Some real brain food:

And by 'food' I mean haemorrhage. Anyway, y'all better get yoself a part bake roll.

The first thing y'all gadda do is to take dat part bake roll and split it down the middle, like I split yo mama's legs - ALL THE WAY!

Then y'all gatta put those two pieces under something real hat, I used yo mama's ass but y'all can use a grayill. Get dem honeyz niiice 'n' toasted.

Then y'all better get yo black asses some cheese on it cos dat's da foundation, man, y'all wouldn't build no house widout dem bricks on er bottom.

Now grill that mutha fucker 'til she's niiice runny, like. Not too runny, we don' want dat bitch sliiidin' owff the toast now, do we?

Next, y'all better get yo asses down to Germany cos y'all gonna need some SALAMI, and lots of it. Layer that mutha up good an' proper.

Now ya gatta get the juices followin', tease that girl, make her wan' it...then put her ass back in the grill.

When she's all ready for yo meat, y'all better rise to the occasion an' put some sweet-ass ham on there.

Last but not least, you muthaz better put some cheese slices on er top.

Now she's got one hat body, real niiice, but she still ain't quite ready. Fire up that grill one more time and melt that cheese aaaaaaaaaaaaaall over her ass, she'll love it.

Now she's ready. This is where you real men come in. Y'all need to go down on that ho and eat the soft, juicy, warm, moist girl like she the only one in the world.

...
...
...
Still a better love story than Twilight.

Integration

Excuse the length of this post...and the grammatical, mathematical and logical errors, and try to see deeper into the depths of the etern...here's the post.

Again, sorry about the length. If you spot any (serious) errors please leave a comment and I'll try to correct it/them. Also post comments and questions about the maths and/or LaTeX used.

Sagging...just no

If one man talks to an invisible man in the sky, he's crazy. If a million do it, it's a religion. Sadly, this can also be said for a number of other things:

One guy getting drunk is a waster, hundreds getting hammered is 'nightlife'.

One girl dressing like a slapper is a slapper, thousands doing it is a fashion.

But I think one thing we can all agree on is that one teenage male wearing his trousers round his arse is an idiot, all of them doing it...yep, they're all fucking morons. Like I've said before, it's not my place to say and you can do what you want...but for fuck sake. Whoever decided that looking like you've either lost about 6 stone and not bought new clothes, or you can't actually read the size numbers on clothes was a good look should be hit with a car. Obviously neither of these are the actual reason people do it, the real reason is because that is what has become 'cool'.

There is a theory (validity TBC) that this 'style' is what people in US prisons do, more importantly what gay people in US prisons do. Now, I'm not against homosexuality (I am against camp-ness, but that's another rant), but I pretty sure that imitating gay prisoners isn't what everyone or even anyone would call cool.

I think that it, amongst other things such as walking with a 'swag', hanging on street corners and talking incoherently, is a way of appearing tougher to one's peers. I don't mean to be impertinent to their dress ritual but how does showing your underwear show that you could beat anyone in close range combat.

Maybe it's to attract the opposite sex, because I'm pretty sure that the ladies show 'the goods' for that reason too, except that's ridiculous because not even a sex crazed woman would be enticed by something as ridiculous as a 'sagging' teenager.

It could be, God forbid, a way for them to 'express themselves'...fuck off.

It's actually quite an ironic thing this trouser malarkey, because it only seems to be teenagers who would be more likely (no offence) to rob a post office maybe, or stab someone, and I don't think that the trousers would be of any particular help when running away from the police.

Maybe it's the same irony as the chinos - try look cool, end up looking like a dickhead.

Gameshow probability puzzle

I read about this a few years ago, but it's only now I thought to write up a nice and neat answer.

Please comment any questions about the maths or LaTeX used.

FOLLOW ME!

If you'd like to see more maths and over-expressed opinions, follow me! I'll be more inclined to keep this thing going.

Proof MLE for variance is biased

The variance of a population is calculated by using:

It seems logical that this formula would also provide a good estimate of the variance of the population when only given a sample. This is what is called and 'estimator'. However, this cannot be used to estimate the population variance based on a sample from it, i.e. it is biased. A proof of this follows along with the alternative, unbiased estimator of the variance of the population.

Please excuse the poor quality.

I can understand if some of this proof is not clear, if you have any queries I can do my best to explain, please leave a comment.

Injury is now a job too

'I was installing a fire alarm and I was give the wrong type of ladder'. So the ladder slipped, I broke my fingers, and now I should have money for my incompetence. These fucking lawyers need to stop encouraging idiocracy. I thought the whole idea of money was that you earned it using your skill and labour, and used that to buy stuff, so how on earth can someone expect money from falling over? Did you injure yourself using equipment at work? Then let that be a lesson to you that you should do your fucking job and check the equipment first.

