A Meta-“Argument” About Arguments

I’m not sure how describe what exactly this is other than a stream-of-consciousness that occurred after someone had intellectually stimulated me. It’s been a really long time since anyone has done that. Ah, intellectual stimulation! Even better than sexual stimulation, in my opinion. Knowledge is wonderful, and I love thinking.

This arose after the person brought up God.

To be honest I’m not sure where I was going with this. Such is the nature of Stream-of-Consciousness.

Again, do realize this is directed towards the individual on ExperienceProject who had brought this up, so if things seem odd in the syntax or sounds out of context (I tried avoiding such), that’s why.

Here’s how I see arguments.

On the bottom-most tier, we have the completely subjective. Things that are literally impossible to prove due to its very nature. We often call this type of thing “philosophy.” Here we have things like “Is reality really real?” Take nihilism for example. No matter what I do, I can’t be sure if I’m the only conscious being in the universe, and everything I experience and discover is just an illusion produced by a consciousness that is me, and that my senses are mere illusions. This among other entirely unprovables, form the bottom-most tier, and are the absolute most subjective things in “existence” (if existence is really a thing).

Then we have things like the concept of consciousness. We can possibly find out what consciousness is and where it resides in our brain (I actually have a very good idea of what it is. It goes against our current postulate that it has to do with the complexity of the system and instead deals with the ability to have short term memory. To explain would take a while, but I’ve already devised an experiment for it I’ll eventually carry out). We can understand what causes consciousness, but we can’t directly prove consciousness itself. I know I’m conscious. I think therefore I am. But I can’t prove to you, nor you can’t prove to me, your own consciousness. It is very easy to program a computer to say “I am conscious.”

Heck, all you need is these two lines of BASIC:

Print “I am conscious.”

End

And oftentimes you don’t even need the second bit. As AI gets sufficiently advanced, a computer would be able to formulate an argument on its own arguing its own conscious–but it can equally argue and defend that it is an iguana. I personally do believe computers are conscious. Whether it recognizes my presence or understands what I’m doing, or acknowledges my interaction with it at all past “hey, I’m getting some input telling me to do something, I should do that,” is a completely different story, but it has short term memory that’s far more complex than our own (we can barely remember more than a few strings in our short term memory… I often joke about how I have a 2kb RAM), and that lasts much longer. I’m pretty sure short term memory is the key to consciousness in humans (if I do prove this, what will this say about the ethics behind killing someone that literally doesn’t have a short term memory), and it might differ for a laptop due to the difference between the way the short-term memories work, but my main point is that one way or another, nothing can prove consciousness directly even if we can find out where it resides.

On the next tier, we start to drift away from philosophy and more into every day arguments. “What color is better, blue or red?” Even though evolutionarily red is far more a warning color than any other color, and if people are scared of a color (namely me) it’s usually red (although I only fear red lights), there’s no way to truly objectively define which color is better in any meaningful way, as the arguments usually relate to the gestalt principle (imagine three black circles on a white background, each with a 60 degree segment taken out of it in a particular way–or is it that a white equilateral triangle was dropped onto the three dots… there’s no way to tell since it’s what one perceives). Does red look the same to me as it does to you? Do you love or hate the scent of hardware stores? These are arguments that cannot be defined objectively simply because of the seemingly superficial point that everyone experiences this world differently.

Next tier would be something like “Which is better, Digimon or Pokemon?” Now this has a few objective points one could argue to directly show how one’s better than the other, even though it’s a weak argument; however it remains largely subjective. For example, most Digimon are direct rip-offs off of Pokemon, among others. I can’t really think of a reason Digimon would be objectively better in any way to Pokemon, but I’m sure there’s probably one or something. We can see this in how Pokemon takes the world by storm while few know what a Digimon is anymore. Again, a weak argument that is still highly subjective in nature, most of the objective points being how Digimon rips off and attempts to emulate Pokemon. (Objective because it’s a directly provable statement, e.g. in the case of Agumon being a clear rip off of Charmander).

On the next tier we have mostly objective, but somewhat subjective matters, as is in the case of the sciences we know some things about. In this case, we can say something along the lines of “We don’t know all it can be, but we do know what it can’t be.” Take for the instance reptiles. We don’t nearly know all the reptilian species in the world, but we know dragons can’t exist because they violate the laws of physics in so many ways. I could see how something could potentially breathe fire (glands full of flammable liquid that squirts really far and combusts when it reacts with some other chemical or oxygen), but the dragons of fairy tales are clearly impossible (I have a dumbass friend that insists they’re real–that’s why I use this as an example).

