It’s common to think of “dimensions” of space and the “dimension” of time, but what if there was more than one dimension of time? I’m not going to present any real theory about this, but just some idea that I’ve been thinking about that offer some interesting possibilities.

First of all, what is a dimension, really? It’s easy to see for space: we live in a three-dimensional world, the three dimensions corresponding to length, width, and height. Everything, from cats to particles, can be located in space with three coordinates (x, y, z). If there was a fourth spatial dimension, we would be unable to perceive it because we are three dimensional beings and so don’t have the capacity to interact with it directly. However, higher dimensions can still have effects upon us (see my previous article on multiple worlds here).

If we were 4-dimensional beings, it would be perfectly normal for us to use 4 coordinates to locate objects in space, so we would have something like a cat at point (x, y, z, *) where * is the coordinate in the fourth dimension. Of course, this can be extended to many more dimensions, as is common in string theory and other physics theories.

So how does time fit into this? We can’t think of it in exactly the same sense as spatial dimensions, because, first of all, there is just one dimension, so it would be a line rather than a 3D grid. Second, we can’t move back and forth along it or even forward along it at any speed we want, but everything moves along it at the same rate. In space, we can stop at a certain point, go forward, backward, change our speed, but time is restricted to forward motion at a constant “speed” along the inevitable conveyor belt of time.

From Einstein, we have learned that it is possible to alter our perceptions of time and the rate at which we pass through time (as seen in his special and general theories of relativity), but it still isn’t possible to truly reverse time. We can’t just stop and head backwards in time like we can stop on a path and reverse our direction. It is possible to greatly alter the rate at which we pass through time by travelling at high speeds or going close to a massive object (massive as in black hole massive), and perhaps even to go to a different time entirely via a wormhole that cuts through the fabric of space-time, but in our general lives, these things don’t happen often, if at all (I’m still waiting for a TARDIS to land in my backyard though…), so we won’t consider that here.

So if time is indeed a dimension, it isn’t at all like the ones of space. Indeed, in physics, time is treated differently than space for other reasons as well. For example, we can characterize motion through space and time with a “metric” that describes an interval of space-time. For example, the metric in flat non-expanding space-time is

where c is the speed of light, ds is the interval in both time and space, dt is the change in time, and dr is the change in space coordinates (x, y, and z). It’s basically just saying that moving in time and space can be written in a combined manner to give the total “interval” that you moved. We can see that space and time are treated differently just by a quick look at the equation: the interval of time is multiplied by c, and it doesn’t have a negative sign like the spatial interval does.

However, we know that space-time is not stationary: our universe is expanding. This doesn’t change the time part of the metric, but it does change the spatial part because every point is moving further away from every other point. It’s like blowing up a balloon with gridlines on it: as the balloon expands, the distance between the gridlines enlarges. In this scenario, the metric is
where a(t) is the scale factor, a function that describes the expansion of space. Already, we see that space and time, even if they figure into the same metric, act very differently (since time doesn’t “expand” as space does).

All this is to say that it isn’t obvious what would happen if there are multiple dimensions of time. If there are more dimensions of space, we just add coordinates to Dr that will also expand with the expansion of space. We can also add additional coordinates of time to the metric, but what would the scale factor be? What is the preferred direction to move in time if there are two time dimensions? It was easy when we had a straight time-line: everything just moves forward along it. But if you have two dimensions, you no longer have a time-line, but a time-grid (see picture). Let’s say we can only move forward along each dimension of time (into the future). So for time 2, t2, time must move up (that is the forward direction) and for time 1, t1, time must move to the right (also the forward direction). But if the times are combined, where can you move? There are plenty of options depending on how fast you go, for example, see the lines on the grid. In each case, you’re moving forward in t1 and t2, but for some, you’re going faster in t1, and for others, you’re going faster in t2. Only the blue arrow has you going forward in time at the same speed in each time.
But what is this “speed” at which we go through time? After all, speed is defined by as the rate at which we cover a certain distance (with “rate” corresponding to a passage through time). So what can we compare the speed of time to? Unless there is a more fundamental time to compare our time to, it doesn’t make sense to talk about a “speed” of time. You can talk about the relative speed of time of one person compared to another (as in special relativity, when one person can appear to age more slowly than another because they’re travelling close to the speed of light), but it doesn’t make sense to talk about the speed of time itself.

However, when we have two times, we can specify the relative speed of the two times with each other: we can have t1 passing more quickly than t2, or vice versa. The orange line in the picture has t2 passing more quickly, since for every step through t1, you go forward 2 steps in t2. The green one is the opposite: for every step in t2, you go forward 2 steps in t1. But you could also have more fanciful patterns on the grid like the pink line: here, although you’re going forward in both times, the speeds at which you move forward in each time keeps changing.

What this would be like for someone experiencing two times is hard to say. Assuming that you can only move forward in both of the directions and at a certain speed (since that is what our one-dimensional time is like now. If not, everything is more complicated!), you probably wouldn’t even notice it unless there were some things that only moved in one dimension of time rather than two. In that case, how would an object just moving along t2 (call it O2) appear to someone two travels through both t1 and t2 (call them P12)? I think there are a few options. The first is that O2 appears stationary for P12: the object would appear to be “locked” in one direction. Since it doesn’t travel along t1, it could be just stationary at all points in t1. This is hard to imagine: what would an object travelling along one time appear to someone travelling in two times? Would it appear “blurred” in part, or somehow less substantial? I really don’t know. This requires a great stretch of the imagination!

