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.

Start Ramble

My passage through life does have a definite path. But unless P=NP, unless I walk this convoluted path, I’ll never know where it’ll take me. I have to walk it to find out where it goes. What appears to be a chaotic dance through many iterations and interactions now could eventually lead to a stable and elegant pattern later. Perhaps I will never figure out what was different in my own initial conditions that led me to an end behavior far different from so many other patterns; it could be anything from the biggest to the smallest of a difference that sent my destined end behavior to play out in a wildly different scenario from many others. If the right condition is met, even after only a few iterations, the entire layout could be drastically different. Why does my native language seem to be math? Why is it that my brain puts things in terms of mathematical jargon first–of which I must translate to let laymen (I make no effort to translate my speech here as, if you decide to read this entire thing, are certainly no layman–really, the fact that you’re interested in my more erudite walls of text is proof enough of that) make sense of what I speak of? Why is it that time and time again I do poorly on SAT essays simply because I have so much to say and no time to write it all; on top of which they do not appreciate the art of rhetorical argument and diction the way the AP Language graders do? There are some things I am genuinely surprised people can’t do in the slightest; those things I had previously thought I was stupid for my slowness at the task. I literally don’t know what goes on in the mind of a layman; I must literally see things differently, for when I walk home from the bus stop, the world occasionally twists and distorts, the colors become more vivid, and I suddenly seem to be in what I can only describe as a “hypermode” of sorts–a period of intensified perception and mental processing speed in which one feels a perceptive high of sorts. Things would pop out at me, and I’d marvel over the extreme interconnectedness of my surroundings. I speak about “the patterns” rather often, but I have never truly defined them; for I cannot truly define them–at most I can describe the nature of the patterns, not what I’m really seeing and how I perceive them. The patterns are the mathematical patterns in nature–the scaling of things, its proportion, length, humidity, temperature, velocity… I’m suddenly this sort of multimeter of nature, of which I’m able to not simply understand the patterns… not simply feel the patterns, but also experience the patterns. It’s almost as a literal sense, much like the sense of touch–more accurately, like proprioception (the sense of where your body parts are in space). It’s an intuitive mathematical sense, I’d say, that I’m not consciously aware of, one that I’m not consciously aware of, or have any true physical method of processing; but rather one that’s ingrained in my subconscience, relying on my other senses to draw a conclusion much the way proprioception does. Of course, my mathematical sense isn’t as developed as some others out there–take the case of two twins that are essentially idiot-savants; they’re human calculators and can generate twenty digit primes in their head within five minutes, see an arbitrarily large number of objects (and that number’s prime factorization) and instantly give you an accurate count, and tell you the exact day of a date arbitrarily long ago, but can at most add and subtract when it comes to applied mathematics. I’m quite lucky to be half way there; whereas I do suck at mental arithmetic (mainly due to short term memory loss), I have weird abilities that rely on some sort of subconscious calculation system. And I’m clearly no idiot… up until you meet me in person, that is, and catch a glimpse at my circumstantial childishness. I’m no savant, but I certainly do have a higher sense of perception than others. Perhaps this is why I am mathematically minded. I initially chose my username simply because it alliterated while holding some truth, but I realize now how true to myself it is. I will never figure out how the majority of the world walks down the street, not in constant awe of the environment around them, regardless of their ability to quantify environmental parameters–it seems so weird and not human. People think I’m weird–autistic, even–when they see me intensely staring at a thin vine hanging from a tree, not realizing what I’m seeing. Even though they instantly take back their assumption of autism after I explain the concept of the Golden Ratio and point out some of its many appearances in the vine, what’s sad is that they still can’t see it, even if they understand it. I wasn’t truly born with this ability; it didn’t truly manifest itself until the beginning of my teenage years. It was developed, once I learned to see the patterns. Why don’t they see the patterns? It’s what confuses me. As far as psychology (a subject which is about as fascinating to me as mathematics is sans the obsessive-fetishistic love I hold for math but pursue as a hobby rather than a career) goes, it’s perhaps my biggest unsolved question. The human brain isn’t a language machine. It is a math machine. I do not mean rote mathematics; I speak of unconscious mathematics–the algorithms that the brain executes to make sense of the world around us. Take for instance, the twins I mentioned earlier. Perhaps the biggest question in the history of mathematics–and also the question that’ll guarantee you eternal fame among the greatest of mathematicians–is a function, simple or not, that tests the “primality” of a number. We know there are an infinite number of primes, but we don’t know whether or not a given (odd-numbered and doesn’t end in 5 for obvious reasons) integer is prime or not without actually testing each integer (from two up to half its value less itself, as its value plus one divided by two will give the last factor pair, itself will give one and vice versa, and anything greater will clearly be a fraction) for divisibility. In other words, as far as we know, primality is NP-Hard (I think). As far as we know, we cannot test for its primality without testing every potential factor of that number. Yet… these two people can generate arbitrary six digit primes (and given their IQ of 60, they certainly didn’t memorize them) instantaneously, and work out primality of a twenty digit number in less than half an hour–a task that would take a computer a fair bit of time (for a computer) to do. They’re certainly not dividing in their head (they don’t know how to divide or even what division is), yet the numbers they’d exchange with each other (and cause the other to smile) are all prime. There have been similar “prime testers” in history–in fact, one idiot-savant found the all the primes up to eight million, all in his head. They’re clearly not using any form of conventional mathematics, yet their brain executes some sort of an algorithm to test the primality of a number. The point in fact is that these people are evidence that there is a way to test the primality of a number simply and accurately (Fermat’s Little Theorem, I think it’s called–not to be confused with the Last Theorem–tests primality, but it isn’t always correct, and hence in mathematics isn’t truly useful). What does an idiot know that I don’t? Only the answer to the biggest question in mathematics of all time–bigger so than Fermat’s Last Theorem was. Of course, I wouldn’t truly want to be them, due to the fact they otherwise are the idiot part of idiot-savant, but I sure would give an arm and a leg to experience the world the way they do–to think the way they do… to experience what they’re experiencing. There is certainly an aura of mysticism surrounding the primes–not simply in mathematics, but also in nature. Primes seem to be extremely natural, second only to the Fibonacci numbers (which exhibit several curiosities relating to primes) in prevalence. Do they see the world literally as numbers? How are they processing these primes? Perhaps they would be the only candidates that could ever love math more than I; and they certainly would if they weren’t otherwise idiots and could consciously do math. I would think that they’re unconsciously processing this information–as with me, the similar things I can do with velocity, time, temperature, humidity, pitch (though perfect pitch is relatively more common than the other curiosities I can do) etc are all unconsciously processed; I cannot consciously process it–only tell myself “this is what I want processed” and such. The number drifts into my head, and I cannot overthink it. That number is the number, and if I don’t grasp it in the fourth of a second it pops into my head, it’ll be replaced with a wrong, biased one. But these people… they’re clearly thinking consciously, else they would only be able to give snappy responses. Personally, I do not find them idiotic. It is like comparing a supercomputer that specializes as a math processing machine to a regular computer. Sure, the regular computer can do more types of things alright, but to call this computer superior to the supercomputer simply because it can do more than just math is clearly illogical. The supercomputer has its insanely great highly specialized function, the normal computer an average, generalized function. In fact, I’d wager to say the supercomputer is superior to the normal computer, and not the other way around. Really, I’d kill to spend a day with their great mind. Perhaps how I view them is how others view me (which makes me wonder how they view them, since most don’t have that degree of sympathy as I do, however small), given that I’ve been told several times that they’d love a day with my own mind. And perhaps, just as the twins viewed the professor that studied them (Oliver Sacks) very strangely when they realized he couldn’t do what they do, that’s