I remembered my abstract dream-ideas from last-night (perhaps only seconds before actually falling asleep) and then re-remembered them again while eating my soup. This is the result.
WARNING: There are many, many flaws to these ideas. I am well aware of this. It’s all complete nonsense, forcing ordinal notation into some quasi-philosophical/spiritual setting. However, I nonetheless found this a lot of fun to write. For whatever weird reason.
Coordinates of success
We can think of our lives as being on different ’levels’ on a scale, or equivalently as different y-coordinates on a graph. Perhaps an “unsuccessful” man (according to some arbitrary standard) is on one arbitrary y-coordinate (e.g. y = 3) but a “successful” man is on another, higher y-coordinate (e.g. y = 9). In general, such men can be represented as y = c, where c is some constant. To people who share this standard of “success” it would seem that climbing as high as you possibly can on this scale (i.e. y = [some huge number]) is a suitable life-goal.
Let’s assume, for example, that the scale represents material luxuries. Owning a nice watch may bump you up a few levels on the scale, as would owning a large house or having a shirt made of gold. Being homeless, not having a watch or a car, etc. could be represented on the scale by lower y-coordinates.
Please note that this is just an example. The other values I list (such as experiences, learning, creativity, etc.) are also just examples given to illustrate the point. The choices of examples are not part of the dream-thoughts, they just make it easier to illustrate where I was coming from.
However, some people may reject this standard of success, they may value something that does not fit neatly on the scale. Perhaps, following the previous example, owning more and more luxury items doesn’t appeal to someone as an end-goal. Such a person may instead value experiences.
The diagonal men
On a graph the experience-valuing man may be represented as y=x+c, for variable x and constant c. Graphically speaking, they are no longer a single coordinate, they are now a diagonal line. They may nonetheless be seen as existing on some fixed, finite point of existence by others. This works mathemetically, for example if we let x=4 then for a man existing as y=x+2, we may see y=4+2=6.
However, God understands the experience-valuing man better than that. He knows that the y=6 manifestation of this man is not the full story, and that below the surface this man is operating as y=x+2. What ‘x’ manifests as is arbitrary and of little importance. In maths we would not reduce a diagonal line to a single constant that it passes through, so I do not believe that God would judge the experience-valuing man according to just his material conditions.
If you’re comfortable with using transcendental ordinals, then you could say that they are on ‘Level ω’, where ω is the first transfinite ordinal. They have transcended all finite levels, and whatever finite level they may be percieved as being on is just the result of an arbitrary, meaningless diagonalisation.
Is there not a hierarchy of experience-valuing men, as there is of luxury-valuing men? Of course there is, and more successful men (according to a standard that values experiences not luxury) could be represented with greater values of ’m’ in the context of y=mx+c. The positive ’m’ constants could represent the richness and varieties of experience. Graphically speaking, these men are represented by diagonal lines of sharper gradients. The ‘c’ term only affects the material conditions a man may manifest in when an arbitrary value of x is substituted into the equation, and is therefore irrelevent to this hierarchy.
Other polynomial men
Some men may see both constant (material) and linear (experience) values as superficial, rejecting both in favour of something more profound. In the material vs experience example, these men may value learning. To the men who place value only in learning, material conditions are ultimately unimportant, as is the richness of experience.
These men may be represented as quadratic equations (i.e. y= ax^2 + bx + c for positive constants a,b and c), or as existing on transfinite Level ω2. Graphically, these men are represented as curves, rather than as lines. Like how the diagonal lines pass through infinitely many y-coordinates at a fixed gradient, the curve passes through stages of infinitely many gradients. The curve may be described as being at some gradient (2ax+b), but this is entirely dependent on an arbitrarily chosen, circumstantial choice of x.
The quadratic men may still be represented as having their own hierarchy by increasing ‘a’ constants in the contexts of y = ax^2 +bx +c or Level ω2+a This constant ‘a’ could represent intelligence or quality of learning.
We can continue much further. Some men will reject the quadratic (learning) values and find higher values representable as cubic polynomials, or Level ω3+a. Perhaps this value could be ‘power’, again with another hierarchy. A higher value-system still, one that transcends basic power-seeking (perhaps ‘creativity’?) could be represented as a quartic polynomial, or Level ω4+a. A higher system still, that transcends basic creativity (‘freedom’?) could be represented by a quintic polynomial, or Level ω5+a. Beyond that, we could have ’nobility’ or ‘honour’ as Level ω6+a.
