Part 1–Equivalence
Today, I want to introduce my concept of “equivalence”. This is an important concept for a theory like mine as my theory rests on a concept of substance that has meaning at its core. It has being and quality at its core as well, as you know (if you’ve been reading), but meaning places it apart from the concept of ordinary matter in such a unique way that it turns our whole understanding of reality up-side-down (not just in what reality contains but what reality–the very fabric thereof–is). Whereas a materialistic picture of the universe would have material objects simply “existing” in an objective sense (independently of any observer), our theory has the existence of material objects, and other non-material things, rooted in the experience thereof. And since experience rests on meaning (as well as being and quality), it not only behaves according to a wholly different set of dynamics, a wholly different set of “laws”, but its essential nature is radically different. For example, we already know it renders a relativistic picture of reality (relative to the experiencer) whereby whether a thing exists or not depends on whether it is being experienced or not and exists only relative to that experiencer. It also renders a picture of reality as fundamentally information as opposed to “objects” or “stuff”, and this has a profound implication for the objectivity of the existence of things. We can no longer simply state that a thing either exists or doesn’t. My concept of equivalence enters the picture to help elucidate these radical changes in how we understand reality under my theory. We’ve already seen, in my previous set of posts, how a question arises as to how the experiences corresponding the molecular and atomic activity relates to the experiences corresponding to the macroscopic objects that those molecules and atoms constitute, and it isn’t clear that a simple description like “summation” or “average” cuts it. While we won’t be returning to this question, we will introduce the concept of equivalence and show how it helps us understand this question, and many others, from a clearer perspective.
Equivalence is meant to be contrasted with identity. Identity is the rule for material/objective universes. If a rock, for example, reduces to a network of atoms, we say that the rock and the network of atoms are identical. They are two ways of thinking of the same entity. Equivalence, on the other hand, denotes the relation between these ways of thinking without deferring to the object they refer to. In other words, while the object may be one and the same, the two ways of thinking about it are (obviously) not. But we can say they are equivalent–you can think of it as a rock or as a network of atoms–maybe both at the same time–but more generally, equivalence is the property that two or more modes or articulations of expression share in common of being interchangeable with each other, with neither one being the “right” mode/articulation or the “wrong” mode/articulation. I can interchange “rock” with “network of atoms” in any statement or utterance and either way is perfectly fine and valid. But the fact that an interchange must occur means they are different, not identical.
My theory of consciousness makes special use of the concept of equivalence because it is a subjectivist theory which removes the divide between perceived and perceiver, between experience and experienced, and merges both concepts into one. Therefore, unlike the rock and the network of atoms in a material/objectivist context, there is no common object or referent that multiple modes of experience can be said to be of, no experience-independent entity that gives rise to a plethora of different ways of being experienced. We only have (sets of) experiences that can be described as (possibly) similar, but not one and the same, and no extraneous entity outside them that can be said to be that which is being experienced. This raises some problems of identity in my theory which need to be fleshed out.
Consider, for example, the binomial theorem:
(x + 2)(x - 2) = x^2 - 4
What is it about the left-hand side of the equation that makes it equal to the right-hand side? Common sense tells us that it is the fact that they are two expressions of the same quantity–so they are identical. But if so, what is this one identity they both share? Is it something that lies “behind” the expressions? Does it lie far off in some mystical realm of numbers and mathematical relations, of truths, a realm akin to Plato’s forms?
Well, one could say this, but not without recognizing the mental status of this realm and everything in it. That is, if these two expressions do correspond to a single number or a preferred mathematical expression, then this entity is no less in the head than the expressions themselves. Thus, it too is but another mode or articulation of experience expressing the same thing–perhaps more succinctly or in a preferred way–but another mode/articulation nonetheless.
