The Myth of Popularity

WARNING: Everything I say forthwith is purely speculative based on a rough approximation of a presented view of how a part of our world works, plus some vaguely related stuff I happen to know. It is very likely to differ from your own personal view of things, so please don’t get angry with me if it does.

Bad TV and cinema is a great source of inspiration; not because there’s much in it that’s interesting, but because there’s just so much of it that even without watching any it is possible to pick up enough information to diagnose trends, which are generally interesting to analyse. In this case, I refer to the picture of American schools that is so often portrayed by iteration after iteration of generic teenage romance/romcom/’drama’, and more specifically the people in it.

One of the classic plot lines of these types of things involves the ‘hopelessly lonely/unpopular nerd who has crush on Miss Popular de Cheerleader and must prove himself by [insert totally retarded idea]’. Needless to say these plot lines are more unintentionally hilarious and excruciating than anything else, but they work because they play on the one trope that so many of us are familiar with; that of the overbearing, idiotic, horrible people from the ‘popular’ social circle. Even if we were not raised within a sitcom, it’s a situation repeated in thousands of schools across the world- the popular kids are the arseholes at the top with inexplicable access to all the gadgets and girls, and the more normal, nice people lower down the social circle.

The image exists in our conciousness long after leaving school for a whole host of reasons; partly because major personal events during our formative years tend to have a greater impact on our psyche than those occurring later on in life, but also because it is often our first major interaction with the harsh unfairness life is capable of throwing at us. The whole situation seems totally unfair and unjust; why should all these horrible people be the popular ones, and get all the social benefits associated with that? Why not me, a basically nice, humble person without a Ralph Lauren jacket or an iPad 3, but with a genuine personality? Why should they have all the luck?

However, upon analysing the issue then this object of hate begins to break down; not because the ‘popular kids’ are any less hateful, but because they are not genuinely popular. If we define popular as a scale representative of how many and how much people like you (because what the hell else is it?), then it becomes a lot easier to approach it from a numerical, mathematical perspective. Those at the perceived top end of the social spectrum generally form themselves into a clique of superiority, where they all like one another (presumably- I’ve never been privy to being in that kind of group in order to find out) but their arrogance means that they receive a certain amount of dislike, and even some downright resentment, from the rest of the immediate social world. By contrast, members of other social groups (nerds, academics [often not the same people], those sportsmen not in the ‘popular’ sphere, and the myriad of groups of undefineable ‘normies’ who just splinter off into their own little cliques) tend to be liked by members of their selected group and treated with either neutrality or minor positive or negative feeling from everyone else, leaving them with an overall ‘popularity score’, from an approximated mathematical point of view, roughly equal to or even greater than the ‘popular’ kids. Thus, the image of popularity is really something of a myth, as these people are not technically speaking any more popular than anyone else.

So, then, how has this image come to present itself as one of popularity, of being the top of the social spectrum? Why are these guys on top, seemingly above group after group of normal, friendly people with a roughly level playing field when it comes to social standing?

If you were to ask George Orwell this question, he would present you with a very compelling argument concerning the nature of a social structure to form a ‘high’ class of people (shortly after asking you how you managed to communicate with him beyond the grave). He and other social commentators have frequently pointed out that the existence of a social system where all are genuinely treated equally is unstable without some ‘higher class’ of people to look up to- even if it is only in hatred. It is humanity’s natural tendency to try and better itself, try to fight its way to the top of the pile, so if the ‘high’ group disappear temporarily they will be quickly replaced; hence why there is such a disparity between rich and poor even in a country such as the USA founded on the principle that ‘all men are created free and equal’. This principle applies to social situations too; if the ‘popular’ kids were to fall from grace, then some other group would likely rise to fill the power vacuum at the top of the social spectrum. And, as we all know, power and influence are powerful corrupting forces, so this position would be likely to transform this new ‘popular’ group into arrogant b*stards too, removing the niceness they had when they were just normal guys. This effect is also in evidence that many of the previously hateful people at the top of the spectrum become very normal and friendly when spoken to one-on-one, outside of their social group (from my experience anyway; this does not apply to all people in such groups)

However, another explanation is perhaps more believable; that arrogance is a cause rather than a symptom. By acting like they are better than the rest of the world, the rest of the world subconsciously get it into their heads that, much though they are hated, they are the top of the social ladder purely because they said so. And perhaps this idea is more comforting, because it takes us back to the idea we started with; that nobody is more actually popular than anyone else, and that it doesn’t really matter in the grand scheme of things. Regardless of where your group ranks on the social scale, if it’s yours and you get along with the people in it, then it doesn’t really matter about everyone else or what they think, so long as you can get on, be happy, and enjoy yourself.

Footnote: I get most of these ideas from what is painted by the media as being the norm in American schools and from what friends have told me, since I’ve been lucky enough that the social hierarchies I encountered from my school experience basically left one another along. Judging by the horror stories other people tell me, I presume it was just my school. Plus, even if it’s total horseshit, it’s enough of a trope that I can write a post about it.

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Hitting the hay

OK, so it was history last time, so I’m feeling like a bit of science today. So, here is your random question for today; are the ‘leaps of faith’ in the Assassin’s Creed games survivable?

Between them, the characters of Altair, Ezio and Connor* jump off a wide variety of famous buildings and monuments across the five current games, but the jump that springs most readily to mind is Ezio’s leap from the Campanile di San Marco, in St Mark’s Square, Venice, at the end of Assassin’s Creed II. It’s not the highest jump made, but it is one of the most interesting and it occurs as part of the main story campaign, meaning everyone who’s played the game through will have made the jump and it has some significance attached to it. It’s also a well-known building with plenty of information on it.

