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About jndiii

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  1. Binary Algorithmic Computational Orthogonal Numbers?
  2. The typical proof of a limit is that you can always find a closer point. When this is on a real number line or a complex plane, it is trivial to prove a limit at a point. Here, because the path is bouncing, it's not a straight line, but geometrically, there is always some point on the path that is infinitesimally closer to any given point (on the square, not just the corners). Let's say you choose point A on the path. It is distance 0.01 from point B, which is not on the path but could otherwise be anywhere on the square, its edges or its corners. Lets say you chose A carefully, so that it is really the closest point on its particular segment of the path (i.e., between two bounces). You can find another point, within .001 or .0001 or .00001, etc., of B, but it isn't on the line segment on which A lies. In other words, any rational slope only fills an infinitesimal amount of space of the square. Any irrational slope will result in a path that completely fills the square, even though there are "rational holes" that are not filled.
  3. Nothing any more special than those with a rational slope, except that all the points on the line that intersects the origin (or whatever vertex) will have irrational coordinates. Another interesting bit: in the case of the rational slope, you can show that except for those lines that intersect a corner, none of the points on that line (bouncing path) get infinitesimally close to a corner. In the case of the irrational slope, however, for any given point on the bouncy path at a given distance from a particular corner, you will always be able to find a point elsewhere on the bouncy path that is even closer. Oh, and the nearer point is often not adjacent to the initial point, but instead is on a part of the bouncy path several bounces before or after the current bounce. (I hope that makes sense. There aren't any good words for the concepts without getting super technical.)
  4. Nope. Can you prove why?
  5. ...... added to this post 4 minutes later: I'd say it's a matter of definition, depending on what kind of problem/context you're trying to describe. If we're literally thinking of a ball bouncing, then the ball would retrace its path back to the origin. If instead we want to explore the overall math, we'd explore how using the extended straight line path traces the sides of the square (using rules we already explored) and see if we can learn anything from it. In this case, I think both of these contexts yield the same result, the retracing of the path backwards and forwards.
  6. This is a great explanation of personality theory (which Peterson interestingly notes didn't start out as a theory), how you measure personality, and a good introduction to the Big 5, what the traits are, what they mean, and so on. I think this is a great resource for people looking into personality theory because it mostly ignores the clickbait-style aspects of finding out what kind of person you are, and instead focuses on putting the concept of personality traits in context. I found myself having to stop and go back a bit every now and again because he's throwing out the ideas so fast, and I'd still be in the middle of processing one thing he says even as he introduces a new idea. There's lots of little interesting tidbits here, too. He briefly discusses what IQ really is, that it's a number measured the same way you measure personality traits, and that it essentially is a personality trait, i.e., it is measured in the same way and that it strongly predicts outcomes. Moderators: if this doesn't belong here, please move it to where it does belong.
  7. Most "randomness" is just complexity. Flipping a coin, whether it's going to rain or not, what number a random number generator will create next ... in all of these, if you could completely understand all the complexity, none of them would be random to you. You'd know which way THAT coin would flip because you could instantly calculate how it was spinning, etc. The only case I know of which is "truly random" would be quantum theory, where every attempt to find the "hidden variables" has failed. So, unless you're trying to predict the spin of an electron, it's complexity, not randomness. And complexity in turn is why all reasonable theories/understandings must be incomplete. To handle all that, we also have theories on how to handle complexity. In chaos theory there are attractors, where you might not be able to predict a certain value, but you'll be able to say that the values tend to hover near certain points/ranges. In physics, there is thermodynamics, where the underlying randomness/complexity of statistical physics becomes very predictable because the randomness cancels out for very large numbers (like 10^23 particles or more). Similarly, in human endeavors, there are principles such as those I've already mentioned where, while not always applicable, help to figure out otherwise "irrational" situations. All you have to do is assume that most people in a system are not idiots, most are not evil, but they are all human and are subject to basic human motivations. A simple but very predictive theory of this sort is "follow the money": it doesn't mean that the money transfers are illegal or unethical or stupid, but taken collectively, they motivate a group/system to do things that make no sense on an individual level.
