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Archive for July, 2014

Today I thought I would share this wonderful song by Buffalo Springfield – “For What It’s Worth”. The song was released in January 1967 and got to number 7 in the US charts. It was written by Stephen Stills (in the centre of the photograph below) who also sings lead vocals on the song. You may also notice in the video that Neil Young was in the group too, on guitar (he is on the right of the photograph).



b.buffalo springfield

The following year, Stills would become part of possibly the World’s first “supergroup” – Crosby, Stills and Nash; which was formed when he, David Crosby (from The Byrds) and Graham Nash (from The Hollies) got together to form the group Crosby, Stills and Nash. A few months later, Neil Young joined them to form Crosby, Stills, Nash and Young.

This song is actually the only Buffalo Springfield song which I know; it is a great song addressing the unrest and uncertainty of the civil unrest and escalating Vietnam war in the late 1960s.


There’s something happening here
But what it is ain’t exactly clear
There’s a man with a gun over there
Telling me I got to beware

I think it’s time we stop
Children, what’s that sound?
Everybody look – what’s going down?

There’s battle lines being drawn
Nobody’s right if everybody’s wrong
Young people speaking’ their minds
Getting so much resistance from behind

It’s time we stop
Hey, what’s that sound?
Everybody look – what’s going down?

What a field day for the heat
A thousand people in the street
Singing songs and carrying signs
Mostly saying, “hooray for our side”

It’s time we stop
Hey, what’s that sound?
Everybody look – what’s going down?

Paranoia strikes deep
Into your life it will creep
It starts when you’re always afraid
Step out of line, the men come and take you away

We better stop
Hey, what’s that sound?
Everybody look – what’s going down?

We better stop
Hey, what’s that sound?
Everybody look – what’s going down?

We better stop
Now, what’s that sound?
Everybody look – what’s going down?

We better stop
Children, what’s that sound?
Everybody look – what’s going down?



Here is a video of the song. Enjoy!





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Today I thought I would share this song “The Passenger” by Iggy Pop (real name James Newell Osterberg). The song was released in 1977 and is on Pop’s 2nd solo album “Lust For Life”, which he recorded in collaboration with David Bowie. In fact, Bowie also sings backup harmonies on “The Passenger”.



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The song was released as the B-side of “Success”, the only single to come from “Lust For Life”, but because “The Passenger” has featured in numerous movies and advertisements it is probably one of Pop’s best known songs.


I am the passenger and I ride and I ride
I ride through the city’s backsides
I see the stars come out of the sky
Yeah, the bright and hollow sky
You know it looks so good tonight

I am the passenger, I stay under glass
I look through my window so bright
I see the stars come out tonight
I see the bright and hollow sky
Over the city’s ripped backsides
And everything looks good tonight

Singing, la la la

Get into the car
We’ll be the passenger
We’ll ride through the city tonight
We’ll see the city’s ripped backsides

We’ll see the bright and hollow sky
We’ll see the stars that shine so bright
Stars made for us tonight

Oh, the passenger
How, how he rides
Oh, the passenger
He rides and he rides

He looks through his window
What does he see?
He sees the sign and hollow sky
He sees the stars come out tonight
He sees the city’s ripped backsides
He sees the winding ocean drive

And everything was made for you and me
All of it was made for you and me
‘Cause it just belongs to you and me
So let’s take a ride and see what’s mine

Singing, la la la

Oh, the passenger
He rides and he rides
He sees things from under glass
He looks through his window side

He sees the things that he knows are his
He sees the bright and hollow sky
He sees the city sleep at night
He sees the stars are out tonight

And all of it is yours and mine
And all of it is yours and mine
So let’s ride and ride and ride and ride

Singing, la la la



Here is a video of the song. Enjoy!



