also thought in terms of “aether.”

The aether was supposed to be a massless object. It was supposed that “aether” existed everywhere, including in the regions of space where there were no massive objects. Thus, the presence of aether ensured that there was no void left anywhere in the universe.

However, as soon as you think of an idea like “aether,” two questions immediately arise: (i) how can aether exist even in those places where a massive object is already present? and (ii) as to the places where there is no massive object, if all that aether does is to sit pretty and do nothing, then how is it really different from those imaginary angels pushing on the planets in the solar system?

Hard questions, these two. None could have satisfactorily answered these two questions. … In fact, as far as I know, none in the history of physics has ever even raised the first question! And therefore, the issue of whether, in the history of thought, there has been any satisfactory answer provided to it or not, cannot even arise in the first place.

It is the absence of satisfactory answers to these two questions that has really allowed Occam’s Razor to be misapplied.

By the time Einstein arrived, the scene was already ripe to throw the baby out with the water, and thus he could happily declare that thinking in terms of the aether concept was entirely uncalled for, that it was best to toss it into in the junkyard of bad ideas discarded in the march of human progress.

The “empty” space, in effect, progressively got “emptier” and “emptier” still. First, it got replaced by the classical electromagnetic “field,” and then, as space got progressively more mathematical and arbitrary, the fields themselves got replaced by just an abstract mathematical function—whether the spacetime of the relativity theory or the \Psi function of QM.

4. Implications of the “Many Objects” Viewpoint and the Supposed Mysteriousness of the Quantum Entanglement:

In the “many objects” viewpoint, the actual causal objects are many. Further, this viewpoint very naturally suggests the idea of some one object being a cause and some other object being the effect. There is one very serious implication of this separation of cause and effect into many, metaphysically separate, objects.

With that supposition, now, if two distant objects (and metaphysically separate objects always are distant) happen to show some synchronized sort of a behavior, then, a question arises: how do we connect the cause with the effect, if the effect is observed not to lag in time from the cause.

Historically, there had been some discussion on the question of “[instantaneous] action at a distance,” or IAD for short. However, it was subdued. It was only in the context of QM riddles that IAD acquired the status of a deeply troubling/unsettling issue.

5. Miscellaneous:


Let me take a bit of a digression into philosophy proper here, by introducing Ayn Rand’s ideas of causality at this point [^]. In OPAR, Dr. Peikoff has clarified the issue amply well: The identity or nature of an entity is the cause, and its actions is the effect.

Following Ayn Rand, if two grey blocks (as given in our example perceptual field) reverse their directions of motions after collision, each of the two blocks is a cause, and the reversals in the directions of the same block is the effect.

Make sure to understand the difference in what is meant by causality. In the common-sense thinking, as spelt out in section 2. of this post, if the block `A’ is the cause, then the block `B’ is the effect (and vice versa). However, according to Ayn Rand, if the block `A’ is the cause, then the actions of this same block `A’ are the effect. It is an important difference, and make sure you know it.

Thus, notice, for the time being, that in Ayn Rand’s sense of the terms, the principle of causality actually does not need a multiplicity of objects.

However, notice that the causal role of the “empty” space continues to remain curiously unanswered even after you bring Ayn Rand’s above-mentioned insights to bear on the issue.


The only causal role that can at all be ascribed to the “empty” space, it would seem, is for it to continuously go on “monitoring” if a truly causal body—a massive object—was impinging on itself or not, and if such a body actually did that, to allow it to do so.

In other words, the causal identity of the empty space becomes entirely other-located: it summarily depends on the identity of the massive objects. But the identity of a given object pertains to what that object itself is—not to what other objects are like. Clearly, something is wrong here.

In the next post, we shall try to trace the implications that the second description (i.e. The One Object) leads to.

A Song I Like:

(Hindi) “man mera tujh ko maange, door door too bhaage…”
Singer: Suman Kalyanpur
Music: Kalyanji Anandji
Lyrics: Indivar

[PS: May be an editing pass is due…. Let me see if I can find the time to come back and do it…. Considerable revision done on 28 April 2017 12:20 PM IST though no new ideas were added; I will leave the remaining grammatical errors/awkward construction as they are. The next post should get posted within a few days’ time.]

