Gravity

At time of writing, I’ve just come home from watching Gravity, Alfonso Cuaron’s recent space-set thriller. And my immediate reaction can be essentially summed up in three words: holy f***ing shit.

OK, OK, I’ll fill in a bit; if you weren’t already aware, Gravity tells the story of a space shuttle mission gone disastrously wrong whilst in orbit, leaving just two survivors: George Clooney playing essentially a spacegoing version of himself as the suave, talkative veteran Matt Kowalski and Sandra Bullock as the inexperienced, depressive and perpetually scared Dr. Ryan Stone. With their craft destroyed, both are faced with the daunting prospect of trying to return to earth alive- without the luxuries of a ship, communications, equipment or much ability to control their own movements. And that’s all I can really say without giving away spoilers- indeed, I feel like the rest of this review may end up giving away a fair few details. However, since the main thrust of what makes the film such an experience is not contained within its plot, so unless you have a burning desire to see Gravity completely unspoiled you’re probably not going to lose out on much by reading on.

The result is something pretty amazing, but Gravity is not flawless by any means- I doubt any film ever was. I don’t know whether the story of former astronaut Commander Chris Hadfield getting thrown out of a Canadian cinema for shouting about the film’s inaccuracies at the screen is true or not, but if so I can see where he’d have been coming from- I am no astronaut, but I know enough about space to say that communications and spy satellites operate at completely different altitudes, neither of which are in the range depicted by the film, and that during re-entry there should not be random objects floating around the cabin like it’s in zero-g. Those are only the more obvious errors- the film does a grand job of delivering the general gist of a spacial environment, but had I so wished I could have spent the entire film pointing out minor inaccuracies or inconsistencies. But then again, I’m no astronaut- and besides, Gravity is hardly the only film to take some rather serious liberties with the laws of physics.

It’s not only in terms of its scientific accuracy where the film has flaws. Its characterisation is almost non-existent, the plot is as stripped-down and oversimplified as it could possibly be whilst still existing, multiple story elements seem decidedly contrived and the whole thing has precisely zero thematic complexity between the tried & tested ‘indomitable human spirit’ arc. But that’s all kinda the point. Gravity is not an actor’s film, nor indeed a writer’s- indeed I have a sneaking suspicion that Cuaron may simply have done three days filming, then locked himself in  a room with his cinematographer and CGI person for a few months putting together the rest of it. The result is nothing less than a jaw-dropping spectacle of a film, something genuinely amazing: to be honest, I’m not even sure that’s even a compliment. It feels more like a simple description of the film’s nature- even if this had been the background setting for something written by Ed Wood, the sheer amazement factor of how the film presents itself would still have left me sitting back in my seat mouth open like a goon.

I mean, just consider the visuals. Alone, they would be enough to make watching Gravity a special experience, capturing as they do both the scale and beauty of the view from space alongside the strange unreality that is sitting in a tin can hurtling at unimaginable speed thousands of kilometres above the surface of our mother earth. The film’s extensive use of CGI (because seriously, how else do you create an action set piece around a ****ing space station) is noticeable, but by keeping the visual style very consistent the film avoids drawing attention to it and maintains a highly immersive experience. Then there’s the cinematography; from the early outset Gravity sets a baseline for weirdness and confusion as a constantly moving, rotating camera reminds us of the nature of space, and the total lack of a reference frame that one has in it. There is no up or down- there is only ‘over there’, and when ‘over there’ is flying around madly as you tumble uncontrollably towards it, as happens frequently during the action set pieces, the whole thing gets decidedly disorientating. I’m rather glad I don’t get motion sick, or indeed scared of heights once the film decides to point out that space flight is, in fact, nothing more than falling very, very quickly.