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At number 6 in Rolling Stone Magazine’s list of the 10 best Bob Dylan songs is “I Shall Be Released”. This song was written in 1967 during the sessions with The Band which were eventually released in 1975 as “The Basement Tapes”. In fact, The Band released a version of the song in 1968 on their album “Music from Big Pink”, but Dylan’s first release of the song was on his 1971 album “Bob Dylan’s Greatest Hits Volume II”, which was one of the first Bob Dylan albums that I ever bought.



At number 6 in Rolling Stone Magazine's 10 greatest Bob Dylan songs is "I Shall be Released"

At number 6 in Rolling Stone Magazine’s 10 greatest Bob Dylan songs is “I Shall be Released”



Dylan recorded a few different versions of the song, in 1967 he recorded a version which eventually officially surfaced in 1991 on his “Bootleg Series Volumes 1-3”. He then recorded a different version of the song in 1971. In the 1971-released version of the song, Dylan is accompanied on harmonies by folk singer Happy Traum, and the song is typical of the “anthemic” songs which Dylan was writing in the late 1960s and early 1970s, which include “Forever Young” and “Knocking on Heaven’s Door”. There are some interesting quotes in caption from Rolling Stone Magazine, including how this song helped David Crosby sustain himself during his time in jail, and how Allen Ginsberg said that Dylan told him in 1968 that he had decided to write songs with shorter lines.


They say ev’rything can be replaced
Yet ev’ry distance is not near
So I remember ev’ry face
Of ev’ry man who put me here
I see my light come shining
From the west unto the east
Any day now, any day now
I shall be released

They say ev’ry man needs protection
They say ev’ry man must fall
Yet I swear I see my reflection
Some place so high above this wall
I see my light come shining
From the west unto the east
Any day now, any day now
I shall be released

Standing next to me in this lonely crowd
Is a man who swears he’s not to blame
All day long I hear him shout so loud
Crying out that he was framed
I see my light come shining
From the west unto the east
Any day now, any day now
I shall be released


As with nearly all Bob Dylan songs, the “original” version of this song (as it appeared in 1971) cannot be found on YouTube, but I have managed to find this interesting live version with Norah Jones duetting with Dylan. Enjoy!





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As most people reading this blog probably know, the area of a circle is given by


\boxed{ \text{ area of a circle} = \pi r^{2} }


where \pi is the ratio of the diameter of a circle to its circumference, and r is the radius of the circle. But, how would we go about proving this well known formula? To do so, we can use something called integration, which is a branch of calculus.

The area under a curve

The area under any curve between the x-axis, the curve, and the lines x_{1} \text{ and } x_{2} (see the figure below) is given by


\int_{ x_{1} }^{ x_{2} } f(x) \; dx


where f(x) is the function (the curve), and dx is an infinitesimally small width. Effectively, what we are doing is summing a series of rectangles of area ydx from the lower limit x_{1} to the upper limit x_{2}.



The area under any curve y=f(x) can be found by summing infinitesimally small rectangles, each of height y and of width dx between the lower x-limit x_{1} and the upper x-limit x_{2}

The area under any curve y=f(x) can be found by summing infinitesimally small rectangles, each of height y and of width dx between the lower x-limit x_{1} and the upper x-limit x_{2}



The equation of a circle

To do this for a circle, we need to write the equation for a circle. To make things easier we will centre the circle at the origin. In this case, if the circle has a radius r the equation which describes this circle is just


x^{2} + y^{2} = r^{2}


Therefore, to find the area of the circle, all we need to do is integrate between x=0 \text{ and } x=r, and then multiply the answer by 4 (as we have only found the area of quarter of the circle).



To find the area of a circle, in principle all we need to do is sum the rectangles ydx from x=0 to x=r between the x-axis and the circle, then multiply the answer by 4.

To find the area of a circle, in principle all we need to do is sum the rectangles ydx from x=0 to x=r between the x-axis and the circle, then multiply the answer by 4.