what’s going on with me. Maybe it’s simply that others are literally unable to see the patterns–for while it took a while for me to see lucidly, I’ve always had my detection abilities–and my brain is literally cognitively wired differently. And conversely such, perhaps it’s because I’m wired that way that I don’t understand how people can become so obsessed over one another, feel jealous, embarrassed–really how people can become so emotionally attached to what seems trivial to I, and especially how anyone would ever let emotions get in the way of what is logical. They literally aren’t wired to appreciate mathematics, and I literally am not wired to let whatever emotions I have influence my logical processes. It does make sense, though, because of my medical condition NF1, which can easily cause the brain to be wired very differently from those without it (for instance, causing genius in one area but retardation in another). Perhaps I am quite literally right when I say that another is blind to the beauty of mathematics, and I waste my time trying to elucidate others on its beauty. I’d initially thought that people are merely shutting their eyes and refusing to open them because they’re scared of what they thought they saw, much like how a child hides under the covers and refuses to leave because they thought that sweater on their chair was a monster… but now I wonder whether they really have eyes at all. It would be somewhat like a dog (anthropomorphic, of course) trying to get a human to smell things the way a dog does, while a human is physiologically incapable of doing such. Of course, this analogy is limited, because it’s a physiological thing, not psychological–and this sense of mathematics I seem to have that seems to be comparable to that of the world of smell to a dog versus a human is not physiologically determined. Due to neuroplasticity, I can in fact improve their ability of mathematical insight, and orient them towards an appreciation of the subject, but this can only be done to a certain degree, and I cannot get them to see the world I do. Similarly, no one can convince me to enjoy romance or even understand what’s so great about it, since not only does romance disgust me, but also I’m somewhat Vulcan in nature by which romance means nothing to me and goes against what is logical in my mind, and whatever romantic neural networks exist in my brain either prewired itself to mathematics or has been taken up for the use of mathematics due to neuroplasticity caused by understimulation, thus causing an overlap which manifests itself by my seemingly romantic love for math. At least, all this I conjecture. I’m not even trying to pose an argument here–all this is merely stream-of-consciousness. While math always is on my un- and subconscious mind, my conscious mind usually focuses on psychology, really, and just trying time and time again to understand how people can be so “stupid” and blind. I used to think that “intelligent” is a wrong term to use on me–in fact, I make the dumbest mistakes a little too often to be called absent-minded. Smart, yes; I’m measurably smarter than others, since “smartness” relates to *relative* intelligence. Intelligent on its own? Not significantly. Perhaps yes, I measurably have a faster “processing speed” to others, but not by a significant amount. In fact, apart from math/science/philosophy concepts, I’m significantly slower than most others. But really, I used to think that people think that I’m so intelligent is because they don’t realize they can be as “intelligent” as I am if they simply tried–and I still believe such. People simply aren’t trying or don’t follow through, that’s all; however, now I do question whether or not they can do what I do the same way I do. But then I realize again that due to psychoneurological reasons, my “smartness” is in due part a high intellect–my intellect, much like the twins, manifests itself in a much different way than what can be measured, simply because not even I know what I’m supposed to be measuring. Others, with some effort, can achieve my level of “smartness,” with the only effort being that my “smartness” is a result of a cumulative set of facts that I’ve collected over my lifetime and have not forgotten them, meaning that they’d need a bit of time. But intelligence? I wonder. Stream-of-conscious break–I’m not trying to be cocky; I literally don’t understand why people regard me as “intelligent” rather than simply “smart,” due to the difference between the terms. I find it fascinating that people will call me intelligent simply due to my use of “SAT vocabulary” and “AP Language grammar.” What they don’t realize is that, while I always had a pretty decent word bank, the only reason I exhibit either of those is because, when learning them, I didn’t care if people saw me as a nerd (for that’s what I was, am, and will always be) for using “big words” and call me a Grammar Nazi for using compound-complex sentences. I knew that if I use such in my normal speech and text, it would become very natural to me when I needed to use them most. I use SAT vocabulary because it IS SAT vocabulary–I practiced using those words to prepare for the SAT, starting from 7th grade when I took it then for CTY. I wasn’t any more knowledgeable or capable than any other student. Anyone could have made the effort to do exactly what I did with exactly the same results. Why then, you may ask, did I not stop using the vocabulary after I finished the SAT? Three major reasons. First is that I had not seen the last of the SAT. In fact, my duel with the SAT ended only today. Just today–that is, October 11th, 2014 for the record–I came home from taking the very last SAT I’d ever have to take, refreshed my EP feed, found a comment, and started typing up a response that ended up being far too long to be a comment all on its own. It’s clear that I have a particular liking of academic things, but I hate tests, and I especially hate the SAT. However, I’m very glad for it because it prompted me to learn all these vocabulary words to use for the following two reasons. The second reason is that even though today ended the initial journey for learning the vocabulary, I’ve only beaten one area in the full game. There are still more levels to come in this game, and these levels aren’t simply easier to beat with my artillery of vocabulary–it’s essential to clearing the area. Even now, there’s a very large list of SAT words that are stored in my unconscious mind from 7th grade (I hadn’t studied vocabulary for this past one since I’ve effectively been practicing perfunctorily by using words–such as perfunctorily–in my day to day speech; it’s something anyone can do, which is why it annoys me when people call me intelligent for using such a diction–intellectual, yes, but not intelligent). There’ll be a time when I’m writing a sentence when suddenly a word pops up into my head, much like auto-suggest in messaging, that I realize I faintly recall but don’t remember the definition of. I then proceed to Google the definition of the word (in fact, 90% of my search queries is composed of “define x,” where x is the word I’m trying to figure out whether I’m using correctly, pardon the self-referentialism) to see whether or not I’m using it correctly. Most of the time I am, so I proceed to use the word, and attempt to use it more and more in order to make a word such as “perfunctory” as perfunctory as “automatic” (for instance, in the sentence “Every morning, John sleepily does his morning chores automatically, without giving them a conscious thought.” In fact, the word “perfunctory” is more perfunctory than the word “automatic” is, because that’s how I trained myself to perfunctorily use words like perfunctory. (I’m sorry about that sentence, but I’m a sucker for self-referentialism, and such a sentence had to be made). The third reason is simple. I like being sesquipedalian–that is, someone that likes using long or complex words, such as sesquipedalian. Very similar to vocabulary is my Grammar Nazism. Of course I’m a Grammar Nazi. The English language is butchered enough; it’s painful to read something that’s grammatically flawed. Needless to say the writing section of the SAT is quite a breeze for me. I do not Grammar Nazi people for not writing in a format that would earn them a nine on the AP Language exam. In fact the only reason I use such grammar is for that reason specifically. It was in fact, my teacher’s suggestion to do so: use this grammatical structure in my normal life, and it’ll be natural to me. I didn’t take this lightly. I struggled to create a sentence that contained a single semicolon at the beginning of the year. In fact, if you look at any of my posts prior to sometime around this time last year, you’ll notice how I greatly lacked the sentence structure I do now, and you can see how I’ve developed since then by reading my posts chronologically from then on (as well as the gradual onset of my mathematical obsession, since it was this time last year–perhaps even the same week or even day last year, that I suddenly realized that I love math even more than I once did) and seeing how my diction evolved. I thought I would fail that class, because I sucked at writing essays because I lacked complex grammatical skills, among the skills needed to use various literary and rhetorical devices… so I practiced. I did what I did for the vocabulary. I continue to use such sentence structures for the same reason I continue to use such vocabulary. I’m not afraid to look like a nerd for using such vocabulary. I never hide who I really am. It would be unnatural if I didn’t use such diction. I’m not trying to show off. In fact, I’m not trying to do anything (I never try to do anything… I’m actually quite lazy if I’m not in the correct environment, which is that of college and not my room) at all. I’m just being me. Anyone that knows me knows that, due to my hardwired necessity of logic, preciseness, and