But what makes Gravity really work is how it creates an atmosphere. The whole thing seems specifically designed to make space seem as utterly, utterly terrifying on all levels to make our hero’s struggle seem that much more daunting and amazing, and the film pulls off on that spectacularly. A key part of its toolbox is its use of thematic contrast: the huge, jaw-dropping visual spectacles that are the action sequences keep the danger and blind terror foremost in our mind, but are offset by the near-silent intimate moments that both give the audience time to process the beautiful insanity playing out in front of them and to remind us all that, surrounded by airless wilderness, ‘in space, nobody can hear you scream’. Cuaron deserves particular credit for his use of music in this regard- it’s one of those things you almost don’t notice, but every set piece is built up slowly, cranking up the tension, before launching into a booming orchestral inferno of noise as the action gets into full flow. And then- silence, save for our protagonist’s terrified breathing. I don’t think any film has ever made me feel a character’s emotion quite so much, and certainly none has done so to a faceless spacesuit.

Ultimately, I’m not sure me spouting words can really do the film justice- it’s one of those things where I could describe the entire storyline, down to the last scene, and it’d still be the barest shadow of what viewing the film in all its glory is. Just let me put it this way: Gravity is an hour and a half of watching people falling out of the sky through the most hostile environment in the universe amidst a chaotic firestorm of broken metal and machinery. And it is every bit as terrifying, jaw-dropping and downright awe-inspiring as that sounds.

One Foot In Front Of The Other

According to many, the thing that really sets human beings apart from the rest of the natural world is our mastery of locomotion; the ability to move faster, further and with heavier loads than any other creature typically does (never mind that our historical method of doing this was strapping several other animals to a large heap of wood and nails) across every medium our planet has to throw at us; land, sky, sea, snow, whatever. Nowadays, this concept has become associated with our endeavours in powered transport (cars, aeroplanes and such), but the story of human locomotion begins with a far more humble method of getting about that I shall dedicate today’s post to; walking.

It is thought that the first walkers were creatures that roughly approximate to our modern-day crustaceans; the early arthropods. In the early days of multicellular life on earth, these creatures ruled the seas (where all life had thus far been based) and fossils of the time show a wide variety of weird and wonderful creatures. The trilobites that one can nowadays buy as tourist souvenirs in Morocco are but one example; the top predators of the time were massive things, measuring several metres in length with giant teeth and layers of armour plate. All had bony exoskeletons, like the modern insects that are their descendants, bar a few small fish-like creatures a few millimetres in length who had developed the first backbones; in time, the descendants of these creatures would come to dominate life on earth. Since it was faster and allowed a greater range of motion, most early arthropods swam to get about; but others, like the metre-long Brontoscorpio (basically a giant underwater scorpion) preferred the slightly slower, but more efficient, idea of walking about on the seabed. Here, food was relatively plentiful in the form of small ‘grazers’ and attempting to push oneself through the water was wasteful of energy compared to trundling along the bottom. However, a new advantage also presented itself before too long; these creatures were able to cross land over short distances to reach prey- by coincidence, their primitive ‘lungs’ (that collected dissolved oxygen from water in much the same fashion as modern fish gills, but with a less fragile structure) worked just as well at harvesting oxygen from air as water, enabling them to survive on land. As plant life began to venture out onto land to better gain access to the air and light needed to survive, so the vertebrates (in the form of early amphibians) and arthropods began to follow the food, until the land was well and truly colonised by walking life forms.

Underwater, walking was significantly easier than on land; water is a far more dense fluid than air (hence why we can swim in the former but not the latter), and the increased buoyancy this offered meant that early walkers’ legs did not have to support so much of their body’s weight as they would do on land. This made it easier for them to develop the basic walking mechanic; one foot (or whatever you call the end of a scorpion’s leg) is pressed against the ground, before being held stiff and solid as the rest of the body is rotated around it’s joint, moving the creature as a whole forward slightly as it pivots. In almost all invertebrates, and early vertebrates, the creature’s legs are positioned at the side of the body, meaning that as the creature walks they tend to swing from side to side. Invertebrates typically partially counter this problem by having a lot of legs and stepping them in such an order to help them travel in a constant direction, and by having multi-jointed legs that can flex and translate the lateral components of motion into more forward-directed movement, preventing them from swinging from side to side. However, this doesn’t work so well at high speed when the sole priority is speed of movement of one’s feet, which is why most reconstructions of the movement of vertebrates circa 300 million years ago (with just four single-jointed legs stuck out to the side of the body) tends to show their body swinging dramatically from side to side, spine twisting this way and that.  This all changed with the coming of the dinosaurs, whose revolutionary evolutionary advantage was a change in construction of the hip that allowed their legs to point underneath the body, rather than sticking out at the side. Now, the pivoting action of the leg produces motion in the vertical, rather than horizontal direction, so no more spine-twisting mayhem. This makes travelling quickly easier and allows the upper body to be kept in a more stable position, good for striking at fleeing prey, as well as being more energy efficient. Such an evolutionary advantage would soon prove so significant that, during the late Triassic period, it allowed dinosaurs to completely take over from the mammal-like reptiles who had previously dominated the world. It would take more than 150 million years, a hell of a lot of evolution and a frickin’ asteroid to finally let these creatures’ descendants, in the form of mammals, finally prevail over the dinosaurs (by which time they had discovered the whole ‘legs pointing down’ trick).

