What Music Do You Listen To?

Asking someone what their favourite type of music is can be problematic for those of us not used to treating conversation as anything other than a method of divulging pertinent information. There seem to be only two accepted answers, both horribly lacking in information.

The first answer is "Single genre". Firstly, this will mean very little to you unless you also like that genre as well. You can express a negative opinion about it but if you don't like the genre then chances are that your concept of it is off. Countless metal fans have been angered by the insinuation that metal is all violence and Satan worshipping (Black Sabbath were predominantly Catholic). Equally as many have cried inwardly when suggesting the exquisite Juno Reactor or such like and been rebutted with a dismissive "I don't like that electronic shit". Secondly, with only one point of data you are going to have to employ some convergent iteration to get an idea of what area of [Genre] they actually like. As far as conversation goes this can be somewhat awkward. It is however information on which you can haphazardly expand, which is more than can be said about the alternative.

"I like a bit of everything" and it's likenesses are woefully inadequate as an answer and do nothing to help the asker ascertain whether or not they have anything to add to the conversation. It's like being asked what course you're studying and replying with the name of your university. While with the first answer you could conceivably start a conversation, as one might start a fire with application of friction to wood, this answer is like pissing on the tinder. You don't help matters and even if no one gets annoyed there is going to be one hell of an awkward silence to come. Ironically it is usually said by those who actually really want to let people know more about themselves. "I listen to certain genres predominantly but don't judge me on that. I probably listen to your music too!" the replier tries to say, but all we hear is "I don't want to continue this conversation."

Clearly the first answer is the better, but it is still infuriatingly lacking. I propose this. When asking, specify that you want 3 genres of music that the recipient listens to the most. When answering, assume that this is what the asker requested. This has the benefit of primarily giving information upon which a conversation can be expanded upon, but it also allows the asker a certain amount of leeway in their answer. "I listen to a lot of Metal, but I do often enjoy Electronic stuff, especially Trip-Hop. I do have a secret soft spot for that Carly Rae song, mind!" If needs be you/they can then clarify that while you/they predominantly listen to these genres y/t do enjoy other things as well. The point of this exercise is to get an idea of someone's taste in music, to establish some basis of a relationship, not to enforce rigid conversational law. And if they genuinely only listen to one genre, they can leave it there.

And if they still try to stall for an answer without offering anything to go on you can rest assured that you're talking to someone who is so lost for personality that they don't quite know which artificial one they want to portray to you.

And for fuck's sake, don't ask what someone's favourite film is. 9 times out of 10 all you're going to get as a reply is an awkward pause as they (I) work through a mental spreadsheet of Genre/Tone/Theme/Acting/Irony/etc. to come to a conclusion that they're (I'm) not sure they want to stick with.

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Notes: The discovery of Uranus, Neptune, and Pluto

Let's take stock. We started out confident in our belief that it was just us, Sol, Luna and the fireflies. Now, we have knocked ourselves down a few pegs. We're not in the centre of the universe, there are other things orbiting the Sun (and not us, the bastards) and we have a bunch of equations that tell us how they move. We also have a brilliant device using lenses and tubes that let us see these things much more easily. Yes, telescopes were a particularly brilliant invention. They allowed us to observe the sky with unprecedented accuracy. Looking around our 5 neighbouring planets, the Moon, the stars, that odd comet...Yes, that one. No, it's definitely a comet, I'm sure. No, no tail as of yet but it's a comet, I'm certain of it.

Comet.

The discovery of Uranus is quite a pleasant one as it happens. It had been seen so very many times over the years but most put it down as being a star. Then a German fellow going by the name William Herschel moved to England, built himself a telescope and had a marvellous time with it until one March night in 1781 he noticed a fuzzy thing and thought to himself "Ah, a comet". Specifically he noted

"In the quartile near ζ Tauri ... either [a] Nebulous star or perhaps a comet"

He claimed as much to the Royal Society and the Astronomer Royal, the latter replying to him not knowing what to call it at all.

 "I don't know what to call it. It is as likely to be a regular planet moving in an orbit nearly circular to the sun as a Comet moving in a very eccentric ellipsis. I have not yet seen any coma or tail to it

Herschel continued to refer to it as a comet, albeit cautiously. By the end of the year however he had concluded that, as others had already begun to suspect, it was a new planet. The happy ending to this story, King George III threw money at Herschel on the condition that he move to Windsor and let the Royal family have a look through his telescopes. There is some more drama to be had about it's name but I'll let you discover that for yourself. It was discovered to have a really very long orbital period. 84 of our Earth years, in fact. Further observation also unearthed some rather interesting data. There was some anomalous factor in the orbit. Now we have dealt with this before. Something is going against our view of the universe and we need to sort it out. Thus we come up with some possible explanations:

• Poor quality observations. This is the favourite of the theorists. Those bloody experimentalists fucking up the data collection. Look at it again, our way is law. Newton's Law.
• Does the gravitational force really obey the inverse square law? Yes, on the other side of the coin, could it be the theorists at fault? Certainly this has been true before. Remember geocentricism, eh theorists? Yeah, choke on that.

Theorists and experimentalists are like that, in the same harmless way that Physicists pick on Chemists pick on Biologists for being a somehow lower form of science. And everyone picks on Psychology. Anyway, the debate raged on, until a couple of people, one French Urbain Jean Joseph le Verrier, one English John Couch Adams, proposed another idea. What if there is another planet, beyond Uranus, who's gravitational force was affecting the orbit of Uranus? Calculations were made, observations done, and low and behold, a "star" making planet like motions was observed. Le Verrier, being the one who actually saw the bloody thing (Seems that Adams did something of a hash job with his data) called it Neptune, and after years of debate, the credit was split between the two. Thus, in some small way, two nemeses came closer, as people, as humans. Yes, we the British could focus on making everyone else hate us instead.

