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Relationships, in the "Are you together?"-sense, are something fairly common to Life, especially that of humans (at least, as far as I can tell; maybe there's a whole culture within humanity out there that doesn't place any significance, positive or negative, on relationships). Whether one is in a relationship or not, the concept of them is pretty much inescapable, I think, especially if living in some form of society (though I don't think it impossible to have a society, at least hypothetically, where relationships are common or even essential; that's not to say I necessarily condone or condemn such a thing).

Consequently, it's something I've thought a lot about in many ways and many times, as well as something that's come up in conversation a lot, so I've thought about it even more! A particular aspect I think I have settled on (for now, at least) and that seems to be quite relevant, given the discussions/events about relationships that I seem to have/come across fairly often, is "What it means to be in a Relationship." I'll try my best to explain my thoughts (and feelings, perhaps), on this with a couple of analogies - the Double-Pendulum system (which might go onto Maypoles...!), and Mountain Climbing. Of course, what follows is my own opinion and almost certainly assumes standards across various things (which'll hopefully be apparent, but even more hopefully be fair/just, at the very least =/). I guess what'll be most obvious, so I'll state it now, is that I'm talking about relationships between two persons; I haven't really given much thought to 'higher-order'-relationships other than that they seem to be rather complicated affairs (that pun was semi-intended, but I am only acknowledging 'honest relationships', rather than those where cheating/adultery is an element), but that's not to rule them out. Anywho, my analogies happen to be 'general' in the sense that they can be applied to 'multi-point' relationships, but I will be talking about them in the sense of 'two-point' relationships, since that seems to be the most stable configuration that I can think of.

The Double-Pendulum: Before describing/considering a double-pendulum, first consider a single-pendulum - a rod of some length with a bob of mass at the end, swinging back and forth about some fixed point/pivot.

As shown in the figure above, a single-pendulum (without friction/energy loss to the surrounding system) oscillates in a very ordered (and regular) manner - it's path is predictable. In this example, the bob of mass is an individual, and the fixed point is said individual's goal - who they are striving to be. Of course, they're not getting any closer (or farther) to their goal in this particular example, but that's not what I'd like to describe with this analogy (that's for the Mountain Climbing one). The point is that the path is relatively simple/ordered.

Now consider a double-pendulum - start off with a single-pendulum, but stick on another bob of mass a fixed length from first bob:

Rather than the first bob (Red) following the same ordered path as it would have done (traced out by the red line), the collective (and individual) motion is now highly-unpredictable to the point of being seemingly random ("chaotic", in terms of Physics). This is because Red's motion is no longer solely determined by its goal, the fixed point. Now, Red needs to take into account what the second bob (Blue) is doing. Red, who is free to move around the fixed point at a certain length from it, has been exerting a force on the fixed point, and that has exerted a force back on Red, but as it's a fixed point, Red's been able to carry on in an ordered motion. However, with Blue now in the system, Red still exerts a force on the fixed point (that still remains fixed and exerts a force back), but Blue exerts a force on Red and Red exerts a force back - resulting in Red's motion deviating from its initial path. Furthermore, within this system, Red is supposedly a fixed point for Blue, so Blue would expectedly oscillate back and forth about Red in an ordered motion...but Red isn't a fixed point, and so Blue's motion deviates from its expected path. The two bobs' motions are coupled to each other, in that where one bob is going to be is determined by where the other bob is, but the other bob's position is determined by where the first bob is also going to be...it gets very messy and unpredictable, which is why we call it chaotic.

[Perhaps another way to try to explain this would be by considering where Red and Blue are and where they're going to be: Red: I'm at position R1, and Blue is at B1, and to get to position R2, I need to know where B2 is.Blue: I'm at position B1, and Red is at R1, and to get to position B2, I need to know where R2 is. Observers: What?]

Regardless, Red is still the aforementioned individual, the fixed point is still their goal, and now Blue is the individual's 'significant other' (I'm not sure what term to settle on that doesn't sound 'clinical', but "significant other" conveys what I mean aptly, I think, hence using it). Conversely, if we were to consider things from Blue's perspective, they'd now be the first bob and Red would be the second bob, rather than Blue still being an 'unhinged' individual being constrained/limited by Red - both have an ordered path in their own 'reference frames'/frames of mind, and those paths are being chaotically perturbed by their significant other.