Then on the next tier, we have highly objective but hard to completely prove. Evolution is a very good example here. We have a LOT of indirect evidence that shows how species are interrelated and we can directly see natural selection at work, but it’d take several hundred to a thousand millenia to see it at work directly. These are things that do have a very definite answer, and even though we don’t have direct proof of it, one would have to be an utter fool to refute the evidence for a particular stance, unless they themselves provided a direct counterexample to it.

On the next tier we get to the next stage–things that do have a definite, completely objective solution we know little about, like a brand new problem. These can also be arguments that have a finite, discrete, and defined set of possibilities, (i.e. no maybe, and the options are clearly listed and cover all possible outcomes). Here we get into the realm where only math, and occasionally other rulesets (although the entirely objective rulesets are actually at the core nothing more than math that’s been prettied up). Take Fermat’s Last Theorem. We now think Fermat never did have a proof, but just postulated it and leave mathematicians figure it out. It left mathematicians scratching their heads for three centuries, and at long last in ’94 it was solved, with math that was unheard of during Fermat’s time. In Fermat’s time, we could have equal groups of people with equal evidence pointing in both directions stating “Yes, there is a solution” or “No there is no solution.” Here we take sides on things that are absolute truths that don’t even need the universe to exist to hold true.

On the next tier, we have absolute objective truths that have massive evidence for one side, but there’s still reasonable and quite possible ways for it to be the other. Take for example, the Collatz Conjecture. Most mathematicians think it holds true. The Collatz Conjecture is dauntingly simple of a question. Pick any whole number greater than 1. If it’s even, divide it by two. If it’s odd, triple it and add one. You’ll get a new number. Repeat it over and over again, and you’ll eventually reach 1. Even a second grader could understand it, but it’s a problem that’s been evading mathematicians for so long, and it’s on the Clay Institute’s “Top Most Wanted” list, with a million dollars and a medal for its head, proven wrong or right. Most evidence points to it being true, but just one counterexample could prove it wrong. We know it holds for all such numbers up to a billion, but it is very well possible that, say, 18478347529347523984 could prove it wrong (now I need to see what the Collatz trajectory for that is out of curiosity, but most online ones only accept 12 digits… eh it’s not hard at all to code this… I’ll do such).

Then on the topmost tier, you have the proven absolute truths. There is no denying these truths are the truth, the truth, and nothing but the whole truth, and these are truths that not even the bottom-most tier will affect–even if literally nothing exists, math would still exist because it is conceptual, and concepts are information that can apply to reality but don’t necessarily need reality to exist to hold true. To say these truths are not the truths would be one of the most idiotic things to do, as there’s absolutely no way for these truths to be false by definition. Everything, anything, and things that we don’t even have words for or could even conceive of–very literally EVERYTHING, even nothing–pure nothingness, that which literally is not anything which if we put a name to would be something, breaks down to being set theory, in some cases, paradoxically. Paradoxes do not violate logic–they instead create a logical latch. “The previous statement is true. The following statement is false.” Logical latches can be physical, too–they’re absolutely necessary parts of computer hardware, actually. But everything in this top tier is absolute PROVEN truth, and anything in this tier has a definite answer, and it is literally impossible to disprove it. Things in this tier include the Pythagorean Theorem, proof of irrational numbers, proof that some infinities are bigger than others (Cantor’s Diagonal Proof, and Hilbert’s Infinite Hotel Scenario, if you’re interested).

I guess I could call the bottom-most tier Tier IX and the top most tier Tier I and such. They’re roughly categorized by a combination of how easy it is to prove something, how objective it is, and how much we currently understand of it. I’ve arranged it in such a way that the higher the tier number, the more acceptable it is to pick sides given one has a substantiated logically-sound argument (i.e. “Red is the best color because it just is” does not work, and even in Tier II even if something is highly likely to be true, you can’t just say something like “The Collatz Conjecture is true because it just is.” Also, the argument has to be logically sound–even if the argument ends up proving false, it is possible for it to still be logical in its own extent, if that makes any sense). Do note that certain arguments can change tiers, except for Tier IX and Tier I arguments by definition. It is very rare for anything to change more than one or two tiers, and it’s only in the case for tiers that differ solely in our level of understanding. For example, if the Collatz Conjecture gets proven, it becomes a Tier I truth, and permanently stays that way. For all but the top three tiers, Tier IX arguments affect them and deconstruct them into arbitrary nonspecifics, but it breaks them down in such a way that would make any position meaningless to our existence (or non-existence, or some superposition of such). If we don’t exist, or if I’m the only one that exists, what does it matter whether red or blue is the superior color? With the top three tiers, i.e. absolute truths i.e. mathematical truths, because mathematics is the absolute most meta (to define how meta or to continue the sentence using a reference point or adjective or similar would be to attempt to define the nature of reality; the best I can do is define these using layman terms to be independent of whatever it is this all is).

