Humans are the most skillful problem solvers. It’s the trait that has placed us at the top of the food chain, the trait that will help us conquer space in the future. Yet, one problem remains unsolved. The most fundamental and essentially the only real one:
Creating a system to solve all problems.
Creating a perfectly consistent algorithmic process that can explain all there is and their relationship with each other. And before 1931, that seemed possible.
Everything Contains Everything
Where does one begin to find the ultimate truth?
Before our logical abilities allowed us to question and investigate our reality, we rested blissfully in a state of ignorance, knowing God was the answer to everything that eluded our primitive deductive reasoning. But human nature is meant to commit hubris in the face of authority.
We rejected the mystery of the unknown and the determinism of our sensorial perception. Instead, we accepted the fact that there’s a system that explains everything. That means we can take any “one” thing, break it down to its core principles and explain the world.
It was the starter pistol that triggered the longest race humanity has ever witnessed; the race to the truth.
What do music, chess, and dancing have in common?
On a surface level, nothing. But in reality, there are common themes and underlying mechanisms that give different forms to the same axiomatic principles. These are closed systems, essentially models, that encompass the content. Our intelligence will work the same way, take the same steps, but adapt to the unique structure of each form.
The reason Bach’s counterpoint compositions don’t allow for augmented intervals, the French defence works against e4, and the Cecchetti method fits beginners better is because, in this case, the truth is performative. It’s “empirical”, tried and tested over many years.
There’s a big difference between knowing and experiencing the truth. Mastery is about the latter. It’s the “Ichigyo-zammai” of the Japanese, the “meraki” of the Greek, the “by the bootstraps”-mentality of the US, the “meditation” of all religious practices.
Whatever you do, commit to it. And you’ll hopefully begin to experience the universal truth through the mechanisms of your intelligence. Using our previous example, we can already sense there’s a Universal Law that governs these 3 seemingly unrelated disciplines:
- Contrapuntal lines are based on contrary motions and independent melodies. This harmonious clash is what creates music
- Chess is about white vs black. Tactical massacre that results in ingenious strategies
- The back and forth, the tension and relaxation of the bodies is what produces the elegance of dance
Opposites, Ordo ab Chao, As Above So Below.
But the question remains:
How can we translate this intimate understanding to an objective statement or theory? It seems impossible! We’d have to define and potentially prove the very axioms that encompass our physical reality. Instead of going inwards, we go outwards.
The Theory of Everything & God’s Hiding Spot
Even though the 20th century was marked by two World Wars, the first few decades were one of the most optimistic time periods for science. Discoveries abound. New theories emerging left and right, hypotheses becoming theorems, applied physics lending credibility to abstraction, revolutions manifesting.
A Theory of Everything, a coherent theoretical framework that explains how all the forces in the universe interact with each other, seemed possible. Merely abstract concepts of philosophy acquired flesh and bones, sparking the self-realization of humanity. What was simply ideation became a dialectical discourse in reality.
An undercurrent of mathematicians began an Icarian journey against infinity; prove consistency and solve paradoxes.
But you know what they say about plans and the divine…
1 + 1 = 2 and Hilbert’s Second Problem
360+ pages were committed in Principia Mathematica to prove this simple arithmetic sentence. But a high school student could easily prove this in a couple of lines using just a few algebraic manipulations. The difference is that Whitehead and Russell, the authors, attempted to define and formalize everything:
“1”, “2”, “+”, “=” and their relationship.
Mathematical logic was born out of necessity because of the paradoxes that were emerging in Cantor’s set theory (see Russell’s Paradox). We were quite literally trying to escape axiomatic tautology and create a logical world without an immaculate conception of said axioms. Building reality from scratch.
Principia Mathematica looks like badly written code. All mathematical logic, including Wittgenstein’s Tractatus Logico-Philosophicus, is based on linear consistency. Consistency is the cornerstone of mathematical validity, but nature tends to operate with paradoxes and opposing forces. Are these paradoxes real or do our original set of axioms necessarily create them?
In 1900, during the International Congress of Mathematics in Paris, David Hilbert announced 23 problems to progress, expand, and solidify the field of mathematics in the next 100 years. Intentionally, the German mathematician steered many of his contemporaries towards mathematical rigidity and consistency.
“The compatibility of the standard axioms of arithmetics.”David Hilbert
That’s Hilbert’s second problem, a hypothesis that hopes to encapsulate all the “math” we know under a certain set of axioms. With that in mind, everyone set out to solve formulas, prove hypotheses, and formalize logic thinking that the solution was hidden in their minds. But in 1931, Kurt Gödel’s incompleteness theorems halted the Race to the Truth.
“In mathematics there is no ignorabimus.”David Hilbert
With this line, Hilbert described the Latin maxim “ignoramus et ignorabimus” (we do not know and will not know) as a pessimistic attitude for acquiring scientific knowledge. Sadly, everyone’s worst fears proved to be very real when the 25-year-old Kurt Gödel showed that (1) every system will contain true statements that cannot be proven and (2) the system cannot demonstrate its own consistency.
In plain words, there will always be unanswered questions. And when we stumble upon a universal truth, a theory of everything or a philosophical absolute, there’s potential that we will not know it’s the truth. God has a nasty humour. Even if we find Him, we won’t be able to face Him. We won’t even know it’s Him.
And that’s the Original Sin. Thinking that we could know everything about our world. The punishment is the insatiable need to try forever, knowing that we never will. An exercise in futility, a war against infinity. But do we need to know?
Obviously, scientific advances didn’t stop when Gödel published his work. The world didn’t stop spinning. Humanity was largely unscathed by this fatal blow. Because human nature is designed to commit hubris. We’re designed to move forward, trying to reach divinity. The very reason we’re doing what we’re doing is precisely because we DO NOT know everything. We can only feel that there’s something greater underneath and above us.
Next time you’re about to enter the unknown, remember that there’s a very good reason you feel uncomfortable. And there are plenty of reasons why you should make the leap.
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