Once again did history repeat itself, it seems, as Neptune's orbit also did not seem to conform to expectation. Ah, but we knew the tricks now. A new "Planet X" was predicted (Planet IX, surely), and eventually, in 1930 something was found. It was named, adorably, by an 11 year old schoolgirl with an enthusiasm for both astronomy and classical mythology. Venetia Burney figured that the name of the god of the underworld was an apt name for such a cold, dark planet. After the name was chosen by unanimous vote Venetia received £5 for her trouble. Adjusted, that is roughly £234 of our Pounds Sterling. Given to an 11 year old.

Fair play

Incidentally, it should be noted that the apparent mass of Pluto was no way near what would have been required to mess with Neptune's orbit. No, Pluto was not the Planet X everyone was looking for. A search for a 10th planet was made but this was all but abandoned following the discovery that the discrepancies in Neptune's orbit were due to a slight overestimation of it's mass. An overestimation of 0.05% in fact, comparable to the entire mass of Mars.

I would like to end the post by reminding everyone that 2012 is not yet over, and there is still every chance that our modern day Planet X, aka Nibiru will swing through the the solar system fucking some serious shit up as it goes before the year is out. Ignore any of those "scientists" or "astronomers" who might tell you that it is kind of impossible for it to actually exist. They're all just in on the conspiracy.

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Notes: Kepler's Laws and the Repercussions

Now where were we? As yes. Imagine you're an avid 16th century astronomer. You make extensive observations of the positions of the planets, and have a fairly comprehensive view of it all. You're even pro-copernicus, though having taken such staggeringly accurate data this isn't much of a surprise. Unfortunately you're also a bit protective of your work (Not an unreasonable stance during the time)  so you don't really tell anyone about it. Congratulations, you're Tycho Brahe. Good news, you have a bitching moustache, and your assistant uses your data to come up with a set of laws that would revolutionise astronomy. Bad news, he does so after you die from a kidney/bladder ailment having refused to go to the toilet at a banquet because it would have been a breach of etiquette. Or you were poisoned with mercury, so there's that.

Speculation aside, your assistant, Johannes Kepler now has access to your lab and notes, and man does he go to town. Within a couple of decades of Tycho's death he had worked out 3 laws of planetary motion:

           1. Planets orbit the sun in ellipses with the sun at one focus

Some maths now. An ellipse, in layman's terms, is a squished circle. If that's good enough for you then just go ahead to the second law now. See you there in a bit.

Mathematically, an ellipse is a set of points that satisfies the equation:

• ^x2⁄_a² + ^y2⁄_b² = 1

Ellipses have an eccentricity 'e', which is basically to what degree they are squished.

• e ≡ √1 - ^b2⁄_a²

Do please ignore the godawful overline job there. That's meant to be all square rooted. But as you can see, if  a=b then eccentricity is 0, and you get a circle. On the other hand as e approaches 1, through oversized a or undersized b, then we're more or less getting a line.

Here is the eccentricity of the planets we've discovered so far:

Earth - 0.017
Venus - 0.007
Mars - 0.093
Jupiter - 0.048
Saturn - 0.056
Mercury - 0.206

Clearly most of our neighbours are fairly normal. Venus is practically Ned Flanders. Mercury on the other hand is down right ovular in it's travels, and this was something that had baffled astronomers who had previously believed that everything moved around in nice polite circles.

This was the equivalent of not thanking someone after they hold a door open for you.

         2. "Equal area" is swept out in "equal time".

This one is simple enough. See the orbit below?

During a value of time t, wherever the planet is in the orbit, the area cleared between it and the star will be area A. Next.

         3. The relationship between period p and distance from the star is:

a³ = p²

^{There's not much more to say on that matter so have some data on it.}

Ah but I wish you could make decent tables in Blogger. 

Now I've already said a lot on the subject of Galileo and his life including the fact that he didn't invent the telescope, as is so often claimed. Thus I shall not dwell for too long on such matters. I did mention that he made a number of discoveries with his telescope however, and I shall briefly expand upon a few of them.

• He discovered mountains on our own moon.
• He had a good look at the celestial Thursday that is Jupiter, and observed that it had four moons of it's own; Io, Europa, Ganymede, and Callisto. These are known as, understandably, the Galilean moons.
• He worked out that the moons satisfy a "Kepler-like orbit", that is to say that the cube of the distance between them and Jupiter is proportional to the square of the orbital period.

All in all everything he discovered kinda fought against the idea of geocentricism. After that, well, like I say, I've gone into it already. Let's briefly move onto someone New...ton.

Sorry. Anyway, Kepler's laws were pretty observation based. They worked, absolutely, but the maths behind it was lacking. So the story goes, having had a crack at it himself this bloke called Christopher Wren made what is known in the business as a Scientific Wager, offering 40 shillings to anyone who could deduce Kepler's Laws from the inverse square law. Alas, while Newton had a stab at it, by the time he had finished he was too late. His only consolation was that his work grew into one of, if not the most important pieces of work in science. The 40 shillings would have been nice though.

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Notes: Epicycles and Planetary Orbits

So far you're pretty sure that you're place is the centre of the universe, and that means that everything in the sky is circling you, as well it should, god's own image, Joshua 10:13 etc etc. However you found something that didn't quite agree with that. The strange wandering stars were moving in a way that didn't exactly suggest  a nice clean orbit around us. So you did what anyone who's sense of place in creation was threatened would do. You made it fit your theory.

What you decide is that the planets are still orbiting you, calling that orbit the deferent, however they're also moving in small circles around that deferent. You call these little circles epicycles, literally 'on the circle'. Alright, everything is sorted. These circles account nicely for the changes in direction, velocity and what not that these planets take when orbiting you.

Source

Except they'd go out and observe a bit more and it didn't quite fit. So they'd add more epicycles. Still not quite right. More epicycles! Still no? Just keep changing stuff until it fits our established theory gorramit!

These days epicycles is something of a swearword in science. I can tell you this with certainty because two lecturers in entirely different parts of the world have told me just that. If a theory comes along that builds into something really unnecessarily and ridiculously complicated it may well be compared to epicycles. Then someone gets punched.