  8. My grandparents slept on separate twin beds in the same room for 50+ years. I never asked why, but I suspect they both slept more soundly that way, and usually went to bed at the same time. Note that this is different from sleeping in a different room, or occasionally sleeping in a double bed and occasionally sleeping separately.
  9. I wasn't saying you don't have courage. I'm saying you already have the tools to deal with it. But yeah, it does suck. The system isn't "flawed" so much as it is human and it is, overall, a complex system. Complex systems MUST have flaws. It's kind of a meta-rule. Check out Godel's Incompleteness theorem: it's easy for simple systems to be "complete", i.e., they work 100% as conceived/designed. Complex systems, however, where "completeness" means achieving every single desired goal, including those no one conceived of before designing it, can never be complete. If you try to make such a system complete, it ends up being contradictory (think of the implications of jargon such as "catch-22" and "SNAFU"). Why does it work this way? Because the system would be entirely useless if it didn't simplify things. You think the internet gives information overload? Imagine having to completely 100% understand something that is complex. You can't. It doesn't fit. At best, you can have a finite set of rules that cover most cases reasonably well, and then lots of special cases that need to be figured out without the rules. I don't blame the players or the game. Rather, once you know that's how the game is played, once you know where the systematic flaws arise due to normal human dynamics, then you can work around them and keep them from fucking you over too much.
  10. How to deal with it? It's called "courage". You just keep on keeping on, knowing that 90-95% of the time, you will be rejected. I work in a very lucrative field in a city where the job prospects are excellent and only getting better. I usually have to go through dozens of phone screens and about a dozen intense 3-hour-long interviews before I get an offer. Even then, I sometimes reject the offer. Last year, I was out of work for about 3 months, constantly dealing with rejections while keeping my standards as high as they needed to be. Emotionally, you just need to know that it is never, ever about you. It is always about them. Most employers absolutely suck at managing job interviews. They farm things out to recruiters, who in turn act like vultures, like scavengers, fighting over the few employable people out their and trying to hawk these people they hardly know to get a commission from the potential employer. When things finally get to the employer, it turns out the person in charge of hiring is being incredibly lazy. Here, they have a candidate which has passed phone screens and clearly knows what he is talking about, and then they give even more tests that prove nothing either way?! Why would you invest emotionally in such a process? Why should these lazy greedy people even begin to affect your sense of self-worth? Now, I'm not saying they're bad people, per se ... but it's a system, and people tend to be as lazy and greedy as the system allows them to be. Oftentimes, it isn't THEIR money that they're spending, so they think that they can spend the company's money over the course of the year on dozens of interviews. As such, I've often found that startups and small businesses are much more direct and no-nonsense. The business owner is entirely conscious of the fact that each extra person interviewed is going to cost hundreds of dollars. That's a strong incentive to hire the first reasonably qualified candidate. In contrast, if it is a middle manager or (even worse!) a technical engineer doing the hiring, such people believe that they can be absurdly picky about their candidates. You can detect which kind of interview situation you have pretty quickly if you keep these dynamics in mind. The lazy employers will give you interview after interview, but the process never quite seems to move forward. The serious employers will probably phone screen you and then bring you in for an in-person interview the next day, and you'll know whether you have an offer almost right away.
  11. I'm more go-with-the-flow than an SJ type, but more about plans than your typical Perceiving type. My plans are always provisional. I don't know what I'll need to change, but I'll adjust them as needed to allow them to move forward, even to the point of deciding to entirely abandon a goal to instead focus on something more productive. P types, especially the xNxP types I am most familiar with, seem to resist having plans altogether. They like to keep their options open. I totally get that, but for me that approach is essentially the same as having no options at all, since you never really choose one. For me, I need to choose options to move forward, but I'm completely open to changing options when the options I've chosen seem to be blocking my progress.
