3500 calories per pound

This looks set to be the concluding post in this particular little series on the subject of obesity and overweightness. So, to summarise where we’ve been so far- post 1: that there are a lot of slightly chubby people present in the western world leading to statistics supporting a massive obesity problem, and that even this mediocre degree of fatness can be seriously damaging to your health. Post 2: why we have spent recent history getting slightly chubby. And for today, post 3: how one can try to do your bit, especially following the Christmas excesses and the soon-broken promises of New Year, to lose some of that excess poundage.

It was Albert Einstein who first demonstrated that mass was nothing more than stored energy, and although the theory behind that precise idea doesn’t really correlate with biology the principle still stands; fat is your body’s way of storing energy. It’s also a vital body tissue, and is not a 100% bad and evil thing to ingest, but if you want to lose it then the aim should simply be one of ensuring that one’s energy output, in the form of exercise  exceeds one’s energy input, in the form of food. The body’s response to this is to use up some of its fat stores to replace this lost energy (although this process can take up to a week to run its full course; the body is a complicated thing), meaning that the amount of fat in/on your body will gradually decrease over time. Therefore, slimming down is a process that is best approached from two directions; restricting what’s going in, and increasing what’s going out (both at the same time is infinitely more effective than an either/or process). I’ll deal with what’s going in first.

The most important point to make about improving one’s diet, and when considering weight loss generally, is that there are no cheats. There are no wonder pills that will shed 20lb of body fat in a week, and no super-foods or nutritional supplements that will slim you down in a matter of months. Losing weight is always going to be a messy business that will take several months at a minimum (the title of this post refers to the calorie content of body fat, meaning that to lose one pound you must expend 3500 more calories than you ingest over a given period of time), and unfortunately prevention is better than cure; but moping won’t help anyone, so let’s just gather our resolve and move on.

There is currently a huge debate going on concerning the nation’s diet problems of amount versus content; whether people are eating too much, or just the wrong stuff. In most cases it’s probably going to be a mixture of the two, but I tend to favour the latter answer; and in any case, there’s not much I can say about the former beyond ‘eat less stuff’. I am not a good enough cook to offer any great advice on what foods you should or shouldn’t be avoiding, particularly since the consensus appears to change every fortnight, so instead I will concentrate on the one solid piece of advice that I can champion; cook your own stuff.

This is a piece of advice that many people find hard to cope with- as I said in my last post, our body doesn’t want to waste time cooking when it could be eating. When faced with the unknown product of one’s efforts in an hours time, and the surety of a ready meal or fast food within five minutes, the latter option and all the crap that goes in it starts to seem a lot more attractive. The trick is, therefore, to learn how to cook quickly- the best meals should either take less than 10-15 minutes of actual effort to prepare and make, or be able to be made in large amounts and last for a week or more. Or, even better, both. Skilled chefs achieve this by having their skills honed to a fine art and working at a furious rate, but then again they’re getting paid for it; for the layman, a better solution is to know the right dishes. I’m not going to include a full recipe list, but there are thousands online, and there is a skill to reading recipes; it can get easy to get lost between a long list of numbers and a complicated ordering system, but reading between the lines one can often identify which recipes mean ‘chop it all up and chuck in some water for half an hour’.

That’s a very brief touch on the issue, but now I want to move on and look at energy going out; exercise. I personally would recommend sport, particularly team sport, as the most reliably fun way to get fit and enjoy oneself on a weekend- rugby has always done me right. If you’re looking in the right place, age shouldn’t be an issue (I’ve seen a 50 year old play alongside a 19 year old student at a club rugby match near me), and neither should skill so long as you are willing to give it a decent go; but, sport’s not for everyone and can present injury issues so I’ll also look elsewhere.

The traditional form of fat-burning exercise is jogging, but that’s an idea to be taken with a large pinch of salt and caution. Regular joggers will lose weight it’s true, but jogging places an awful lot of stress on one’s joints (swimming, cycling and rowing are all good forms of ‘low-impact exercise’ that avoid this issue), and suffers the crowning flaw of being boring as hell. To me, anyway- it takes up a good chunk of time, during which one’s mind is so filled with the thump of footfalls and aching limbs that one is forced to endure the experience rather than enjoy it. I’ll put up with that for strength exercises, but not for weight loss when two far better techniques present themselves; intensity sessions and walking.