accuracy (in other words, hardwired to be a scientist), I must use the most accurate word as possible. Part of it is my natural mathematician side kicking in–in mathematics, verbosity is considered unclean, childish, and unnecessary. It makes one look like they don’t know what they’re doing. A proof consists of steps in the most concise way possible; although unless one is familiar with the necessity of accurately describing what seems obvious in a proof, the conciseness is not immediately obvious. I highly value precise and concise mathematics and language (since I do argue that both are one of the same thing in different forms with mathematics being a parent level of generality to language, which has nothing to do with why I seem to use mathematics jargon often). Simple Wikipedia is a highly simplified and layman version of Wikipedia, both usually accurate in content. It is concise, but is not precise, whereas the opposite is true for Wikipedia. What I do is use Wikipedian erudition with Simple Wikipedian length. I trim out the unnecessary bits–well, aside from stream-of-consciousness, since that would not, by definition, be stream-of-consciousness– and convey the message I need to convey curtly and effectively. I don’t intend to obfuscate my language in order to show off my vocabulary skills. Whenever I use such language, people mistake it as an attempt to “flash my intellect” at them, and call me pretentious (yet they’re calling me pretentious for using words like “pretentious,” which is pretentious and hypocritical on its own… I’m never going to stop making self-referential jokes), while it’s really me… being me. A similar thing goes towards my math enthusiasm. People mistake my enthusiasm as pretension, not realizing that just because I talk about an academic subject at a higher level, it doesn’t mean I’m being pretentious. As a matter of fact, I’ve said it fifty times and I’ll say it again, I’m not nearly as good as math as people think I am. I know the concepts, but when it comes to actually working it out, I’m no better than any other AP student is. Above average, yes, but not exceptional in the least sense. If I were really good at math, I wouldn’t have gotten Bs (and even one C) in all my math classes, getting an A only in Geometry–that too, it was an online class (oddly enough I took it before I took Algebra, which is usually not allowed due to prerequisite reasons; I don’t remember why they allowed me to do this…) , and my grade was bumped to an 89.5 simply because my teacher loved my enthusiasm and quality of the work I produced for the class, especially during the module projects. There’s a stark difference between those who are egotists and those who are passionate; in fact, I wager that they’re mutually exclusive. Did I spend three hours straight writing this wall of text to impress someone? Or did I do it because I just started typing, and this is what naturally poured out–a stream-of-consciousness? If I were pretentious, I’d be talking about how I’m so much better at math than everyone else. Of course I know more math (when it comes to the math they don’t teach in school, also known as math, because they don’t teach “real” math in school) than most people my age, but that’s not the point I’m trying to make with my points. I don’t even see how my posts could even be considered pretentious, given that my posts are out of pure enthusiasm. When I post factual information, I’m expressing my enthusiasm of teaching mathematics, as well as trying to open the eyes of the public laymen community–and it HAS worked not once, not twice, but countless times to stimulate a greater appreciation of math from those who don’t act like the illogical and immature child that hides under the sheets and refuses to look again at what they thought was a monster with the lights on to see that their fear was irrational. Shed a new light unto what appears formidable and terrifying, and the more mature and logical of the children will be willing to take a peek and open their eyes to see that there was nothing to fear. A few children will begin to question the logic behind their other fears, and begin to examine their closet and under their bed for “monsters” using a flashlight, and realize soundly that when illuminated, all they feared to be “monsters” was nothing more than a product of their imagination. And perhaps, under the bed, instead of finding a monster, they’d find their beloved long lost toy, or a forgotten book, or that 100 dollar bill their mother hid under there to reward them for conquering the fear that lies beneath what they lie on. I hadn’t expected more than one or two people to open their eyes to mathematics. What I got was more than I expected: a few crybabies that pout and cry and refuse to lift the sheets off of their head even after I turn the light on; many that take a peek and then goes back to sleep content with the fact that there is nothing to fear, but don’t care to investigate further; and a tiny fraction of those that get up, grab their own flashlight, and shine it on other things they’d been too scared of or too unwilling to look at before the light was turned on. And that tiny fraction represents far more than I expected to convert. The crybabies and neutrals were expected, but to me, the very fact that I led so many people to appreciate mathematics makes me feel as if I’ve already succeeded in life. There are some that already have their light on, but they don’t seem to try and show their peers that there is nothing to fear. They hide their feelings and are unwilling to spend four hours typing up a wall of text to show people what exactly goes on in their mind in a four hour period. With I, this is only a fraction of the topics that go on in my mind, because I obviously don’t need to explain things to myself, but it’s a sample of what my stream of consciousness is like, less a bit of math and interjections. And part of what goes on in my mind, apart from math, is the idea of clearing up misconceptions and introducing new ideas to the public. I don’t care to show off. I don’t want to show off. I want to teach. I want to educate. I want to make people think. I want them to dust off those gears which they try to operate as little as possible, and show them that the only reason the gear system isn’t working is because they’re missing one cog–which I provide–that’ll make the entire system run smoothly, that makes everything suddenly make sense. I give them this missing cog–whether they install it or not is up to them. What pleases me is not flattery–in fact, flattery is quite unflattering. I don’t want people to call me “brilliant” for writing erudite walls of text. I already know that I’m above average, and I don’t like being told what I already know. I don’t want to be tagged with any superlative, because more often than not, the superlative is inaccurate, and as such, it is something I do not appreciate. I do not like being told inaccurate information. I’ve never written anything to show off, unless I’m explicitly stating I’m doing such (usually, in a lighthearted manner or to troll a troll; academic trolling works best with those who harass me at school, since it usually makes them feel incompetent and thus stop). Apart from writing walls of text (this one included) for fun, I write them with deliberation–I intend to educate. In fact, I find it very insulting if all someone does is compliment me on writing a wall of text and nothing else. It’s even more insulting than comments that are illogical or irrelevant, because I know that most who compliment me are intelligent enough to understand at least part of what I’ve written, and as such, take something from what I’ve written and discuss it with me. If someone wants to flatter me, they’d tell me not about how they love my writing, but instead how it opened their mind, and what they’ve taken from it. If they really want to flatter me, they’d challenge me. They’d challenge me with an argument. It’s direct proof that they got the point of my post, that it made them think. That it made them grab their own flashlight and go monster-hunting and such. Regardless of whether their point is valid or not, it is the comments like those that keep me in business. It is the comments that make ME think that I value the most, because to me, thinking is my favorite hobby. Thinking is what has made me as apparently intelligent as I am. No one should sit around and compliment me for thinking. I want to get them thinking. There was a point I could hardly draw stick figures. My drawings all looked like those of a third grader up until tenth grade, when I started to draw. I used to marvel at even the most simplest sketches by the artists in middle school and I’d ask them how they’d learn to draw like that, and they all tell me the same thing. Practice. Within three months, and now a few years, I’d draw two or three full quality line art drawings during a single period… or so people think of what really are absent-minded doodles. I learned to draw by practicing drawing, not by complimenting people on how well they draw. I think the way I think not by complimenting the people that think on how well they think, but by thinking for myself inspired by the way they think and what they think of. I do not spend four and half hours typing just any wall of text for fun. I now say this with deliberation: I’ve mentioned a countless amount of topics that one can dwell on, challenge, bring a new point of view to, and so much more. This is perhaps the largest wall of text I’ve ever written for EP yet. Surely you will have something intellectual to contribute. It is those types of comments that actually make me post walls of texts. In fact, even this one was spawned from a completely unrelated comment that I’m not even sure is directed to me or not. Even if you don’t take anything from this wall of text, I ask that if not anything else I’ve mentioned in here, you take at least this mantra with you:

Think. And when you’re done thinking, think some more. Thinking soon becomes addictive, and you soon become a thinkaholic. Thinkaholism is what brought us the greats in this world. Think responsibly, of course, and do not commit logical fallacy. And if you cannot think of anything to think about, think about how you’re thinking about how you cannot think of anything to think about, and are thus thinking about thinking about how you cannot think of anything to think about, and get a good laugh out of the experience. Never stop thinking. It’s perhaps the most dangerous thing anyone could ever do.

End Ramble

Because the post is so recent, there’s only one real significant comment thread. I think I’m on 14 when it comes to anonymous censoring.

**User 14 [October 29, 2014]: **

I wonder if you are really 17, and then I wonder the extraordinary amount of randomness that made me come here, read the post to the bottom, and if you think about the coincidences it’s bewildering.From now, THIS moment,I feel a strong desire to ACT on the thoughts, the longings, the dreams and the fantasies of being able to UNDERSTAND the mathematics that I appreciate as beautiful, as seducing becuase without learning additon you can not know about Arithmetic Progressions or the convergence or divergence of a series, and to learn is to ACT where thinking acts as the initiator, and when you’ve learned enough a specific topic(for one can NEVER learn enough) thinking is what pushes you further, and leaves you at the cusp of voracious realization that you know too little.For longer than I can recall, I have been just ignoring the deafening ramblings of my mind, which theologians would argue is the soul or self, and this period of ignorance up until now(more specifically up until the moment I was at the end of your post) has extended so long that I have forgotten: I was born for mathematics , for psychology , for just wondering(I prefer this word to thinking, however I am not aware of the differnces between them) how the world works , just how does a child learns so much , how language evolved, and a myriad of other things which are seemingly so simple that you don’t need to put a conscious effort to achieve. Too much of laziness , excuses has put me off my track( I blame school and college and parents and society; just about everyone else except my own) which has resulted in my forfeiture of learning, which in consequence has resulted in my lack of understanding mathematics.