Coming back to the second “world”…

[Four updates added on September 24, 2013.]

0. Coming back to the second “world,” I would like to briefly note a few points concerning it. … But before coming to these points, first, in case you have joined late and so don’t know what I mean by the term “second ‘world’,” let me tell you that in brief.

1. The term “second ‘world'” means: a view of the physical world which would correspond, roughly speaking, with the Newtonian physics. In particular, it refers to a broad, objective view of the physical world as is implied by, or is implicit in, the state of physics as it existed after Galileo and Newton, but before the discovery of the laws of electromagnetism. Roughly speaking, the mid-17th century to, say, the early 19th century.

This “world” consists of uncharged bodies not only colliding with each other but also sucking up the gravity field-fluid. The first “world,” in contrast, would be this second world, minus the phenomenon of gravity. I had written about these ideas in my recent post here [^].

The first world really speaking doesn’t pose much of a conceptual problem to any one, because it is a local theory, and a relatively simpler one at that. The only kind of entities making it up are all definite objects—either discrete objects like apples and planets, or such continua that their defining properties always are defined in reference to a definite portion of that continuum, as in the classical fluid and solid mechanics. Further, all entities in this world are material (i.e. mass-possessing) ones. And, all the interactions are via a common surface between the directly touching bodies.

The second world, as I indicated in my earlier post, posed conceptual problems back then (and it continues to stump people even today—if they at all care to think about it) because gravity adds two difficult features: (i) forces acting through a “void,” and (ii) instantaneous action at a distance (IAD).

I had then sketched a possible solution involving a hypothetical, massless, gravity field-fluid.

In the follow-up post [^], I had referred you to Wang’s papers, and had asked if scientific papers like these would be enough. And, also what additional input would be necessary for you to be convinced that a hypothetical massless fluid indeed makes for a first-class object of physics.

2. The main paradox:

For convenience, let me now more or less fully reproduce, paraphrasing only a bit here and there, what I said by way of the question, right in that first post about the conceptual trouble with that kind of a “fluid.”

The first issue that arises in the second world, viz., forces being transmitted through a void, is a more serious challenge, because it spoils the neat view otherwise built for our first world—a view of localized, definite objects exchanging momenta/energy through direct contact via a common surface (collisions or fluxes).

So, now, a question arises: Where do we place the field of gravity? Is gravity an attribute of the distinct material objects (such as apples or planets), or is it an attribute of the “void” in between them.

The issue is not as simple as it might sound to you.

If you say that gravity is an attribute of the void, then an immediate next question is: does gravity exist in a world devoid of the material objects like apples and planets? If so, what does the field do? Forcing nothing is a contradiction in terms—the definition of force involves the change of momentum of a material object like an apple or a planet.

There cannot be a force in a field if there is nothing to force from/to. Assuming unit masses for all entities, mathematically, “forcing” is nothing but another name for “accelerating.” Even if you hypothesize the existence of a definite, lawful, but massless physical object for the Newtonian gravitational field, i.e. one with identity, a question still remains: how do you define forces (i.e. accelerations) within this object? A massless forcing object can make sense but only when there is some mass to be accelerated.

Naturally, you have to attribute the phenomenon of gravity to the usual material objects: the stars and planets, for example. If so, you have come back to square one: you can no longer explain interactions via simple direct contacts between material bodies. If gravity is to be attributed to the material bodies themselves, then no mechanism is left to explain how it can act over the “void” (or “free space” or whatever).

This theoretical complication is what Newton himself should have commented upon. But, he didn’t. His shortcoming.

3. The (other) candidate solutions:

My further ‘net searches threw quite a few fascinating ideas. I will note down just a few of them (i.e. apart from Wang’s papers that I have noted earlier in this series).