Another option is that O2 appears at a single moment in P12’s time. It’s like you have a straight line to represent O2 on the grid and a slanted line to represent P12, like this:
They only cross at one point, so they would both see each other for only an instant, or more likely, not at all, because it would correspond to an infinitesimally small interval when they cross each other, which wouldn’t be perceptible for living beings. If we make an analogy with space, it’s as if you had a 2D object that had no height (see image to the left). It’s located at a certain height in 3D space, but it doesn’t have height itself. Though the problem with this option is explaining why O2 appears at a particular instant of t1. Why not shifted to another time? Since it isn’t travelling in the t1 direction, that time is meaningless to it, so it shouldn’t prefer to be at one time rather than another.

Here’s another scenario that’s easier to understand. Let’s say you’re confined to one dimension of time, but that there are really two dimensions in the world around you. This would mean that things that can travel in both time dimensions could appear to come in and out of existence. Making another analogy with space, it’s as if you were on a 2D sheet and a sphere was passing through you. You wouldn’t see it as a sphere, but as a series of disks that start out small, become larger as the centre of the sphere passes through you, and become small again as the sphere finishes passing through your sheet.

And if there were things that travelled in t2 while you only travelled in t1, they would either appear to you to be stationary, since you can’t perceive their motion in the other dimension, or you just wouldn’t see them at all (like in the first example).

You could also have three dimensions of time, and then you’d get a 3D grid of time like you do in space. There will be many more possible directions of travel through this grid, leading to much stranger things! But whether any of these are really possible isn’t that clear. After all, could someone even exist in multiple dimensions of time? Our bodies function in one dimension of time, relying on cause and effect for our bodily systems to function, and this wouldn’t be straightforward in more time dimensions. Our thoughts are also sequential: we think one thing after another (“discursive thinking”). Yet introducing more dimensions of time might actually correspond to what philosophers and mystics have strived toward throughout the centuries, namely, “noetic thinking,” where we can grasp multiple concepts at once without having them being fragmented them due to the restricted nature of our thoughts. This, however, might only be possible if we can travel anywhere on the “grid” of time: forward and backward, which encompasses a more complete view of existence. Though whether or not this is possible is another matter entirely.

So, having more than one dimension of time is certainly not as clear as adding more dimensions of space. But there’s nothing that says it’s impossible. It’s possible that we already live in two dimensions of time, or three, or ten, and that things that we’re unable to explain with our current science could be due to the fact that there are multiple times.

I can’t believe I only read this book recently: I probably should have found it and loved it long ago. In any case, Peter Beagle’s fantasy classic The Last Unicorn is a wonderful story about a unicorn in search for her missing people and two humans who accompany her on her journey. The first part of the story focuses on the unicorn’s point of view, which is important to help us understand at least a glimmer of how the unicorn thinks and understands the world, but the majority of the story follows the magician Schmendrick and the woman Molly. The story was written beautifully, and many of the descriptions held me in awe, making me read them again and again. It’s not a predictable story either, although it has the feel of a heroic adventure story, Prince Lir being the hero, though he comes into the story quite late and in many ways is not a typical hero. I’m not going to summarize the book, but I’ll point out some of my favourite parts and some interesting themes the story evokes.

First off is the magic within the story. Besides magical creatures such as the unicorn, magic is possessed only by magicians who study it or who have a particular gift for connecting to its powers. The unicorn is the embodiment of pure magic and eternity, not aging and not affected by the turmoil in the world around her (for the most part). Her magic is more subtle than that of humans, who have to study it rather than having it outflow from them naturally. However, it is also possible for humans to have a direct connection to magic in vision-like bouts of power. Schmendrick is usually unable to perform real magic (he performs tricks and illusions mostly), yet there a true power comes through him at times, and instead of letting him direct the magic himself, uses him as a vehicle. The magic works through him rather than being directed by him. This is interesting because it shows that the most powerful magic lies in magical beings who use it naturally as well as a higher power that can work magic through others as is deemed fit. Yet as to the identity of this power, we can only speculate.

A further consideration of magic lies in the manipulation of time. The talking skull in King Haggard’s castle speaks about this when he says:
 “When I was alive, I believed — as you do — that time was at least as real and solid as myself, and probably more so. I said 'one o'clock' as though I could see it, and 'Monday' as though I could find it on the map; and I let myself be hurried along from minute to minute, day to day, year to year, as though I were actually moving from one place to another. Like everyone else, I lived in a house bricked up with seconds and minutes, weekends and New Year's Days, and I never went outside until I died, because there was no other door. Now I know that I could have walked through the walls.”