Intensity sessions is just a posh name for doing very, very tiring exercise for a short period of time; they’re great for burning fat & building fitness, but I’ll warn you now that they are not pleasant. As the name suggest, these involve very high-intensity exercise (as a general rule, you not be able to talk throughout high-intensity work) performed either continuously or next to continuously for relatively short periods of time- an 8 minute session a few times a week should be plenty. This exercise can take many forms; shuttle runs (sprinting back and forth as fast as possible between two marked points or lines), suicides (doing shuttle runs between one ‘base’ line and a number of different lines at different distances from the base, such that one’s runs change in length after each set) and tabata sets (picking an easily repeatable exercise, such as squats, performing them as fast as possible for 20 seconds, followed by 10 seconds of rest, then another 20 seconds of exercise, and so on for 4-8 minute) are just three examples. Effective though these are, it’s difficult to find an area of empty space to perform them without getting awkward looks and the odd spot of abuse from passers-by or neighbours, so they may not be ideal for many people (tabata sets or other exercises such as press ups are an exception, and can generally be done in a bedroom; Mark Lauren’s excellent ‘You Are Your Own Gym’ is a great place to start for anyone interested in pursuing this route to lose weight & build muscle). This leaves us with one more option; walking.

To my mind, if everyone ate properly and walked 10,000 steps per day, the scare stats behind the media’s obesity fix would disappear within a matter of months. 10,000 steps may seem a lot, and for many holding office jobs it may seem impossible, but walking is a wonderful form of exercise since it allows you to lose oneself in thought or music, whichever takes your fancy. Even if you don’t have time for a separate walk, with a pedometer in hand (they are built into many modern iPods, and free pedometer apps are available for both iPhone and Android) and a target in mind (10k is the standard) then after a couple of weeks it’s not unusual to find yourself subtly changing the tiny aspects of your day (stairs instead of lift, that sort of thing) to try and hit your target; and the results will follow. As car ownership, an office economy and lack of free time have all grown in the last few decades, we as a nation do not walk as much as we used to. It’s high time that changed.

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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 :).

What we know and what we understand are two very different things…

If the whole Y2K debacle over a decade ago taught us anything, it was that the vast majority of the population did not understand the little plastic boxes known as computers that were rapidly filling up their homes. Nothing especially wrong or unusual about this- there’s a lot of things that only a few nerds understand properly, an awful lot of other stuff in our life to understand, and in any case the personal computer had only just started to become commonplace. However, over 12 and a half years later, the general understanding of a lot of us does not appear to have increased to any significant degree, and we still remain largely ignorant of these little feats of electronic witchcraft. Oh sure, we can work and operate them (most of us anyway), and we know roughly what they do, but as to exactly how they operate, precisely how they carry out their tasks? Sorry, not a clue.

This is largely understandable, particularly given the value of ‘understand’ that is applicable in computer-based situations. Computers are a rare example of a complex system that an expert is genuinely capable of understanding, in minute detail, every single aspect of the system’s working, both what it does, why it is there, and why it is (or, in some cases, shouldn’t be) constructed to that particular specification. To understand a computer in its entirety, therefore, is an equally complex job, and this is one very good reason why computer nerds tend to be a quite solitary bunch, with quite few links to the rest of us and, indeed, the outside world at large.

One person who does not understand computers very well is me, despite the fact that I have been using them, in one form or another, for as long as I can comfortably remember. Over this summer, however, I had quite a lot of free time on my hands, and part of that time was spent finally relenting to the badgering of a friend and having a go with Linux (Ubuntu if you really want to know) for the first time. Since I like to do my background research before getting stuck into any project, this necessitated quite some research into the hows and whys of its installation, along with which came quite a lot of info as to the hows and practicalities of my computer generally. I thought, then, that I might spend the next couple of posts or so detailing some of what I learned, building up a picture of a computer’s functioning from the ground up, and starting with a bit of a history lesson…

‘Computer’ was originally a job title, the job itself being akin to accountancy without the imagination. A computer was a number-cruncher, a supposedly infallible data processing machine employed to perform a range of jobs ranging from astronomical prediction to calculating interest. The job was a fairly good one, anyone clever enough to land it probably doing well by the standards of his age, but the output wasn’t. The human brain is not built for infallibility and, not infrequently, would make mistakes. Most of these undoubtedly went unnoticed or at least rarely caused significant harm, but the system was nonetheless inefficient. Abacuses, log tables and slide rules all aided arithmetic manipulation to a great degree in their respective fields, but true infallibility was unachievable whilst still reliant on the human mind.