  12. That's what I was trying to get at with the STOP sign analogy. Another analogy might be walking into your living room and smelling poop. You don't analyze the poop smell. You instead look for the source of the poop smell. When you discover the source, then you have enough information to do something about it. You were crying about fighting with people you care a lot about. You don't want to give more info, and I respect that, but that other info is going to tell you where the source of the need to cry comes from. That you cried in THAT case, but not for movies and other trivial things is saying that there is something you really care about going on there. There are typically two paths: one where you compromise something to keep that which you find more important, or you realize that someone or something you really care about is asking far too much from you and that you should give any more. Oh, and sometimes, it's just raw hurt, an empty spot in your life that you can't do anything about, but you have to live with it, but that doesn't seem to be this case. In the poop analogy, your dog probably pooped in the living room: you'll either do the dirty work of cleaning up the poop and work harder at house training, or you'll do clean up the poop and get rid of the dog as soon as possible. The parallel here is that "somethings gotta give". Things cannot stay as they are. A strong emotion like crying means that you need to resolve things one way or the other. The context of your crying tells you what it is that needs resolving. Crying isn't the problem, it's the signal.
  13. All decisions are comprised of a trade-off. You can choose A or B. At best, science can tell you the consequences of both A and B. Where does the confusion come in? Science doesn't actually tell you which choice is better. That's a personal choice/belief, not science. The word "pollution" is a good example. Typically, one might consider that a city isn't pollution, but what a city's sewer system handles is pollution. But some people might argue that the city itself is pollution, because without it there would be no sewer. Alternatively, one might regard the city's sewer system as a major source of pollution, in spite of the fact that it mitigates the damage of sewage. None of these are scientific questions, but that won't stop people from saying "science works, bitches" as the solution to all such disputes.
  14. @justpassingby ^^This is what emotional intelligence looks like. Taking what ENFPEACE is saying a bit further, think of your emotions as a kind of information, as a kind of truth. You don't "analyze" them any more than you would "analyze" a STOP sign. There is nothing to analyze. Instead, just as the "STOP" sign is a very critical piece of information about how to navigate a road, a strong emotional reaction such as crying is a very critical piece of information about your true self. Paying attention to emotions is a key part of self-awareness. Emotions aren't "ultimate" truth, any more than the STOP sign is. There isn't some ultimate spiritual meaning, for example. Instead, like the STOP sign, emotions are entirely contextual. A STOP sign at an intersection means you need to stop at that intersection. It doesn't mean you need to stop anywhere else. If you need to stop somewhere else, there will be a STOP sign there, too. Emotional truths work the same way. Example contextual emotional truths that might be conveyed by crying: This person is important to me. This principle, this abstract value is important to me. I really care about this, moreso than other things. This is the kind of thing I am looking for in life. (Yeah, these are all different ways of saying the same thing, but that's because it's all the same "crying" emotion. The contexts differ, but the "this is important to me" meaning is what crying means, in a very abstract way.) One thing to keep in mind is that everyone is driven by emotions in this way. In fact, people who have brain damage to the centers that convey emotion find it very difficult to make decisions, even as they are perfectly capable of logic. Logic is merely how you decide. Emotions are why you decide. Emotions point out what is important to you and what is not. That doesn't mean that such things should be important to you. Sometimes they shouldn't. Sometimes when an emotional issue comes up over and over and over again, it's a signal that you're prioritizing something that really shouldn't have much priority at all, e.g., being worried and anxious about things you cannot control. Either way, the first step is listening and letting your emotions tell you the underlying reasons as to why you favor A over B. In terms of MBTI and T vs F, this picture of how emotions work help to explain the real differences between "T" and "F". It isn't "thinking" vs "feeling" so much as how you deal with your awareness of emotions. F types tend to trust their emotions. They believe that their priorities and values come first, and then logic and reasoning follow. T types instead tend to distrust their emotions. They find that when they follow their emotional priorities/values, their life gets worse, not better. They learn to ignore their emotions insofar as possible, because they cannot trust them the same way an F type can. Both T and F types can be very emotional, but F types tend to go with their emotions and T types often go against their emotions. Both types, however, are very much driven by and make decisions based on their emotions. After all, even if one is a T type, "distrust" is an emotion, not logical reasoning.
  15. Just to drop in and say a random hi.  :)

    1. jndiii


      Is that truly random, or just pseudo random?