At this point, please note I am not saying significant others automatically introduce chaos into our lives/are inherently negative or anything of the sorts; bear with me a little longer on this analogy. Also, neither case involves getting closer/farther to the respective goals, and this still isn't what I'd like to demonstrate with this particular analogy. Rather, the particular aspect of relationships I'm trying to get at with this analogy is the notion of Change, in the sense of the individuals in the relationship changing. "You're not who you used to be.", "I don't like who you've become.", "You've changed." These sorts of reasons seem to be relatively common for relationships ending (where there aren't clear reasons for it to do so i.e. abuse, dishonesty, etc.), and a lot of the time, I get the impression that there was a presumption of a person never changing =/

As you may have surmised, I find this presumption to be unjustified, and ultimately, destructive (at least as far as the relationship is concerned). People change all the time (hopefully for the better), and should do so (for the better), in my opinion - I don't think it's possible for us to 'max out' on how good we can be, even if it's seemingly tiny improvements here and there - we should strive to be the best we can be. Regardless of my opinions on changing (that it should be an ongoing thing and always for the better), people themselves are pretty much always changing according to their own metric and for their own reasons. To expect an individual is going to remain the same as they were at the formation of a relationship (with them) is unrealistic and wildly inaccurate, in my opinion - the second bob effectively gets thrown all over the place as they try to keep up with the first, who in turn is trying to 'balance' the two 'forces' acting on them. As such, the relationship itself suffers, in that (from the point of view of either, but not both simultaneously, individual) one is trying to achieve their goal and change in some particular direction to accomplish said goal, but they are also changing in another direction because their significant other is pulling them in that other direction (even if it's meant to 'restore' them back to their initial position i.e. so they don't change), so neither direction wins, and the individual ends up doing something different to what either intended/wanted (or at least doesn't satisfy either's intended movement). And when both of the individuals are going through the same thing, they both suffer even more.

Having said all of this, I think I've botched up my explanation of this, though when I say it in person, it seems to make sense to others - how peculiar, and my apologies if I have indeed messed up my explanation and it doesn't make sense...though thank you for sticking with me through it. And yes, there are those who like to sit in a 'comfort zone' and not move in any particular direction, and whilst it's probably very rare to find another not wishing to move where they are in Life yet still be in the same place as our individual selves already, it almost certainly does occur (though I still think we should always strive to better ourselves, even if it's effort/means facing inconvenient truths). Also, whilst chaotic systems are highly unpredictable, that's not to say they are completely beyond recovery, so I'm not saying it's impossible for a relationship like the one described [or at least attempted to...] above with the double-pendulum to work; perhaps very 'gifted' individuals/couples may be able to make it work, though I think it will require a lot of effort, and not necessarily in proportionate amounts for the individuals i.e. a significant strain is placed on one/both.

Anywho, I'm gonna wrap up the Double-Pendulum analogy there before I confuzzle any more. The 'take-away' message of this analogy (or at least what I was trying to get at with it) is:

People change (for better or for worse) all the time, so a relationship based/built on the assumption that other will never change (static) will 'naturally' lead to a chaotic system, given that neither is static (i.e. individuals are dynamic functions) and so the 'observed' relationship will deviate from the 'predicted/intended' relationship, generally leading to an unhappy relationship (I'm not talking about relationships that are/went "better than expected", by the way, as that's a different context).

The implication for relationships this has is that, since the components/individuals in the system are dynamic themselves (i.e. they're evolving over time) and that they themselves are each converging towards some goal (i.e. they tend towards some value/asymptote as they evolve), the relationship itself either converges or diverges over time i.e. the individuals ultimately grow closer or grow apart). If they have the same goal, they converge, and if they have different goals, they diverge (this is a generalisation at the 'limits', so to speak - it could be that the individuals have roughly similar, rather than exactly identical, goals and still get close enough; I'm not saying it's "All or Nothing" on goals matching for a relationship to work harmoniously). And this is what my second analogy is about...

Mountain Climbing [Part I]: Your life-long goal is to scale a particular mountain in a particular mountain range. You intend to do it or die trying. You arrive at this specific mountain range with all your gear on your back, where there's no unique path for scaling each mountain, rather there're general starting points for the range, and the paths will sometimes cross and whatnot. Nobody else is around, and you start your journey up the mountain. Sometimes you grow tired from the stuff you're carrying as well as minor injuries along the way [personal problems in Life], and so each time you have to stop to rest/recover. Eventually, some way up the mountain, unexpectedly meet somebody else with all their gear on their back, unaware of where they started climbing from; you both talk and find out that you both want to climb the same mountain, so agree to set carry on the rest of your journey together [two people, initially strangers, that are already on their respective ways to their goal, meet and find that they have the same goal, and consequently begin a relationship together, regardless of their background].

