The whole world, absolutely the the whole world can be classified into two groups. Now, read that sentence again and check out how "the" was repeated, and you didn't notice (Some, may even re-read everything again, just to check that I will not fool you again with the same cheap trick).
Are you mad that you fell for such a childish trick? I hope so. I am taking advantage of a particular trait your brain has: discarding redundant information. Cheap, I admit it, but it allowed me to put your brain into a recursive loop disguised as an inocuous paragraph. I am very proud of that paragraph, check it out again... Note that if you strictly followed the instructions it gives, you'd have no escape from it. Your brain had a bug, and it fixed it all by itself.
What just happened?
You made it here thanks to that other trait your brain has, the ability to break recursivity. Recursivity itself is not a bad thing. As a matter of fact, you could've broke it simply by not re-reading at all. That recursive phrase will remain there; iron casted into the blockchain; until another innocent victim comes to read it, or a hard-fork removes it as a whole: triggering and shuffling synaptic contacts in left and right, exhausting the circumstantial entropy of the victim... Feeding the eventual thermal death of the whole Universe that dared to give a chance to its mere existence. Which is a cosmic irony, wrapped up into an existential paradox... Or something like that, just In case, I didn't re-read.
We're so skilled handling recursive loops, that mechanism that allows us to create matryoshka, that are dolls from Russian origins, a migthy Asiatic country, that is a continent formed out of the supercontinent named Laurasia, after it separated from Gondwana, with 11 time zones, they all are within one another, with sentences of any level, that we can make our brains play with sentences as long as this one even when they surpass the length of our working memory. (HATE ME)
Recursivity ABC's
Now, when recursivity is based in a self reference, things can go wild. First, we need to understand "how it looks": It would be something like, you hear me say "I am Renzo", or the infinitely more interesting one "This sentence has thirtynine characters". Both are self referential and true. Let me warn you, there's self referential false sentences. There's even self referential drawings. Sometimes, even "Ideas".
The complexity of self reference shows when something that is neither true or false is claimed. Please, follow me towards the canonical example: "this phrase is false". Pure-breed self referential phrase, do not be fooled by its low profile, because it'll smack all your teeth off your mouth. Lets see: if what it claims is true, then the sentence is false. If it is false, then the sentence is true. There's no way the circle can be broken. It is, inherently complex, yet, simple (I warned you!). Take a break, let go of that ego your aunt always said you had too inflated, the same aunt that says that "your" science cannot explain miracles. Now, go and read that sentence again. it's true, it's messed up. But, there's no big deal... Unless it creates a problem in the center of math and physics themselves. In which case we should all start running in circles (no pun intended).
A monster, someone named Gödel created a self referential mathematic object. It refers to itself, but in math. and, yes, it is hard to imagine, but it is nothing else than the formal description of the problem itself. The analysis of the logic bug that led us into this conclusion: Math has a hole.
"Houston, we have a theorem", that creates a problem at the heart of math itself.
"Bullsh1t, how can that be possible?", would say someone that always assumed the idea of math as something incorruptible, pristine, ideal, infinite, immaculate. After all, it is a group of axioms and logic rules from which we build the largest conceptual skyscrapers, how can it fail? Well, yes, and no. but SOMETHING is wrong. We did not look for it, but it's there. It HAD to be there.
One imagines math as a mental construct that is, at least, consistent. This is, that has no internal contradictions. Starting from true premises and applying propositional logic rules, one "should" not be able to claim that "A equals B" to later say "A is not B". One, also imagines that it is complete: each formula has a proof, for either true or false results. Since there's not such thing as "kinda pregnant" there's not such thing as "kinda true"; there's no shaded zones. In math, either you like it or it hurts. True or false, it can always be proved with a theorem. OK, no. Well, yes, sort of. The part were everything is true or false is "OK". There's no shades. But sometimes, we cannot prove it. It is not that we do not know the possible demonstration, it's that the demonstration does not exist within the system. To fully understand you HAVE to read THIS.
This is not over, it never is!
The legacy this monster left was, we need to pick a path. If the math cannot prove itself, yet it did somehow, then it is a contradiction; if it did not prove itself, then we need to accept them as true, even when we cannot prove it! Therefore, math is consistent or complete, and both properties exclude each other. Chose one! BOOM! Our brains obviously pick the one that is consistent, leaping off that recursive loop. Nobody wants to travel in a plane that can fly or not depending on how did the reasoning line perform. As a consequence, we've an unavoidable gift from the Universe for all those bright minds that dare to study it, we have formulas that we cannot claim as true or false. Like that funny "this phrase is false" and the playful "I am a liar" or... the title of this article.
Ha! I just triggered another recursive loop in your brain, forcing you to re-read the title of the article. A HUGE loop. Not only that, the title itself is self referential. And, as you may have already noticed, is neither true or false. You've no option, you cannot break the circle, just like before. And here comes the CRAZY part: The brain, is self referential. It can even study itself.
If the brain could ever finish understanding itself we would trigger a black hole in the same backbone of our universe. It is not wise to study our brain with out brain. But we will keep doing it, because we love it, just as weekend barbecues, kittens, Internet and the phrase you're for sure waiting for: "This whole article (ALL of it) is false".
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