When humankind were first trying to develop walking robots in the mid-twentieth century, the mechanics of the process were poorly understood, and there are a great many funny videos of prototype sets of legs completely failing. These designers had been operating under the idea that the role of the legs when walking was not just to keep a body standing up, but also to propel them forward, each leg pulling on the rest of the body when placed in front. However, after a careful study of new slow-motion footage of bipedal motion, it was realised that this was not the case at all, and we instead have gravity to thank for pushing us forward. When we walk, we actually lean over our frontmost foot, in effect falling over it before sticking our other leg out to catch ourselves, hence why we tend to go face to floor if the other leg gets caught or stuck. Our legs only really serve to keep us off the ground, pushing us upwards so we don’t actually fall over, and our leg muscles’ function here is to simply put each foot in front of the other (OK, so your calves might give you a bit of an extra flick but it’s not the key thing). When we run or climb, our motion changes; our legs bend, before our quadriceps extend them quickly, throwing us forward. Here we lean forward still further, but this is so that the motion of our quads is directed in the forward, rather than upward direction. This form of motion is less energy efficient, but covers more ground. This is the method by which we run, but does not define running itself; running is simply defined as the speed at which every step incorporates a bit of time where both feet are off the ground. Things get a little more complicated when we introduce more legs to the equation; so for four legged animals, such as horses, there are four footspeeds. When walking there are always three feet on the ground at any one time, when trotting there are always two, when cantering at least one, and when galloping a horse spends the majority of its time with both feet off the ground.

There is one downside to walking as a method of locomotion, however. When blogging about it, there isn’t much of a natural way to end a post.

F=ma

On Christmas Day 1642, a baby boy was born to a well-off Lincolnshire family in Woolsthorpe Manor. His childhood was somewhat chaotic; his father had died before he was born, and his mother remarried (to a stepfather he came to acutely dislike) when he was three. He was later to run away from school, discovered he hated the farming alternative and returned to become the school’s top pupil. He was also to later attend Trinity College Cambridge; oh, and became arguably the greatest scientist and mathematician of all time. His name was Isaac Newton.

Newton started off in a small way, developing binomial theorem; a technique used to expand powers of polynomials, which is a kind of fundamental technique used pretty much everywhere in modern science and mathematics; the advanced mathematical equivalent of knowing that 2 x 4 = 8. Oh, and did I mention that he was still a student at this point? Taking a break from his Cambridge career for a couple of years due to the minor inconvenience of the Great Plague, he whiled away the hours inventing calculus, which he finalised upon his return to Cambridge. Calculus is the collective name for differentiating and integrating, which allows one to find out the rate at which something is occurring, the gradient of a graph and the area under it algebraically; plus enabling us to reverse all of the above processes. This makes it sound like rather a neat and useful gimmick, but belies the fact that it allows us to mathematically describe everything from water flowing through a pipe to how aeroplanes fly (the Euler equations mentioned in my aerodynamics posts come from advanced calculus), and the discovery of it alone would have been enough to warrant Newton’s place in the history books. OK, and Leibniz who discovered pretty much the same thing at roughly the same time, but he got there later than Newton. So there.