This is what the greatest magicians can accomplish, to be able to sidestep time itself. As Schmendrick says, the essence of being a wizard is “seeing and listening,” and so it is necessary to see and listen to the world in order to go beyond the bounds of time. Normally everyone, no matter how great their powers are, is bound by the forward motion of time. It is a train we are all confined to, taking us from the past to the future. Yet what if we could step off the train and go backward to another time along the tracks? Or forward? This is not the natural spontaneous magic of the unicorn, but another dimension of magic. Though with the unicorn’s healing powers, it may very well be that she is also tapping into this magic of time: restoring someone’s body to a time before they were injured. She is not entering a different time herself, but the person she is healing might be imperceptibly travelling back in time. Likewise, her agelessness could also tie in to this power of time, for although her memories accumulate from the past to the present, her body exists in some eternal state unbounded by the moving train of time. She “walks through the walls” and is not bound by this “house bricked up with seconds and minutes,” for she can enter and exit it at will.

Yet despite the unicorn’s powers, King Haggard’s Red Bull still proves to be a formidable enemy that has trapped many of her kin. We never find out what the Red Bull really is, though I take it to be a manifestation of fear and hate in contrast to the unicorn’s pure magic. It’s not that she has the magic of love and the Red Bull that of hate, because, as we see in the story, apart from the time that the unicorn becomes human, she is not a force of love, but is beyond human emotions and concerns. This is expressed clearly when she says, “How can I be cruel? That is for mortals…so is kindness.” This might seem callous from a human’s point of view, but for an eternal being, it is inevitable that they see things from a more remote viewpoint since they are essentially outside of the endless cycles of life and death. This is a very different take on unicorns than we normally see in fiction: it isn’t until the unicorn becomes (part) human that these sorts of sentiments arise in her, and this seems more realistic.

But back to the Red Bull: since the unicorn is not omnipotent, he still has an effect on her by evoking a deep fear in her, forcing her under his sway, as he did with the other unicorns before her. It is a more primal force on par with the unicorn’s own powers, not the “parlour trick” magic of humans such as Schmendrick, but the manifestation of a deep power, the only kind that can threaten a unicorn. We also see this with the harpy, which is another ancient creature with great powers that the unicorn fears. It is fear that these evil creatures evoke in the unicorn, yet when she can overcome this fear, she is able to realize that she is more powerful than they are. And this, surprisingly, was only possible after she had turned into a human: even after returning to unicorn form, she retains some human aspects, one of which is the love for someone else and a passion to pursue her mission to save her kin. This allows her to overcome her fear, something she was unable to do while in a purely “unicorn frame of mind.”

And lastly, to give you a sense of the amazing descriptions in the story, some of the particularly good ones are:

“The sky was low and almost black, save for one spot of yellowing silver where the moon paced behind thick clouds.”

“The thin night wind lifted and spilled her mane, and the moon shone on the snowflake crafting of her small head.”

“the murderous smell of it seemed to turn her bones to sand and her blood to rain.”

“Fear came back to her eyes like a great stone falling into a pool: all was clouded and swirling, and quick shadows were rushing everywhere.”

“The horns, the seashell shining of the horns! The horns came riding in like the rainbow masts of silver ships.”

And one of the many humorous quotes:

“Prince Lir bowed to her; a quick, crooked bow, as though someone had hit him in the stomach.”

There are lots of others, but you’ll have to read the book to see!

Although I’ve only touched on a few themes, the book is much richer than this and I’d highly suggest reading it.

Neoplatonism is an important school of thought that formed to resolve enigmas in Plato and Aristotle’s philosophies, Plato in particular. Indeed, Neoplatonists claimed that they were only explaining Plato in more detail, fleshing out what he really meant. The quote today is from the Roman philosopher Plotinus, who lived from 204 – 270 AD, and was one of the founders of Neoplatonism (though at the time, they just claimed to be Platonists). The quote is one of my most favourite ones in all of…well, everything, so be prepared for a long blog post!

From Plotinus’ Ennead V (~ 250 AD):
“We must turn our power of apprehension inwards, and make it attend to what is there. It is as if someone was expecting to hear a voice which he wanted to hear and withdrew from all other sounds and roused his power of hearing to catch what, when it comes, is the best of all sounds which can be heard; so here also we must let perceptible sounds go (except in so far as we must listen to them) and keep the soul’s power of apprehension pure and ready to hear the voices from on high.”

Such a beautiful quote, though to know exactly what Plotinus is talking about requires us to know a bit about the metaphysics of Neoplatonism. Neoplatonists view the world in terms of three hypostases, or levels of reality. This includes the One/God/Tao/Ain Soph/Brahman, Intellect/Nous/the Divine Mind/Atzilut, and Soul/Psyche/Universal Soul/Beriah&Yezirah. There’s also Body/the World/Nature/Physicality that comes after the soul, but it isn’t a real hypostasis (we’ll see it at the end). I’m listing various names for all these just to show that they correspond to many other religions and philosophies, but the first terms are those that Plotinus uses, so I’ll stick with those.

At the base of all existence, subsuming all other hypostases, is the One. It is the source of everything, transcending “being” as we know it. We usually think of the verb “to be” as determining something qualities. A dog is a dog because it has a specific form, a particular code of DNA, and so on. This is determinate being, but the One is infinite and indeterminate, containing all things, so it can’t be described in this way. If you describe it as one thing, you’ll leave something else out. Determinate things can be described because you can say they are “x” rather than “y.” Toto is a dog, not a cat, or a duck, or a hippo, etc. Yet the One is everything. Just like the Tao, it cannot be described: we can only gesture to it in metaphors and perhaps glimpse it in insights that go beyond our reasoning mind. The human mind can only grasp determinate things, so the One will remain out of our grasp unless we go beyond seeing things in sequences and in time.