You set off with this person whom you still don't know that well, but you've got the journey up the mountain together to get to know each other better. As you're going up the mountain, there are still times when the path becomes quite difficult for you. Some of those times it's 'simply' that climbing the path is too much for you, given the load of your backpack or [minor] injuries you might sustain along the way, and so the other person carries some of the stuff in your backpack for you, even though it's not their stuff, or they even carry you. This way, you can both keep on going towards the summit, rather than stopping - something you did whilst travelling solo. Of course, the other person can only carry you/your things for some time. They, like you, are finite in strength and stamina. They, like you, have limits. Another "of course" is that this goes both ways - sometimes the other person finds the climb too difficult, they lean on you for support, and you help them through those times of difficulty as best as you can. And so you both need/learn to appreciate each other/not take each other (and each other's help) for granted, as well as not letting the other become overwhelmed by your own troubles. If this means having to take those troubles off the other person and back onto your shoulders, then that's the case, but it is possible for you both to stop/slow-down your climb and deal with the problem at hand first (ideally you'd then be able to 'recover' and resume your journey stronger than before). Additionally, there'll be times when you both have problems to deal with, and sometimes you're able to 'swap' burdens and carry on, whilst other times you'll both have to, as before, stop until it's figured out.

Now, it's possible that either person might feel inconvenienced by having to wait for the other whilst they themselves could carry on, but they should remember that they, too, have times of weakness where they have and will require the other's support. Everybody has ups and downs, be they for the same things at the same time or not, and so we ought to be patient (within just parameters) with others - "...Sometimes you're ahead, sometimes you're behind..." (the rest of this quote comes later). (I think I will deal with the case where one person is significantly more adapted/ready to climb the mountain than the other in a separate post, insha Allah.)

So far, the problems you've faced are 'external' - they're not brought about directly by the other. However, occasionally, you come across forks in the path [arguments]. Sometimes you both agree on which path to take (and it's important to not take these agreements for granted, in my opinion), sometimes you don't. During the times you don't, you both try to figure it out together so that you can carry on travelling with each other, since you've come to not just depend on, but enjoy, each other's company more and more as you progress on this journey ["learning to love", rather than "love to lust"]. Sometimes you do (and you learn quite a bit more about each other during this initial disagreements, with how you both handle said disagreements and the motivations behind each other's choice of path), and you climb much better together as a result (since you know more about each other's climbing habits/techniques, thereby anticipating and working with the other better, as well as bettering your own style from the other's techniques). Other times, though, you can't seem to agree on a path and go separate ways [falling out]. Now, given that you're both trying to get to the top, you should end up meeting each other again, so whilst you might not travel together on some particular stretch, you're comforted by the fact that, at the very least, you'll hopefully still get to seem them again at the top. The other possibility, though, is that one of you picks the wrong path, and you either press on out of pride, even if it's unnecessarily more difficult, or you admit your mistake and turn back before it's too late to catch up with the other and resume your journey together (of course, it's possible that both paths were wrong and you discover/make a new path together!). Hopefully, you admit your mistake and backtrack (if we make mistakes that weren't born from carelessness, they can be recitified as long as we learn from them, don't repeat them, and, with due understanding, help others from making the same mistakes).

You rejoin each other on this common pursuit of the summit, and these things happen fairly often. You're both trying to get to the top, you both face difficulties by yourselves that you can turn to the other for help, you sometimes drift apart, but you ultimately get closer to each other. The thing is, you didn't grow closer based on wanting to be closer with each other from the start (which may have resulted in the problems expected in the Double Pendulum analogy), rather it was a consequence of both going towards the same goal, so the time spent journeying with that person could (generally speaking, at least) never have been in vain. Eventually, you both get to the top and get to share that accomplishment, but also the accomplishment that you both came out of this journey together, despite all the difficulties faces, and became better people for it (by learning from/with each other). And even if you didn't make it all the way to the top together (considering a reality of Life is that it's not forever), all is not lost, I'd like to think; it's like one of those clichés about "the journey being more important than the destination". I don't agree with this saying completely; I think both are important and both need to be justified in their individual parts as well as collectively (so not "the ends justify the means" or "the means justify the ends", but "the means and ends need to justify themselves as well as the other", I think), but the point is that the journey itself wasn't in vain. And, back in terms of 'reality', rather than our analogy, perhaps the goal is something abstract, and we can never attain it, but approach it asymptotically, and that's okay, in my opinion, as long as we remember that (that it's abstract and so we may never be able to actually reach the goal, but get infinitely closer to it).