If I think about what I do , and what I think I would or shall do, I realize that I contradict myself too much, and am a great hypocrite.

Take me in, I want to think, to know you.

**User 14 [October 29, 2014]: **One hour ago, I replied and since then, I have realized that for 8 long years I have wasted myself(although I knew this before your post, was just reluctant to admit so), past three months I have been in a disturbed state of mind becuase with every single pico-second I am decaying and I have yet to learn mathematics, reading your other post about topology and chaos and mathematics, and all the mathematics articles, wiki pages and the lives of other mathematicians in the past hour,that I had bookmarked for a long time(I mean some not ALL) has made me embarassed and I have ‘cried’ (although now that I have stopped doing so, it seems extremely illogical to do so) that I do not have the least idea about topology, about fermat’s last theorem, game of life, fractals and mandelbrot set.Altough I have came across all of these many many many times over, but never have been able to acquire the pre-requisite knowledge to truly understand them. TEACH ME 😦

**Me [October 29, 2014]:
**

Yup. I’m 17. Here’s a (somewhat blurry) picture of me:http://i.imgur.com/vFYXywF.jpg.

The act of thinking can be related to Newton’s Third Law. An object at rest tends to stay at rest. An object in motion tends to stay in motion. Likewise, unless you start thinking, you’re not going to learn anything. But once you do start thinking, you’ll get absorbed… you won’t be able to stop. You’ll be hungry… VORACIOUS for more knowledge. And even after you’ve thought a lot, you’ll be starving for more, because when you’re hungry for knowledge, you’ll never have to worry about “overeating.”

People have a tendency to tell themselves that they’re not good enough, and that they should just leave it up to the “smart people.” Now while some people have a greater ability to learn than others, it’s only by a marginal amount.

It’s not that they’re incapable, or that they’re not intelligent enough, or that it’s truly difficult… because it’s not. When I was 10, I thought that calculus was extremely difficult, and that it would take forever to understand it. That’s because, at the time, I didn’t know algebra. Algebra would look hard to a preschooler, simply because they haven’t learned to do any math past addition and subtraction if at all. I have a few books on fractal geometry that confuse the heck out of me, but I’m slowly moving through them, teaching myself along the way. Especially when it comes to mathematics, there’s a lot of extraneous information that’s just there for formality. It only sounds hard because of all the extra words, but at the bare-bones level, it’s rather simple, actually.

Mathematics has never, ever, been hard for me, if I’m learning something that’s at my level. Of course this book on fractals is hard. I had to teach myself a branch of math that’s not so much as mentioned in math classes in high school–set theory. If I didn’t know set theory, then of course I’d find that section that assumes I know basic set theory very difficult. But if I do know set theory, then it isn’t so difficult after all. Right now, the Schrodinger equation is nothing but symbols to me. I don’t know how to work with it in the least sense. All I would be able to tell you is that it involves partial differentiation–something I know of, but barely know how to work with. I know what it’s supposed to represent, and I could tell it on a heartbeat–it’s a probability function that’ll tell you the likelihood that you’ll find an electron in a given place. But… within a few years perhaps, the Schrodinger equation might be but child-play, and I’ll be attempting to solve the Navier-Stokes problem or something of the like. It’s all a matter of perspective.

Jargon obfuscation is seen in two fields in great amounts–mathematics and law. In law, they do so primarily to confuse a typical person, so that they can land them in traps (or sneak them out of one). In mathematics, it’s primarily done for formality, because of how conditional certain circumstances may be.

For instance, let’s say that I’m describing the Collatz Conjecture to someone, and I demonstrate it first. I cannot simply say “pick a number,” because this “trick” (one that someone would earn a million dollars and a Fields medal if they figured out how it worked) only works with a certain type of number–positive integers greater than 1.

Now, I could simply state it this way:

Pick a whole number greater than one. If it’s even, halve it. If it’s odd, triple it and add one. Repeat this process over and over again, and you’ll eventually always reach one.

So simple, that even a first grader could do it. Right?

How about this?

Let (n_0)∈(ℕ>1). For (n_1) given (n_0), if mod2(n_0)=0, then n_1=(n_0)/2. If mod2(n_0)=1, then n_1=3(n_0)+1. For n_k where k is the iteration depth, if mod2(n_k)=0, then (n_k+1)=(n_k)/2. If mod2(n_k)=1, then (n_k+1)=3(n_k)+1. With enough k, n_k will always eventually equal 1, so goes the Collatz Conjecture.

The same thing, put in formal terms, suddenly became a LOT more complicated, right? It now looks like something you wouldn’t see until the third year of college–and you’re right. It’s not something you’d see in formal terms until then. But this is describing the exact same process as the simple version! They’re playing kid-under-the-covers. They’re so insistent that what they saw looks scary, that they’re not even ready to listen to an explanation of what it means behind all the symbols, formality, and jargon.

Schools often fail to teach math properly. The teacher will show on the board the formula for differentiation. “f'(x)=[f(x+Δ)-f(x)]/(Δx)” writes the teacher on the board. The student asks, “Why?” The teacher replies, “It’s not going to be on the test. It’s in the book. Go look there.” The most the teacher is willing to teach is draw a graph with points a and b with a line connecting between them, and show what happens to that line as b approaches a. No more. Nothing about how the function is derived. No proofs, nothing. The only time schools ever seem to ask you to prove anything is in Geometry, and that too, for rather unspectacular things.