So the One is both everything and nothing: it doesn’t lack anything, it gives rise to all things, but it also is nothing in particular, not possessing any determinate qualities. Plotinus says that “The One is all things and not a single one of them: it is the principle of all things, not all things, but all things have that other kind of transcendent existence…the One is not being, but the generator of being.” Yet you can describe the One as perfect, or fully actualized. One of the most important Neoplatonic ideas is that a fully actualized being will create an external reflection of itself, also known as a second actuality. Plotinus says that “All things when they come to perfection produce.” This production is an expression of the One, an image of it that isn’t as perfect because it is more restricted.

The best analogy for this is the dispersion of white light by a prism (which I described in a few other posts): the white light of the One splits into various colours upon entering the prism, so there is more variety in what is further down in the hierarchy. However, the One is undiminished, for like the white light from which the colours arose, it remains pure and simple, even though its dispersed beam appears to be multiple. This process continues down to much more complicated levels of existence until the physical world comes into being.

An analogy Plotinus uses is that of fire, snow, and perfume: “fire produces the heat which comes from it; snow does not only keep its cold inside itself. Perfumed things show this particularly clearly. As long as they exist, something is diffused from themselves around them, and what is near them enjoys their existence.”

The One gives rise to infinitely many things, particular beings unlike the source from which they arose. This first expression of the One is the second hypostasis, Intellect. This is also known as the Good in Plato, the highest Form. All other Forms exist within the Good.

This process of creating Intellect is called emanation. The first step is when the One sends out a reflection of itself, which is less perfect and so is multiple rather than unified: “The One, perfect because it seeks nothing, has nothing, and needs nothing, overflows, as it were, and its superabundance makes something other than itself.” The next step occurs in Intellect, which is when Intellect actualizes itself as a distinct level of existence. The nature of Intellect is to think, and by thinking, it strives to return to the One. This doesn’t occur in time, because time only enters into existence in Soul (as we will see below). Intellect strives to return to the One, its perfect source, though because it is limited, it is never able to reach the One by thinking. It is Intellect’s nature to think, yet the One cannot be thought since it is not a determinate being.

Yet this failed attempt to grasp the One actualizes Intellect as its own level of existence: it becomes perfect as a reflection of the One by thinking of itself—the only thing it can think of. In thinking itself, the Forms are generated, and so although Intellect doesn’t return to the One, it actualizes itself by creating a system of Forms that each express different aspects of being. These are infinite aspects of the One that exist in a hierarchy with the Form of the Good closest to the One and more specific Forms that derive from it further down. They are all connected, and each Form derives its nature from all other Forms. It is a lot like Hua-yen Buddhism (see my previous post), where each dharma (or in this case, Form) is defined in terms of the whole system of Forms. One cannot exist alone. Each Form is a partial grasp of the One: a different aspect of it. Returning to the dispersion analogy, the different Forms, represented by the colours of the rainbow, are generated when the white light of the One is dispersed through a prism (which is in this case the act of Intellect thinking).

You’ve probably heard of Platonic Forms before: really anything you can think of has a Form that it’s modelled after (though not perfectly). The Form of the Good, Beauty, Number, Colour, Motion, Rest, and even specific things like Dog, Grass, and Table (note that I’m referring to Forms in capital letters, so the Form of Dog is in Intellect, while specific dogs are physical creatures that imperfectly partake in the Form “Dog”). Yet in Intellect, these Forms are unchanging objects of thought and not physical things that grow and change.

The next level of existence is Soul, which “is a ghost of Intellect.” Because Intellect actualizes itself in the act of thinking, it also produces an external image of itself, a second dispersion (add another prism!). Soul is thus more multiple than Intellect, further from the eternal existence of the One. It is here that we introduce time and change, which measures the thinking activity of Soul. The Forms are eternal and unchanging, but the souls that exist in Soul, although they partake in the Forms above, change and evolve, which is less perfect than Intellect. “For around Soul things come one after another: now Socrates, now a horse, always some one particular reality; but Intellect is all things. It has therefore everything at rest in the same place.” The very fact that Soul changes means that it isn’t perfect: if it was already perfect, change would bring it away from that perfect state, and if it wasn’t yet perfect—if it was improving or regressing—then it still isn’t in a perfect state.
Likewise, Soul actualizes itself by trying to unite with its source, Intellect. Soul, however, can only think discursively, which is the kind of thinking we usually talk about. It is thinking one thing after another using a chain of reasoning. Intellect, however, thinks noetically, which is more of intuition: an immediate insight that can grasp all Forms at once. Such thought is only possible, however, when one is outside of time, so Soul can never fully reach Intellect. It tries to grasp the relationships between the Forms, but is only able to think of them sequentially, for it is “ever-moving,” so misses the interconnectedness of the Forms. For instance, if you imagine the Form of Beauty and try to understand it, you will be thinking of certain qualities rather than others, and so will necessarily leave parts out. Even if you were to think of all aspects of Beauty sequentially, that would still not be grasping it as a whole, and it would also be missing its position in relation to the other Forms. This fragmented way of thinking is intrinsic to Soul’s nature, and it must be transcended in order for Soul to return to Intellect. Yet Intellect is still at the centre of Soul. It is its essential nature, just like the One is the essential nature of Intellect.