The integration to do this is


\int_{0}^{r} y \; dx \; = \; \int_{0}^{r} \sqrt{ r^{2} - x^{2} } \; dx


This is not an integral which we can do, so we appear to be stuck!

Changing variables to use “polar coordinates”

Luckily for us, there is a way around this problem. Rather than using x-y co-ordinates (more correctly known as Cartesian co-ordinates), we can change the co-ordinate system to something called polar co-ordinates, and when we do this we get an integral that we can do.

To see how to go from Cartesian to polar co-ordinates, consider the figure below.



The point (x,y) on the circle can  be written in terms of the radius r and the angle theta. We can write that x = r cos theta and y = r sin theta

The point (x,y) on the circle can be written in terms of the radius r and the angle \theta. We can write that x = r \cos \theta and y = r \sin \theta




We write the x \text{ and } y coordinates in terms of two new variables r \text{ and } \theta, where r is the radius of the circle and \theta is the angle between the line from the centre of the circle to the point and the x-axis. When we do this, we can write that x = r \cos \theta and y = r \sin \theta.

Then, to determine the area of the quadrant were x \text{ and } y are positive, we can instead integrate using r \text{ and } \theta. To see how we do this, consider the figure below.



To find the area of the circle, we add a series of slices, each with an infinitesimally small angle dtheta and radius r between an angle of theta = 0 and theta = pi/2, then multiply the answer by 4

To find the area of the circle, we add a series of slices (the shaded region), each with an infinitesimally small angle d\theta and radius r between an angle of \theta = 0 and \theta = \pi/2, then multiply the answer by 4



One of the reasons the method of using polar coordinates is easier is that we now have only one variable, \theta, as the radius r is a constant. When we were using x \text{ and } y as our variables, moving along the circle involved both variables changing, but with polar coordinates only one variable changes, \theta.

Instead of finding the area of a rectangle and summing those, we instead consider a slice of the circle, where the angle in the slice is d\theta, an infinitesimally small angle, and the radius of each slice is r. This is shown by the shaded region in the figure above. We then sum these slices between an angle of \theta =0 and \theta = 90^{\circ}. But, when using calculus, we do not use degrees, but rather we have to use radians, which as I explained in this blog, are a more natural unit for measuring an angle.

As d\theta becomes infinitesimally small, the slice becomes a triangle, and the area of a triangle is given by \text{ half the base } \times \text{ the height}. The height is, of course, just the radius r, but what about the base? The base is the length of the arc, which you will recall from the definition of a radian is just \text{ base } = r \; d\theta.

The integral we wish to do is therefore


\int_{0}^{\pi/2} \frac{1}{2} r \times r \; d\theta \; = \; \int_{0}^{\pi/2} \frac{1}{2} r^{2} \; d\theta = \frac{ r^{2} }{ 2 } \int_{0}^{\pi/2} d\theta = \frac{ r^{2} }{ 2 } [ \frac{ \pi }{2} - 0 ] = \frac{ \pi r^{2} }{ 4 }


But, remember, this is the area of just the positive quadrant, so the area of the whole circle is going to be 4 times this, or


\boxed { 4 \times \frac{ \pi r^{2} }{ 4 } = \pi r^{2} }


just as the famous formula states!

When I derived the acceleration of an object moving in a circle (the centripetal acceleration)


\vec{a} = \frac{ v^{2} }{ |\,\vec{r}\,| } \hat{r}


one of the comments stated that I could have derived the same formula using polar coordinates. Now that I have introduced polar coordinates, I will in a future blog re-derive the formula using them.

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Today I thought I would share this song by the British band Dire Straits, “Private Investigations”. The song was released as a single in the summer of 1982, and got to number 2 in the Dinsunited Kingdom singles charts.