The “truth” of religion is a Tier IV argument that very heavily favors religion being false, due to how contradictory and illogical it is. However, the pure concept of God i.e. there being a penultimate creator (penultimate to mathematics itself, as the God itself, being an entity, would still be defined by a set of rules that which is the absolute truths of mathematics–i.e. the true “God” is literally maths) is a Tier III argument that we have insufficient evidence to neither prove nor disprove.

Here’s the slightly shorter TL;DR version of all of this applied to religion as objectively as possible. Such does not necessarily reflect upon my exact beliefs, but instead is based on how possible something is from an objective viewpoint based on our current understanding and pure logic:

Is religion the truth (including any and all ideas that we actually mean something in this universe and that any God, if one exists, interacts with us in any meaningful way in our perspective)? No, it’s self-contradictory, far too variant, highly illogical, and goes against objective reality. If reality doesn’t exist, then it wouldn’t matter one way or another. We have sufficient counterevidence against religion. Is God as nothing more than a creator, the truth? We can’t be sure about that, although we’re pretty sure the God(s) don’t really give a crap about us or is anything like we’d perceive them to be from statistical reasoning alone. God could easily be nothing more than a conceptual necessity of reality, or could be a physical entity comparable to a programmer with varying motives. I could go quite in depth into the topic of “Assuming God exists and created this universe, what is it, what was its motives in creating the universe, what is it observing, etc. etc.” What does God look like? Could be anything. Some weird alien, something we can’t describe, a space unicorn monkey toad–whatever it is, it has statistically no chance of looking anything remotely human. Any one thing I describe has statistically no chance of even remotely describing what a God would look like. The statement “God built us in his image” can be directly proven false. We are imperfect. If God built us in his image, then God must be imperfect. Because by definition, God is perfect, then God cannot look like us without being imperfect i.e. it would not be God, as it would be imperfect. It is sometimes fun to picture God as a vagina, as many would argue that vaginas are the epitome of perfection, haha! Hey, intellectuals can make sex jokes too!

The extremely TL;DR version of THAT:

Is religion the truth? Nope because it goes against logic.

Is God as nothing more than a creator the truth? We’re not sure.

Well, that’s my two cents on this. Yes, two cents–this only scratches the surface of all I could say on this.

—–

To be even more meta, I suppose this argument is a Tier V style argument. I try to be as objective as possible all the time, and I suppose I was slightly less objective in this case because the length of the post happened on accident, and I didn’t completely add in all I could have to each stance so some things seem undefended, and went off on many tangents.

I suppose these Tiers are more along the lines of a cross between Classes and Types, although since they are somewhat ordered, “Tier” isn’t too wrong of a term to use.

A Meta-“Argument” About Arguments

“The Significant Insignificants” — Our Place In The Cosmos [Happy New Year!]

Happy New Year! WOOOOOOOOOOOOOOO 2015!!!
My resolution for this year? Pull up my grades, I suppose. Graduate, go to college, and all that jazz.

But anyways, to usher in the new year, I’ve narrated my post “The Significant Insignificants” to bring forth new hope and optimism, and inspire people to be more appreciative about their existence!

“The Significant Insignificants” — Our Place In The Cosmos [Happy New Year!]

The Significant Insignificants

I was re-listening to Carl Sagan’s “Pale Blue Dot” speech, and then I found myself channeling him again, in writing a comment… I tend to do that a lot… but heck, it’s not a bad thing that my words end up emulates those of Carl Sagan… that’s a good thing. And I’m not going to stop it.