Thus, a better way of looking at the hypostases are that they form a circle with the One at the centre, Intellect a layer around it, and Soul a layer around that. At the centre of Soul’s circle is Intellect, and at the centre of Intellect’s circle is the One. Everything is really just an aspect of the One, emanating outward in circles that stray from the central point as they are created. This also means that it is possible to reach Intellect and even the One because it is at the centre of our being, for “Nothing is separated or cut off from that which is before it.” This is related to Plato’s doctrine of recollection: even if we aren’t taught mathematics or other principles related to the Forms, we have the Forms within us, so we understand them on an intuitive level even if we’re not taught them.

Soul does, however, actualize itself as a distinct level of existence in its act of thinking about the Forms. So, as Neoplatonism dictates, it produces an external reflection of itself. And thus, we reach the physical world, Body. Soul “looks to its source [Intellect] and is filled, and…generates its own image.” As time was introduced at the level of Soul, space comes into being at the level of Body, so we now possess space and time (space-time).

Body is not really a hypostasis in itself, though it does emanate from Soul like Soul came from Intellect and Intellect from the One. The difference is that although Soul actualizes itself in thinking and can return to Intellect if it transcends its discursive thinking, Body is unable to overcome the limitation of physicality and so can never actually return to Soul. It is not conscious, but rather consists of material things that can’t think, called logoi spermatikoi, or seminal reasons. Materiality cannot be overcome, and so Body is not really another level of existence like Soul and Intellect are from the One, because it does not have the One as its ultimate nature.

As a whole, Soul is also known as the Universal Soul, yet within Soul are also individual souls, centres of consciousness. Like the Universal Soul, the primary purpose of souls is to contemplate Intellect in order to ascend to a more perfect level of existence. There is a hierarchy of souls within Soul: those more enlightened tending toward Intellect, and those more tied to the material world toward Body. Yet a secondary purpose of souls is to incarnate in the material world, to form living beings like humans, which means that we are a combination of two worlds: Soul and Body. Yet since every soul has at the innermost centre of its being the Universal Soul, each soul can be said to have made the physical world. Plotinus says, “Let every soul, then, first consider this, that it made all living things itself, breathing life into them…it grants life to the whole universe.” This can be understood in two senses: the first is that souls incarnate into the material world directly, giving life to it, and second is that they are in essence the Universal Soul from which the world emanated.

Higher souls do not get caught up in the material world that they animate, yet lesser ones can easily get distracted by it and fail in their primary purpose of contemplating the Forms. Souls are supposed to govern the body, not become attached to it, a doctrine we see in many other philosophies. The soul suffers when it identifies itself with the body, because everything in this world is transitory and far from the true source of existence. It is just a reflection from Soul, an “illusion,” and so placing importance on it and treating things here as permanent only leads to suffering.

In order to ascend back up the ladder of being, Plotinus gives us two ways: “One shows how contemptible are the things now honoured by the soul…the other teaches and reminds the soul how high its birth and value are, and this is prior to the other one.”

The first way is asceticism, condemning physical existence and detaching oneself from material things. They are imperfect, they are transitory, and so should not be objects of veneration or sources of happiness. This closely aligns with Stoicism and Buddhism in particular. The second way ties in to the first, which is to recollect one’s true nature. To realize you are a soul in a body rather than a body. Your soul defines you, and that soul is part of the Universal Soul, and that part of the Forms, and so on to the One. This shift in consciousness can help you become what you already are, to shift the eye of the soul to what is both beyond and within it. It’s not something that we can fully comprehend given our limited minds, but we can try, at least. Plotinus speaks of seeing the order in things around us: how various beautiful things in the world are only imperfect instances of the greater Form of Beauty, for instance. Even though we must necessarily think discursively, eventually, we can overcome that and think of the Forms noetically as Intellect does. The final stage is to return to the One, where all thinking is put aside, and there is only unity and no longer determinate being. It may seem impossible, yet at the very core of your being lies the One: “Since the soul is so honourable and divine a thing, be sure already that you can attain God by reason of its being of this kind.”

Much of Neoplatonism has parallels with various other religions: Buddhism, Kabbalism, Taoism, and mystic Christianity, for instance. They are all speaking of the same underlying universe, which, although expressed in various symbols and metaphors, is a hierarchy of reality with truer levels of being closer to the One.

This is all a simplified version, because within Intellect, Soul, and Body are many levels that make it clearer how one hypostasis gives rise to another other. If we look at these, we can see a correspondence to the Kabbalah, since in the Kabbalah there are many Sephiroth within each level of existence. The Neoplatonic scheme of existence is also a good way of understanding mathematics and physics. Numbers themselves, as well as mathematical laws based on them, exist as Forms in Intellect. In order for mathematics and physics to describe the world we live in, there must be some fundamental physical laws that exist: otherwise, the world would just be chaotic. Since these laws obviously don’t exist physically (you don’t find the number 4 floating around), they must be nonphysical, and hence, exist in a nonphysical realm above ours (“above” being a higher level of existence). A law only presides over that which is below it, so the laws in Intellect don’t affect the One, its greater source, though they do affect Soul and Body. There is a hierarchy where more specific laws are subsumed by more general ones that are closer to the One. The further down something is in the hierarchy of existence, the more restricted it is, being subjected to a more laws that restrict its movements or thoughts. Thus, if one transcends the physical world, through purifying their soul and attending to that which is above it, they will transcend some of the limitations of the world around them. This is how some people have, through meditation or other practices, appeared to transcend the common-sense laws that govern the world. Walking on water, perhaps? Telepathy? This is just speculation, but it could certainly be explained in this way. Of course, this is common in Buddhism, but even Greek philosophers such as Plato and Pythagoras were said to have certain powers.