As far as I can tell these 'lawyers' steal money from other people to give to clumsy people. I live in the UK where we have the NHS, i.e. free health care, so if you get injured they fix you up for nothing, no money out of your pocket for being at a hospital. Also the lawyers help you claim up to 5 years after the accident happened, so even if you've recovered and are back working, you can still rob people. I'm not claiming to have been round the block a few times, but I have one little fact about life: it isn't fair.

If you don't know your own job well enough to know what ladder to use, should your employers have their reputation damaged and profit margins dented? If you're playing golf and lighting strikes the club, should you sue the manufacturers because they're made of metal? If you slip on ice on the street because you weren't watching where you were going, should every tax-payer give you money for the 'trauma' the street caused you? Damn right you shouldn't. I can understand that if you're on a plane and it crashes, you should have your damages paid for (and maybe your money back...and some free flights), or if you buy a laptop and it explodes when you take it out of the box then you should have a free (working) laptop. But if you're just an idiot, I hope you've learnt your lesson.

Moment Generating Functions - Binomial

The last of the moment generating functions for the three main distributions. the Binomial Distribution is as follows:

Any comments or questions just add a comment.

Moment Generating Functions - Poisson

As I did for the Normal Distribution, I will show how you can derive the moment generating function for the Poisson Distribution:

Again, if you have any questions about the LaTeX or mathematics used, please just comment.

Time signatures

One thing I really love in music, but just don't see enough of, is interesting time signatures. I'm not saying that a good ol' 4/4 or 2/4 are dreary, but when an obscure band whips up a crazy sound in 26/4 it just adds another element to the music, it brings out something that would normally be missed. This might sound stupid but let me explain. 

A lot of bands would use drums to just keep the rhythm and rely on other elements of the song, such as AC/DC, to create the sound the artists are after. I'm sorry if you're a fan but just flick through Black Ice, the drums in every song boil down to dun, tss, dun, tss, dun, tss, with minor variations (granted, with the exception of the last track, Black Ice, which is a little more lively). Now, sure enough you can tap along to this music and it's very easy to listen to, but if you really want to push your listening experience, you have to move into something with a bit more vigour and technicality. A good example of making good use of a set of drums would be Tool's Lateralus when the vocals start at around 1:40. Rather than keeping the rhythm alone, it also helps to tell the story, making it a much more satisfying experience because everything in the song works to submerge the listener into it, in the same way that a film does. Instead of actors working in a white room, the background is brought to life to convey a mood, a setting, part of the story. Something we'd not usually notice directly is what's doing a lot of the work to get the audience in the best place to experience the whole product.

This is why time signatures have a certain something about them that can be exploited to add many more layers of sounds to a song. As we usually don't think about them, we don't notice that they seldom vary much in mainstream music, we're happy tapping along to the same basic rhythm because we're too easily pleased by the superficial aspects - primarily the melody followed very, very closely by the vocals and lyrics, then by the sexually suggestive dances and facial expressions. It seems a lot of chart-topping stuff is they same template repeated over and over, because that is what works, it's what people like. It's a shame that most of these people wouldn't want to stray into music that mixes things up because you can't dance to it, and it takes a little more work to get the full experience. But I assure you, there's a whole other world to music if you're willing to put the effort in, and the enjoyment you get out of it will be ten-fold what it is with today's most popular.

Anyway, back to time signatures. I'm not an expert on the matter but I can understand the basics, which has been enough for me to pick out some more interesting rhythms. For example, Meshuggah's (who have built up a reputation for odd time signatures) "Future Breed Machine" (http://www.youtube.com/watch?v=vOd-T58qHLA), at around 3:40 in has a solid 7/4 for the guitar laid onto a 4/4 drums. The drums follow the basic tss tss tss dun tss tss tss dun... and the guitars follow two lots of three beats, which is some kind of djent chugs, followed by one beat of rest. I count it as:

1, 2, 3 - 1, 2, 3 - 1 -  1, 2, 3 - 1, 2, 3 - 1. 

This may be a little more difficult to grasp at first, but don't worry it gets obscenely worse. If the previous song seemed easy enough to follow, have a listen to "Rational Gaze" (http://www.youtube.com/watch?v=rkrjE4QRsys) which has been said to follow a 23/16 during the second part of the intro, from around 0:29. If you're trying to count this and follow the beats, try counting it as three groups of 7/16 and one of 2/16, so:

1,2,3,4,5,6,7,  1,2,3,4,5,6,7,  1,2,3,4,5,6,7,  1,2.

