Forgiving Us
Dynamical Systems and you and I
Reality exists outside the realm of time and space, and there was love. Maybe, I am finally out of my mind — maybe I had too much granola yogurt for breakfast at the temple — too much of ascetic and hermit life has perhaps forever doomed me to a life of endless contemplation and no real action, but hey, I am writing this after 11 hours of meditation today, and I feel nothing but deeply grateful to be alive and typing this up at this moment.
Before discussing the spacetime, yeah, I admit — I have been deluded enough to think that I could be some kind of harsh and uptight dharma for someone when I was the one that needed a dharma the most (I did go to the dharma talk today and it reaffirmed that I cannot be an overbearing dharma).
Well, here’s some mathematical physics I picked up at Brown haha. Think of dynamical systems — the phase space. Basically, make a 2D plot that shows every possible state of the pendulum — every possible thing it could do in one graph. On the x-axis, plot the angle of the pendulum, and on the y-axis, its velocity. Each point would be a unique state of the system and it will tell you the behavior of the system over time. The angle — x-axis — would measure the angle it makes with the vertical line, and the angular velocity shows the rate at which the angle is changing and in this phase space, any point (θ, ω) shows a state of the pendulum. If the pendulum has friction, it slows down and stops — drawing itself inward and making slower swings, reaching the final state at rest to the fixed point at the fixed point attractor. The closed loop, however, makes periodic and predictable repeats. Each point uniquely identifies the complete state of the system — and the demon has also summoned — all the Laplacian future is predetermined for you.
See Lorenz’s system, it has a sensitive dependence on initial conditions. There are three variables and plot the phase space in 3D. Take any point and see how it moves. They evolve together so far but start to diverge. They start from close points but end up in totally different trajectories. This is also completely deterministic — as long as you put the exact same initial conditions, you will end up with the same end result. Well, you know, very simple cases like tiny causes like a flay of butterfly’s wings in Brazil could have huge effects like the setting of a tornado in Texas. This means even tiny and insignificant choices I make now as a dumb 23-year-old can have huge consequences in my life. Does this not mean that I am forever doomed? If that’s the case, then I need to make sure that every single thing I do need to be right somehow (then I get frantic about, making the right choices, looking for the source for it, scouring for the answer) so I can prevent some huge regrettable future events. Then you start following the right tracks, listening to all the right people, talking to the right mentors, meeting the right person for a successful partnership and marriage, and getting on the right track that you ought to be on. Because there’s one right thing to do. In that case, I cannot allow any room for mistakes!
Then I kneel and pray, O Bodhisattva, what’s the best possible way to optimize my life to securely set up for the future me? Because there’s a great amount of fear of lagging because you’re marked for eternal punishment or determined to meet by tragic fate. And it’s all you, your fragile nature, that’s the problem, and cannot make it because you’re the issue. Then I murmur, O dear Laplacian demon, please spare some clemency.
They all say yeah, things are pretty determined by the time you hit the age x, but does life follow laws of motion and universal gravitation — like how Newton has foreseen? Laplace’s demon has all prescribed you and your future events for you and if the superintelligent being has all the malicious things planned for you, you might as well surrender to it and see the ugliness and injustice around you be as it is, because it’s just how it’s meant to be. Everything is fixed, you are bound to follow the cosmic rules, and if not, there’s a preordained failure awaiting you. You know that you will end up in a completely different final state, and you got to make sure to study the right subject now that will somehow bring you happiness ~30 years later like the cozy 401k or stock options waiting for you.
But, Lorenz’s system is deterministic but unpredictable. It’s tricky to predict the weather more than a week in advance even with supercomputers. Then there’s a set of predictions of all possible courses of temperature changes and movements of hurricanes and such. Chaos puts fundamental limits on how far we can look into the future. Then what the heck, let’s go and eat tons of red meat, because, it tastes really good and why would I care what happens to me or to the environment?
There’s a whole bunch of different initial conditions but observe their evolution. Initially, the motion is messy but soon moves towards or onto an object — an attractor that looks like a butterfly. All the paths never cross like a closed loop or they never connect to form one. Hence each path makes an infinite curve in a finite space — and there lie fractals. These unique structures illuminate how the smallest things are necessary components of the greater whole — something analytics can easily overlook. If magnified it could go on forever and ever. You zoom in, and boom, there’s an elaborate and complex structure.
Cauliflowers (my favorite veggies!) — look closely at the hypnotic fractal spirals — you can measure and measure and measure. Each time you’re closer, it gets bigger down to very very minuscule distances. Look at the gorgeous coastline of these lakes, and try measuring the distances. The closer you go, the longer measurement you are going to get. There is no straight trend and there’s an interesting structure in every corner you would look.
Fractals remind you, that you must consider actual random processes with few inputs to fit the data to yield a degree of understanding. Rather than taking calculus, taking a smooth derivation of lines, take Mandelbrot’s thoughts and come closer and look at the finer details of the thing you’re modeling. A rough and overarching estimation won’t cut it.
Acts of God — we cannot put aside and that lies the crux of the problem. Self-affine nature doesn’t take into account of that. In the face of adversity, man finds it hard to escape oscillating between overestimation and neglect. The unrelenting faith in the invariant and identifying stationarity and scaling show invariances with respect to translation in time and change in the unit of time.
Stationarity is if shift in time does not cause a change in the shape of the distribution — mean, variance, and covariance would stay constant over time.
M 1963 fractal model — the price variation must be discontinuous within every interval of time. And other fractal models mix continuous and discontinuous variations. The parameter α determines the state of continuity. It shows that concentration is mostly due to isolated discontinuities — like periods of market turbulence.
You might feel the same, but I did not see any of this happening exactly a year ago. I was too fearful of the Laplacian future which led me to my distasteful attitudes. I am sorry, because now I think this conception engrained in me has negatively affected so many people around me. Foolish me now realizes that what governs our perception is so illusively entangled in a web that we (or those who have not become Bodhisattva) cannot clearly discern what’s actually going on with all the interpretations. I, too, have been gravely suffering from and many times clouded by delusions. Foolish me is late to realize just the very essence of all of us is joy and love.
So, this is all to say, the invariant you and I experienced will come to fruition and we will flourish in our prospective ways. I will take in my heart to bring kindness and gentleness wherever I go next. It seems like, now that I have a better understanding of this intricate structure, that you were the dharma for me, not the other way. Thanks for this lesson, and I will keep that in me tightly. For that reason, there’s nothing I can send but a bounty amount of gratitude and love. I realized today during Zazen that much resentment I harbored towards you in me has turned out to be just deep sadness and grieving a grave loss on my end. But I have let that go, and now I only see gratitude and compassion for you. I understand now, and I forgive us — and it seems to me, that I and, hopefully, you too, can finally see the reality outside the spacetime with pure love.