First, the obligatory Wiki articles, and the references therein: Aether the Classical Element [^], Aether Theories [^], Mechanical Explanations of Gravitation [^], and, though meant for electromagnetism, if you wish to use similar ideas also for gravity, Luminiferous Aether [^]. …

BTW, the coverage of the aether-related ideas on the Internet in general, and on Wiki in particular, has improved a significantly great deal since the time not so long so—around 2004/05 times, when I was doing my PhD. At that time, most pages were amateur or even worse—crackpot! The only exceptions were a few groups like a nonlinear studies center in an Austrian university, or so. [Update on September 24, 2013: Link, here[^]]. BTW, my PhD papers had assumed an aether hypothesis, but quite different from what people meant about it. Which brings us to the next set of material.

  • The “MountainMan” collection of links [^]. Very comprehensive. (They didn’t miss Dirac’s surprisingly pro-aether viewpoint either!)
  • The “Cellular Universe” Web site, with an excellent summary of the views of the aether idea, throughout history (right in the format of a table/timeline!) [^]. You may want to spend some time exploring some related material (like that on cosmology) on this site; consult the links given in the side bar of that site.
  • There were quite a few others too, though the links already given would cover pretty much the entire territory one way or the other. … For instance, see this blog post [^]. Its presentation is good, but all those points are one or the other already covered in the links (and the sub-links) given above.

Comment: Realize that none of these solutions, IMO, fully satisfactorily resolve the main paradox which I have noted above.

For many of these aether theories, if you wish to use a simple heuristic to expedite your reading (though I wouldn’t advise you to outright dismiss any idea out of hand), just ask yourself this simple question:

If it is a continuum aether, is it massive or massless? If the former, how does the theory account for Newton’s three laws for the massive objects? Are they modified too? Must they? And, if the latter, then what specific characteristics of aether are proposed here that would go on to provide a mechanism for the gravity force?

For certain other, particles-based theories (i.e. particles of aether), always ask yourself: Is this theory philosophically satisfactory? What exists in between those aether particles? void?

Have fun.

4. “But why should I pursue it in the first place? What is the fallout?”

You may now wonder, of course, where the fun is, in all this “back-dated” enterprise.

You may perhaps say something like: “All we seem to be doing here is to dig through the errors of the other people, and, that too, of those who are long dead. There is no fun in going through the wrong theories of the ancient people [like Newton and all!], how they thought. Einstein proved them all wrong, and the 20th century—including all the finest and costliest experiments performed till date—has proved Einsten right.” And, continuing, you may then ask me: “How is your paradox relevant to solving the really important problems (or even paradoxes) facing today’s physics? Why dig up old paradoxes when new ones are available, and old ones are already resolved?”

I won’t argue a lot here. By way of my answer, I will only note down a couple of points. [Many other smart people, I am sure, would have already noted these by now, without me having to tell them about that…. But still…].

(i) The second world is important because it is the simplest toy world that still carries an important, defining feature of the standard model of the modern particle physics: viz., the division of all things (they call it “particles”) into two mutually exclusive and collectively exhaustive classes: the massive particles (i.e. the fermions) and the massless particles (i.e. the bosons). If you know how to (properly) quantize a continuum (the way I have done in my published papers and also writings on the blogs etc.), then, in solving the toy problem of the gravity-fluid, you create a platform that would be very directly useful in solving some of the really difficult conceptual riddles concerning the modern standard model. … I won’t name them. You should know what those are. [LOL! Why? Because you were concerned with the modern standard model, that’s why!]

(ii) If you can resolve the main paradox, by giving a logically consistent and complete (i.e. fully satisfactory) aether-based description even if only for the second world, then, that accomplishment, by itself, would mean that you had overcome the greatest hurdle in resolving the most difficult paradoxes related to the relativity theory as well. They would go out the door in one go. Web pages like, e.g., this excellent set [^], would be taken down, though the Web sites themselves (including that Web site) will still continue to thrive—by focusing on other, better, more authentic problems of physics. Why?

Because, this way, you would be able to give an “engineer’s” description for the physical world, a description that, at its most fundamental level, requires only a 3D Euclidean geometry for space, and a basically separate scalar for time. (Time would no longer be a “dimension” in the theory; it would be just a parameter, really speaking.)

Imagine what kind of a simplification in the conceptual structure of physics that would represent.

