The Calculus of Dreams

Ever since 2005, I have been pondering the subject of dreaming greatly, and have finally came to some useful philosophical conclusions (but I still haven’t found sure proof that this world is real), but one particular milestone is when I watched Inception, the second greatest movie I’ve seen. Out of many interesting things I noted while watching the movie, by far the greatest idea was a model for dreams that I came up with while watching it. It is the representation of dream levels as functions, and the representation of dream transactions as calculus.

Let’s, for purposes of introduction, call real life 1, and by “1” I mean the function f(x)=1, not the number 1. This is a sensible assignment, initially because the simplicity of “1” represents how reality makes sense straightforwardly, but also because of reasons to be explained later. What happens after you die? Well, nonexistence quickly leads to thinking of “0” (or d(x)=0)  to represent what occurs when life ends.

What would be a good expression to represent your dream? (I’ll just call it ‘dream’ for now and ‘Dream Level 1’ later.) A dream is mysterious and doesn’t always make sense—much of it is a representation of unknown, so a sensible expression for a dream would be “x” (as a function, g(x)=x).

Of course, some things about “x” don’t make sense, like what the slope represents in terms of properties of the perceived mental world; for example, what does the slope represent? Insanity?

In any case, let’s go back on track. What if we had a dream within a dream? Would that just be x²? That would make an intuitive guess, but these new dreams are very weird…they are more unstable and have greater time dilation. Perhaps h(x)=x²/2 is a better representation for Dream Level 2.

At this point, something just has to be noticed. h'(x)=g(x), g'(x)=f(x), and f'(x)=d(x). That’s right, the relation between worlds of existence is analogous to the relation between dream levels. Philosophically, it makes sense, in terms of the derivations of spontaneous actions from the unconscious. The factor that the power rule tells us to bring around represents closely the shift in apparent time speed, although in this case it’s by factorials rather than powers of 2, but both of these functions show the correct exponential growth of time dilation in deeper dream levels. Knowing this, it can be seen that entering a dream is not just inception, but also integration—integration of our secret emotional reserves into our interaction with the world around. The world of “1” is thus distinctly different from dream worlds, because attempting to derive the source of entering the f(x)=1 world leads to death (or perhaps limbo, but see later), where more attempts of deriving are futile for change and integration from 0 (reincarnation?) leads to too much uncertainty for returning to where one was. The integral of d(x)=0 is just “C,” and who knows which world will be picked for you: 2? 9001? π?

Once a full connection is made though, the next thing to do is extrapolation. What exactly is limbo? Think about the delicate nature of how the process of transferring between levels uses the discrete package of a difference of “1” between dream levels. When the framework of meta-dream mechanics is sabotaged or vandalized, perhaps the error of inputting a fractional difference could occur. What does this imply? One could end in a world with a fractional exponent of x, and unless or until another such mistake occurs of coincidental fractional fix, one must wander this stack of functions related by integrals and derivatives. This is like limbo. Why? There is only mindless wandering here. Unlike the case with dream worlds of positive integral degree, looking down the dream stack reveals a well with no bottom. Differentiating again and again leads to worlds that are indeed one exponential degree apart, but there is no stopping at zero, no getting rid of the x in representation, and an infinite descent down the negative degrees. There isn’t really any dream level more dreamy than another now, as they are all infinitely far from any world that can be distinguished as reality. All the worlds are equally dreamy: it is dreams all the way up and dreams all the way down.

But what if this, instead of representing limbo, represented an alternative structure for a universe over the parameter of dreams? It shows that perhaps there isn’t really any reality (which I could talk about more but would be tangential here), thus in some way nulling the meaningfulness of the distinction of a world as “dreaming.” That would be a pretty weird alternative world, but one worth thinking about.

Yet we could extrapolate further. Consider each function as possible of representing a world in reference to dreaminess. What happens in an f(x)=sin x world? In that interesting hypothetical world, entering a dream consecutively four times leads you back to where one was—a cyclical dream stack. That is a possibility that deserves some thinking as well. What about an f(x)=e^x world? A dreamless world? What does integrating in f’(x)=1/x to f(x)=ln|x| represent? What would doing these things in polar coordinates represent?

And most importantly, what do all of these imply about the juices that mold life and its meanings and properties—the elusive top that has been spinning in the minds of humans for millennia?


So as we all know, QWERTY is pretty inefficient. Incidentally, it’s actually by far not the most painful layout possible, so I made a personal attempt to produce a truly egregious keyboard layout. In this keyboard, I tried my best to put the keys in the most unbearable positions possible. Try typing (okay, maybe hovering your fingers over the keys to represent typing the keys) something using this keyboard layout, like perhaps your name, or a quote you like. Enjoy the torture.

On the Boredom Problem

When I was 5, my parents introduced me to the concept of death. Yes, I was very frightened, because dying sounded very scary (you literally just end and then you can do nothing afterwards)—more scary to me apparently than to other children. In fact, it scared me so much that I started trying to find all ways possible to prolong death as much as can be done, yet grieving over the fact that it must eventually happen. When I was 10, however, on a day in February in 2005, I was in the bathroom thinking and reached some dramatic conclusions about life, the first of which was the realization that death is a great thing. Without death, we will suffer the alternative, a never-ending consciousness of the world which eventually intuitively will get painfully boring and miserable. But then I realized that death is the equivalent as well (although, thankfully, we won’t be conscious of what’s happening, although I was worried where our consciousness goes after death), and I reached a horrible dilemma that haunted me for two years: both death and living forever seemed like abysmally bleak results—are we completely doomed in this world?

As I said, the problem was painfully in my mental back burner for two years before I finally reached a comforting conclusion. I realized that a more concrete explanation of the problem with death is that it is actually foreverness in a sense—one is in the same boring state with no end in sight (or, heck, in reality). The source of the problem of both cases is the eventual settling to an unwanted existence: boredom is the actual greatest enemy of the conscious. But this boredom seemed inevitable until I discovered that there is a possibility of an alternative.

Here’s how the alternative comes about: imagine the set of the decimal numbers. Death can be represented as a terminating decimal—for example, 4.62—the 2 marks the point of death after which the decimal halts. Non-terminating life can be represented as a repeating decimal—for example, 3.33333333333… (I mean 10/3 in decimal form)—there is no end to the series of 3’s. First, we can notice that this confirms the notion of how death and non-terminating life are related in boredom: the 4.62 is actually 4.6200000000000…, but 0 represents nonexistence. In both cases, the problem is having to deal with something with no end in sight, a horrid prospect.

But more importantly, we can finally be consoled that there is a third path, as there exists irrational numbers. A π-life would not have these horrendous issues. Of course, it was hard for me to imagine what such a life would be like, but the analogy was strong enough to convince me and finally have some rest in the part of my brain that until then was continuously stomped on by this problem. I was relieved even though this dogma is highly unrealistic (although later, when I was 15, I found an alternate theory that is as convincing of relief and already is in place in the “real” world). But of course, as you probably know, when picking a random number, chances are it’s irrational.

In fact, if you put the mathematics aside, think for a moment: the world contains irrationality after irrationality. Can you imagine how horrible life would be without them?