As I said earlier, what value-systems, moral-characteristics or behaviours we attribute to this model are arbitrary. You may consider ‘purity’, ‘friendliness’, ‘humour’ or even ‘sexual attractiveness’ to be more fitting value-systems to assign polynomials to. It doesn’t matter.
The time analogy
If we imagine x to be the passing of time, then we could say that the material men are stationary, competing to be the furthest along the track. Meanwhile, the experience-valuing men are running, each at constant rates, each competing to be the fastest-running man. They do not care how far along the track they are, they just want the thrilling sensation of speed. The material men may feel ‘better’ than them for being further along, but they are not understanding the experience-valuing man’s game.
The learning-men are not interested in being the furthest ahead, nor in travelling at the fastest speed. The learning-man is competing to have the fastest acceleration. Imagine a sprinter practicing his starts. That is the learning man. How fast he can run is not important, what is important is the acceleration: how quickly greater speeds can be reached. The experience-seeking man may be running faster than the learning man at a given moment, and therefore feels that he is doing ‘better’, but he is fundamentally missing the point of the learning man’s exercise.
By the way, for the cubic case (the power-seeking example) the time-equivalent would be the differential of acceleration over time, known as JERK. So the most powerful people in the world will just be constantly JERKING. While the thrill-seekers rocket down the track and the learners practice, the truly powerful BIG BRAINED folk will be sat there, jerking. The lower people will think they are losers for not being as fast, nor as explosive in their acceleration. Haha, the fools, they will never understand the transcendent, incomparable importance of jerking it. All day long, constant jerk. The most powerful men are those with the greatest jerk-strength (‘a’ in the context of Level ω3+a). Similarly, creative people are those who learn not how to jerk more, but how to jerk faster and faster.
That’s all that this squid-ink has been building up to. 🤡 Why aren’t you laughing? I suppose we can continue, but the funny bit is over now.
This time analogy is quite fitting if one thinks about eternity. If we assume that in the afterlife ‘x’ will eventually increase past any arbitrary point, then we can say that all learners “eventually dominate” (using a googologism) all experience-seekers in value, and all experience-seeks will “eventually dominate” all luxury-seekers. Similarly, better learners will “eventually dominate” lower learners, regardless of their richness of experience (x term) or material conditions (constant term). This pattern holds generally: anyone higher up the transfinite “Levels” system will eventually dominate anyone below. If we believe that God will judge us, then maybe it would be useful to think in terms of which behaviours “eventually dominate” which other behaviours?
Transcendence as a goal
Okay, so what if the men in our model become aware of a well-thought-out hierarchy of value-systems, and therefore start studying higher-value systems? Such men would have the meta-goal of adopting new goals that transcend lower value-systems. I suppose we could model these as exponential curves, y=a^x, or really any other super-polynomial functions. These would fit nicely on Level ω^2+a of our transfinite levels-system.
But is transcendence really the highest possible goal? Are there not, somewhere, higher values (that we perhaps do not have well-known or any words for, but float around nonverbally in the minds of monks)? Maybe, but surely the question is only being asked for the sake of transcending the goal of transcendence, which is in fact limiting the deepest, authentic goal to just transcendence. We seem to have hit a ceiling.
Now, I would love to take this idea further and extend this system deep into the ordinals. Indeed, when I was sleepily dreaming these thoughts last night, I was happily wondering what a Level-ω^ω, Level-ε0, Level-Γ0 or possibly even Level-BHO man could aspire to. But I don’t think that such an extension would make sense, as transcending the transcendent values would really just make one better at transcending. There is of course a hierarchy amongst men with the goal of transcendence, but this can already be addressed in the Level-ω^2+a model by increasing the constant ‘a’.
Maybe it is possible to have a goal that systematically transcends the polynomial-tier value-systems without valuing transcendence in itself. We could crudely call this ‘religion’, but then I fear transcendence could be stuck just one step above that. Maybe ‘religion’ could be somehow be divided into sub-values like ‘piety’. I don’t think that this could be stretched very far at all, but maybe hypothetically these values could get deeper into the ordinals, maybe justifying something crazy like a Level-Ω designation for transcendence. I think that this is VERY wishful thinking, and that in making such stretches I would just be hoping for an excuse to play with more infinities rather than actually saying anything. This article is barely saying anything worth reading as it is!