Watch this first:


Then listen to this while reading my little spiel…


Saganist: A sentient product of dying stars that follows the wise, echoing, timeless words of the great, legendary Carl Sagan, and dreams of carrying these words and enlightening the world with his resonant philosophies in order to stop this senseless selfishly driven violence that serves no purpose but to drive our world into chaos…

import carlsagan.lgd

A cosmologist may not be god, but one comes as close as possible to godly understanding, of knowledge and truth—harboring the answers to the ultimate questions in existentialism, seeking the Grand Unifying Theory of Everything, to make sense of this 13.7 billion light year ball we call the universe.

It isn’t until we gaze up at the stars do we truly realize that we are awfully insignificant. We are a mere infinitesimal on the scale of the cosmos. We are not even a dot. We are not even a pixel. Our reach only extends so far as our atmosphere. We may have stroked the surface of a few planets and moons, a comet, and the far reaches of our solar system, but we are but a pixel in our solar system, which is a mere pixel in our galaxy, which is a pixel among our galaxy clusters, which are pixels among our superclusters, which are pixels in our universe, which is a literal infinitesimal among the infinite number of universes in the multiverse. Even considering chaos theory, our existence simply isn’t, on the scale of the universe.

Yet, here we are so awfully insignificant, legends in our own fraction of a pixel of a pixel of a pixel of a pixel of a pixel of an infinitesimal, many unable to appreciate the vastness of the universe. We are inebriated by our own ego; delusional that we are significant. We are far too drunk to realize that we are in fact drunk and drowning in our own flattery. We refuse to realize the truth that we don’t in fact matter in the cosmos.

Still, there are a few of us that have woken up. We are the cosmologists, the mathematicians, the stargazers; we are the philosophers, the existentialists, the few privileged individuals on this pale blue dot that have sobered up and know that we will never play a significant role in the cosmos; however, even more sobering is the thought that we even begin to comprehend the cosmos at all. While it is almost certain that life could have evolved elsewhere in the universe numerous times, only a handful of the spawns of life would even come close to understanding the vast cosmos as intimately as we do.

Despite being as tiny and insignificant as we are, we’re able to understand something as vast and mysterious as the universe. That is something significant on its own. We are one of the few lifeforms in existence capable of truly comprehending the cosmos, and that makes our existence significant. We may not be able to do much to the cosmos, but we can do all we can do to understand it. We can affect our own world–our pale blue dot. I could not be more privileged than to be blessed with the appreciation of the cosmos and everything in it. If I had to choose between ruler of the world blind to the truth and cosmologist with existential philosophies, I would choose the latter without hesitation.

I’m only a 17 year old girl. There is only so much I can do right now. But I am blessed to have developed an appreciation for this universe at such a young age; that means I have even more time to bring as much new understanding about the cosmos as I possibly can within my lifetime. To others, the sky is the limit. I see no reason to limit myself. I may never physically leave the earth, and it is possible that this is due to unfortunate technological, economical, and political reasons; however, nothing is going to stop me from doing my best to peer into the cosmos to understand something more… something beyond, something bigger, something that created this pale blue dot.

The Significant Insignificants

The Story Of My Life From The VERY Beginning (As In, The Big Bang)

Someone asked a question on EP wondering if they’d understood the universe from the Big Bang to the present day. There were a few flaws in his thought process, but instead of trying to… hang on, it’s 11:11PM on 11/11 heh heh… correct individual parts, I thought I’d just start from the very beginning and elaborate as much as I felt like concentrating. One could go very, very, very in depth with this, but then it gets too long and uninteresting as part education, part philosophy, and part humor.

This is basically the story of my life from the VERY beginning… only I don’t really elaborate on my conscious life as much.

I could go into the Multiverse and Parallel Universe and Many Worlds hypothesis and state what might have happened before the Big Bang, and other possible nuances in what could have happened afterwards, but hey, I was just having a little bit of fun with this, How-The-Universe-Works style!

Wooo #spaceweek!