Consider a chalkboard on which the binomial equation was written except that no equal sign conjoined the left- and right-hand expressions so that one who is unfamiliar with the binomial equation would have no indication that they are indeed equal. Visually apprehending each expression, one who is familiar with the basic rules and notations of algebra understands that (x + 2)(x - 2) means that a quantity x with 2 added to it is multiplied by the same quantity x with 2
subtracted from it. Likewise, one understands that x^2 - 4 means the quantity x is raised to the second power and has 4 subtracted from it. Therefore, the visual apprehensions of each lead to two different conceptual apprehensions.
Nonetheless, these conceptions cannot be identical since the one apprehending them still fails to appreciate the central implication of the binomial theorem–namely, that the two conceptions are equal. But this remains true even for those who do appreciate the binomial theorem, for the conceptions in their heads should be no different. Everyone with a rudimentary understanding of algebra should conceptualize (x + 2)(x - 2) the same way–as x with 2 added multiplied by x with 2 subtracted–as they should x^2 - 4, regardless of whether or not they recognize the equality between them. The only difference is that those who recognize the binomial theorem
understand the two expressions to represent a single mathematical entity.
If we were to denote this entity with another variable, say y, then we could write it out, appending it, with an equal sign, to the right of the two expressions above. We would then see that it is just another expression, succinct as it might be.
(x + 2)(x - 2) = x^2 - 4 = y
What this means, however, is that, whether written out or simply held in the conceptual recesses of our minds, this entity is merely another expression–another way of articulating (x + 2)(x - 2) and x^2 - 4–that has no more claim to the underlying reality of the entity being expressed than the latter two expressions. It is no more the bearer of the formal identity of these expressions than the expressions themselves. The question now is: if each one harbors its own unique identity, in what way can we still say they are equal, for we most certainly don’t want to deny this?
Enter “equivalence”–what we ought to say about the equation above is, not so much that the equality denotes an identity–as though they are one and the same thing underneath the diversity of expressions—but that they are equivalent. We ought to say this about certain other experiences as well. Some experiences bear a special relation to each other such that they are, like the mathematical expressions above, not identical but interchangeable.
I maintain that this is only possible for information, for meaning, for description–not for objective material reality. One does not interchange physical objects the same way one does information–that is, one does not swap out the rock for the network of atoms–they are both there simultaneously, constituting an identity, a single thing. But with information and meaning, one can swap out one expression for an equivalent other without disrupting the overall identity of the whole of which they are parts.
Well, this all makes sense when it comes to mathematics (maybe), but when would this apply to experiences? A prime example is when we consider what I describe in my book as the “uniform and homogenous” quality of an experience, and then imagine it being broken up into its component experiences. The blue of the sky on a clear day, for example, is uniform and homogenous–not a lot of qualitative diversity therein, not a lot of details–unlike the experience of seeing a park–in which there is plenty of qualitative diversity and details. Nevertheless, we can imagine the experience of seeing a park as a single uniform and homogeneous experience if we consider “seeing a park” as the defining property of that experience–as if we lacked the capacity to analyze it and break it down into its details. Yet, we can also imagine, much more easily, that this experience is decomposable into more basic experiences–such as seeing a playground, a park bench, a pond, and children playing. In this case, it would be more accurate to say that the latter set of experiences, taken together, is equivalent to the singular experience of seeing a park.
But it might seem that an identity is also formed here. After all, isn’t seeing a park just the sum of the component experiences thus considered? When we talk about “seeing a park”, are we not also talking about the collective experience of seeing a playground, a park bench, a pond, and children playing?
A better example will show how this is not necessarily the case. Consider the sight of the park bench. We can decompose this experience even further–we can talk about the sight of wood planks, of bolts, of metal stands. Consider one of the bolts. We can decompose this sight into scratches, dents, chips, and other blemishes. Consider a tiny speck. Now comes the crucial step. Can the sight of the speck be decomposed even further? Well, if it’s barely visible, it wouldn’t seem so. A speck, for all intents and purposes, is about as small as you can get, at least for the visual experience.
