100 years ago Albert Einstein came up with the brilliant idea of representing the world as a four dimensional, infinitely-differentiable, pseudo-Riemannian manifold, with a metric tensor, obviously. It was an impressive achievement, of course, because it’s not obvious that this would work, because while all three physical dimensions are reversible, time itself is unidirectional, at least that’s how I see it.

But Einstein’s idea only concerns the physical world. There are more things in heaven and earth than are dreamed of in his physics and all those things are part of the world. So that begs the question, what do we make of the rest of the world?

Now Laurence Tribe, constitutional law professor at Harvard Law School, himself a former undergraduate student at Harvard math department, often uses those–what would be considered–esoteric terms and concepts borrowed from math and physics to explain the mechanism within constitutional law.

So I don’t see why I shouldn’t be doing the same. After all, “physics envy” is perhaps the strongest among modern philosophers.

The metaphysics of Jennifer Suzuki:

The physical world

Since ancient times people have concocted various ways to comprehend the world, and the most successful ones–well, the ones that survived to modern days–have always involved the separation of the world into a few distinct worlds, involving Heaven, Hell, different layers of hell, etc.

Those mythologies, folklore, and fables have reflected a greater truth, that there is much more to this world than what we see.

The world as I see consists of three distinct entities: the physical world, which is governed by logic; the world of ideas, which is the world formulated by the mind to comprehend the world, and the world outside the realm of ideas.

The physical world is what we consider to be the natural world, Nature, if you will. And the entire physical world is governed by logic. If it’s natural, i.e., physically possible, then it must be logical, i.e., deducible using logical reasoning from a certain set of axioms. This is very easy to see. Consider the contra-positive: if it’s not logical, then it cannot be physically impossible. Yesterday I forgot my key at the house. Because Aliens erased my memory and tried to abduct me. It’s of course not true, and it’s illogical. Therefore, it cannot have really happened.

But there is a limit to our logic. As Kurt Godel has shown that given any finite set of axioms, there would always exist propositions that cannot be proven to be either true or false.

We will probably never be able to reach the limit to our logic. Even if the progress of science accelerates at an exponential speed, limit can only be approached, but never be reached. That’s literally the definition of limit from, like, Calculus I.

So we will never be able to know what lies beyond our logic, and that is, what lies beyond our natural world.

The world of ideas

The world of ideas is embedded into the very definition of the physical world that I just defined. The world of ideas are the conceptions of the physical world concocted by humans to comprehend the physical world; they are like the continuous functions on a smooth manifold mapped from itself back to itself, forming a category onto itself. The world of ideas is always mapped back to itself, forming a feedback loop, like an automorphism, which, as you know, is another category, for those of you who is into category theory.

Without the world of ideas, we are blind, deaf, and mute, living like animals. Our ideas of the world informed us how to comprehend the world and which in returns catalysts our actions in the world.

The world of ideas itself is as boundless as the sea and just as deep. Anyone who thinks can formulate his or her own ideas of the world. But successful ideas are few. For instance, the idea that eating your own poop is definitely out there, but not many people practice it.

And in this world of ideas, logic is only secondary. While some rudimentary logic is prerequisite, the most successful ideas always do without it. Flip open the Bible, and you are bound to find contradictory passages in very other page.

In fact, in the realm of ideas, the more logical, and the more rational an Idea, the more likely it will fail. Marxism is widely regarded as one of the most well formulated, pseudo-scientific ideas to have ever been germinated, but it has always failed catastrophically. On the other hand, Christianity is full of contradictions, but it seems to have survived and fared well around the world. And so do many other ideas, such as “God is benevolent” or that “All men are created equal” or “live according to Nature.” All those ideas–if Kurt Godel were to examine them, and he did–are not perfectly logical, but they seem to be the most dominant ideas around the world and many people adhere and live by those ideas.

Of course one can freely choose to adhere to whichever idea he or she likes, because there is Will in the world of ideas.

In the realm of ideas, there resides also will. Without will, ideas will never be propagated and inseminated. Ideas and will are like the Killing vector forms acting on top of the manifold that is the physical world. I use Killing vector form because we assume, like Einstein, that our world is a pseudo-Riemannian manifold. Were we living in a projective space, I would have used affine vector field, obviously.

Ideas are like the points on this manifold floating in mid-air, not going anywhere, and Will is like the group action that pushes this point around the globe. Without Will, Ideas stay stationary and motionless.

The world outside the world of Idea:

This world that I have just concocted is my Idea. I have imagined their existence. I have imagined the existence of this pen and this paper, as Jean Paul Sartre would say. I have imagined the existence of all the people who are reading this little philosophical treatise. Without my imagination, none of you would even exist, subjectively speaking of course.

This world of my construction is running in parallel with the physical, objective, natural world. It is somewhat connected by logic, at least when the world of my Idea is applied purely to the physical world, but logic becomes fuzzy when the world of my Idea is applied to itself, that is, when it interacts with other ideas through my will. It is not always clear that logic is useful.

But then, what is outside of this world of ideas?

The world outside the world of ideas is wholly without logic. The world outside the world of ideas does not adhere to the rules of the physical world. The world outside the world of ideas is the world of the poets; it is the world of our raw desire materialized.

The world outside the world of ideas is the world of puissant energized sexuality, deepest hatred; seething, murderous passion, and dreadful abyss.

The world outside the world of ideas is not visible to the eye, but will without eyes see pathways to its will. The world outside the world of ideas is tyrannous and rough in its proof. It is what one will find more often in Greek tragedies and East Asian horror tales.

The world outside this world of ideas is like the ocean bubbling underneath the Dirac sea, the Dirac sea being everything we can see on the surface of this physical world,and like a bubbling cauldron, ghosts, sparks, frogs, vermin, baboon’s blood and lizard’s leg, and many many other things constantly emerge onto the surface from the cavernous undersea terrain. The world of ideas and the world outside of the world of ideas have porous boundaries. Carl Jung might call it the Unconscious, Freud might call it the Id, neuroscientists might call it the Lizard brain. Those are their ideas, but to me, it’s simply outside the world of ideas, things that we cannot rationally and logically comprehend, and for me, this world is the most important, because it’s so mysterious, so forbidden, and yet so entertaining. It’s full of intriguing sexuality and romance, blistering emotion and raw sexy feelings.

All our thoughts and ideas are mere shadows of this world, much simpler, darker, and emptier.