Incidentally, this is where one of those fables I keep writing about come in. In fact this is the first one in that first lecture series where I got the whole idea. Basically the idea that they kept making things more complicated is true, but they didn't so much keep adding epicycles as they did arbitrarily change the velocities of the planets, or make the epicycles move side to side, anything that might help get it to work. The end result is the same though. An arcane mess of a theory that you just want to curl up and ignore.

Kitten break.

So you do. You decide you're fed up with this nonsense. Clearly something is wrong, and a new theory is needed. So thought a fellow named Copernicus, who had a look at the data and thought "Ok, this needs some work". So he proposed Heliocentric cosmology, and published his theory in a book called De revolutionibus orbium coelestium, On the Revolutions of the Heavenly Spheres. Initially it didn't sell so well. Copernicus has made it really rather technical, so that only the most learned of astronomers could really understand it. This allowed it to disseminate into their ranks before it roused any of the more zealous geocentric types. Eventually however it did become fairly popular, enough so that the pope had it put on the Index of Forbidden Books in 1616. Copernicus didn't really mind so much at the time, though mainly because he was dead. Probably best. If he was still alive when it was banned he might have been taught the error of his ways, as it were. And then died.

Now this theory works, you think, though probably only in your head, lest you be put on trial for heretical thinking or whatever. It fits the data. The planets all orbit in the same direction, the outer planets take ages to get anywhere, everything fits. What this also means is that we can take a decent stab at working out how far away the other planets are:

I'm tired, hungry, and have been at this all day. You be happy with my illegible scribbles.

So finally, we have some proper idea of our universe. There's us orbiting the sun, along with other planets, and the fireflies that got stuck up on that big bluish black thing.

Next time, the uneventful adventures of Tycho Brahe.

Not that one.

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Notes: Stars and Planets

So far we have made some basic observations, and come to a conclusion about our place in the universe that, as far as we're concerned, is flawless, and frankly kind of gratifying. Centre of the universe huh? Who'd have guessed it. Enough back patting for now though, we have more looking at stuff to do.

For example, the fathomless depths of my eyes.

You may have noticed that while the moon is floating about, it's joined by a bunch of other tiny points of light. To save you the trouble of counting I will tell you now that there are roughly 4000 stars visible to the naked eye. Almost all of these move across the sky in a fixed pattern that, if you were of a type, you might want to sort into patterns and what not.

I am momentarily amused that iTunes, in an act of solidarity has just shuffled in Metallica's 'Orion'. Simple things. Excellent track though.

Alas, things are not as perfect as you might have liked. There are 5 points that don't seem to want to stay in place with the rest. And because you're an ancient Greek, you go ahead and call them astēr planētēs which sounds lovely until you realise it literally means 'Wandering star'. You decide to stick with 'planets' because you're English now and frankly we seem to have a properly hard time not nicking other cultures' words. They are named:

• Mercury
• Venus
• Mars
• Jupiter
• Saturn

Now I'd like to point a little something out. It's not quite so obvious in English where our days of the week are fairly Germanic in origin (There is something quite enjoyable about going to lectures on 'Thor's Day') but some of you may know the more Latin based, French  Check out their names for the days of the week starting on Monday:

• Lundi
• Mardi
• Mercidi
• Jeudi
• Vendredi

Now switch back to English for the weekend and we have:

• Saturday
• Sunday

It all has the same kind of root which is why I'm being fairly inconsistent with language. Point is that our 7 day week is based on the 7 key objects observable in the sky with the naked eye. Some languages name them with their Germanic roots, some Latin, some Gaelic, but on the whole they're all from the same thing, showing just how far back this astronomy business goes.

Right, enough linguistics¹. Back to the observational SCIENCE! So, these wanderers pique your curiosity, and you devote some time to observing them. What you notice is odd. They really do wander, sometimes completely randomly.

A composite view of Mars from Earth

It looped. Mars bloody looped around in the sky. This is nuts. This completely goes against your world view. Everything is meant to be nicely orbiting us and there is Mars pissing off doing it's own thing. What a wanker.  But nonetheless, you have new data to be interpreted. If it's not circling around us neatly it can only mean one thing.

Epicycles.

[1] If I wasn't a physicist I would absolutely go into studying linguistics and etymologies and what not, and not just so I could make hi-LAR-ious oral sex jokes.

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Notes: The Moon

Back onto the astronomy thing. As mentioned last time, we are moving onto the second most obvious thing in the sky, The Moon.

To begin with, it's worth knowing a little about something called the ecliptic. This is basically the path the sun took during the day. Secondly, you need to know that everything has an angular position. There is a brilliant rule of thumb for this. I urge you to try it, it works for damn near everyone. Simply hold your arm out in front of you, with your hand up straight, like a traffic cop telling you to stop or something. Your finger is roughly 1°. With this in mind, know that the Moon can be found within 5° of the ecliptic.

Incidentally, both the Moon and the sun are roughly 0.5°, meaning you can more or less cover them with one finger, though if you want to test this one I'd recommend trying it on the Moon first. The Sun is very formal, and pointing is quite rude.

Alright, so you see the Moon, you observe it over some time, and you notice it changes shape with a certain regularity. These are called the phases of the moon and proceed like so:

Incidentally, in the same manner as with Dara O'Brien's slip up, I had my reservations about the accuracy of this particular advert that some of you may remember from our youth.

That clearly should be "Full moon, Waning crescent, No moon", but I guess marketing departments have no time for scientific accuracy.

Anyway, distraction aside, this cycle repeats itself more or less every 29 days.

Interpretation of the Data

Ok, so you're a blank sheet of potential human observation. Telescopes and what not have yet to be invented and all you have seen so far is the Sun and the Moon, going around and around in an eternal game of celestial kiss chase, one full of fiery passion, the other kinda turning invisible half the time. I don't know, I never played kiss chase.

Using this data you try to craft a model of the universe, and eventually settle on one that fits your Sun-Moon-Earth data perfectly. Thus came about the Ptolemiac system, from which arose much of Geocentric cosmology, a view that persisted for a good 1400 years, and one that has clouded much of western philosophy, religion and science.