… And, yes, if you wished, you would still be free to play with the “spacetime” continuum, manifolds, their contortions… all those concepts as well, though you wouldn’t have to use them. You may find reasons (perhaps even good reasons) to continue using them for mathematical convenience in (some, not all) applications, that’s all. [For instance, you may find some convenience in error analysis of some numerical analysis code, or in presenting a more concise deductive formulation.] But not in the basic physics theory.

[Update on September 24, 2013:

This update on September 24, 2013, over.]

Of course, your intermediate step would still consist of first resolving a similar riddle for the third world (that of EM) as well. Yet, the nature of the issues is such that if you can resolve the paradox even if only in the second world, then that by itself would be a great step forward. You see, the paradox concerning the third world (i.e. the one concerning the EM field) is only mathematically a bit more complicated—conceptually, not so much, though some conceptual advancements would still be necessary, too (other than what I have already explicitly noted or hinted at).

3. One more reason why you can give it try. It’s because… the paradox—at least that in the second world—most certainly is resolvable.

And, how do I know that?

…[Suppresses laughter] …

Time to run through the description of the main paradox, again? See the main point 2. above. (… It could be put in a better, more precise way, but what I have already noted down seems to be enough. At least to me, and at least for a blog-post, and at least for the time being. It puts the issue directly enough. … So, there!)

* * * * *   * * * * *   * * * * *

Updates on September 24, 2013:

Update 1. Why the classical fluid mechanics belongs to the first world:

In the classical fluid mechanics, there also is a flux of mass (in addition to that of momentum) which, at the first sight, seems unlike the first world, because with the solid colliding balls of the first world, there is a transfer of only momentum, not of mass.

However, we can still regard the classical fluid as belonging to the first world, because mass of the fluid is a property defined for both the parts of the material continuum sharing their common surface, and both these defining parts are definite material objects.

The classical fluid is nothing but just a limiting case, obtained by applying a mathematical homogenization (or “squishing” i.e. “continuum-ization”) procedure to a collection of what otherwise are only discrete material objects occupying a defining volume in the first world. For instance, a grosser-scale volume of air is taken as the classical fluid material, even though the reference volume itself is made up of a large number of tiny, discrete, gas “molecules” which themselves can be taken as the usual solid objects of the first world; ditto, for water and other liquids.

Left as an exercise for you: Figure out why also friction (e.g. Newton’s law of friction) does not pose any deep conceptual issue in the first world.

Update 2: A link to the Austrian university which was doing research on aether-based descriptions in the mid-naughties, has been inserted inline; it was the AINS [^]. BTW, I had made a reference to Prof. Gr\”{o}ssing’s papers, in one of my PhD research papers, too.

Update 3:  The additional beneficial fallouts of a new conceptual perspective:

Another point. I wish to note a bit more on the beneficial fallouts of a new conceptual perspective such as the resolution of the main paradox concerning the second world, as noted in these blog posts.

Though the final quantitative predictions of both the mainstream theory of Newtonian gravitation and an aether-based theory may outwardly seem to remain quantitatively the same, it still is not proper to dismiss the aether-viewpoint.

A plain epistemological fact is that with a new (objectively valid) conceptual viewpoint, new progress into the as-yet-not-even-imagined territory also becomes at all possible.

The progress of physics does not always depend only on new experimental observations; crucial to the inductive process of discovery also is the advancement in the conceptual perspective. (Claiming otherwise is a direct case of MBD—the mind-body dichotomy.)

Remember, consciousness is finite, not infinite. In other words, we have limitations to how much of a further progress we can make, given an already existing level of knowledge, and, given a particular conceptual vantage point that goes with it (at least implicitly).

Due to the finitude of our consciousness, given a particular conceptual viewpoint (implicit in a particular state of knowledge), some as-yet unknown facts, even if logically not inconsistent with that older viewpoint, still become so conceptually distant as to fall out of the limited range of any possible mental grasp, and hence, out of the range of any possible application involving them—or even the more basic discoveries of those facts.