The Big Bang was more of a huge expansion than an explosion. It created pure energy–equal amounts matter and antimatter that for the most part annihilated each other. Why matter reigns is a big problem in cosmology. We think that there’s an antimatter universe twin somewhere across the universe. Once the universe was cool enough to start making bonds, energy converts into mass (because E=mc² allows this to occur), and starts making primitive subatomic particles, which in turn start making electrons, protons, and neutrons, forming primarily hydrogen atoms and such. With all this hot gas swirling around, many enormous stars formed, living fast and dying young with the true bangs of the universe, far more explosive even than a hypernova (which is itself more explosive than a supernova). This creates many black holes, which then eat each other up to form supermassive black holes, which become the seeds to start forming galaxies. Hot gas starts swirling around these seeds and form the protogalaxies in which solar systems start to form. Each star starts off as a swirling mass of hot gas. This begins to have some gravity, which pulls the gas closer together and pulls in even more gas. This creates an even more massive cloud with even more gravity, and even more gas is pulled in. This keeps going on until the gravity causes enough pressure at the core of the protostar to ignite fusion. Fusion starts colliding hydrogen atoms together to form helium atoms, in the process releasing radiation, and this star burns for millions to billions of years–a battle between the intense gravity pulling the star together, and the intense fusion pushing it outwards–before finally running out of fuel. After the star uses up all its hydrogen, it starts fusing together helium atoms. Once all the helium atoms are fused together to form carbon, it starts burning the Carbon. It eventually gets to a point where it creates iron. Iron is the most lethal thing to a star, since it requires an *intense* amount of energy to fuse it. The star keeps pouring in energy into the iron atoms, but it doesn’t give. Once it produces iron, it has only seconds to live. With no more fusion to fuel the star’s fusion reactor, the battle between gravity and fusion ends. Gravity always wins. The star’s dead before it even hits the ground. In the final moments of the dying star, the star’s core shrinks to a size that’s less than a thousandth of its original size. This creates an incredible amount of energy in which the stars eject two powerful beams of gamma ray energy–its death cry (sometimes the birth cry of a black hole)–out of its sides. In this few second release of energy, iron fuses together and forms heavier elements, and so on. The energy released in this moment is more than the star will have ever outputted in its entire lifetime. This is known as the gamma ray burst, and while this death ray hurtles through the universe, blasting gas and stardust all around, leaving a nebula behind. This stardust contains the heavier elements needed to create life. Sometimes the star leaves behind a neutron star, others, a white dwarf, and others yet a black hole. From this cloud of dust and gas, a new star can be born from the unused hydrogen. The process repeats. This time, when the clouds of gas and dust circle around the protostar in order to create the new star, the heavier elements are flung outwards in an accretion disk. These tiny particles eventually collide-but don’t necessarily fuse–with each other, which, over time, builds up to form mini asteroids, which continue to build up. Eventually a proto-solar-system is born, in which there’s but chaos throwing planets around left right and center. Over billions of years, this system stabilizes. One of these planets was the right distance from its star–its Goldilocks zone, and collected the right elements from its surroundings. It was in perfect conditions to avoid asteroid collisions and collected the most amazing chemical in existence–dihydrogen monoxide, more affectionately termed as water. This, along with carbon, nitrogen, oxygen, and phosphorous, and a little zap of energy, created the first amino acids–the first organic molecules. Eventually, these amino acids arranged themselves into a particular pattern–RNA, surrounded by a protective phospholipid bubble–the first cell. Gradually, over time, these cells became more complex, eventually forming the first prokaryotic cells–bacteria. These became ever more complex, creating eukaryotic cells. From this stemmed the process of evolution, the ever fractally branching process of a genetic algorithm that either survives or doesn’t, allowing only the best of the generation to go on. Replication isn’t a perfect process, causing small mutations per generation, that can either help or debilitate the species as a whole. Eventually there’ll come a time when the species branches into a completely different species… with enough time, due to Chaos Theory, the tips of the tree will be vastly different. One of these paths involved one branch of the bacteria evolving into strange aquatic creatures, which one branch evolved into fish, which one branch evolved into amphibians, which one branch evolved into a rodent-like mammal, which one branch evolved into the first primate, which one branch evolved into ape-like primates, which one branch evolved into the hominids, which one branch evolved into the homo-sapiens, which has since evolved into a better developed version of the homo-sapiens (homo sapiens sapiens), which became us today. These humans originated in Africa, from which they migrated to different locations as the earth’s plates shifted and such. One such group migrated to India, and generations later, developed civilization. Further civilization by other humans (the British) developed certain areas in a certain way. Two of these humans in a developed area arranged a marriage between two individuals that after having one son later migrated to the United States in Minnesota, and had a daughter. After a few years, they moved to Orlando, and the daughter grew up there, facing severe bullying but learned to develop apathy, as she fell in love with math and science, and learned not to care about what other people think. Over time, she fell in love with cosmology and mathematics in particular, and loved teaching such. Having joined a site called ExperienceProject, she then vowed to educate people as much as possible. One day, she stumbled across a question that involved the origin of the universe, and she started typing a self-referential wall of text, of which she can’t say anything more since it hasn’t happened yet. All this to remind you that she and everything around her is literally stardust, since everything around her and herself at an atomic level was forged in the belly of a star.