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The song is from Dire Straits’ 4th album, “Love Over Gold”, and was written by lead guitarist and lead singer Mark Knopfler. I first came across Mark Knopfler’s name when Bob Dylan used him on lead guitar for his 1979 album “Slow Train Coming”, which he recorded just after Dire Straits had released their first single “Sultans of Swing”, a song which illustrates wonderfully Knopfler’s superb guitar playing. Dylan picked up on this, even though the song had not been a hit in the US, and I think it is fair to say that Knopfler is now recognised as one of the great rock guitarists.

As you can see from the lyrics below, there are not many, although the song itself stretched to nearly 6 minutes in the single version, and nearly 7 minutes in the album version. The song features Knopfler playing classic guitar, and is more instrumental in nature than most of their single releases. The song has a moodiness and melancholy feel which does not lend itself naturally to being a hit single, but by 1982 Dire Straits were one of the biggest bands in the Disunited Kingdom.


It’s a mystery to me, the game commences
For the usual fee, plus expenses
Confidential information, it’s a diary
This is my investigation, it’s not a public inquiry

I go checking out the reports, digging up the dirt
You get to meet all sorts in this line of work
Treachery and treason, there’s always an excuse for it
And when I find the reason I still can’t get used to it

And what have you got at the end of the day?
What have you got to take away?
A bottle of whiskey and a new set of lies
Blinds on the window and a pain behind the eyes
Scarred for life, no compensation
Private investigations



Here is the official version from YouTube. Enjoy!





Which is your favourite Dire Straits song?

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I thought it was about time I gave another update on currently the most important story in astrophysics – the BICEP2 team’s possible detection of B-mode polarisation in the cosmic microwave background. I have previously blogged about this story, for example here, here and here. But, just to quickly recap, in March the BICEP2 team announced that they had detected the B-mode polarisation in the cosmic microwave background (CMB), and argued that it was evidence of gravitational waves and cosmological inflation in the very early Universe.

Since then, controversy has been the order of the day as other astrophysicists and cosmologists have argued that the BICEP2 detection was not due to the CMB at all, but rather to emission from dust in our own Milky Way galaxy. BICEP2 on their own do not have sufficient data to rule out this possibility, something they concede in their published paper. However, it would seem that the European satellite Planck do, as it has not only observed the whole sky (including the part of the sky observed by BICEP2), but has done so at five different frequencies, compared to BICEP2’s single frequency measurement.

In the last few days, it has been announced that the BICEP2 team will formally collaborate and share data with the Planck team, which I think is good news in sorting out the controversy over the BICEP2 detection sooner rather than later.



The BICEP2 team and Planck team have announced that they will collaborate and share data to help clear up the controversy over the source of the B-mode polarisation detected by BICEP2.

The BICEP2 team and Planck team have announced that they will collaborate and share data to help clear up the controversy over the source of the B-mode polarisation detected by BICEP2.



Although the Planck measurements of the polarisation of dust in our Milky Way will presumably become public at some point (as is normal with publicly funded science projects), this would not be for many more months. By formally collaborating with Planck, the BICEP2 team will get not only earlier access to the Planck data, but just as importantly will get the experts in the Planck collaboration working with them to properly interpret the Planck measurements. It is hoped by all in the astrophysics and cosmology communities that this collaboration between BICEP2 and Planck will lead to the issue of the origin of the detected B-mode polarisation being sorted out in a timely fashion, possibly even by the end of this year.

We shall have to wait and see!

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At number 7 in Rolling Stone Magazine’s 10 best Bob Dylan songs is “It’s Alright Ma, (I’m Only Bleeding)” which, like the song at number 8 (“Mr. Tambourine Man”), is from his 1965 album “Bringing It All Back Home”. The song was written in the summer of 1964, and Dylan performed it live in late 1964, several months before recording it in the studio, which he did in January 1965. It is the penultimate track on “Bringing It All Back Home”, and is surely one of his darkest and most evocative songs.