[*Interesting fact; apparently, both Altair and Ezio translate as ‘Eagle’ in some form in English, as does Connor’s Mohawk name (Ratonhnhaké;ton, according to Wikipedia) and the name of his ship, the Aquila. Connor itself translates as ‘lover of wolves’ from the original Gaelic]

The Campanile as it stands today is not the same one as in Ezio’s day; in 1902 the original building collapsed and took ten years to rebuild. However, the new Campanile was made to be cosmetically (if not quite structurally) identical to the original, so current data should still be accurate. Wikipedia again tells me the brick shaft making up the bulk of the structure accounts for (apparently only) 50m of the tower’s 98.6m total height, with Ezio’s leap (made from the belfry just above) coming in at around 55m. With this information we can calculate Ezio’s total gravitational potential energy lost during his fall; GPE lost = mgΔh, and presuming a 70kg bloke this comes to GPE lost= 33730J (Δ is, by the way, the mathematical way of expressing a change in something- in this case, Δh represents a change in height). If his fall were made with no air resistance, then all this GPE would be converted to kinetic energy, where KE = mv²/2. Solving to make v (his velocity upon hitting the ground) the subject gives v = sqrt(2*KE/m), and replacing KE with our value of the GPE lost, we get v = 31.04m/s. This tells us two things; firstly that the fall should take Ezio at least three seconds, and secondly that, without air resistance, he’d be in rather a lot of trouble.

But, we must of course factor air resistance into our calculations, but to do so to begin with we must make another assumption; that Ezio reaches terminal velocity before reaching the ground. Whether this statement is valid or not we will find out later. The terminal velocity is just a rearranged form of the drag equation: Vt=sqrt(2mg/pACd), where m= Ezio’s mass (70kg, as presumed earlier), g= gravitational field strength (on Earth, 9.8m/s²), p= air density (on a warm Venetian evening at around 15 degrees Celcius, this comes out as 1.225kg/m3), A= the cross-sectional area of Ezio’s falling body (call it 0.85m², presuming he’s around the same size as me) and Cd= his body’s drag coefficient (a number evaluating how well the air flows around his body and clothing, for which I shall pick 1 at complete random). Plugging these numbers into the equation gives a terminal velocity of 36.30m/s, which is an annoying number; because it’s larger than our previous velocity value, calculated without air resistance, of 31.04m/s, this means that Ezio definitely won’t have reached terminal velocity by the time he reaches the bottom of the Campanile, so we’re going to have to look elsewhere for our numbers. Interestingly, the terminal velocity for a falling skydiver, without parachute, is apparently around 54m/s, suggesting that I’ve got numbers that are in roughly the correct ballpark but that could do with some improvement (this is probably thanks to my chosen Cd value; 1 is a very high value, selected to give Ezio the best possible chance of survival, but ho hum)

Here, I could attempt to derive an equation for how velocity varies with distance travelled, but such things are complicated, time consuming and do not translate well into being typed out. Instead, I am going to take on blind faith a statement attached to my ‘falling skydiver’ number quoted above; that it takes about 3 seconds to achieve half the skydiver’s terminal velocity. We said that Ezio’s fall from the Campanile would take him at least three seconds (just trust me on that one), and in fact it would probably be closer to four, but no matter; let’s just presume he has jumped off some unidentified building such that it takes him precisely three seconds to hit the ground, at which point his velocity will be taken as 27m/s.

Except he won’t hit the ground; assuming he hits his target anyway. The Assassin’s Creed universe is literally littered with indiscriminate piles/carts of hay and flower petals that have been conveniently left around for no obvious reason, and when performing a leap of faith our protagonist’s always aim for them (the AC wiki tells me that these were in fact programmed into the memories that the games consist of in order to aid navigation, but this doesn’t matter). Let us presume that the hay is 1m deep where Ezio lands, and that the whole hay-and-cart structure is entirely successful in its task, in that it manages to reduce Ezio’s velocity from 27m/s to nought across this 1m distance, without any energy being lost through the hard floor (highly unlikely, but let’s be generous). At 27m/s, the 70kg Ezio has a momentum of 1890kgm/s, all of which must be dissipated through the hay across this 1m distance. This means an impulse of 1890Ns, and thus a force, will act upon him; Impulse=Force x ΔTime. This force will cause him to decelerate. If this deceleration is uniform (it wouldn’t be in real life, but modelling this is tricky business and it will do as an approximation), then his average velocity during his ‘slowing’ period will come to be 13.5m/s, and that this deceleration will take 0.074s. Given that we now know the impulse acting on Ezio and the time for which it acts, we can now work out the force upon him; 1890 / 0.074 = 1890 x 13.5 = 26460N. This corresponds to 364.5m/s² deceleration, or around 37g’s to put it in G-force terms. Given that 5g’s has been known to break bones in stunt aircraft, I think it’s safe to say that quite a lot more hay, Ezio’s not getting up any time soon. So remember; next time you’re thinking of jumping off a tall building, I would recommend a parachute over a haystack.

N.B.: The resulting deceleration calculated in the last bit seems a bit massive, suggesting I may have gone wrong somewhere, so if anyone has any better ideas of numbers/equations then feel free to leave them below. I feel here is also an appropriate place to mention a story I once heard concerning an air hostess whose plane blew up. She was thrown free, landed in a tree on the way down… and survived.

EDIT: Since writing this post, this has come into existence, more accurately calculating the drag and final velocity acting on the falling Assassin. They’re more advanced than me, but their conclusion is the same; I like being proved right :).