This incidentally is fine. It's all very well to look back and scoff about how uneducated past folk are, but do remember that given the data they had, this view fit perfectly  They were using what we might now call a "non-inertial reference frame", which in this case is kind of a nice way of saying they didn't know the Earth was also moving.

I'm not strictly holding to the lecture by lecture notes thing at this point instead opting to separate them into similar sub-subjects. So, I'll cut these notes half way through and next time I'll say a little about stars and what not.

Now if you'll excuse me, I need to go buy some Jaffa Cakes.

Heaven.

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Notes: Thermometric Properties

A thermometric property is one that varies with temperature. For example, most objects will expand as temperature increases. The volume of the object is a thermometric property.

It is from these properties that we get our temperature scales. Now, we can't just measure every degree between 1 and 100. The problem there is that different materials expand at different rates. An alcohol thermometer will not agree with a mercury one. So what you do is you get two points that are definitely what it says they are, then you just split everything in between evenly. Mostly the two points will be the temperature at which water freezes and boils at 1 atmosphere of pressure. Celsius for example used to be defined as such, putting freezing at 0 and boiling at 100 degrees, then defining a single degree Celsius as 1/100 of the boiling point..

These days things are a little more...precise? It's not changed too much but now Celsius handily ties into the Kelvin scale which has the fixed points as absolute zero and the triple point of water, the triple point being defined as the temperature at which a substance (in this case water) can exist as it's 3 phases (solid, liquid and gas) in thermal equilibrium. These points are given the numbers 0 K (-273.15 °C) and 273.16 K (0.01 °C), with a single Kelvin being defined as 1/273.16 of the temperature of the triple point of water.

Incidentally, avid QI fans like myself will remember this particularly contentious issue:


To be perfectly honest, I may not have actually gotten as far as writing in, but I was definitely bothered that he had gotten points for it the first time around.

I'm sorry Mal, I'm just bit sad like that.

Anyway, that was 2 lectures worth of notes. Christ, this particular module drags on a bit.

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Notes(or not): Dynamics, Algebra and Calculus

The problem with these subjects (more obviously for the latter two) is that they are fairly maths based, not to mention how much of it so far has basically been A Level recapping. As such, they don't really translate into typed format very well, and, to be honest, even if they did it's more about practice than information. So, I will not be blindly pumping out equations unless it's particularly interesting. Complex numbers for example, I might do something on them.

But until then, if there's something you think I might help with, and for some reason you can't ask your own lecturer, give me a shout and I'll see what I can do to assist you. Together we will help us help you help us all.

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Notes: The Sun

Part of what makes science kinda great is that it's constantly being worked on and improved, tempered in the forges of experimentation. Astronomy is one of those odd sciences, in that we can't exactly go out and do that. Going up to stars and measuring stuff poses certain logistical problems. So instead what we do is look at stuff. A whole lot. And would you believe that looking at stuff is really gorram interesting? Think about it, it's one of the oldest sciences and it still has a pretty massive presence. Something about the vast expanse of unknown is still sparking the old human curiosity...thing.

Ok, so let's explore what we can observe with just our naked eyes. I mean let's face it, not everyone has an awesome 8" reflective equatorial telescope. And while that is a shame, it's not the end of the world.

For starters if you look up during the day, and are not in Wales, then you may see an incredibly bright thing. We call this The Sun, or Sol, if you're the kind of person who calls the Earth Terra in casual conversation. If you give it a while, you may also notice that the sun takes a path across, and further careful observation reveals that the path the sun takes is a little different every day. In fact this happens all year around, the path being a little bit shorter each day at this time of year until the 23rd of December, or the Winter Solstice.

Source

Side note: You may notice that that is a fairly familiar date. That is no coincidence. Fun fact, the Bible doesn't actually give a specific date for Jesus' birth. Thing is that at their most expansionist, the Roman Catholics decided they needed a date to celebrate the event of their saviour's birth, and they also wanted to get rid of the pagan celebrations of the solstice. And as my lecturer so put it, you don't get popular by cancelling parties. So, the logical thing to do was to co-opt the existing "unholy" celebrations for their own righteous and godly one.

Ok, so that's one glowy orb seen, how about the other? During the night, when they sky is arguably at it's most stunning we have the bright white disk we call the Moon, and that's what we shall cover next time.

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Notes: Thermodynamics

Posts with the heading Notes:[subject] are more for my benefit than yours, just a little something to reinforce what I've already written down. There is only so much I can do to make dynamics a source of humour, for instance. But by all means read on, and I'll certainly do my best to spice things up a little.

Kicking things off with a bit of basic classical mechanics. This is the part that deals with the energy transfer of stuff on the macroscopic scale, that is to say, things we can measure easily enough in a lab. Key word in this area is systems.

A system has been defined for me as a collection of matter in a boundary, though truthfully I prefer Wikipedia's disambiguation page's suggestion "the portion of the physical universe chosen for analysis". It makes it sound like we are undertaking something fairly special, selecting a single part of the entire universe to study and observe, when in fact we are just considering energy transfer in engines and what not.

There are, generally speaking, 3 types of system; we have open systems, where matter can cross the boundary, closed systems, where matter cannot cross the boundary, and isolated systems, where both energy and matter are unable to be exchanged.

Generally speaking CT deals with systems in thermal equilibrium.

Extensive and Intensive properties

Extensive depends on amount of matter in a system
Intensive does not.

Well that was easy.

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Wading Slowly Down Into The Deep End

Ah, it has been (another) while since I opened this site up. Yeah, sorry about that, been kind of busy lately, getting results, working and more importantly, finally, and so very wonderfully, getting into university. Yes, I am finally here, fulfilling my physics based dreams. And so it is from here in my small but comfortable room in halls that I come to you now. What does this mean for you? Well, I imagine that I shall continue using this as a revision tool, which means I will be posting about topics of marginally higher complexity. It is a well known truth that, when it comes to scientific subjects at least, the first line of any high level course is more or less "Hey, you know what you just spend ages learning for those previous exams? It's all bullshit. Here's where it's really at."