Even if we don’t know what the ultimate laws are that govern the world, we already understand physics in terms of a hierarchy of laws that are applicable in more specific or general situations. For example, Einstein’s theory of gravity is a general theory that applies to the universe on a large scale as well as the world around us. Newton’s theory of gravity works well for things on Earth and much of the solar system, but it fails on larger scales. Thus, it is a subset of Einstein’s theory that is applicable in more restricted situations. An even more general theory would include both quantum mechanics and general relativity (see picture below from the physicist Max Tegmark). This law would be a higher Form that more specific laws are derived from. But this law, ultimately, will arise from even more basic principles: Number, Symmetry, Order, etc. For instance, Max Tegmark said that all mathematical structures are abstract, immutable entities. The integers and their relations to each other, all these things exist outside of time.” Existing outside of time doesn’t correspond to the world around us, or even Soul, but to more basic principles in Intellect. Additionally, they are not mere fictions that we have created to describe the world. I won’t get into that here, but see my previous post.
Diagram from Max Tegmark

Another physicist, Roger Penrose, believes that Platonism is a correct description of reality. For example, in an interview, he said that “mathematics has to have been there since the beginning of time. It has an eternal existence. Timelessness, really: it doesn’t have any location in space, it doesn’t have any location in time.” He also explains how there are three different kind of existences: the physical, mental, and mathematical worlds, which would correspond to Body, Soul, and Intellect (the One doesn’t “exist”: it is beyond existence). Likewise, our access to the world of mathematics, the fact that we can understand things as basic as numbers and addition to more complicated things like differential equations and general relativity, is only possible because, as Plato said, it is already within us. Within the core of our souls is Intellect, providing the laws that created us and govern our existence.

Now, the laws that govern the physical world (quantum mechanics, general relativity, electromagnetism…everything), although they derive from the Forms within Intellect, are “filtered” through Soul and so exist in the Universal Soul rather than Intellect. As I quoted in my previous post, the physicist John Spencer said, “All the laws of physics are partial reflections of the one eternal mathematical law, which is a kind of super-law, the foundation of all the mathematical laws in the universe.” This law exists in Soul, the “?” in the diagram of yellow boxes above, and all laws that derive from this exist in Soul below it. If a soul transcends above this level, it will no longer be subjected to these laws, and so may appear to do miraculous things.

This eternal law, which describes how the physical world works, partakes in higher Forms of Symmetry, Number, etc. Plotinus says that “Even in seeds it is not the moisture which is honourable, but what is unseen: and this is number and rational principles.” Thus, physical laws (rational principles from the eternal law) and number (mathematics in Intellect) form the basis of everything in the world around us. More specific laws arise when the eternal laws is applied to, say, the microscopic realm with quantum mechanics, or the macroscopic realm with gravity. But if you could understand the greater laws above it, you would be able to describe both quantum mechanics and gravity with a single law, and even more generally, both souls and bodies.

Thus, the metaphysics of Neoplatonism can help us understand all sorts of aspects of existence from souls to time to mathematics and physics. Like many other philosophies that include a hierarchy, or even those like Hua-yen Buddhism, it describes a universe that is united and tells us that even though the world may see chaotic and disconnected, everything derives from the One, and we all can return to it, for it still exists as an invisible core within us. Listen, and you may hear “the voices from on high.”


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It’s not surprising that quantum mechanics, the branch of physics that studies the smallest level of reality, has many conflicting interpretations to what’s really happening and what actually exists. A book I read recently, The Anthropic Cosmological Principle, discusses many areas of science that relate to the anthropic principle, some of the most interesting of which are the interpretations of quantum mechanics (QM), in particular, the Many Worlds Interpretation (MWI). This is what we’ll look at today:

From The Anthropic Cosmological Principle by John Barrow and Frank Tipler (1988):
“The question of why does this universe rather than that universe exist is answered by saying that all logically possible universes do exist. What else could there possibly be? The MWI cosmology enlarges the ontology in order to economize on physical laws.”

By the way, I have a lot of “stars” in the text below, which correspond to notes at the bottom that give a bit of physics details for those who are interested (it’s not necessary to read though).