But now consider the idea of epistemic awareness. Is the experience of seeing a speck really un-decomposable? Or does it simply represent the limits of our epistemic awareness of the details? In other words, could there be further details below the level of the speck that we are simply incapable of knowing about? (Sure, we could move closer, but I’m talking about the visual experience of seeing a speck–what details can we make out in that?) After all, the neural circuitry in the brain corresponding to the sight of the speck must consist of at least a few neurons. And even a single neuron consists of complexity and a diversity of parts–microtubules, proteins, DNA, a protective membrane, a nucleus to house the DNA–which suggests that any experience corresponding to the neuron’s firing must equally consist of a complexity and diversity of parts, of details, of heterogenous qualities, like unconsciously seeing a Persian rug.
The reader might note that we are using epistemic awareness here to explain more clearly what I mean by the “uniformity and homogeneity” of experiences. That is, when I say that experiences ought to be conceptualized as uniform and homogeneous, I am talking about what it feels like to be epistemically aware of an experience. If we notice meticulous details in an experience, such as when we look at a Persian rug, this reflects the multitude of experiences being acknowledged, acknowledgements being entailed by each detail in question. In other words, a complex, heterogeneous experience like this is actually a collection of more simple, homogeneous experiences of which we are epistemically aware. If there are no more fine-grained acknowledgements below the level of the smallest details, the details must be considered uniform and homogeneous. We can only be epistemically aware of so much detail, and beyond a certain limit, we can make out nothing more. (Conversely, I point out in my book that some experiences, such as that of seeing a cup, are more than the sum of their parts–the essence of the cup–and therefore are already uniform and homogeneous by virtue of being something distinct from the details or the whole, but that’s a slightly different concept.)
For our present purposes, if we can get away with thinking of the essential quality of these homogenous experiences as the “average” of the unique and diverse qualities of all their components–much like the overall colors of the pixels on a screen are the average of their red, green, and blue components–then we are lead to conclude that we are only epistemically aware of this average. And there you have it. The uniformity and homogeneity of an experience amounts to an average. The sight of the speck is the average of all its component experiences, the latter hidden in epistemic unconsciousness.
While it may not seem so, the experience of “seeing a park”–plain and simple as that–must be a uniform and homogenous experience because all its details–a playground, a park bench, a pond, children playing–must average too. And that average would be the whole experience of seeing a park. It may be hard to imagine the experience of seeing a park as uniform and homogenous because our brains are wired to acknowledge the details–to be aware of them–and so it seems intuitive that seeing a park is a complex of diverse qualities and parts–but I maintain the uniform and homogenous experience of simply “seeing a park” is in there too. It’s what we experience when we pay no attention to the details–like recognizing a car coming when we want to cross the street–we aren’t interested in the car’s details, we just mean to identify oncoming traffic to be sure it’s safe to cross the road–and so we experience simply “a car”. The same can be said about seeing a park. We can talk about its myriad details but we don’t have to–we can also talk about just the wholistic experience of seeing the park–plain and simple–and in such cases, it’s best, I maintain, to consider it the uniform and homogenous average of all its details.
But here’s the catch–there isn’t really an average. If you take a bunch of test scores and derive the average, chances are that no one test taker scored it. A similar reasoning applies to the color of a pixel. A pixel may look orange from far away, but there are only certain degrees of red, green, and blue–no orange. It other words, when we look at the details, we don’t see the average among them, like an extra test score or an extra color among the group.
But perhaps it’s too much of a stretch to say that the average doesn’t exist. After all, in the case of test scores, the average comes into existence when the tester calculates it. Likewise, the color orange comes into existence when the viewer sees it from a distance (or the colors mix). But how does the average experience come into existence from its components? How does the speck we see on the bolt actually exist as a visual experience if no such experience exists at the level of its components, at the level of molecular and chemical activity in our neurons? It’s like supposing that a group of 10 people come with a collective mind that is the average or sum of all the individual minds. But if so, who experiences this collective mind? It’s not any one of the individuals because each one experiences only his or her mind. The only possibility is that this collective mind must constitute its own person or being, as if there is an eleventh member of the group. But an eleventh member just means there are really eleven people, not ten, and one must then consider the collective mind of all eleven members, a twelfth mind. I’m sure the read sees the infinite regress that lurks in waiting in this scenario. And more to the point, what is the mechanism by which the minds of the 10 original members yields an eleventh mind? In the case of the rock and the network of atoms, this question is answered easily: the network of atoms gives rise to the rock because the former is identical to the latter–it necessarily is the latter–but with equivalence, we are talking about the experience of the atoms and the experience of the rock, and these are not identical.
