scale invariance

On recycling

(Or on the risk-mixinfinitum problem of metaphors and entropy with damping)

Life is or is not or it may be a can of let’s be healthy and say sparkling water and already this is unraveling: open the top and there’s carbonated liquid inside and gas escaping and the can remains a solid boundary for the liquid but the gaseous liquid is subject to complex dynamics and the bubbles are pretty fascinating describing their movement and flow and thinking of Perelman’s description of deformations of objects at singularities like beads of water or universes meeting making grown adults cry probably in the mind-enhancing revelations kind of way to prove a conjecture over a hundred years in the making but kind of the homology the pockets of gas in a fluid some of which adheres to the solid boundary the fluid I mean and the evident fact that water can bead or bounce, roll and pinch on a solid surface on various solid surfaces and liquids more generally on solid surfaces like rain and jet fuel and additive manufacturing and ideally not fracking because not all applications are good for the world learning and trying to choose the good ones and defining good is as useful or more than knowing of them and gas can bubble in water quite randomly and life can form in or on deep ocean vents the randomness of which is a question wars can’t answer but the probability of which is small enough to require the spacetime of a dynamic universe…but just drink it already this life-sustaining liquid who cares obviously not really that dismissively but overwhelmed (and thirsty) and it’s gone the fluid the can is still there unsurprisingly hopefully and it’s a pretty interesting shape (aren’t they all): how to replicate it or even just the shape with a different material or why it exists at all then just twist and crush it that’s humanly natural proving sort of time’s irreversible orientation in the evolution-of-a-volume-element-in-motion-through-fine-grain-phase-space entropic way (hardly) and human ego and more like proving the ability to manipulate real objects human-made or otherwise requiring an application of the aforementioned evolution concept in reality and the scale-invariance of the theory and the responsibility that implies and don’t cut a finger by the way and recycle and move on but the can though crushed and more like a nondescript thin aluminumostly object that quite recently served as the container of a liquid volume and don’t forget some carbonation and can be viewed as a covering surface of a semi-cylindrical-like space or mesh and the canny-like peel can it be called a can if it was once a can and no longer appears to be this is not our problem but it is and that’s fine

Etc

Bb

Why 2 (or Self-Similarity; or orororororor……. ;)

I was fortunate to take an intermediate-level survey course in thermodynamics with one of the most influential scientists of the post-WWII generation, I mean this guy was at the center of research for combustion and fueling, kind of combining modern thermo and fluid dynamics, at NASA through the rise of the space age and jet propulsion. Early in the quarter he gave this lecture, just in a small class of 20 or so young engineers, that began with an explanation that while he can’t possibly fit a lifetime of knowledge into a single class over a relatively small time period, we should trust that we will learn plenty of the material deemed necessary to get good grades in the class itself by default if we just go to class and do the work.

What he meant was he would touch on topics that we weren’t prepared to fully grasp, teaching us far more than we would need to pass his tests. His philosophy is that the mind is the most complex closed object in the universe, and if we listened to him with an open mind, the brain has an incredible capability to keep knowledge stored away until it could be used properly even if it’s a decade down the road, and by implication the brain also has an innate ability to know when knowledge that I would never have imagined I am able to retain can help me understand life better in the future.

He called this inspiration, and I indeed think about that lecture now. Then he shared with us a tool to understand the universe, a concept generally termed scale invariance over a metric space in mathematical language, and he told us we might not fully appreciate this concept for a very long time, but if we remember to think about it and look for its representations, we will have an essential skill for understanding why things are the way they are. Scale invariance, or self-similarity, and ideas about connectedness or more deeply gauge symmetry or mirror symmetry and S-duality: these are essential properties that allow matter and energy to have structure at sub-atomic levels, and explains why this structure scales up to describe molecules and life and consciousness and planets and stars and galaxies.

In its most intuitive form, it’s the metric we define as distance or size in a given dimension, measurements we can make to determine how far away something is on earth but also how far things are in space; and then how can we define a radius of an atom or how solid ice takes up more volume than liquid water despite having the same molecules. It can go even deeper to relate to particle theory and gravity and spacetime, human memory and computer memory, dimensionality and rank of things called number fields crucial to encryption security; economic theory, human behavior, evolution; why there is no such thing as ‘zero or nothingness in the most general sense’ but rather different scales of infinity.

Now I’ve diverged from the actual point here, and that is: don’t worry about understanding all of this (I don’t) or concluding: cannot now and will not ever understand it because a lot of intelligence is convincing ourselves of our own immense brainpower, then using it positively towards oneself and others. True knowledge while we are here on Earth reduces quite nicely to human interaction, shared experience, happiness, kindness, altruism, empathy, compassion and all that good stuff. Society can make progress, but time scales as well and it took billions of years to achieve consciousness in real time yet we have the power to destroy the Earth many times over in an instant. It takes a lot more than money and people yelling at each other on TV or the Internet. It takes genuine cooperation and a mind open to dynamic adaptation and learning and filtering out noise and synthesizing experience.

It takes fundamental change in the way we think about ourselves and the world around us.

It takes unity and diversity.

-BB