I'll still be trying to post those Bailyn's Fables, because I personally find it fascinating to look into, and I plan on joining the uni's RP society so hopefully I'll be able to make good on my mission statement to bring you posts of that nature.

Basically while I anticipate a massive increase in workload, this will have the paradoxical effect of making this blog, or whatever it is, busier, and ideally more entertaining.

Wish me luck!

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The First Time I Was Conned

I am an inexplicably trusting creature. If a stranger comes up to me in the street and asks for money because she needs to feed her child and she can't afford baby formula then I will probably end up emptying my wallet (This may or may not have happened). However once I catch on to your con game, I will never fall for it again. Character development, people.

This takes place in a dark time in my life. I was naive and gullible in a world full of crooks who could smell weakness on me like oregano on pizza. It was irresistible to them. Yes, of course I am talking about Primary School. It happened on a cold, wintry mid-summer afternoon, and I was playing with my new pack of Pokémon Cards. 1st edition Starter set, I was chuffed. Everyone else had them and I was finally going to join in. Filled with hope and child like frivolity I went to school, looking to socialise in whatever way my awkward young self could. I passed the day, blindly trading energies for cards that would do nothing without said energies, standard kid stuff, when, during break, one of the older kids came up to me. What he offered me? A Pokémon comic, 1st issue. Well, I could hardly believe my luck. What did he ask for in return, why it was only a small thing. Nothing much. Just the shiny Machamp that came with all starter packs. How could I say no?

Believe me, I am cringing right along with you as I write this. Well, it turned out, it wasn't even a proper Pokémon comic. Some translated Pokémon Special, that would have been fine, but no, all I got was what amounted to an officially produced print out of screenshots from the first animé episode. I was devastated when I realised my error. From that day on, I resolved to change. I changed from the 7-8 year old child I once was and became an 8-9 year old boy! Never again did I blindly walk into deals I hadn't thought through or checked thoroughly for validity. I still have that comic, if only to forever remind me of that day, to feel the same sting of resentment, and to remind me to always be wary of deals that seem too good to be true.

Until I was 12 when my friend assured me that that girl I liked would totally go out with me if I just asked. I feel I coped with that "No." better than many my advanced age would.

What sorrow these 12 year old eyes know. Death and suffering walk with me arm in arm, cloaks black as my VERY SOUL.

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The Steam Sale, and Why I Haven't Updated

There are times when it is a good thing to have not really very much money at all. One of those times is during the Steam sale when you can feel much better about having spent all your money on games your computer cannot and will not ever run.

Why must you taunt me so?

There is a very obvious question that comes up every year, "How can they afford this?", the answer to which is the equally obvious question, "Would you buy it anyway?". Would you really look at that game at it's RRP and think, "Yeah, I want that.", or has the thought process turned into "Well fuck, it's only £3"? Steam is still making money here, money that they wouldn't have otherwise, because they take that sense of "Hey, I'm saving money!" and apply it to absolutely bloody everything, and suddenly for a week or two, you have a host of people going "Well I wouldn't usually play that, but damn, it's so cheap" for a whole host of non-usual product. Voilà, you have a new customer, who may even end up being a fan of the series/genre/theme music and stick around to buy more at regular price.

The trouble of course is when the regular buyers think "I'll just wait for these Steam sale". Luckily for those on the production end, as we all know the gamer is a horribly impatient breed.

In short, Valve know their markets, their demographics, and know how to work them. They are probably one of the best, if not the best software developers of the age, but it is always worth remembering that they are a company, and they are out to make money. Even if they do take the much more endearing route of actually building a loyal fanbase and not being complete assholes all of the time.

In other news, I haven't updated in a while because I have been trying to remedy the no money situation through the method of working 12 hour night shifts. Very nice pay, but it completely wiped me out when they were finished. I have just gotten my sleep schedule back into something like normal, so ideally there should be some more activity here soon.

Now if you'll excuse me, Thief II is going for under £2. I think my computer should just about handle that.

Sweet, sweet polygons.

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You All Meet In An Inn

There is a tendency in certain mindsets to dismiss a certain popular wiki known as TVTropes as an over-analytical media dissecting machine, and while I think there is truth in that argument, there is also truth in the idea that Tropes Are Not Bad, and I would like to take a moment to justify one of the more well known tropes in RPGs.

So you start your game, all your characters are ready, and the GM has donned whatever piece of clothing makes himself feel that touch more important (I have a particularly nice top hat). You are awaiting the GM's first words eagerly/absently doodling on your character sheet when you hear the words: "You are all sitting in a pub/bar/space bar in space". Instantly the table erupts in groans and accusations of a severe lack of originality are thrown around. But why? The way I look at it, your GM has chosen one of the most likely places for a group of people to meet up. If they know each other, what better place to hatch your plans that in your favourite local? If you have all just met, how better to loosen up than with a round of drinks/futuristic hallucinogenics.

You all meet around an array of novelty shots.

I will grant that in the everyone-knows-each-other setting maybe someone trusted's home would suffice, though in all likelihood, someone will still call out for the host to provide at least a glass of water, in startling resemblance of the RL group itself. But the usual setup in the cliché is that a group of people bound by common cause meet from afar at an inn, a well known landmark in any town. Your character who is not from town can easily ask a passing stranger "Where is The Juggling Tomcat?" and get a positive answer. There is however little chance in all but the smallest towns of getting where you need to quickly with a "Where is Urist McHammerdorf's home?"

My final point lies in the often all too looked over effort required of the GM to come up with somewhere for a bunch of characters who really have no business being together to meet. This ties back to the previous points that really, the best place for an upbeat sniper specialist and a depressive technomancer with Occult (Herbalism) to meet up is somewhere neutral, somewhere both can easily locate and no-one feels overly uncomfortable.

"Do you reckon they know any Michael Buble?"