They’re not interested in teaching you why a guess-my-number game works. All they care about is “this number trick will always equal this number–just know this for the test… to hell with why it works because it’s not going to be on he test.” That’s how you can tell math teachers and mathematicians apart. Math teachers only care about the test. Mathematicians actually care about the math, and want you to understand why something is the way it is… because THAT’S where the beauty of math lies. Remember. While the view the end of the trail is spectacular, what’s most memorable is the journey that took you there. They condition students to believe that there is no beauty in math–in fact, giving the impression of the exact opposite. Of course people aren’t going to enjoy it… they don’t know what real math is. Of course people find it difficult. They’re not getting the “why” behind what they need to learn. They’re not shown where it’s applicable, and why it’s so important. Sure, there are some parts of math that are purely recreational–for instance, perfect numbers, where the factors of x add up to x (like 6, because 1+2+3=6, and 28, because 1+2+4+7+14=28). But ironically, the math that people actually find “fun” has little to no practical use, and the math that is integral (pun intended) to the modern world is despised, and spawns the all-too-often-asked “when am I ever going to use this” question, as if implying they’d like “useful math” better.

Schools don’t teach math properly. It’s not an individual’s fault that they don’t like math. What they really mean is that they don’t like “school math.” As do I–it can hardly be called math. I want people to know what real math is. I want to inspire people to achieve greatness. Knowledge is not something meant to be hoarded. Knowledge is something that should be spread as much as possible–liberally so. Most of what I will develop (software-wise) will be open-source. If someone can improve something–by all means, they should do it! The only thing they shouldn’t do is plagiarize, or take something open-source and try to profit from it.

Of course my career goal is as follows: Go to MIT and do research on various theoretical and applied aspects of mathematics, particularly of dynamic systems in the quantum and cosmic level, as well as that of the brain and how it affects us and how we can use this knowledge to treat mental illnesses and perhaps develop a true AI (one that doesn’t have access to any neurotoxin or unethical human-testing research facilities), as well as perhaps direct a documentary series that brings the beauty of math and science to the public in a way that is not so much pedantic as it is didactic and philosophical, which will assist in forming an emotional attachment to the subjects that’ll aid them towards pursuing academic interest and overall inspiring children to find true academic subjects as interesting, fascinating, and fun as they find the opposite (or same/different/lack-of) gender, toys, sports, and pop culture interesting.

But that’s my *career* goal. I have only one goal in life. I want to change the world. Yes–this cliche statement, millions of times overused… but I really mean it. But when I say it, I don’t mean that I want to invent a new technology that revolutionizes the world. Of course I want to do that, but I’m not necessarily going to die with regret if I don’t. What I mean is that, more specifically, I want to inspire the world. One person might be able to get a lot done with their life… but imagine what could be done if that one person inspired others to do greatness. Even if it’s just one other person that I inspire… two greats can do more in total than one can alone. I’ve inspired more than just one person before I even graduated high school. Most of them simply become less sour towards a subject. There is, however, a small fraction of them that actually understand what my pedagogical posts are trying to say.

When I explain to people the Collatz Conjecture, I’m not trying to show off that I know what it is. I’m not trying to state it matter-of-factly. I try to show them that such a simple problem has such an elusive answer. Of course, I don’t expect them to suddenly want to be the person that solves the Collatz Conjecture. When I explain to people the Mandelbrot Set, I’m not trying to show off that I know what it is and can make some pretty pictures. I’m not simply trying to show them pretty pictures, or state it matter-of-factly. I try to show them that such a complex figure has such a simple construction. I want to show them what schools don’t–that not only that looks can be deceiving, but also that there is beauty behind it all. Why it’s beautiful. How to see that beauty.

A novice wine taster will not be able to tell the difference between wine from a gas-station and the finest wine from the finest winery in all of France. A wine connoisseur will be able to taste the difference between two of the same wines where one is a year older than the other. Of course, the same can be said for five hundred pictures of Joe Biden eating sandwiches, but my point is that once someone learns how to see the beauty in something, they’ll realize how much they’ve been missing out on. The wine connoisseur will be able to tell you how to taste the subtle differences between wines… they don’t simply drink the wine. They experience the wine. Of course, I’ll have to wait another four and half years before I can taste any wine for real, but if the wine connoisseur describes the wine in the right way, I’ll be able to appreciate and see why some wines are better than others. That way, when I do turn 21 and start sipping some wine, I’ll know that I shouldn’t simply drink the wine, but I should also experience the wine. I’ll know what qualities I should look for, and truly enjoy the wine as not simply fermented grape juice, but as a symphony of parameters; the instruments of tartness, kick, strength, color, aroma, and so many more, all playing together to orchestrate the music we drink as wine. Some music sounds beautiful; others, not so much. I’ve heard people describe wine before, and I’m able to not only imagine what wine may taste like, but also describe it as though I’ve been drinking it for years, even if I’ve never had a sip of alcohol ever before. That is to say, even if I don’t really know what wine tastes like, I’m able to appreciate it as an artform and craft, where others that have never tasted wine can’t even begin to imagine what it might be like. Many others that have tried cheap wine will judge the flavor of “real” wine before they even taste it, and even if they do, they don’t know how to tell the difference between wines, and mark them off as equals.

The same is true of math–only instead of the occasional glass of wine this would be the equivalent to being a fish that lives in a sea of wine, because we’re *surrounded* by it. If someone sufficiently describes how to see the beauty in math, one doesn’t even need to know the math itself to see why it’s so beautiful, just as one doesn’t need to drink wine to be able to relate to what it tastes like and why it’s enjoyable. One simply needs to inspire the other person, and to train them in how to see the math around them, and why the math is so beautiful.

I don’t need to go into depth explaining how the Mandelbrot Set is made to show that it’s beautiful. I don’t need to explain much of the math behind the Golden Number to show why it’s so beautiful–all I need to do is teach them how to look for it; most of the time they’re awestruck about the patterns that’s right under their noses (somewhat literally so, too, because much of the face conforms to the Golden Ratio), and they then can’t stop seeing it everywhere. All I need to do is give them a very succinct and simplified version of the math, and then explain to them why it is beautiful. Perhaps they’d even be interested in the math behind it all, if they’re sufficiently impressed with what I have showed them.

Now while it would be very difficult to explain to them the beauty behind Euler’s Identity (it takes some experience before one realizes why a function that uses e, i, pi, 1, and 0 is interesting), I can get them to realize that math isn’t the monster they thought it was, but instead it is an elegant, seductive, exhibitionist maiden that dances for those that find her… for She blends into the background until spotted. Then, once top-down processing has occurred, you won’t be able to stop seeing Her, and you’ll get seduced by Her performance, desperate for more… eventually one will see that the background is a part of Her dress, and once you strip everything away, She is nothing but Herself–pure mathematics–underneath.

