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 you would never have imagined you were able to retain can help you understand life better in the future.

He called this inspiration, and I indeed think about that lecture nearly every day. Then he shared with us one of the secrets of the universe, a concept loosely termed scaling invariance over a metric space, 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 tool 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 or concluding that you cannot now and will not ever understand it because a lot of intelligence is convincing your brain of its own immense power, then using it positively towards yourself and those around you. 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.

-BB