More or less.

The Story Of My Life From The VERY Beginning (As In, The Big Bang)

Space Week: Because Science!

I’m not sure if hashtags work on blogs or not. But either way, hey, #spaceweek! So much more awesome than Shark Week!

I just watched today’s special “Which Universe Are We In” and of course, having followed the Multiverse Theory since I was 12, I already knew the stuff they were talking about. But it still warms my heart and reminds me of my dreams and goals. I want to solve the universe. Even from the perspective of Chaos, we are absolutely insignificant to the rest of the universe; however, the very fact that we’re absolutely insignificant yet we’re able to not only comprehend the universe but also what lies beyond is more than astonishing–there simply exists no word to describe exactly how astounding, amazing, and awesome this is. We live in the Golden Age of cosmological and quantum mechanical discovery, and I want to be on its frontier, riding the wave forwards into further discovery–perhaps even being the one that helps propagate these waves into deeper knowledge. Why? This is one question that I actually tend to avoid elaborately, for it can succinctly be summed up into two words: because Science. Does there really need to be any other reason, other than Science–just, you know, because SCIENCE? It speaks for itself. I don’t care about fame. I don’t care about fortune. I care about science. I care about discovery. I want to KNOW. To me, knowledge is the most valuable possession one could have, for with knowledge comes discovery, and with discovery comes progress–and that, I feel, is what is the human endeavor.

Space Week: Because Science!

Think

This post is very recent.
All I can think of saying is that I just let things go in this one, and just went on and on and on, because it was, after all, a stream of consciousness to try and explain all that goes on in my head (and what better way to do that than stream of consciousness).

Original Post Date: October 11, 2014
Original Post: http://bit.ly/1vjqEAz


Sometimes I’ll get a reply to a post, which I reply back with what starts out as a long comment, then ends up being too long to post as a comment, so I decide to post it as an experience, and allow it to be as long as it turns out to be.

When I do that, I’m essentially typing up a stream-of-consciousness, where I type whatever comes to my mind at the time, even if it seems like I’m jumping from topic to topic, and then eventually reach a conclusion that sums up everything I’ve mentioned through all the verbosity and redundancy and inconsistency of the text just to make it appear consistent while having definite deliberation as does the rest of the passage.

This is perhaps the longest passage I’ve ever written for EP, and I’d particularly like you to pay attention to the very last paragraph at the least, if this is TL;DR for you.
Continue reading “Think”

Think

The Beauty of Chaos and Mathematics

Original Post Date: Jun 20, 2014
Original Post: http://bit.ly/1DjhRCZ

I don’t know what else to add. This is one of my posts where I pretty much have my own ideas. Well, I guess I should have mentioned the Three-Body-Problem, and more about Godel’s Incompleteness Theorem…


The Beauty of Chaos and Mathematics

Mathematics is not itself about numbers and symbols. Those numbers and symbols are a part of the grand metaphor for the absolute truth of what is mathematics.

Given two particles of identical mass that only but gravitationally interact with each other, it seems obvious how they’d mathematically interact. The force that draws them together is simply Newton’s gravitational constant times both of their masses divided by the square of the distance between them. It’s nothing more than hardly high-school physics. An infinitesimal of time ticks by and the particles move accordingly. They have a new position and a new trajectory. The function is applied again, and the particles move accordingly, again, with a new trajectory. This process goes on and on.

It still appears to be a simple system. After all, with two particles, it seems that complexity is completely nonexistent in the system. It might seem complicated to a layman, but it is not complex, by definition—nor is it complicated to any high school student with a basic understanding of physics and math. In fact, this system is a far less complex system than reality; reality would include far more forces than just the gravitational force, and far, FAR more particles. Either way, this particle system seems rather simple.