Just as imagining what wine tastes like is nothing in comparison to the real thing (so I assume), simply enjoying the math without truly knowing how to do it is nothing compared to actually knowing how to do it while knowing how to see its beauty. The closest thing I can describe it is ASMR combined with true Enlightenment. We don’t need to give up all of our material goods (though extreme materialism that is the “American Dream” is awful and appalling) and live in the middle of nowhere to achieve it. It is when one learns to see how everything relates to one another (via the language of Mathematics) one has become truly Enlightened. It is when you experience the gestalt and the details at once–that is, being able to see how everything interconnects and how everything is perceived as a whole. The more detail one is able to perceive, the more interconnected everything is, adding to the experience–and nothing describes the world in greater detail than mathematics, especially when one learns to see the connections between it all. It is then when one’s able to truly understand and experience their surroundings. Such an interconnection is far more intricate than the integration of all life forms on Pandora, mathematically connecting everything, not simply life, together as one. To see this integration as well as be a part of it then becomes something of extreme euphoria. This feeling of knowledge… this knowing… this intuition of the surroundings! Oh, how everything interconnects! The beauty of it all! These are the patterns! This is Enlightenment! Oh, if only I could just show them the patterns from the get-go! Perhaps then they’d be as infatuated, fixated, and seduced by Mathematics as I! Oh how lucky I am to be Enlightened at such a young age! How much more of life I can experience being Enlightened! And how much more of life I can spend Enlightening!

Sadly, I can’t just show others the patterns from the get-go; however, I do make it my every effort to set people on a track towards seeing the patterns. Why do I post to a site like EP? What use is there posting to forums where people are already Enlightened or are already on their track towards being Enlightened? I reach out to the layman community to see who’s willing to take my hand and trust me to show them the road to Enlightenment. The roads may be dangerous to travel alone, but with one that has conquered the road, there is nothing to fear. The first segment of the road is rocky and barren, but past that, it’s a smooth and very scenic and serene route. And perhaps they’ll love the scenery so much, that they’ll deviate off of the road to go discover more on their own, and perhaps even discover a new scene entirely. After all, the Enlightenment can be found along any part of this road. I come onto EP looking for prospective explorers. Whether they’re tourists that drop by just to check it out, or travelers who want to gain some experience, or true explorers, and want to go out on their own, I want to show them what and all they’re missing out on, and inspire them to do greatness. There is much land to explore, and we need explorers to reach into the unknown. Even if I recruit just one explorer, who knows? That one explorer might be the one that discovers a vast expanse of waterfalls, jeweled caves, and new species. The more explorers I recruit, the greater the chances of one or more of us discovering something significant. And if you ask me, THAT’S what makes my life worth living. Be it I or someone who I inspired, nothing matters more to me than see this world progress intellectually. And with that, I’d be able to die happily.

I wish to inspire greatness. It’s true what they say–it’s lonely at the top. That’s why I’m reaching down to make some friends and inspire them to climb the ladder to join me and to see the view.

And today, you have brought a tear of joy to my eye, because, for the first time in the past year and a half, my posts served more than their intended purpose: I’ve not simply inspired someone to appreciate and look into mathematics more, but I have also now brought someone’s train back onto its track, and I may have brought forth an epiphany in someone, inspiring them to take action and pull themselves out of the darkness.

I would be more than happy to take you in, teach you, and open up to you. I must warn you, though. The first part of the road ahead is rocky. It might jar you around so much, that you may want out. But I promise you, the road ahead is smooth and beautiful. There may be some rough spots along the way, but the scenery is oh so beautiful.

So I ask you this. I reach my hand out to you, and offer to show you the way towards this incomparable beauty. At one point, I must let go, and leave you off to explore on your own, be it known areas or an expedition into the unknown. But for now I ask you to trust me, and bear through the rocky introduction. My hand is extended towards you. The question is… will you take it?

Of course, given how recent the post is–especially my reply to his comment that, as of this post, was posted about 10 hours ago. If necessary, I’ll update this thread. But this sums me up like nothing else, from a philosophical perspective.

** **

A quick point about the primes!

Primality tests aren’t nearly as elusive as you make them out to be, I’m afraid. We /do/ have very efficient primality testing algorithms — I recommend looking up the AKS algorithm. It’s a bit involved, but it’s very fast, and is in fact in P. (Given an n-bit number, AKS allows you to determine its primality in n^6 time.)

And when you say that “there’s no way to determine if a number is prime or not, other than testing each factor” — well, it all depends on how you’re dealing with notation. If I gave you a function from R to R, and asked you to determine if it was an even function or not, one could argue that “there’s no way to tell for certain that it’s even at ALL points unless you try all of them!”. And in some cases that might be compelling, if I gave you a very very complicated function with no clear simplifications. But if I give you the function f(x)=x^2, you can immediately tell that it’s even.

Similarly, if I give you the number

2186975371034984108708031312226086440343946183034312578845248165029983\

7224223958498251722557711882625578162418269864051129621129352976610631\

2723916710697558805391637497871620579209

it’s not very straightforward to determine if it’s prime or not, but if I give you

2186975371034984108708031312226086440343946183034312578845248165029983\

7224223958498251722557711882625578162418269864051129621129352976610631\

2723916710697558805391637497871620579209^2

then you can immediately tell that it’s not. Or less trivial expressions, like phi(607251906256126427388165319700), where phi is the Euler totient function — phi never has a prime output except for phi(3), so even though evaluating the above might be very difficult, you can tell me right away that it’s not prime.

What if I ask you, is the number 607251906256126427388165319700 even? You can look at the last digit and immediately tell me yes. So telling if a number is even is “easy”. What if I asked about being a multiple of 7? A lot less easy, and you need to develop long division to figure it out. But at the same time someone who works in heptenary says the divisibility by 7 is easy! And someone who works in unary would say — “ah, not there’s no way other than to try it out! Count the 1s, going in groups of seven, and see if there are any left over!”

Primality is not mysterious, it’s all a matter of wording. Primality determination, given the number in some low-base digital system, on a Turing machine, takes a lot of steps to compute. But that’s only a matter for Turing machines. From a purely mathematical perspective, it’s hardly even a question.