The solution is to remind ourselves that if the average experience (or the sum) is equivalent to the collection of the component experiences, then it is interchangeable with them. If the details of the speck on the bolt are beyond the reach of our epistemic awareness, but we nevertheless see the speck as a sort of collective experience of the whole, then what is happening is simply that the component experiences (the collection thereof) are being swapped out for the average (or sum). We are not saying that the component experiences are, collectively, identical to the average, that they constitute the average; we are saying they are equivalent to the average, interchangeable with it. To understand how this brings the average experience into being, or onto the same ontological footing as the component experiences, we have to understand, in a very profound way, what it means for these experiences to be expressions of the same meaning. It means that it doesn’t matter which expression–whether that of the component experiences collectively or their average–we employ. We could either express those experiences corresponding to the molecular and chemical activity–or–the average, the speck on the bolt. Neither one has priority over the other. The two are interchangeable.
There are two conditions under which this holds: 1) when one whole experience, uniform and homogenous, reduces to a set of component experiences, and 2) when the meaning of a set of experiences is identical to that of another set of different experiences. In both cases, we are justified in describing the meaning of each set of experiences as identical–not equivalent, identical–because when it comes to sets of experiences, the meaning of such sets must be an average or a sum (or whatever best describes the unification of their meaning). So whereas each experience in the set has its own unique meaning, the meaning of the set itself cannot be attached to any one experience and must be understood as the derivative of the averaging or summing of all meanings therein. In that case, the singular meaning of each set, though their members might have no similarities to each other whatsoever, can be said to be one and the same–like the same meaning in two poems–and therefore identical–much like the averages of two sets of test scores, if equal, are said to be identical. The same holds for the equivalence between one set of experiences and one single experience on its own. It is by virtue of this point that we can say that the same meaning can be described by a variety of qualitatively distinct sets of experiences.
It is no different with mathematics or with meaning in ordinary language. With mathematics, one could take, say, a single number like 1 and substitute it with an expression like .5 + .5, and it would still signify the same quantity. One could choose from a whole variety of expressions such as .1 + .9, or .25 + .25 + .25 + .25, or 10 - 9, or 1 - 1 + 1, and so on. With meaning, one could take, say, a single word like “horse” and replace it with any of the definitions found in a typical dictionary, such as “a large four-legged animal with solid hooves and a mane and tail of long, coarse hair.” In both these cases, neither mode of expression takes precedence over the others. No one is more “real” or more “true.” There may be one whose use is more convenient or succinct than the others, but certainly not any less valid or “correct”.
It is the same with the meaning of experiences. For all conditions under which equivalence is the type of relation two or more experiences bear to each other, those experiences are interchangeable and it doesn’t matter which one is described–either by us or by the experiences themselves.