Will it follow a predictable pattern? It might seem like it does at first glance. That is the beauty of mathematical chaos. This one simple pattern follows a seemingly unpredictable nature, even though it is defined by one simple function. This Lorenz Attractor system is a good example of mathematical chaos. If we change any of the parameters by just a tiny bit, no matter how small, given an enough amount of time, the systems appear to have no similarity in their trajectories. It’s simply beautiful.
Throw in a third particle. How about a hundred particles? Maybe we’ll throw in the few googols or so of subatomic particles that we know of into the mix, and all of the strange ways they behave, just to add to the complexity. The beauty is that these systems are theoretically governed by a set of a few mathematical rules. Whether we have discovered these patterns or not yet, these patterns do exist.

Gödel’s Incompleteness Theorem states that there might be problems that we will never be able to solve. From a philosophical sense, this is true. For all we know, solipsism could be the truth, and everything is but a mere illusory projection from an observer’s mind. The thing is… math is absolute truth. Everything can be mathematically defined in some way. The Pythagorean Theorem will always hold for any right triangle on a perfectly flat surface, and methods of topology and the Law of Cosines can compensate for other distortions of triangles and other angles. It’s truly beautiful.
The traditional definition of chaos—where things run uncontrollably and rampant—is the antithesis of beauty. Mathematical chaos, on the other hand, is the epitome of beauty. Take the Mandelbrot Set, for example. It’s nothing more than taking a point on the Complex Plane, putting it into a function where one term is squared and added to the initial term, then fed back into the squared term, and looping—iterating it—for enough times that the point either goes out of bounds or doesn’t. Yet this simple generation does not generate a simple shape. In fact, it generates one of the most complex structures in all of mathematics—a fractal.

Due to the principles of Chaos Theory, with “time” being the number of iterations done to the point, a point that is a billionth of a billionth of a billionth of a billionth of a pixel away from the one right next to it might be in the Mandelbrot Set, while the neighboring point isn’t. The Mandelbrot Set is almost unanimously agreed to be the most be the most beautiful object in all of mathematics, as it is an extremely elegant demonstration of Chaos Theory.

Now think about Conway’s Game of Life. Imagine an infinitely huge sheet of graph paper. Each cell can either be shaded in or not shaded in—that is to say, alive or dead… and no, there are no Schrodinger cells. Each cell has eight neighbors. Let’s say we have a living cell. If there are one or no neighbors, the cell dies, as if of loneliness. If there are two or three cells, the cell lives on to the next generation. If there are any more neighbors, the cell dies, as if by overcrowding. If three neighbors surround a dead cell, the cell comes to life. From these simple rules, we can again use the principles of Chaos Theory to create a game board that essentially looks… living, hence its name.

To a layman, this may not seem all too fascinating. To a mathematician and mathematical biologist, these patterns take us one step closer to describing our own universe. Could we not be the byproduct of a very large array of an n-dimensional version of the Game of Life? Who is to say we aren’t? While this theory lies forever in the Conjecture Limbo of Gödel’s Incompleteness Theorem, it is certainly a sobering thought to think that our universe may be governed by a set of rules that an elementary school kid could understand.

Most people think of math as the horrible way schools teach it. I do not like school mathematics. I do not like it one bit. Why don’t I like school math? All of the classes—even Geometry—manages to squeeze out all of its elegance and beauty, and show us a framework that looks—let’s face it—ugly. It’s horrible—it’s like teaching that art is all about painting different types of fences. Math is an art, and its beautiful constituents—ESPECIALLY when it comes to geometry—are ripped out of the subject and presented to us in school. No wonder why kids do not like math. They don’t know what math is.

Math is an absolutely beautiful topic. Chaos Theory and fractal geometry are some of the many elegant, absolutely lovely mathematical topics. If I were to invent a math class, I’d teach all about these amazing concepts of math—what real math is, mixed in with some geometry. In an art class, people learn about the life of the artist. Why shan’t we say the same for math classes—let’s learn about, at least in part, the life of the mathematician. After all, math is none other than an art that uses symbols as metaphors to represent reality.

I may be only 17, but one does not have to be old to be wise. It simply takes a little elucidation to what really is to be captured by its allure, drawn towards not a Siren Song, but the calling of absolute truth and reality. Mathematics is not the greatest human invention. Mathematics has always existed and always will exist as absolute truth. Mathematics is the greatest human discovery. It may not seem like it at first glance, but it’s like a chocolate éclair—looks are deceiving, and all you need to do is to take one bite and you’ll have wondered why you ever hesitated to dig in.


I don’t know what else to add. It’s 6AM. I should get ready for school.

The Beauty of Chaos and Mathematics