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Archive for December, 2014

At number 24 in Rolling Stone Magazine’s 500 greatest songs of all time is “People Get Ready” by The Impressions. This song is from 1965, and I thought that I did not know it when I saw it listed. But, once I listened to it to write this blog, I knew that I had heard this song many times before. It was written by Curtis Mayfield, and it reflects Mayfield’s increasing social and religious awareness. It has strong gospel overtones, and reached number 14 in the US singles charts.



At number 30 in Rolling Stone Magazine's '500 Greatest Songs of all Time' is "I Walk the Line" by Johnny Cash.

At number 24 in Rolling Stone Magazine’s ‘500 Greatest Songs of all Time’ is “People Get Ready” by The Impressions.



This song has been covered by many other artists, including Eva Cassidy, Bob Marley and Bob Dylan. Jeff Beck and Rod Steward recorded a version in the mid-1980s which is possibly one of the better known cover versions.

People get ready, there’s a train comin’
You don’t need no baggage, you just get on board
All you need is faith to hear the diesels hummin’
You don’t need no ticket you just thank the lord

People get ready, there’s a train to Jordan
Picking up passengers coast to coast
Faith is the key, open the doors and board them
There’s hope for all among those loved the most
There ain’t no room for the hopeless sinner whom would hurt all mankind
Just to save his own
Have pity on those whose chances grow thinner
For there is no hiding place against the kingdoms throne

People get ready there’s a train comin’
You don’t need no baggage, just get on board
All you need is faith to hear the diesels hummin’
You don’t need no ticket, just thank the lord


Here is a video of this song. Enjoy!





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At number 25 in Rolling Stone Magazine’s 500 greatest songs of all time is “God Only Knows” by the Beach Boys. I have already blogged about this wonderful song here, but you can’t get too much of a good thing!



At number 30 in Rolling Stone Magazine's '500 Greatest Songs of all Time' is "I Walk the Line" by Johnny Cash.

At number 25 in Rolling Stone Magazine’s ‘500 Greatest Songs of all Time’ is “God Only Knows” by The Beach Boys.




I may not always love you
But long as there are stars above you
You never need to doubt it
Ill make you so sure about it

God only knows what I’d be without you

If you should ever leave me
Though life would still go on believe me
The world could show nothing to me
So what good would living do me

God only knows what I’d be without you

God only knows what I’d be without you

If you should ever leave me
Well life would still go on believe me
The world could show nothing to me
So what good would living do me

God only knows what I’d be without you
God only knows what I’d be without you
God only knows
God only knows what I’d be without you
God only knows what I’d be without you
God only knows
God only knows what I’d be without you
God only knows what I’d be without you
God only knows
God only knows what I’d be without you
God only knows what I’d be without you
God only knows
God only knows what I’d be without you
God only knows what I’d be without you
God only knows
God only knows what I’d be without you
God only knows what I’d be without you
God only knows
God only knows what I’d be without you


Here is the Beach Boys’ version of the song. Enjoy!





Here is a version which the BBC recently put together with an “all star cast” (see how many you can spot).




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In this blog here, I tried to explain Newton’s 1st law of motion, the so-called law of inertia. Then, the following week, in this blog here, I tried to explain Newton’s 2nd law, the one with the equation F=ma, which tells us how a body accelerates if there is a (resultant) force applied to it. This week, I will finish up this series by trying to explain Newton’s 3rd law.

His 3rd law is very important. Without it cars wouldn’t work, we wouldn’t be able to walk forwards and rockets wouldn’t work in space. The 3rd law is often stated as “to every action, there is an equal and opposite reaction”. Another way of saying this is that, if you push on something, it will push back. It is the reason you get a recoil from a gun when it fires a bullet. The explosion of the bullet propels the bullet forward, and an equal force propels the gun back into your shoulder.



Due to Newton's 3rd law, when you fire a gun and the bullet comes hurtling out of the front, an equal and opposite reaction means the gun recoils into your shoulder.

Due to Newton’s 3rd law, when you fire a gun and the bullet comes hurtling out of the front, an equal and opposite reaction means the gun recoils into your shoulder.



You might be asking yourself “hang on, the gun doesn’t come back at the same speed as the bullet goes out of the front, so how can it be equal and opposite?”. Well, remember it is the force which is equal and opposite. Force is mass multiplied by acceleration (Newton’s 2nd law), and the gun is many times more massive than the bullet. This means that the force applied to the bullet produces much more acceleration than the equal force applied to the gun, so the gun moves back much more slowly than the bullet goes out of the front (thankfully!).

When we walk, we are actually using Newton’s 3rd law to move ourselves forward. We push our foot onto the ground, but also slightly backwards (the difference between walking and just standing). The backwards push of our foot leads to the ground pushing us forwards. Try walking on slippery ice, and you quickly realise that it doesn’t work too well when friction is reduced and your foot slides as you try and push backwards on the ground.