Now, you do have one point about it being slow. Factoring an integer is hard. Pretty hard, for a Turing machine. And right now we have only algorithms that run in time significantly higher than polynomial — almost exponential, in fact. We don’t think it’s NP-hard, though. It’s certainly /in/ NP — everything doable in P is, for instance — but to be NP-hard would mean that any problem could be rewritten in terms of factoring, and that’s very unlikely. It’s hard, yeah, but I think right now people /are/ expecting it to be broken /eventually/. It will just take time to find it. AKS took a very very long time to find, anyway.

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When I said “There is no way to determine a number is prime or not,” I implied that there was no straightforwards formula. We know that if it ends in an even number or a 5 that it isn’t prime, but past that, there is no one true formula to test for primality. I know there’s also Fermat’s method of calculation. 😀

Can you tell me exactly what NP and P problems are? I’ve been trying to understand them, but I’m not exactly sure what polynomial time is. And why exactly are we not sure if P=NP or if P != NP?

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First off — these are questions formulated on a Turing machine, which is for all things we would most likely consider equivalent in power to classical physics. There are some problems which a Turing machine (classical physics) can’t solve efficiently, but which a quantum computer can.

P represents the set of problems that can be solved in time polynomial with some parameter. A “problem” is set of inputs and corresponding yes/no answers. For instance, in terms of checking if a number if prime or not: the problem is a set, usually referred to as PRIMES, which has the elements { (1, No), (2, Yes), (3, Yes), (4, No), (5, Yes), … }. There’s an algorithm, called AKS, that can take an n-bit number and determine in n^6 steps whether or not it is prime. Because of the existence of this algorithm, for each element in the set, you can figure out the second element from the first in time polynomial in the size of the first element. (Read that a couple times, maybe.) Other things that are in P are, for instance, sorting a list (this can be done pretty easily in n^2 time, if you have n things to sort), finding the shortest path between two nodes in a network (can be done in n^2 time, if there are n nodes connected), finding the two nodes in a network that are the hardest to get to from each other (n^3 time), and stuff like that. Factoring is currently not believed to be in P, as there is no way to get from a number in binary (or decimal) to its list of factors.

NP looks at a very different kind of machine. Suppose you had a machine that could “guess lucky”. For instance — I want to factor an integer. The machine “guesses” one set of factors, and checks if it was right. And then in one possible path, that machine ends up finding that it was correct, and so we have the answer. In a slightly different way of understanding it, we ask the machine, “Is the smallest factor less than 1 billion?”. If it says no we double our guess, if it says yes we cut it in half. Clearly we can home in on the correct smallest factor very easily. This is also a form that adheres more strictly to the “yes/no” form of computation, but it still lets us find the actual factors very quickly. Our magic computer splits into a huge number of universes, in each one picking some trial number, like 123456789123. If that number is more than 1 billion, it’s not worth checking, so the computer shuts down. If the computer has a number less than 1 billion, it tries dividing by that [guessed] factor, and if it works, it spits out “YES”. The way this machine works, if any of the possible universes spit out YES, then the whole thing spits out YES. If none of the universes spit out YES, then the whole thing spits out NO. This is a form of “nondeterminism” because it is, in a sense, doing different things unpredictably. If you think about it a bit you’ll see how “try everything, see if any of them work” and “try to guess lucky” are the same thing. There are a lot of questions that /can/ be answered efficiently if you’re always guaranteed to guess a lucky key. This kind of computer is called a non-deterministically accepting computer, and we’re still interested in things it can guess+check in polynomial time. Thus, this set of problems is known as NP, for Nondeterministic Polynomial.

Everything in P is also in NP. Anything a regular computer can do, a nondeterministic one can as well. So P is a subset of NP. On the other hand, there are some problems, like “is there a way of choosing numbers to simultaneously satisfy all these (nonlinear) equations?”, that are known to be in NP, but are not believed to be in P.

This was all fine and dandy, and then a mathematician named Cooke found a very surprising result: there are some problems in NP that are as hard as anything else in NP. If you Google 3SAT you’ll find the one he used. It’s pretty simple, it’s about trying to plug true/false into a boolean expression to satisfy different requirements. Cooke proved that any problem in NP could be rewritten in terms of 3SAT of a similar size. Thus, if someone could quickly solve 3SAT, they could solve anything! This was called “NP-hard”. NP-hard means it’s as hard as the hardest things in NP. 3SAT is also within NP itself, so it’s called NP-complete. There are some other things that are NP-hard but we don’t think they’re in NP (they’re /very/ difficult problems), so we just leave them alone — they’re NP-hard, but not NP-complete. But because many people don’t talk about that kind of problems, some people us NP-hard when they mean NP-complete, unfortunately. Over time, people showed that 3SAT could be re-written in terms of other problems. For instance, there’s a way of turning the “true” and “false” notion into different structures of triangles, so you can re-write 3SAT as a problem about network structure; and then you can rewrite that network structure problem as something about solvability of NxN sudoku puzzles! And because anything can be re-written in terms of 3SAT, and 3SAT can be re-written in terms of these other puzzles, they’re all NP-complete! http://en.wikipedia.org/wiki/List_of_NP-complete_problems is pretty comprehensive. If you could find an efficient solution to any of these, you would be able to do anything in NP very quickly, and you would basically win the whole world. 😀

So, if anyone finds a way to do an NP-complete problem in polynomial time, that problem would be in P, so all of NP would be in P, and P and NP would be the same set! However, this is is widely viewed as unlikely.

Some other sets of problems, similar in spirit to P and NP, but easier or harder or just different, have been proven to be separate. This is usually through establishing that there is some problem in one set B, that is just soooo hard that it’s impossible for it to be in A. There also have been some major surprises, like L and SL, which are sort of like dumbed-down versions of P and NP. No one thought they would be equal, but then Omar Reingold found a very surprising and complicated algorithm that lets you solve SL problems in L. It’s been a long time now, and no one has found a way to put NP in P, and no one really expects to. And even if someone did, they would have so much power to control the planet, that they would definitely not let anyone know. On the other hand, no one has found any NP problems that are provably not in P, no matter how obvious it feels.

Maybe you’ll find the proof, good luck! 😀

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