For instance, Newton’s original formulation of the laws of dynamics, which is essentially a formulation in terms of vector mechanics (though the concept of a vector had not yet been explicitly grasped in his time) does remain applicable, in principle, to every dynamical problem of the first world. Yet, a very large range of problems become tractable only via the variational/energy-based approaches (or the Lagrangian/Hamilton reformulations). [BTW, Newton was also the first person to correctly pose and solve a variational problem.] In the classical physics, the law of conservation of energy does not add anything new to the already known dynamics at its most fundamental level.  [Incidentally, I still remember how discovery of this fact had come as a shock to me!] But try to use the original Newtonian mechanics in calculations of, say, the heat of a chemical reaction!

And, my point here is deeper than that. Among two or more conceptual viewpoints explaining the same set of facts, the most fundamental among them is the most crucial—abandoning it affects the scope of any new possible discoveries the worst. Physical observation is basic to mathematics—and not vice versa. Hence, abandoning a more fundamental physics viewpoint affects the new discoveries the worst.

Thus, not only inventions of new mathematical principles, but also new physical discoveries themselves become at all possible only when you actively adopt a new conceptual perspective—even if its initial scope seemingly refers to the same old set of facts.

As an example of this latter fact right in our present context, see the ease with which Wang’s paper suggests the possibility that the exponent “2” in the inverse-square law may not be a constant—and the ease with which you can understand it, too! Otherwise, precisely due to the much-prized mathematical “tightness” of the Poisson-Laplace equation—and, if you want, you can also throw in here any supposed beauty of the harmonic analysis, the beauty of its symmetry, et cetera—the very idea of a variable exponent in a law verified in as many separate instances as Newton’s Law of Universal Gravitation, would look wacky and crackpot to any one—especially if the paper were not written using LaTeX! …

When Dirac in fact made a similar suggestion concerning the possible variability of the universal “constants” of physics, he was rightly held in high regard and admiration for that idea. Understandably so. Abandoning aether, it would take a genius to think of varying just that part of, say, the “spacetime” (i.e. without using even the hyphenation mark [whether using LaTeX or not]). Since most physicists by then had abandoned that idea of the aether, the suggestion did look awesome to many of them. From their viewpoint, it would take not just a normal genius but, say a genius^genius, to conceive of so “bold” and such “daring” an idea.

Well, there is some boldness and daring in here, but it’s not in the detail of suggesting the possible variability of what we take as universal constants—I mean to say, it’s not an issue limited to making a variable out of a constant; it does not concern an apparently marvellous piece of a mathematical thought. Instead, the boldness and daring is in trying to keep a more fundamental physics hypothesis, that of aether, in the physics theory, despite its denials by the authorities of the day. Once you put aether back into the physics theory (or never fully abandon it as probably was the case with Dirac—at least privately to his own mind), it then looks a plain and relatively simpler consequence of that theory.

Now, you can always put such a consequence in precise mathematical terms, which, taken out of context, is guaranteed to look unbelievably awesome. [Morally lesser professors at the world’s leading universities have always employed this trick.] Further, once the concrete suggestion comes out, you can always go back into the woodwork (or near your blackboard), deduce—in part using the new suggestion—and then, come out of the woodwork and say that it was already deducible even from the plain old mathematics, and use that claim both to make the new advancement look lesser, and to continue justifying your dogma. [Morally lesser professors at the world’s leading universities are known to employ also this trick.]

…And, this variability of the supposed universal constants was just an example. .

.. New conceptual perspectives, even if based on the same set of observational referents, enable new discoveries that would otherwise remain out of the reach of the human mind that uses only an existing conceptual framework which contains some unresolved “merely philosophical” paradoxes. Every fundamentally new field of mathematics—i.e., if it is authentically new (and not just a deductive avatar of an existing one) has, in fact, depended precisely on such conceptual advancements coming from physics (or the “physical” thinking).

The Objectivist epistemology even has terms for such things: the DC [not that one!], the CCD [and now you believe me, don’t you?], the rule of fundamentality, and all that. … OK. More, later.

Update 4: Added the usual section about a song I like.

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A Song I Like:

(Marathi) “hari bhajanaaviN kaaL ghaalavu nako re…”
Singer [of the version I like]: Dashrath Pujari
Music [of the version I like]: Dashrath Pujari (?)
Lyrics: Sant Sohirobaanaath

[PS: Just a stray thought…. Should I have put these updates in a separate post? … May be I will… I will think about that later on… For the time being, enough is enough!]