At number 7 in Rolling Stone Magazine's 10 greatest Bob Dylan songs is "It's Alright Ma, (I'm Only Bleeding)"

At number 7 in Rolling Stone Magazine’s 10 greatest Bob Dylan songs is “It’s Alright Ma, (I’m Only Bleeding)”



I find this song simply stunning. The rhyming is very complex, and the lyrics are both dark and profound. It always strikes me that Dylan was only 23 when he wrote this song. How can someone so young write such profound lyrics? It is beyond me, but all I do know is that it is one of the masterpieces of Dylan’s “poetic, surrealistic” period. One of the most memorable lines for me in the song is “But even the President of the United States / Sometimes must has to stand naked”, a reminder that we are all human, irrespective of our importance.


Darkness at the break of noon
Shadows even the silver spoon
The handmade blade, the child’s balloon
Eclipses both the sun and moon
To understand you know too soon
There is no sense in trying

Pointed threats, they bluff with scorn
Suicide remarks are torn
From the fool’s gold mouthpiece the hollow horn
Plays wasted words, proves to warn
That he not busy being born is busy dying

Temptation’s page flies out the door
You follow, find yourself at war
Watch waterfalls of pity roar
You feel to moan but unlike before
You discover that you’d just be one more
Person crying

So don’t fear if you hear
A foreign sound to your ear
It’s alright, Ma, I’m only sighing

As some warn victory, some downfall
Private reasons great or small
Can be seen in the eyes of those that call
To make all that should be killed to crawl
While others say don’t hate nothing at all
Except hatred

Disillusioned words like bullets bark
As human gods aim for their mark
Make everything from toy guns that spark
To flesh-colored Christs that glow in the dark
It’s easy to see without looking too far
That not much is really sacred

While preachers preach of evil fates
Teachers teach that knowledge waits
Can lead to hundred-dollar plates
Goodness hides behind its gates
But even the president of the United States
Sometimes must have to stand naked

An’ though the rules of the road have been lodged
It’s only people’s games that you got to dodge
And it’s alright, Ma, I can make it

Advertising signs they con
You into thinking you’re the one
That can do what’s never been done
That can win what’s never been won
Meantime life outside goes on
All around you

You lose yourself, you reappear
You suddenly find you got nothing to fear
Alone you stand with nobody near
When a trembling distant voice, unclear
Startles your sleeping ears to hear
That somebody thinks they really found you

A question in your nerves is lit
Yet you know there is no answer fit
To satisfy, insure you not to quit
To keep it in your mind and not forget
That it is not he or she or them or it
That you belong to

Although the masters make the rules
For the wise men and the fools
I got nothing, Ma, to live up to

For them that must obey authority
That they do not respect in any degree
Who despise their jobs, their destinies
Speak jealously of them that are free
Cultivate their flowers to be
Nothing more than something they invest in

While some on principles baptized
To strict party platform ties
Social clubs in drag disguise
Outsiders they can freely criticize
Tell nothing except who to idolize
And then say God bless him

While one who sings with his tongue on fire
Gargles in the rat race choir
Bent out of shape from society’s pliers
Cares not to come up any higher
But rather get you down in the hole
That he’s in

But I mean no harm nor put fault
On anyone that lives in a vault
But it’s alright, Ma, if I can’t please him

Old lady judges watch people in pairs
Limited in sex, they dare
To push fake morals, insult and stare
While money doesn’t talk, it swears
Obscenity, who really cares
Propaganda, all is phony

While them that defend what they cannot see
With a killer’s pride, security
It blows the minds most bitterly
For them that think death’s honesty
Won’t fall upon them naturally
Life sometimes must get lonely

My eyes collide head-on with stuffed
Graveyards, false gods, I scuff
At pettiness which plays so rough
Walk upside-down inside handcuffs
Kick my legs to crash it off
Say okay, I have had enough, what else can you show me?

And if my thought-dreams could be seen
They’d probably put my head in a guillotine
But it’s alright, Ma, it’s life, and life only

Here is a live performance of this amazing song, made around the time of its release in the summer of 1965. Enjoy!





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