Comprehending this concept may prove difficult. We are used to thinking of things as objectified entities residing in existence in the sense that a model of reality based in objectivist materialism would portray them. It is extremely difficult, therefore, not to do this for experiences, but we must try to remember that in a subjectivist model of reality, such as my theory, experiences play the role of the basis for things to be real. Experiences are not objects in existence any more than the meaning of words on a page are physically there in the page itself. Experiences are the very fabric of reality–the material of the box itself, not its contents–and determine, in the final analysis, what is real and what is not. If one is experiencing red, green, and blue (taken metaphorically), it would make no sense to say that the person is really experiencing orange even though he may not know it. In a context like objectivist materialism, this might make sense because the “true” character of an experience can be one way objectively even though it may not seem so subjectively. But in a subjectivist context, the subjective experience itself is the only thing defining what’s real. So if the individual only experiences red, green, and blue, then only red, green, and blue exist. What the foregoing discussion on equivalence says about the orange that these red, green, and blue experiences are equivalent to is that this orange is a separate experience, not a mix of the red, green, and blue, not what the red, green, and blue “really” are, but that as the average or sum of the latter, it is being experienced too–not by the individual but by (we might say) a consciousness on a higher level in the reductive hierarchy, that is the average of the individual’s experiences of red, green, and blue. And so orange does indeed exist but not because that’s what the individual is “really” (objectively) experiencing (unbeknownst to him), but because the experiences of red, green, and blue are equivalent to that of orange (their average), and so they share the same meaning and are interchangeable, and there is no fact of the matter which actually exists and which doesn’t.
(We avoid the infinite regress problem mentioned above here because we are describing the relation between experiences at different levels of the reductive hierarchy, where as the derivation of the 12th person in the scenario above didn’t concern itself with relating lower levels of the hierarchy to higher levels; it grabbed the 10 minds of the original individuals from one level, the mind of the 11th individual from a higher level, and inferred a 12th from that in (what?) a realm on the side?).
The reason why the analogies of mathematics and the meaning of words found in a dictionary work so well is because experiences are more similar to these than they are to physical objects (primarily because they are founded on meaning and information). To imagine experiences as objects (objectification) makes it all the more difficult to understand how there could be one particular experience, yet another experience standing in for it without coexisting with it–that either description of the universe is a proper one. Yet there is no basis upon which we can identify any one experience as the “real” one and the others simply waiting to pop into existence should there be a need to replace it. Where their being is concerned, they are all on equal footing; yet this is not to say that they coexist–like two poems written differently yet with the same meaning–just that it is either/or–that is, it is either one experience or the other, but without a determined answer to the question “Which is it?”
Something else that depends solely on its description, taken straight out of physics, is the relative motion of objects. Einstein’s relativity theory tells us that for an object to move relative to another, to say which object is moving and which is fixed really depends on one’s description (or frame of reference). If one describes the first object as moving relative to the second–whether in words or merely by his or her own senses–then that is a legitimate description and is, for all intents and purposes, true. If, however, he or she describes the second object as moving relative to the first, that too is a legitimate and true description. It’s not as though one description is the “right” one and all others “wrong”, but it isn’t as though both descriptions are true simultaneously either. It’s that they are interchangeable. The same reasoning applies to time dilation. When one approaches the speed of light, his or her time passes more slowly than does the time of someone else who remains at rest. Yet neither one’s clock measures time at the “right” rate. It depends on whose description we consult. Thus, the theory of relativity is yet another useful analogy for understanding the notion of interchangeable experiences and the concept of equivalence.
To offer yet another analogy, we can revisit the concept of the statue in the rock we considered in a previous post. We noted the difficulty with which we can talk about the actual existence of the statue before it is carved out. In one sense, the statue doesn’t exist yet. There is only the rock. The sculptor has yet to create it. In another sense, the statue is there inside the rock, always has been, and only needs to be exposed by chiseling away at the excess surrounding it. In fact, an infinitude of statues exists in the rock, each exposable by the sculptor’s choice of what to chisel away, her choice of how to describe the rock. Do we say that the rock and all the possible statues the sculptor can carve out “coexist”?–as if they are each distinct objects in their own right crammed together in the same space?–or do we say their existence depends on the description we bring to bear on it? We can describe it as simply a rock–there is only the rock, plain and simple–or we can describe it as a statue hidden by excess rock debris that surrounds and clings to it until the sculptor chisels it away. Whether a plain rock or a statue concealed by excess rock debris, these descriptions are equivalent but not identical.