I have yet to find out myself or from anywhere what the rest is timed in. Regardless, I think I can fully appreciate it. One way to get the most out of one of these songs is to listen different instruments and try to zones out others. For example, if the drums are very prominent in a song, try to listen more to the bass guitarist. Maybe he's playing a different rhythm or is bouncing between the lead guitar and the drummer, enhancing both at the same time. Once you've done this to all the instruments, go back and listen to it as a whole and you'll see that there is much more to some (albeit, rarely chart-toppers) songs that you would've never noticed. 

This may seem to be approaching the limit of complexity that a mere human can identify, but there's one more level - math rock. These guys know how to knock out something that will leave you in awe of it's sophistication and technicality. Some of them border on the random...some are random, but there are some that have written their music and sheets and made tabs and all the rest, so it these guys that are the masters. A brilliant song with a very interesting signature is "26 is dancer than 4" by This Town Needs Guns (http://www.youtube.com/watch?v=IhPljk5EZ0Q). Here the song title acknowledges the life that more complicated rhythms breath into music. It says that 26/4 has more feel and can please the listener more than a 4/4. Yes, that does mean:

1,2,3,4,...,24,25,26.

each measure (but there is only one from the start to the first chorus). It's a slow beat in the song dispite the pace of the melody, taking from the start until around 23 seconds in to count the 26 beats. 

Okay, I lied, there is another level (maybe two). I've a few pieces of music that offer an other worldly approach to music and seek only to demonstrate how the pitches and volume of notes and tones, and their distances apart, at the most fundamental level can give a very rewarding experience to the listener, if only s/he has the patience to find it. Some examples are Stockhausen's Klavierstück I - X (especially IX) which feature a very interesting approach to music, as well as incorporating very odd time signatures, including a mind melting 142/8. Returning to math rock, there is Tera Melos. Give them a listen and see what you think. They've passed the point where humans can tap their foot to feel the rhythm, I think if you tired tapping your foot along to "A Spoonful of Slurry" you're likely to give yourself and injury. However, to those brave souls that do, I will offer a KitKat (fo' serious) as a reward to anyone that can figure out all of the time signatures for this song, first one to comment with the correct signatures wins. God speed and good luck.

I thought someone should point out...

The irony of chinos: blokes wear them to look cool and to impress the ladies, but just end up looking gay or like Olly Murs.

The irony of tube mini skirts: women wear them to look good and feel confident, but just end up looking wider at the middle and needy.

...not that it's my place to say. You can do what they want, but you can't expect me to like it. Granted most if not all will not expect me to, but as they don't care what I think, this post shouldn't bother them. If it does and you feel like commenting, congratulations for voicing your opinion...just like me. Good day.

...on religion

If there's ever a time for a more philosophical blog then it is now, while I'm sitting in the late hours with Beethoven's 9th playing, sipping on Laphroaig out of a gorgeous pewter hip-flask (courtesy of a very, very special person).

As a man of science, or more specifically mathematics, people are usually taken aback when I express anything other than pure distaste towards any religious ideologies. Now don't get the wrong idea, I'm not what most people would describe as a theist but I have thought a lot about what exactly it is all about. I tend to avoid the subject because it's a potential minefield of political correctness. I find the best way, if you really want to sit down and think about religion on the whole, is to argue both sides fairly, if not biased towards what you're arguing against. I will try to do just that.  To start with I will make it clear that I'm comparing two groups of people; those who believe in a 'higher power', and those who don't. One of the main problems with this is that theists view themselves as superior to atheists. They feel like they have the ability to have faith or that they have broadened their minds to see beyond, on the same token, atheists look down at their rivals, seeing them as gullible, closed-minded, and insecure. This is seen their arguments for their own position such as, an atheist would argue that if a higher power or 'God' exists, then we should be able to find him/her/it, we should be able to find evidence. This instantly becomes an argument of swings and roundabouts. Both think they're better, but for reason that don't apply to the opposing group. Such an atheist would ask theists for evidence of God, and as these theists wouldn't be reliant on the scientific method, they would say something along the lines one of two things:

1. Evidence is not relevant. That an all-powerful being can easily evade all human attempts to track Him down, should He not want to be found. This seems like a childish attempt to avoid answering the difficult questions, but you have to put yourself in their shoes, believe that the being they describe exists. They believe this to be the absolute truth, which undercuts all that science could throw at it. How do you measure something that can appear to not even exist? From here all sorts of questions about the motives of God can be brought in. Why is He hiding? Does He show Himself to anyone? Why won't He reveal Himself to remove all doubt? But remember, such an all-powerful God would be infinitely more intelligent than any human, so it's pointless to question Him. 'Evidence is not relevant' is a check-mate response that shouldn't be used because it leads nowhere towards a better understanding for either parties.

