Roots, Branches and Offshoots — Derivative
An expression representing the rate of change of a function with respect to an independent variable.
Some phenomena are not about themselves. They take you one level, one dimension down into the substance of things, they are measurements of change, gauges of the inner workings of the world, consequences of movement.
Every atom in existence is a player in a giant set of games of variability. Imagine the collection of all of these games as threads, clusters, and fabrics. These threads of things happening, let’s say, are not even, they display changes in speed; they have lumps and thinnings; they stop and change direction, they soar, plummet or disappear. Their changes imprint a secondary metric into our world, a measure of variability, a smoothing over of its irregular nature. These measures show trends and directions, they clean the world of detail to reveal only the impulses of motion. They are diagrams of change.
Take, for instance, the line of highest slope. The water always follows it when it flows down the hill. Or the line of lowest slope. A donkey will always find it when it carries burdens up the hill. These lines are not obvious, they are abstract measurements of the change in incline and they only become visible when the water, or the donkey, reveals their existence.
You will say to yourself that it is not reasonable to guide yourself by the wisdom of lesser things, and that is a vanity of human thought, which deems itself the arbiter of things only because it gathered a few droplets from an infinite sea of knowledge constantly refreshing itself.
There are no lesser things, and there are many respects in which the donkey is wiser than you. The wisdom of the donkey is also part of the larger game of life, for which it received different tokens to play than you.
We are not unchanging entities either; we are not like earthen pots, which once shaped and hardened in the fire are no longer subject to the motions of the world. We are tentative stems that emerge and grow and move and transform.
We always wonder why a thing happened to us, or why life favored one way instead of another, and we do not understand that we obey the same rules as the rest of creation. Everything needs energy to keep going and when it depletes its supply, it stops.
If you understand the underlying rules of these secondary measures of motion, which run flat when things cease to change, it will become obvious why every time your life doesn’t seem to change anymore it is approaching either a summit or a bottom.
We all know these things in our gut and take them for granted, we have feelings of elation or foreboding we can’t explain to ourselves, but which most of the time emerge from our awareness of these change measurement undercurrents that run through everything.
We all know instinctively that accelerating change leads to untenable outcomes.
There is no such thing as an infinite soaring or an infinite decline.
Infinite expressions don’t feel at home in the world of matter. This world needs ebbs and flows to stay on course and it can’t function when changes start happening faster and faster. A wheel rolling down an endless hill will eventually gather such momentum it disintegrates all on its own, even if no obstacle hits it. The unlimited increase in its speed reaches the inner workings of the wheel, those things that keep it together, and forces them into motion too.
In the same way, speeding up towards progress, which in the human heart reflects as hubris, brings people to emotions and situations inside which they can no longer function. It is as true for the things unseen as it is for the visible portion of the world. These points of extreme, where things become too fast, too far, when there is no limit to the building up of speed, break the fabric of existence. They create holes where reality should be. They are places where things no longer work as expected and where life can’t thrive.
There are a lot more laws to existence than those that we know, and these laws are consistent and inexorable.
One of these laws is that any coherent mechanism will self-regulate, refusing to allow local disruptions in its inner workings that could end up in the breakdown of its function.
Existence is such a mechanism.
It puts a limit on these sharp peaks and smooths them over, so they continue to be gentle waves and folds in the fabric of being, rather than rips and holes: all soaring civilizations experience decline, the stars that burn too hot consume themselves to nothing, there is no unlimited love, or unlimited pleasure, or unlimited fervor, every emotion slowly dampens itself in a series of diminishing returns.
Expect this to happen in your life, we amass so much misery while yearning for impossible things!
I can’t say this enough: life is motion. Ideals are gauges of that motion, among many others, instances at the top of a range. They are like temperature readings: just because you can measure the temperature at which the water freezes that doesn’t mean you can stay in it indefinitely.
A couple more things before we stop for questions.
Sometimes the footprint of subtle things is more obvious than they are. For instance, you can’t track the warming and cooling of every gust of air, but you can infer those changes from the stirring of the wind. You can assess the speed and the steering on a boat on the open seas just by looking at its wake.
You can tell winter is coming just by noticing how soon the plants go into dormancy.
All living and non-living things have tokens to play in this large game of existence, and these tokens are very different.
One that us lucky humans get to use is the ability to interpret the moves of other players, human and non-human alike.
Second, there are things that only change because they are tethered to other things: ocean tides to the moon, deserts to movements of dessicate air, lush forests to rain. They wouldn’t exist in the absence of their nurturing factors. We are such things ourselves, we wouldn’t be here if it weren’t for sunlight, water, air, an environment that offers us sources for the energy we need to keep going. We are consequences, corollaries of the rules of a larger game, which involves celestial bodies, forces and fields independent of our understanding, and which have been in place long before we came to be, and longer still before our eyes were open to their workings. It is a good way for us to stay humble and not presume ourselves to be the wake that moves the ship.