At this point, it should be obvious where equivalence is best applied: to the reduction of experiences from higher scales to lower scales. If it were physical reduction we were considering, we could still speak in terms of identity. We would still say that a rock and the network of atoms that make up that rock are identical, one and the same. But where the reduction of experiences is concerned, we need to speak in terms of equivalence–at least, when we want to describe the experiences at higher scales as uniform and homogenous (or less heterogenous, at least), and those at lower scales as the heterogenous pieces whose average or sum amount to the homogenous whole at the higher scale. We would say that the uniform and homogenous experience at the higher scale–say that had by a galaxy–is equivalent, but not identical, to the experiences of its atoms and molecules considered collectively. Nowhere among the latter do we find the former, and visa-versa, so to describe them as identical is not an option. But they share a common meaning and are therefore interchangeable. That is to say, it doesn’t matter which we consider real, and in fact there is no fact of the matter which is real. Yet it is not as though they coexist–side by side–like a set of test scores and the average the tester derives from a bit of computation–their interchangeability tells us it is either/or but without a determined answer to which it is.
This isn’t to say that the reduction from higher scale entities to lower scale entities is the only example of equivalence but it is definitely one such example. Another might be one set of experiences that entail another set of experiences–as in how the energy in our brains flows from one state to another, corresponding to our experiences flowing from one state to another. This is entailment. But not all such examples of entailment are examples of equivalence, obviously, as the case of seeing a shiny green bike might remind me of a bike I had when I was a kid (the bike I see before me is obviously not interchangeable with a memory of a bike I had long ago… otherwise how would I distinguish between my memory and my current visual beholding of the bike?), but seeing as how two sets of equivalent experiences share the same meaning, one of the sets must obviously entail the other. So while not all cases of entailment are cases of equivalence, all cases of equivalence are also cases of entailment (though they may not always manifest as such in our experiences). What this means is that the universe is always entailing its higher levels from its lower levels (convergently) and visa-versa (divergently).
Returning to the question of how higher scale experiences relate to lower scale experiences, the question of how to describe such relations (as a “sum” or “average” or whatever else), the concept of equivalence sheds a certain light on the question (though it doesn’t answer it). It tells us that we ought not to think of the higher level experience as, in some way, a “mix” of the lower level experiences (like red, green, and blue paint mixing to get orange) such that we get a sum or average. The lower level experiences remain separate, unmixed, while the higher level experience stands on its own, not existing among the set of lower level experiences but apart from them. And yet they don’t “coexist” either–they are interchangeable, either/or, but without any determination as to which it really is. So something binds the two together such that they are equally entitle to claim a part in existence, and that something is obviously their shared meaning. But how to articulate a formula by which the description of one can be entered as input and the other expected as output still eludes us (or me at least). The constancy of their meaning is obviously key and guides us in determining this formula, and the assessment we arrived at in previous posts–that both descriptions must serve equally as justifications or reasons for the behavior of the physical systems at each level–tells us that we must look at the relation between descriptions of behavior at each level as well.
Perhaps the formula takes the experiences from one set as input and computes the overall meaning of the entire set as output. That output would give us the uniform and homogenous experience we’d expect at the higher level of scale. To determine if two sets of experiences are equivalent, we’d do the same for each and compare the meanings in the output. If the meanings are the same, the sets are equivalent. Otherwise, they are not.
But the key take away here is that equivalence prohibits us from imagining that the experiences at the lower level somehow go through some kind of transformation where the law of the conservation of matter and energy hold and only the form changes. We ought not to think of the experiences at the lower level somehow “mix” to become that at the higher level. So stop doing it! 
). The reader might note that the word “behavior” has come up a lot when describing how physical objects or systems act or undergo change. This is important because, as stated in the OP, it is behavior that mind and experience serve the role of explaining–that is, mind (as we said) serves the role of justifying behavior, or giving reason for it, or a purpose for it. The reason I might engage in dancing when a song plays, for example, is explained by my love of the song and the way it drives me to wanna perform these bodily movements called “dancing”. Note the difference between the cause of my behavior, which is accounted for by the physiology of my body (the muscle contractions, the signals from my brain, the chemical reactions throughout the entire process that make each step possible, etc.) and the 
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