In summary, there is nothing particularly wrong with the trope. If your GM pulls it out, and you really have a problem with it, just consider it an unoriginal starting point for an adventure that you can make brilliantly original yourself. And GMs, if you are really stuck for a logical starting point for your diverse set of characters, you can do worse than an inn.

If nothing else your PCs can start a bar brawl. That should keep them entertained while you figure out which crime lord they pissed off doing so..


NB: You'll thank me, dear Reader, for not actually linking you to any TVTropes pages. It would have resulted in hours of lost productivity for both of us, I'm sure.

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Thermal Physics: Ideal Gas Equation and Laws

pV = nRT

That equation is gorram everything to this section.

Learn it. Love it.

Wear it into town.

Pressure, p
This is caused by the gas particles colliding with the wall of whatever container they're in. Measured in pascals, Pa

Volume, V
The space occupied by the gas. Measured in m³

Number of moles of gas, n
That's fairly self explanatory, really. Measured in numbers.

Molar gas constant, R
= 8.31 J mol^-1K^-1

Temperature, T
The measure of the average kinetic energy of the molecules of a gas. It is the absolute temperature and is measured in kelvin, K


Now, a little something about temperature scales. The temperature of gas is measured by the change in another substance at the same temperature. The obvious example of this is a glass thermometer, and the expansion of a length of mercury or alcohol within. This is known as a thermometric property.

The thermometric property is measured at two fixed points. Often this is at the change of state of a property. It is well known for example, that the Celsius temperature scale was made to be fixed at 0 °C and 100 °C, the then defined freezing and boiling point of water. So let's come back to our glass thermometers. They are designed so at 0 and 100 they are both accurate. It is assumed therefore that the two will progress linearly up and down the scale. Alas as is so often the way, things are a little more complicated.

Mercury and alcohol expand at different rates as they heat. The consequence of this is that while they both agree at 0 and 100 °C, these are the only points they can be guaranteed to agree on. But fear not. It was to overcome this that a standard scale was devised. May I thus reintroduce: Kelvin.

William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE

The Kelvin scale is actually based on our post subject, the behaviour of an ideal gas. It uses the pressure of an ideal gas as it's thermometric property, it's two fixed points being the point at which there is 0 pressure, known as absolute zero and the triple point of water, where water can exist as solid, liquid and gas, defined to be 273.16 degrees on the Kelvin scale.

Gas laws

Remember that equation I ordered you to remember? These 3 are what combine captain planet style to form it.

  1. Boyle's Law

For a fixed mass of an ideal gas at constant temperature p ∝ ¹⁄_V
∴ pV = constant  or p₁V₁ = p₂V₂

 2. Charles' Law

The volume of a fixed mass of an ideal gas at constant temperature is proportional to it's absolute temperature, V  ∝ T

 3. The pressure-temperature law

The pressure of a fixed mass of an ideal gas at constant volume is proportional to it's absolute temperature,  P  ∝ T.

Now, you do need to know these. At the very least, you need to associate the name with the key components, because then you can just look at the equation up top to work out what they're meant to be doing.

More constants!

The Avogadro constant

The corresponding law states that at the same temperature and pressure, equal volumes of gases contain equal numbers of molecules.  Lot of words, sure, but it's not that bad at all. Let's refer back to our beloved equation. Rearranging for number of moles give us:

n = ^pV⁄_RT

It is clearly apparent that if p, V and T are the same for two gases then yes, they will have the same number of moles.

We take this a step further by considering 12g of Carbon-12. It has as many atoms as there are particles in one mole of a substance. This gives us the Avogadro constant, N_A = 6.02 x 10²³

The Boltzmann constant

This is literally just a constant gained by taking our two current constants and dividing them:

k = ^R⁄_NA

k = 1.38 x 10^-23 JK^-1

• Back to Heat Capacity and it's related paraphernalia.
• Onwards, to kinetic theory!

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Thermal Physics: Heat Capacity

In Britain's own peculiar way it is bloody freezing, in the middle of June. So, what better time than now to do a little something on thermal physics.

As with most physics, this all comes down to energy, and the transfer, exchange and general movement of same. The effect of this is generally kind of obvious. The more thermal energy something has, the larger it's temperature is. What's interesting is that various materials have a greater inclination to be heated that others. This is easier demonstrated. Find a metal surface, and consider it's temperature. Unless you already know what I'm about to get at and are purposefully being difficult by considering the inside of an oven, you should agree that said metal is at room temperature. Now if you touch said metal, you should notice that it is quite cold. "Gosh James, how can this be?" I hear you ask. Well, as we all know, heat tends to flow to colder areas. Things like to reach an equilibrium, that's just they way of things. So when you touch metal, you aren't feeling cold metal as much as you are feeling the heat energy in your fingers being SUCKED OUT FROM YOUR BODY.

Dramatic reconstruction

The way we measure how willing objects are to drain the life from your very body is called the specific heat capacity, c. This is defined as the energy required to cause a temperature rise of 1K per unit mass, usually 1 kg. From it we can work out a bunch of stuff with the equation:

ΔQ = mcΔT

In words, the change in thermal energy of an object is equal to the mass by the SHC by the change in temperature. T is measured in kelvins really but given that 1 K and 1 °C is exactly the same it doesn't really matter once you stick that Δ there.

All important equations are given to you but I feel it's helpful to get to know them beforehand. So let me throw this one at you:

 ΔQ = ml

This is where we bring in latent heat, l. Again this comes with a "specific" alternative. Two actually, and as such we have two definitions to remember. Both are pretty similar however, so I don't imagine you will have too much trouble.
Specific latent heat of fusion

the energy required to chance 1 kg of solid into 1kg of liquid, with no change in temperature.

Specific latent heat of vaporisation

the energy required to change 1 kg of liquid into 1 kg of gas with no change in temperature.

What this means for you is that when working out the energy required to  get a substance from one temperature to another, and there is a state change in between, you are going to need to make more than one calculation. One for the first temperature increase, one for the state change, then another for any further temperature increase. Keep yourself aware of this and you should be fine.