[This portion of the manuscript, together with several others, was sent to an independent agency for authentication, because the instruments we had turned out inconclusive results.
This imposed a one year break in our research, time we endeavored not to waste by immersing ourselves in a thorough study of the rest of the documents.
Our efforts were not in vain.
We discovered alternate interpretations for the remaining text which wouldn’t have occurred to us did we have to allocate time to the unavailable portion of the manuscript.
These interpretations become obvious once gleaned, and they make us wonder whether there might be other things we missed, because of a superficial reading of the work.]
Questions.
How is the knowledge of the variable speed of change useful?
It always pays to notice when things speed up or slow down, especially if that happens over a stretch of time, because they point to a peak or a trough.
This is true in fields you wouldn’t normally consider, like fortune, favor, inspiration, stamina.
It is also a good thing to know that, short of death, your circumstances won’t evolve towards an infinite outcome in either direction.
You can track these changes in yourself and in your surroundings, and both circumstances yield useful information.
Another use for this second metric, which is often more obvious than the truths it derives from, is to help you understand phenomena that seem to have no rhyme or reason associated with them because the rules of the game they are part of are outside your reach.
For instance, you can trace the movements of the things unseen through this, our lower reality, by the traces and the footprints they leave behind. Sometimes we can’t see things in their higher dimension, but we can see the changes in their motion, which, as I said, are always one level, one dimension down.
Let’s say you can only see things that live inside the piece of paper in front of you. If I place this goblet on the paper, you will see a circle. If I could press it through the paper you would see the circle’s circumference change with time. Now, there is no such thing on your piece of paper as a circle with variable circumference. You can never see the goblet, because you don’t have the senses with which you can interpret it, but you can interpret the varying lengths of the circle radius by representing them differently and suddenly you get an elevation of the goblet, a clear picture of an object that can not exist inside your world, just by tracking the changes in its footprint.
Can I give you examples of such things?
Sure. Take this lens and let sunlight run through it. A ray of light comes in and a rainbow comes out. You didn’t know that light and rainbows were the same thing, because you couldn’t, possibly. You can never see light as a rainbow without the instrument that bends it so much it makes its strands unravel. Also, this bending only happens when you hold the crystal at specific angles. If the only information available to you was a static image taken at those angles, you would never think of light as white. But you can change the angle and thus understand that there are intrinsic properties of light which you can’t see, and its different appearances are all reflections of the same governing law.
[We can see another version of the optical illusion of the three dimensional rose at this location in the document.
The trompe l’oeil of this sketch is inescapable, from any distance and at any angle. Sadly, the drawing technique is still puzzling the experts and will remain shrouded in mystery for now.]
What if you don’t care about light and rainbows? What does this concept have to do with real life?
The same principle described above applies to all the things shaped by unseen rules: the workings of society, love and relationships, the gaining of a skill.
Can I be more specific? Mastering a skill takes a long time during which your proficiency in that skill increases, which encourages you to work harder to improve. After a while the amount of work becomes disproportionate with the increase in skill, which means you are approaching the top of your range. You stay there for a while, but there is no incentive to work harder, because you can no longer improve. You have accomplished what you set to accomplish, and after enjoying your skill for a while you start losing interest in it, and as a result of your lack of practice your skill wanes.
Does this mean you will always abandon your current interests in search of ever changing ones?
No. It just means you should pick an interest complex enough it can keep you engaged for the length of your lifetime. This way you risk having your life run short of the top of your range, but this is a better problem to have than its opposite.
Can you manipulate the higher dimension by changing things one level down in its rate of change? I have to confess that I never contemplated the possibility.
Could you, for instance, cut a crystal in such a way that no matter where the light comes from, it always enters it at the angle of your choice, and live inside that crystal? If you did that, in theory, all light would come out rainbows for you, no matter what. I guess the answer to your question is that you can’t change the laws that govern the higher dimension, but you can shape your own experience of those laws, and that may be enough for you.
Come to think of it, we experience this all the time: parallel lines don’t meet at the horizon and things don’t get smaller as they get farther away. We change from infancy to old age, but we always think of ourselves as the person we are in the present.
We pay no attention to the movements of things that happen inside time frames significantly different from our lives — the shaping of mountains, the movements of plants, the intricacy of a raindrop.
We all live in a reality warped by our senses and the speed of our life, one that eliminates the details we can’t use.
[This page ends with a series of symbols, which seem to be components of a language, but which match none of the writing conventions we have encountered so far.
They are combinations of only two elements: a circle and a line.
It was beyond our ability to interpret the meaning of the script. We can’t tell whether the pictographs represent words or phrases and there aren’t enough symbols in the sample to yield any discernible patterns.]