One of the many problems in QM we still need to solve is how to make sense of observers. Namely, us, the ones who perform experiments. We seem to have a peculiar influence over what happens to particles at the subatomic level just by observing them. Indeed, before a measurement of a particle is taken (usually something like its position or speed. I’ll just talk about position though), the usual interpretation, called the Copenhagen Interpretation, says that the particle exists in a “superposition” of states: not at any particular location. It is spread out over a certain area and is described by a wavefunction (usually denoted by ψ). Although the particles is more likely to be found in a particular area, it can still be found outside this region.*1

The interpretation favoured by the Copenhagenists is that when an observation is made, the wavefunction “collapses” to a particular value. When we weren’t looking, it was spread out over a large area, existing, in a sense, in many places at once, but now, it is nicely settled at a single point in space. In the picture below, the graph on the left shows the probability of observing a particle in a particular location (in x and y coordinates, so two dimensionally). This is represented by the particle's wavefunction (ψ) on the vertical axis.*The particle isn’t “in” any one spot, but spread out over an area, though it is most likely to be found at the peak.

However, when an observation or measurement is made, the wavefunction collapses so that the particle is now in a particular spot (the spike on the graph to the right). So, as the physicist Niels Bohr said, “an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor the agencies of observations.” Observation, in a sense, brings the properties of particles into being—they never really “existed” beforehand.

This interpretation seems ludicrous, and there are some serious issues with it as well.*3 This might just be how nature works, but fortunately, there are also other options available to us. First, the uncertainty in our description of QM (for example, of locating a particle) is probably just that: it is only an uncertainty in our description, which is tailor-made for human experience. It describes our uncertain knowledge of the world, not an uncertainty in the world itself. There is an inherent limitation to what we can know (from our limited senses and the fact that we have to interact with the world when we observe it) but that doesn’t mean that the world is actually “uncertain” and existing in many states before it’s observed. It’s naïve to assume that we can know everything through our senses and the mathematics we have created; it’s more reasonable to assume that as creatures living in three spatial dimensions, able to travel one direction in time and being mostly limited to our five senses, if we dig deep enough, there may be some things we can only understand probabilistically—but that’s not to say that this is the way they are, just the way they are to our perceptions. There must be a physical reality independent of our observations even if we can’t observe it, because otherwise, what would our probabilistic descriptions be describing? Thus, it’s important to distinguish between the mathematics we use to describe the world, and the world itself, which need not be constrained by our theories and human limitations.*4

This ties in with a different interpretation of QM called the Many Worlds Interpretation.*5 In this theory, each quantum mechanical possibility occurs in a different world. Introduced by Hugh Everett and endorsed by many physicists today (for example, Max Tegmark, said, “Accepting quantum mechanics to be universally true means that you should also believe in parallel universes.”), in the MW interpretation, every quantum mechanical possibility happens, but each occurs in a different world.*6 So everything happens, and there are nearly infinite possibilities! So think about every possible universe, those that are only slightly different to ours (e.g., one in which your favourite colour is red instead of purple) and ones that have entirely different planets, solar systems, and galaxies. In this scenario, the observer has no magical ability to make wavefunctions collapse, but rather, when they make a measurement, they only measure the particle’s position in their particular universe. Everett said that “it is not so much the system which is affected by an observation as the observer,” so the MW approach is a realist view of QM (meaning, in this context, that each world exists whether we observe it or not).
So when a measurement is made on a system, all the possibilities that could happen will “split” into different worlds. If one views the universe as a whole, however, (though here, it might be better to say multiverse) there is no real splitting and no change in the particle’s wavefunction: the general wavefunction represents all the different particles that exist in every universe, even though in our particular universe, it only follows one option. The real difference is in the measuring device (or ourselves, since we perceive the particle to be in one state or another), because we measure different values depending which universe we’re in. Indeed, it’s more apt to say that the measuring device splits rather than the particle and the universe around it, because it’s the measuring device that is registering different values depending upon the state of the particle. Barrow and Tipler say that, “There is only one Universe, but small parts of it—measuring apparata—split into several pieces…upon the act of measurement.”

I find this hard to imagine physically, since, if anything in the universe splits into multiple states, where do these copies exist? They have to be somehow distinct from each other or else it wouldn’t make sense to talk about a “split” in the first place. And it isn’t as though there is “the” universe, and then off in some other plane of existence, there are various measuring devices with different readings existing in and of themselves. I can’t explain why there wouldn’t be as many universes as there are splits, even if, at the moment of the split, they all start out the identically except for the reading on the measuring device and the particle’s state. So the view of having many worlds seems to make sense only if there are many fully-fledged universes distinct from ours.*Yet later on, they mention multiple “worlds,” each with different states for the particle that is measured, which makes more sense. They say that “each measurement splits the apparatus (or equivalently, the universe).” There is only one “Universe” (capital “U” to denote all the worlds together), but this Universe represents a collection of “universes” (each with the different possible outcomes). It is the measuring device that causes the world to split, but it is not the only thing that exists in these other worlds.