(Other things I didn't cover in-depth in this post about this analogy are when people change their goals [deciding/realising this mountain isn't the one they want to climb, but another is], as well the idea of being almost complete strangers at the start of a relationship, as is the case with arranged marriages [hearing from family and friends about somebody wanting to climb the same mountain and looking for a climbing-partner], or looking explicitly yourself for your own climbing-partner [some online forum or something for somebody to climb a particular mountain with, I guess]. Also, as already mentioned, I didn't cover the case where the two climbers are quite different in their initial ability, and so one may end up supporting the other much more often/significantly than the other; another time, insha Allah.]

To be honest, if I wanted to skip the details, I probably should have just compared a maypole with two separate bobs being swung around it, ultimately getting closer to each other as they wind up closer to the top...

This post took much longer to write than expected/intented (maybe this is my 'signature style' =/) and I wrote it in parts, so apologies for gaps, inconsistent writing-styles, incoherence, and whatnot (please particularly point out inconsistencies in the analogies if you spot them, though!). Also, this is, as I've stated already, just my opinion, and I'm open to correction and whatnot, plus I certainly mean to cause no offence or sadness with it! Lastly, I leave you with an essay by Mary Schmich, titled "Sunscreen" (made famous by Baz Luhrmann in 1999); something that has meant a lot to me since I first heard it, and I find myself reflecting over often:

Ladies and gentlemen of the class of '97:

Wear sunscreen.

If I could offer you only one tip for the future, sunscreen would be it. The long-term benefits of sunscreen have been proved by scientists, whereas the rest of my advice has no basis more reliable than my own meandering experience. I will dispense this advice now.

Enjoy the power and beauty of your youth. Oh, never mind. You will not understand the power and beauty of your youth until they've faded. But trust me, in 20 years, you'll look back at photos of yourself and recall in a way you can't grasp now how much possibility lay before you and how fabulous you really looked. You are not as fat as you imagine.

Don't worry about the future. Or worry, but know that worrying is as effective as trying to solve an algebra equation by chewing bubble gum. The real troubles in your life are apt to be things that never crossed your worried mind, the kind that blindside you at 4 p.m. on some idle Tuesday.

Do one thing every day that scares you.

Sing.

Don't be reckless with other people's hearts. Don't put up with people who are reckless with yours.

Floss.

Don't waste your time on jealousy. Sometimes you're ahead, sometimes you're behind. The race is long and, in the end, it's only with yourself.

Remember compliments you receive. Forget the insults. If you succeed in doing this, tell me how.

Keep your old love letters. Throw away your old bank statements.

Stretch.

Don't feel guilty if you don't know what you want to do with your life. The most interesting people I know didn't know at 22 what they wanted to do with their lives. Some of the most interesting 40-year-olds I know still don't.

Get plenty of calcium. Be kind to your knees. You'll miss them when they're gone.

Maybe you'll marry, maybe you won't. Maybe you'll have children, maybe you won't. Maybe you'll divorce at 40, maybe you'll dance the funky chicken on your 75th wedding anniversary. Whatever you do, don't congratulate yourself too much, or berate yourself either. Your choices are half chance. So are everybody else's.

Enjoy your body. Use it every way you can. Don't be afraid of it or of what other people think of it. It's the greatest instrument you'll ever own.

Dance, even if you have nowhere to do it but your living room.

Read the directions, even if you don't follow them.

Do not read beauty magazines. They will only make you feel ugly.

Get to know your parents. You never know when they'll be gone for good. Be nice to your siblings. They're your best link to your past and the people most likely to stick with you in the future.

Understand that friends come and go, but with a precious few you should hold on. Work hard to bridge the gaps in geography and lifestyle, because the older you get, the more you need the people who knew you when you were young.

Live in New York City once, but leave before it makes you hard. Live in Northern California once, but leave before it makes you soft. Travel.

Accept certain inalienable truths: Prices will rise. Politicians will philander. You, too, will get old. And when you do, you'll fantasize that when you were young, prices were reasonable, politicians were noble and children respected their elders.

Respect your elders.

Don't expect anyone else to support you. Maybe you have a trust fund. Maybe you'll have a wealthy spouse. But you never know when either one might run out.

Don't mess too much with your hair or by the time you're 40 it will look 85.

Be careful whose advice you buy, but be patient with those who supply it. Advice is a form of nostalgia. Dispensing it is a way of fishing the past from the disposal, wiping it off, painting over the ugly parts and recycling it for more than it's worth.

But trust me on the sunscreen.

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