On the practicality side of things, this area of physics is widely used, mainly in the area of cooling, by dissipating thermal energy. It can been seen in power stations, and closer to home, us when we sweat.

Continue into the world of ideal gases

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Bailyn's Fables: Chandrasekhar's Limit

First, we need to know a little something about white dwarfs and electron degeneracy pressure. You see, the normal way stars manage to not collapse into their incomprehensibly massive selves is thermal pressure. Basically, while gravity is pulling everything in, pressure is pushing everything back out, and so the two balance, at least, for a while. Eventually the star runs out of hydrogen in the core, which contracts, raising temperature of a shell of hydrogen outside the core, causing it to start fusing. This expands the star into a red giant, until all remaining hydrogen has been fused, making the star contract again.

What it doesn't do is collapse into a black hole. It seems that for high density objects other kinds of pressure arise. In this case it is electron-degeneracy pressure. Very, VERY basically, this is a result of no two particles being able to occupy the same space, and the pressure that results as the volume these particles are occupying decreases. Long story short is that this pressure fights against the gravity of the collapsing star, balancing at roughly the radius of the earth. This is called a white dwarf, and this is where we pick up the main subject of this post.

In the 1930s an Indian-American called Subrahmanyan Chandrasekhar discovered that electron-degeneracy pressure isn't always enough. If the mass of the star is more than 1.44 solar masses gravity overcomes the pressure and the star continues to collapse. He presented his findings to the Royal Astronomical Society. Upon finishing however Sir Arthur Eddington stood up and opposed Chadrasekhar's findings, stating:

 I think there should be a law of Nature to prevent a star from behaving in this absurd way!

A full account can be found in , pages 37-39. It is apparent that while he could understand the theoretical idea of a black hole, Eddington simply could not conceive of Chadrasekhar's findings, that beyond a certain mass a star could essentially collapse into nothing.The result of this was that a number of physicists who would otherwise have publicly agreed with Chadrasekhar did not, due to Eddington's status. Chandrasekhar spent the rest of his life holding to his beliefs, even until 50 years later when he finally got the Nobel Prize for his work.

The moral of this tale is that maybe one should believe their student, rather than their own intuition. Had Eddington allowed for Chandrasekhar's work to be possible, we might not have lost a good 40 odd years of research into black holes. It also demonstrates the dangers of being too convinced of one's own intellect. As Eddington got older he became more and more convinced that he could just guess the answer to questions using gut instinct, a method I imagine most of us would agree to be utterly useless scientifically.

Further reading

A review of the meeting in which Chandra presents his findings and Eddington tears them down. Relevent pages are 37-39
The highlights of Chandra's life
A brief biography, and image source for this post

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Transit of Venus 2012

Early this morning I became part of history, and witnessed the like of which will not be seen again for over a century. I saw the transit of Venus.

I thought I'd break my unintentional hiatus just to express to the aether just how I felt at such a prospect, not to mention witnessing the historic event itself. I switched on the NASA EDGE livestream at 20:45 GMT, and watched for the entire stream from then until 06:00 the next morning. For most of the night I had been resigned to the fact that all the weather sources had said just how cloudy it was going to be, so I contented myself with the stream, which was incredibly informative and entertaining, I must say. However, as 04:00 approached and the sky became lighter, I noticed that the cloud was breaking.

Then came a good hour and a half of fervent hope, that the sun might breach the horizon before the dark mass of cloud to the north reached us. I happened to have a decent pair of welding goggles ready (bolstered with a pair of sunglasses, just in case) and sure enough, for a few minutes at around 05:45, just before 3rd contact, direct sunlight broke through the clouds, and after a few seconds, I could make out a speck of black at the edge.

I was struck by how beautiful the whole thing was. It really pulled into view the idea of the Earth and it's place in the Keplerian dance that is our Solar System, and our fiery sister planet, so alike but so different to Earth.

It was cloudy over most of Britain, so I imagine that yes, a significant number of people in this country did not get to see what I did, and may who could likely didn't care. But that's not really the point. I didn't so much become part of a select few, as I did join so very many people in celebrating this event. Not only the millions watching the same stream I did, or the other streams across the world, but the further so very many who have witnessed the same event over millenia. This event connects us to the past and the future, and that in itself is incredibly humbling.

The Science

Of course it is a great deal more than just a stunning celestial event. The transit has provided much for scientists, significantly in the area of studying exoplanets, one key method of discovering such is looking for the periodic dips in light from other stars that mean something is passing in front of it. As the sun is reaching a maximum in it's activity cycle it has more sun spots that usual. The transit means that astronomers had a chance to practise observing similar events in other stars.

Further practise can by made into estimating exoplanet diameter, through the measurement and comparison of Venus' apparent diameter and known diameter

Observations of Venus' atmosphere can help us understand more about it, more than can be cleaned from normal observation. It can also be compared to exoplanets to help determining atmospheres yet unknown.

All in all this was a highly significant event for all involved, from the amateur observers, looking at the pretty colours in a filtered livestream, to those dedicated scientists who missed the event, opting instead to sleep in anticipation of the huge amount of data and work that is about to be flung their way.

Images courtesy of NASA and SDO, link below

Now if you'll excuse me, I have to go get my sleep schedule back in order.

P.S.
If you missed it, or you just want to see more, I have a few links to share:

• NASA's Transit Data, a number of short clips and composites of the event in various filters, taken by the Solar Dynamics Observatory 
• Helioviewer, an impressive tool that, in short, shows you the sun. 
• Sun-Earth Day, the NASA sub-site with a large amount of information and images on and of the transit.
• NASA Edge, The guys who provided/hosted the livestream. They were clearly effected by the lack of oxygen up at the top of Mauna Kea, and they plugged it enough themselves, so I see no harm in linking to their stuff in appreciation.
• MMS, nothing to do with the transit, but a highly interesting upcoming mission that was mentioned in an interview during the livestream.