To return to the quote at the start: “enlarging the ontology” simply means that there are many universes rather than one, which might seem to be superfluous. The ontology is just our description of the universe at large, and to have all possibilities happen rather than just one is certainly enlarging it. To “economize on physical laws” means that we need not evoke a strange quantum collapse that deviates from the equations of physics to describe how a particle’s wavefunction evolve: you have a wavefunction to describe the Universe, and it never splits. And if every possible universe exists, there is no need for us to specify why the universe exists the way it does: we happen to live in this universe because it is habitable to life. Of course, we wouldn’t expect to find ourselves in a universe so vastly different to ours, or else it wouldn’t harbour life.*8

This ties in with a similar explanation of the MWI described by Max Tegmark in various papers (using Everett’s original ideas). There is no “collapse” of the wavefunction: it proceeds according to physical equations.*9 It isn’t that the wavefunction “splits” into many worlds, but that all possibilities exist, even though we only perceive one of them in a given scenario (so it looks like a split). There is “apparent randomness from the inside viewpoint…[but] strict causality from the outside viewpoint,” which means that although we can’t know which state of a particle will be in when we measure it in a given experiment, we know with 100% certainty that all outcomes will happen. From an “outside” point of view, we would be able to see all the possibilities occurring, which is where the many worlds come in, since each happens in a different “world.” This is called decoherence, when you go from a quantum (small-scale, one world) description to a classical (large-scale) description within one of the worlds. So it “is essentially indistinguishable from the effect of a postulated Copenhagen wavefunction collapse from an observational (inside) point of view.”

Thus, there is no real randomness to the universe: it only appears so to us because we cannot predict which outcome we will end up with in our universe. Tegmark says “whenever a quantum event appears to have a random outcome, all outcomes in fact occur, one in each branch [universe].” There is nothing random or uncertain about the wavefunction itself: it follows certain physical laws just like the objects in the macroscopic world, but “observers subjectively experience this splitting merely as a slight randomness.”

The MW theory thus has two descriptions: the inside view, and the outside view. Tegmark describes this as the bird’s point of view looking down on the world below (or in this case, worlds), and the point of view of a frog within one of the worlds. From the bird’s point of view, there is only universe described by a single wavefunction, and it does not split into many worlds. All these “worlds” and possibilities occur simultaneously, splitting and merging according to fixed physical laws. It is only on a smaller scale, with the frog, that ideas about randomness and probability make sense. The frog experiences a small portion of the full reality, perceiving only a single world within the entire multiverse.*10 At every instant, when there are multiple outcomes that can arise in a given situation, the bird can see each of them playing out, all in different worlds, whereas the frog only experiences the different worlds “as a slight randomness.” There is no real randomness, but since the frog doesn’t have access to any other worlds, it can only understand the world in terms of probabilities rather than certainties. This is why mathematics is so powerful: it allows us to temporarily rise out of the frog-level of existence and understand what’s really going.*11

This is the basic idea of how you can explain QM mechanics with the MW theory. It does, however, introduce many philosophical puzzling questions, such as:
  • If there are many copies of “you” in different worlds, each slightly different, which is the “real” you? Are they all you, are they all different people, or is it meaningless to talk about a unified self at all?
  • If the soul exists (and we have good reason to believe that it does), then is it spread out over the different copies of you, or are all copies but one “soulless”? This, however, depends on the answer to the first bullet point.
  • Is there a theory of everything to describe the many worlds as a whole, or, even from the bird’s eye view, is probability the best we could ever get?

In a future post, I’ll talk about how this can be understood within the framework of Neoplatonic philosophy, but for now, that’s another story 

*This can be seen clearly in Heisenberg’s Uncertainty Principle: ΔxΔp ³ ħ/2, where Δx is the uncertainty in the particle’s position, and Δp the uncertainty in its momentum. So the more accurately you know the position, the less accurately you know its momentum/speed, and vice versa, so you can never localize a particle precisely.

*To be more accurate, it’s actually the particle’s probability density, |ψ|2

*For instance, how can our knowledge, something that exists in our minds and is, in a sense, nonphysical, affect particles outside our bodies? If there are no observers, will the world exist? Does, say, a fruit fly count as an observer? What about an unconscious measuring device operating without any human influence? And, as in Schrodinger’s cat scenario, how can a cat be both dead and alive until we observe it?

*Some physicists don’t like this idea, saying that the unknowable properties of particles are “hidden variables” and that the underlying reality of the world involves statistics rather than certainties. But philosophically, this makes little sense. For a related topic, check out my previous blog post Platonic Realism in Physics.

*Another interpretation that could also be philosophically sound is having an “Ultimate Observer,” but I won’t get into that.

*A simple example is a system with a particle that could be spin up or spin down. Although we describe the particle as being in a superposition of the two spin states, we only measure one of these two possibilities when the spin of the particle is measured: one in which the particle is spin up, and the other spin down, each corresponding to two different universe.

*It may make sense to mathematically describe only the apparatus splitting, but when you think about what physically happens, you can see that the rest of the universe will be “copied” in the other world.

*This is the weak anthropic principle: “weak” not because it is lacking in some sense, but because it doesn’t make any grand statement about the universe. In fact, it really just states the obvious, since everything we perceive in the universe is restricted by the fact that we exist and are able to observe it, so it must be conductive to life, otherwise, we wouldn’t be here to observe anything.

*The system evolves according to the Schrodinger equation at all times. If there was a collapse, the Schrodinger equation would be violated.

*10 Decoherence “prevents them from seeing…parallel copies of themselves.” (Tegmark)

*11 I don’t mean that we can get out of probabilistic interpretations, because that is embedded in our mathematics as well, but rather, we can conceptually understand the general structure of reality and what this means for the existence of other worlds, probability, and determinism.


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"A Soul Wanderer never knows. He wanders; he makes his own path through the
heights of the universe."

-Sio Larwick

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