Enter Blaise Pascal, 17th century mathematician and pioneer of probability theory (among other things), who invented the mechanical calculator aged just 19, in 1642. His original design wasn’t much more than a counting machine, a sequence of cogs and wheels so constructed as to able to count and convert between units, tens, hundreds and so on (ie a turn of 4 spaces on the ‘units’ cog whilst a seven was already counted would bring up eleven), as well as being able to work with currency denominations and distances as well. However, it could also subtract, multiply and divide (with some difficulty), and moreover proved an important point- that a mechanical machine could cut out the human error factor and reduce any inaccuracy to one of simply entering the wrong number.

Pascal’s machine was both expensive and complicated, meaning only twenty were ever made, but his was the only working mechanical calculator of the 17th century. Several, of a range of designs, were built during the 18th century as show pieces, but by the 19th the release of Thomas de Colmar’s Arithmometer, after 30 years of development, signified the birth of an industry. It wasn’t a large one, since the machines were still expensive and only of limited use, but de Colmar’s machine was the simplest and most reliable model yet. Around 3,000 mechanical calculators, of various designs and manufacturers, were sold by 1890, but by then the field had been given an unexpected shuffling.

Just two years after de Colmar had first patented his pre-development Arithmometer, an Englishmen by the name of Charles Babbage showed an interesting-looking pile of brass to a few friends and associates- a small assembly of cogs and wheels that he said was merely a precursor to the design of a far larger machine: his difference engine. The mathematical workings of his design were based on Newton polynomials, a fiddly bit of maths that I won’t even pretend to understand, but that could be used to closely approximate logarithmic and trigonometric functions. However, what made the difference engine special was that the original setup of the device, the positions of the various columns and so forth, determined what function the machine performed. This was more than just a simple device for adding up, this was beginning to look like a programmable computer.

Babbage’s machine was not the all-conquering revolutionary design the hype about it might have you believe. Babbage was commissioned to build one by the British government for military purposes, but since Babbage was often brash, once claiming that he could not fathom the idiocy of the mind that would think up a question an MP had just asked him, and prized academia above fiscal matters & practicality, the idea fell through. After investing £17,000 in his machine before realising that he had switched to working on a new and improved design known as the analytical engine, they pulled the plug and the machine never got made. Neither did the analytical engine, which is a crying shame; this was the first true computer design, with two separate inputs for both data and the required program, which could be a lot more complicated than just adding or subtracting, and an integrated memory system. It could even print results on one of three printers, in what could be considered the first human interfacing system (akin to a modern-day monitor), and had ‘control flow systems’ incorporated to ensure the performing of programs occurred in the correct order. We may never know, since it has never been built, whether Babbage’s analytical engine would have worked, but a later model of his difference engine was built for the London Science Museum in 1991, yielding accurate results to 31 decimal places.

…and I appear to have run on a bit further than intended. No matter- my next post will continue this journey down the history of the computer, and we’ll see if I can get onto any actual explanation of how the things work.

Isn’t legalised violence wonderful?

OK, back I am after unscheduled break, and since I have some time, I thought I would try to spread the word of something very close to my heart- the sport of rugby.