2. You're the scientists, why don't you prove God doesn't exist? Seems fair, if the scientific method works then God will be disproven or proven outright, or if it doesn't, all remains a mystery, right? Except it's not that simple. I remember a nice analogy for the problems when proving the existence or non-existence of God: imagine a teapot orbiting the sun at some arbitrary distance. No one would've ever seen it or know of it's existence, but regardless of this, a man pipes up one day and claims just that. His says there is a teapot orbiting the sun. Soon enough the populating splits in two, those who believe and those who don't. The theists of the teapot ask the non-believers to prove that there is no teapot if they're so confident. This task would mean searching every cubic foot of the space around the sun and not finding anything, but an atheist responds by saying that if the teapot exists it would be much easier for one the believers to point it out. Clearly here, the teapot represents a God, but the arguments are strikingly similar. These would be, crudely speaking, the atheists asking the theists to use an atheist method for proving the theists are correct. Whereas the theists would be asking the atheists to use a method they don't believe in to prove an idea they don't believe in. Something isn't right. Neither group can prove to the other group their beliefs because they don't use a universally agreed method.

I believe that so far science is on track. It has made countless discoveries that would appear to be independent of a greater intelligence, whilst remaining true to form in its method. But the simple fact is that, even if science finally believes it knows everything, it may still be missing out on one thing - the higher power that doesn't want to be found.

This is just a brief introduction to my opinions, but discussions, counter-arguments, general comments are welcome and encouraged.

Accidental maths

I'm not sure of the uses of the following equation, but either way it's quite novel and the proof quite nice because in mathematics the factorial function, f(x) = x!, can be quite frustrating sometimes. Using it often results in using the Gamma function which is getting into mathematics quite a bit beyond Joe Bloggs. Anyway, after stumbling across the following and proving it, then realising someone had already done it and getting over the disappointment of finding out I hadn't discovered something new in maths, I've written a nice, neat version of my findings:

Again, if you have any questions on the maths used or if you like to know more about the LaTeX used, or have anything suggestions on extensions or improvements of this proof, just leave a comment.

The One.

You know you've found the one when she'd travel around the world just to be with you, but would never have to, because you'd already be on your way to be with her.

Moment Generating Functions - Normal

If I ever find anything interesting in the world of mathematics that I want to share, I will try my best to understand it then post my interpretation here, the first of these being:

Moment generating functions generate what are called moments of a random variable X. I am blogging about this because I think it is a beautiful piece of mathematics. The following is written using the program TeXworks (tek-works).

If anyone has any questions on the mathematics above or the LaTeX code used, please just comment.

Do what you want, just don't expect me to like it.

Recently I was roped into watching America's Next Top Model, sadly it was not about Airfix models. Instead it was about these people who have some crazy obsession with not eating for an extended period, then having some other people take snapshots of them doing weird things. Fair enough, it's your body, do what you will with it. However, there is another 'show' that really gets up my nose, I mean really up there. Signed by Katie Price, hosted unsurprisingly yet disappointingly, by Katie Price aka Jordan. Now this I watched with a little more curiosity, in the kind of 'what's she doing with her life?' way. As it turns out, a lot. Not only has she discovered a way to sit on a chair without it sliding up her fanny, but she's also finding these people ranging from the everyday eating disorder-types to the fairies. Actually, that's mean, and I'm not against homosexuality, it just the whole camp as a row of tents thing, and that's before the guy-liner. Anyway, she finds these, or rather they find her (why?), and turns them into models of some description. Brilliant, finally we can have some good looking celebrities, right? With Katie's expert page 3 guidance we can have a new group of glamourous women and some Pumping Iron-esque blokes to form the next generation of the super-good looking people. Sadly, nope, you just end up with girls (and some guys) that put on a stone of make-up, wear skirts that aren't a great deal longer than the belts that hold them up, and that bitch and moan for an hour, and apparently this is worth paying god knows what a month for. If you are one of these people (or Katie Price herself) please just stay away from me or I bloody well might swear at you. Good day.

Coming soon...nothing

As I'm someone with a laughable social life, I spend a lot of time trawling the internet, and when I say trawing, I mean visiting the same tedious sites over and over, hoping one day there will be something worthwhile. So rather than look at other peoples' funny pictures, witty comments, rants, and other shit, I decided to make my own stuff.

If you're interested in anything funny, mentally stimulating, or just plain cool, I hope you will enjoy this blog. However, if you think Michael McIntyre is funny, Jay-Z is music, or Pluto is a planet...please, for your own good, leave now.

Anyway, after a few hours of revision I decided it was time to fire up Phun for the first time in a while. If you've never played Phun...download it...now. It's free and awesome.

This blog is just to see what the page looks like...

Sorry.