However, discovering the most important mathematical tool to modern scientists and engineers was clearly not enough to occupy Newton’s prodigious mind during his downtime, so he also turned his attention to optics, aka the behaviour of light. He began by discovering that white light was comprised of all colours, revolutionising all contemporary scientific understanding of light itself by suggesting that coloured objects did not create their own colour, but reflected only certain portions of already coloured light. He combined this with discovering diffraction; that light shone through glass or another transparent material at an angle will bend. This then lead him to explain how telescopes worked, why the existing designs (based around refracting light through a lens) were flawed, and to design an entirely new type of telescope (the reflecting telescope) that is used in all modern astronomical equipment, allowing us to study, look at and map the universe like never before. Oh, and he also took the time to theorise the existence of photons (he called them corpuscles), which wouldn’t be discovered for another 250 years.

When that got boring, Newton turned his attention to a subject that he had first fiddled around with during his calculus time: gravity. Nowadays gravity is a concept taught to every schoolchild, but in Newton’s day the idea that objects fall to earth was barely even considered. Aristotle’s theories dictated that every object ‘wanted’ to be in a state of stillness on the ground unless disturbed, and Newton was the first person to make a serious challenge to that theory in nearly two millennia (whether an apple tree was involved in his discovery is heavily disputed). Not only did he and colleague Robert Hooke define the force of gravity, but they also discovered the inverse-square law for its behaviour (aka if you multiply the distance you are away from a planet by 2, then you will decrease the gravitational force on you by 2 squared, or 4) and turned it into an equation (F=-GMm/r^2). This single equation would explain Kepler’s work on celestial mechanics, accurately predict the orbit of the ****ing planets (predictions based, just to remind you, on the thoughts of one bloke on earth with little technology more advanced than a pen and paper) and form the basis of his subsequent book: “Philosophiæ Naturalis Principia Mathematica”.

Principia, as it is commonly known, is probably the single most important piece of scientific writing ever written. Not only does it set down all Newton’s gravitational theories and explore their consequences (in minute detail; the book in its original Latin is bigger than a pair of good-sized bricks), but he later defines the concepts of mass, momentum and force properly for the first time; indeed, his definitions survive to this day and have yet to be improved upon.  He also set down his three laws of motion: velocity is constant unless a force acts upon an object, the acceleration of an object is proportional to the force acting on it and the object’s mass (summarised in the title of this post) and action and reaction are equal and opposite. These three laws not only tore two thousand years of scientific theory to shreds, but nowadays underlie everything we understand about object mechanics; indeed, no flaw was found in Newton’s equations until relativity was discovered 250 years later, which only really applies to objects travelling at around 100,000 kilometres per second or greater; not something Newton was ever likely to come across.

Isaac Newton’s life outside science was no less successful; he was something of an amateur alchemist and when he was appointed Master of the Royal Mint (a post he held for 30 years until his death; there is speculation his alchemical meddling may have resulted in mercury poisoning) he used those skills to great affect in assessing coinage, in an effort to fight Britain’s massive forgery problem. He was successful in this endeavour and later became the first man to put Britain onto the gold, rather than silver, standard, reflecting his knowledge of the superior chemical qualities of the latter metal (see another previous post). He is still considered by many to be the greatest genius who ever lived, and I can see where those people are coming from.

However, the reason I find Newton especially interesting concerns his private life. Newton was a notoriously hard man to get along with; he never married, almost certainly died a virgin and is reported to have only laughed once in his life (when somebody asked him what was the point in studying Euclid. The joke is somewhat highbrow, I’ll admit). His was a lonely existence, largely friendless, and he lived, basically for his work (he has been posthumously diagnosed with everything from bipolar disorder to Asperger’s syndrome). In an age when we are used to such charismatic scientists as Richard Feynman and Stephen Hawking, Newton’s cut-off, isolated existence with only his prodigious intellect for company seems especially alien. That the approach was effective is most certainly not in doubt; every one of his scientific discoveries would alone be enough to place him in science’s hall of fame, and to have done all of them puts him head and shoulders above all of his compatriots. In many ways, Newton’s story is one of the price of success. Was Isaac Newton a successful man? Undoubtedly, in almost every field he turned his hand to. Was he a happy man? We don’t know, but it would appear not. Given the choice between success and happiness, where would you fall?

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 :).