In Europe (or Britain, anyway), rugby is subject to a lot of misconceptions due to lack of knowledge- across the rest of the world, Australasia and South Africa excepted, it is hardly known. For those of you unfamiliar with the game, rugby is an ancestor of American Football, and shares several of the same broad features- big meaty players, an oval-shaped ball (although rounder than an American football to make it easier to pass and kick), physicality and the idea of touching the ball down in the end-area. However, below the surface, the similarities end. For one thing, rugby players do not wear full body armour, and for another they do not run around for 3 seconds at a time interrupted by a 2 minute break. I would try and explain the rules differences, but rugby is recognised as having some of the most complicated laws (when gone into in detail) of any major sport. A few basic rules include- there are two groups of players, big, strong forwards who win possession and be physical, and light, fast backs who score most of the points. Points are scored either by touching the ball down over the end line for 5 points (not just by running over it or throwing it down), or kicking the ball through the posts at either end- this can either be done either after a try (touchdown) has been scored (worth an extra two points), when a penalty is awarded (3 points), or from a drop kick in general play (also 3 points). You can only pass backwards & sideways (but can kick or run forwards in open play), you can only tackle a player with the ball, and once a player has been tackled to the ground the forwards (or whoever happens to be nearby), all pile in to try and push each other off the ball in what’s called a ruck, in order to win possession. If the ball is ‘knocked on’ (spilled forwards), a scrum is formed (both sets of forwards pushing against each other to win the ball), and if it is kicked out of the field on either side, a lineout is formed (the ball is thrown in and both sets of forwards jump and lift one another in order to try and catch it).
Considering I probably could have summarised football in a sentence, this gives you some idea of just how complicated the game can get. If you want to learn more, I suggest you try to watch some- the Six Nations tournament is starting in February and will be on TV, while one of the American networks (I think it may be NBC) has recently started broadcasting rugby 7’s (7 players on each side rather than 15, and only 7 minutes each way rather than 40- this leads to very fast, high-scoring games).
I should probably also take this point to clear up a couple of misconceptions about the game. 1) Rugby is not a ‘posh man’s sport’. Yes, it is named after an English public school and yes, most of the current England squad will have got sport scholarships at private schools, but rugby is an inclusive game, and anyone can join without fear of class boundaries- I have been in a squad where one guy with a dad earning upward of 100 grand  has been struggling for his place while our first choice centre’s dad has been struggling for work. 2) You are not guaranteed to break eery bone in your body. I have played rugby for numerous years now and have yet to receive a serious injury, and while it is true the injury toll in rugby is far greater than in football, it is far less than sports like American Football, and the rugby community is very good at looking after its members.
However, I didn’t post this just to be a laws description or a whinge against those who don’t understand the game, because rugby is so much more than a complicated set of rules. To my mind, there are 4 reasons why rugby is the best game on the planet. One is that it is a game for everyone, regardless of shape, size or skills. The big chunky ones who may not be the most intelligent or skilful but like to push each other around can go up front in the forwards (probably the front row, who are an entity unto themselves), the big tall ones can be really good in the lineout, the fast ones can go on the wing, the skilful and aware ones at flyhalf (the rugby equivalent of a quarterback), and the tiny, annoying little gob*****s who like to annoy the referee are born scrum-halves. Two is that rugby can, at its best, be superlatively spectacular and beautiful in a myriad of different forms. This: http://www.rugbydump.com/2011/12/2271/biarritz-score-a-sensational-team-try-against-montpellier, is just a teamwork spectacular showing a ‘backs try’, but just as beautiful to a rugby aficionado could be a 60-metre maul (like a loose scrum), pushed all the way up the pitch. And then you’ve got this which, well… it was the world cup final, England v Australia (the old rivals), England had never won the world cup before, it was 17-17 well into extra time, there were less than 30 seconds left and- this:http://www.youtube.com/watch?v=XuKHtcIdD4M&feature=related. It was a hell of a lot better than the video and commentary makes it look.
Thirdly, and perhaps most importantly, rugby is a social sport. It’s a friendly game, and getting drunk in the bar with your opposite number is a celebrated post-match ritual, even if he’s sporting a broken nose you gave him in the match earlier. On the pitch, you may be worst of enemies- on it, everyone has a laugh. Rugby fans are allowed to drink at matches, unlike football fans, because the authorities can trust them to basically behave. Rugby abhors violent play, and abuse of the referee is especially frowned upon. It is a game founded on trust and friendliness, on camaraderie, on team spirit, to an extent that no other sport can match, and it is a thing more beautiful than even the greatest of tries.
And fourth (watch all the replays of these) and finally there is… well this: http://www.youtube.com/watch?v=XuKHtcIdD4M&feature=related
and this: http://www.youtube.com/watch?v=XuKHtcIdD4M&feature=related
and this: http://www.youtube.com/watch?v=DPMZrPjW5cs
… and also this: http://www.youtube.com/watch?v=9wq_PL-GDTI&feature=related
Yeah…