A rocket moving through empty space is an example of Newton’s third law which often confuses people. This is because people don’t see what the rocket is pushing against. The answer is – nothing! But that does not mean there isn’t an equal and opposite reaction. The rocket sends gasses out of the back of the rocket through burning fuel (essentially a controlled explosion), and in pushing the fuel out of the back the equal and opposite reaction to this push is that the rocket is pushed in the opposite direction, forwards. The gasses coming out of the back do not need to be pushing against anything, the mere act of their coming out of the back means the 3rd law reaction is to push the rocket forwards.



When a rocket in empty space moves forwards the gasses coming out of the back do not push against anything, but Newton's 3rd law means that the gasses being pushed out through the exhaust cause an equal and opposite reaction - the pushing forwards of the rocket.

When a rocket in empty space moves forwards the gasses coming out of the back do not push against anything, but Newton’s 3rd law means that the gasses being pushed out through the exhaust cause an equal and opposite reaction – the pushing forwards of the rocket.



So, that is it. With these three laws of motion, which Newton outlined in his 1687 masterpiece The Principia (which I blogged about here), the foundations of mechanics had been laid down. These foundations are still in use today, more than 300 years later. Despite Einstein showing that Newton’s laws of motion have their limitations (written in its simple form, Newton’s 2nd law of motion is not entirely correct), we still use them on a daily basis because we so rarely experience the situations where relativistic mechanics is needed.

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At number 53 in BBC Radio 2’s 100 greatest guitar riffs is “Beat It” by Michael Jackson. This song, released in February 1983, is taken from his album “Thriller”; one of the best selling albums of all time and an album which could well hold the record for the largest number of singles released from it. I blogged about “Thriller” here, as it is number 20 in the Rolling Stone Magazine list of the 500 greatest albums.

This song is, for me, quite different from most of Michael Jackson’s songs from this period, and is one of my favourites. This is due, in no small part, to the great guitar riff in the song, which is played by Eddie Van Halen; “Beat It” is much rockier than most of MJ’s songs. The song got to number 1 in both the Disunited Kingdom and USA’s singles charts; in fact it was a huge hit around much of the World.



At number 53 in BBC Radio 2's list of the 100 greatest guitar riffs is "Beat It" by Michael Jackson

At number 53 in BBC Radio 2’s list of the 100 greatest guitar riffs is the 1983 hit single “Beat It” by Michael Jackson




[1st Verse]
They Told Him Don’t You Ever Come Around Here
Don’t Wanna See Your Face, You Better Disappear
The Fire’s In Their Eyes And Their Words Are Really Clear
So Beat It, Just Beat It

[2nd Verse]
You Better Run, You Better Do What You Can
Don’t Wanna See No Blood, Don’t Be A Macho Man
You Wanna Be Tough, Better Do What You Can
So Beat It, But You Wanna Be Bad

[Chorus]
Just Beat It, Beat It, Beat It, Beat It
No One Wants To Be Defeated
Showin’ How Funky Strong Is Your Fight
It Doesn’t Matter Who’s Wrong Or Right
Just Beat It, Beat It
Just Beat It, Beat It
Just Beat It, Beat It
Just Beat It, Beat It

[3rd Verse]
They’re Out To Get You, Better Leave While You Can
Don’t Wanna Be A Boy, You Wanna Be A Man
You Wanna Stay Alive, Better Do What You Can
So Beat It, Just Beat It

[4th Verse]
You Have To Show Them That You’re Really Not Scared
You’re Playin’ With Your Life, This Ain’t No Truth Or Dare
They’ll Kick You, Then They Beat You,
Then They’ll Tell You It’s Fair
So Beat It, But You Wanna Be Bad

[Chorus]
Just Beat It, Beat It, Beat It, Beat It
No One Wants To Be Defeated
Showin’ How Funky Strong Is Your Fight
It Doesn’t Matter Who’s Wrong Or Right

[Chorus]
Just Beat It, Beat It, Beat It, Beat It
No One Wants To Be Defeated
Showin’ How Funky Strong Is Your Fight
It Doesn’t Matter Who’s Wrong Or Right
Just Beat It, Beat It, Beat It, Beat It, Beat It

[Chorus]
Beat It, Beat It, Beat It, Beat It
No One Wants To Be Defeated
Showin’ How Funky Strong Is Your Fight
It Doesn’t Matter Who’s Wrong Or Right

[Chorus]
Just Beat It, Beat It, Beat It, Beat It
No One Wants To Be Defeated
Showin’ How Funky Strong Is Your Fight
It Doesn’t Matter Who’s Wrong Or Who’s Right

[Chorus]
Just Beat It, Beat It, Beat It, Beat It
No One Wants To Be Defeated
Showin’ How Funky Strong Is Your Fight
It Doesn’t Matter Who’s Wrong Or Right

[Chorus]
Just Beat It, Beat It, Beat It, Beat It
No One Wants To Be Defeated
Showin’ How Funky Strong Is Your Fight
It Doesn’t Matter Who’s Wrong Or Right
Just Beat It, Beat It
Beat It, Beat It, Beat It


Here is the official video of this song. Apparently Eddie van Halen was prevented from appearing in the video by his record company. It is also before Michael Jackson became a freak, and was at his best.