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Decision Maths: List of Definitions

The D1 exam is but a week off, friends, and hopefully you've been practising all the algorithms and stuff. There is one aspect that I'm having trouble with, so I thought I'd try and right up a little revision sheet for us all, unless you're reading this in the future, in which case I have undoubtedly become a shining blogging god, and thanks to my own last post no one ever took a Decision Maths exam again, instead opting for nicer, more productive modules like Mechanics, or Further Maths. Indeed, anyone taking a D𝒙 exam is actually brought into a psychologist's lab to help further understand why someone would subject themselves to such a thing. Good luck, strange person I just made up. May you find peace in your future.


Anyway, the thing I want to work on right now is definitions. I haven't had to properly equate lists of uncommon words and phrases with arbitrarily specific meanings since learning all the Italian for Music Theory, so I'm not looking forward to it. Best get it done though. I'll try to keep things minimal, and only go into the particularly arcane ones. You should be able to remember something like "A subgraph is part of a graph" yourself. For the more tricky ones I'll try to single out the words to remember that might help jog your memory.

Graphs and Networks

Graphs understandably hold a whole bunch of the words you need to remember, taking up most of the course as they do.

Path - A finite sequence of edges such that the end vertex of one edge in the sequence is the start vertex of the next, and in which no vertex appears more than once

Ok, you see what I mean? It's not enough to just say that it's a bunch of connected vertices. You have to be ultra specific, to the point of obfuscation. I'm pretty sure Decision is Mathematicians' way of trolling Biology and Law students.

Keywords: finite sequence, no more than once

Walk - a path where you are permitted to return to vertices more than once.

So, a path can only visit each point once, whereas if you are walking along said path, you can go wherever the devil you like.

And with scenes like this, why not?

Keywords: more than once

Cycle - A closed path

a path where you could conceivably go around in a circle if you followed it. These are the things you want to avoid in them there Prim and Kruskal problems.


Spanning tree - A subgraph of graph G containing all the vertices of graph G and is a tree.

Define tree with tree. Stay classy Decision Maths.


Keywords: subgraph, tree


Isomorphic Graph - Shows the same information but differently.

If you're coming at this from a more scientific background you should recognise the prefix iso, meaning "equal". Isotope is a variant on an element that occupies the same τόπος (tópos, “place”) on the periodic table. Isomer is something that has the same molecular formula, but a different structure (μέρος (meros, “part”))¹ .

Keywords: Iso-same, morphic-shape

Complete graph - a graph in which every vertex is directly connected by an edge to each of the other vertices.

Everything is connected to everything, lines are everywhere.

Keywords: Every vertex, connected

Bipartite graphs 

This is a fairly important part, as almost every bipartite question I've done has asked for some definition or another. As such I've seperated it from the other graph definitions.

Not to be confused with...

Bipartite graph - consists of two sets of vertices X and Y. The edges only join vertices in X to vertices in Y, not vertices within a set.

Pretty simple one, it's just describing the set up of your average bipartite problem.

Alternating path - starts at an unmatched node on one side of a bipartite graph and finishes at an unmatched node on the other side. It uses arcs that are alternatively 'not in' and 'in' the initial matching.

This is another one of those definitions that really takes the piss. It basically means that an alternating path is a path that alternates, specifically between the two sets of nodes. It is what you end up with after applying the maximum matching algorithm.
It is probably best split into it's two parts. Try to associate everything in red with "path" and everything in blue with "alternating". The second one should be easier as "alternatively" is right in there already.

Keywords: Starts unmatched, finishes unmatched, initial matching

Matching - The one-to-one pairing of some or all of the elements of on set, X, with elements of a second set, Y.

The main thing I can recommend for this one is DO NOT FORGET the "one-to-one" bit. That is worth , well, probably only a single mark, but any mark you can grab in this exam is a good one. It is simply not enough to just say that it's the pairing of the two sets.


Keywords: one-to-one pairing, some or all


Complete matching - This is the same as a compete graph but with matching replacing the word graph, and taking into account the two separate sets. It is possible that you cannot obtain a complete matching if some tosser in the question refuses to do some task or another. In this case you simply get as many pairs are you can and call the a maximal matching.

Route Inspection (aka Chinese postman problem)

I prefer to think of this as the envelope problem, because it reminds me of that puzzle we all did when younger of trying to draw an envelope without pen leaving paper or redrawing lines. It didn't take too long to work out that this was impossible without adding an extra line to make it look like an open envelope. If there is one thing I can say I enjoyed about D1 it's the joy of finally knowing why this was. Anyone, on to the definitions.

Valency - This is essentially the number of arcs that are connected, or "incident" to a particular vertex. This can be either odd or even, because, you know, integers work that way.

Eulerian - A graph has this property if all the valencies in it was even. If precisely 2 valencies are odd, and the others even then this is known as being semi-Eulerian

Leonhard Euler. This guy has had an insane amount of stuff named after him

Traversable - A graph is traversable if it is possible to traverse every arc once without removing pen from paper. This fits with the Eulerian definition as is a graph is Eulerian, it is traversable. Indeed, if a graph is semi-Eulerian is it semi-traversable, with the start and end points being the two odd valencies.

Critical path analysis

Source node - The first one.

Sink node - The last one.

Dummy activity - A virtual line with no time value, used to show that an activity depends on another before starting, if said activity has already been drawn leading to another node.

Early event time - The earliest time of arrival at the event allowing for the completion of all preceding activities. Calculated during the forward pass/scan.



Late event time - The latest time that the event can be left without extending the time needed for the project. Calculated during the backwards pass/scan.



Critical activity - If any increase in an activity's duration with cause an increase in the total duration of the project then it is a critical activity. The path leading from source node to sink node following these activities is the critical path.



And that, as they say, is that. I've left out linear programming as that is basically algebra, and we all know algebra terms. Inequalities and all that. I have on the other hand added a few potentially superfluous ones just for completions sake. I can't say I've heard much call for a definition of source/sink node. 



Good luck, all.






¹I could go on, and I really want to because etymologies are fascinating, but I kinda committed to this revision thing.

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