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Christmas is nearly here, and I have to say that Cardiff makes a pretty good job of decorating its streets and buildings with lights. Here is the castle, which is right in the centre of the city.



Cardiff Castle

Cardiff Castle



In the Disunited Kingdom, there is a superstition to remove Christmas decorations by “Twelfth night”, which is January the 5th. In the USA, where I lived for 9 years, no such tradition seems to exist which means that people often leave their house decorations up until late January, which I liked as it helps brighten the dark days of December and January.

Here is a gallery of some of Cardiff’s decorations. Enjoy!






What is your favourite tradition at Christmas time?

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At number 26 in Rolling Stone Magazine’s 500 greatest songs of all time is “(Sitin’ on) the Dock of the Bay” by Otis Redding. This song was recorded on the 22nd of November and the 7th of December 1967, and sadly on the 10th of December Redding tragically died in a private ‘plane crash in Wisconsin. He was 26 years old. “Dock of the Bay” was released in January 1968 and got to number 3 in the Disunited Kingdom singles charts, and to number 1 in the US.

This is my favourite Otis Redding song. I first heard it as a teenager, I found its wonderful soulful vocals and plaintive sound mesmerising. Redding also wrote “Respect”, the song made more famous by Aretha Franklin (which is also in this list). Possibly his other best-known songs are a more bluesy version of The Temptation’s song “My Girl”, and “Try a Little Tenderness”; but “Dock of the Bay” is, for me, his best song.



At number 26 in Rolling Stone Magazine's '500 Greatest Songs of all Time' is "I Walk the Line" by Johnny Cash.

At number 26 in Rolling Stone Magazine’s ‘500 Greatest Songs of all Time’ is “(Sitin’ on) the Dock of the Bay” by Otis Redding.




Sittin’ in the morning sun
I’ll be sittin’ when the evening comes
Watching the ships roll in
Then I watch them roll away again, yeah

I’m sittin’ on the dock of the bay
Watchin’ the tide roll away, ooh
I’m just sittin’ on the dock of the bay
Wastin’ time

I left my home in Georgia
Headed for the Frisco Bay
Cuz I’ve had nothing to live for
And look like nothing’s gonna come my way

So, I’m just gon’ sit on the dock of the bay
Watchin’ the tide roll away, ooh
I’m sittin’ on the dock of the bay
Wastin’ time

Looks like nothing’s gonna change
Everything still remains the same
I can’t do what ten people tell me to do
So I guess I’ll remain the same, listen

Sittin’ here resting my bones
And this loneliness won’t leave me alone, listen
Two thousand miles I roam
Just to make this dock my home, now

I’m just gon’ sit at the dock of a bay
Watchin’ the tide roll away, ooh
Sittin’ on the dock of the bay
Wastin’ time


Here is the official video of this wonderful song. Enjoy!





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Next year, 2015, marks the centennial of Einstein’s theory of gravity, what we now call the General theory of Relativity (or just “General Relativity” – “GR”). It is widely recognised as one of the greatest achievements in science, and when Arthur Eddington validated one of its predictions in 1919 Einstein was catapulted to the status of an international star. It is often said that, whereas Einstein’s 1905 special theory of relativity (or “special relativity”) would have been thought of by someone else had Einstein not come up with it, general relativity was so far ahead of its time that we may still be waiting for it if it were not for Einstein’s unparalleled genius.



A portrait of Albert Einstein from around the period that he started developing his theory of gravity, General Relativity.

A portrait of Albert Einstein from around the period that he started developing his theory of gravity, General Relativity.



As it turns out, the development of Einstein’s new theory of gravity was not an easy one. Over the course of several blogs I will trace this tortuous path, which took the best part of ten years, mainly because he had to learn the mathematics of curved space and Tensor calculus to be able to express his ideas in equations. Today I will discuss the beginnings of GR, and in particular what we now call Einstein’s “principle of equivalence”, which he thought of in 1907.

Einstein’s 1905 Special theory of Relativity

I have already blogged about Einstein’s ground-breaking Special theory of Relativity here. Just to recap, based on two assumptions

  1. There is no experiment one can do to distinguish between one inertial (non-accelerating) frame of reference and another
  2. The speed of light is constant in all inertial (non-accelerating) frames of reference

Einstein was able to show that these two postulates require that strange things happen to space and time when one travels an appreciable fraction of the speed of light. Lengths get shorter, and time passes more slowly. One of the other consequences of this theory is that Einstein predicted that no information can travel faster than the speed of light.

Einstein soon realised, after he had developed his theory, that Newton’s theory of gravity was in violation of special relativity because it violates both of the postulates on which special relativity is based. In Newton’s theory of gravity, the gravitational force between two objects acts instantaneously. So, according to Newton, if the Sun were to disappear, we would instantly notice its absence (the Earth would move in a straight line rather than continue in its orbit).

Secondly, you could have two inertial (non-accelerating) frames of reference in two different gravitational fields (e.g. one on the surface of the Earth and the other on the surface of the Moon), and a simple experiment like the swinging of a pendulum would yield a different result. This is because the force of gravity (which, along with the length of the pendulum’s string, determines its period of motion) would be different in the two places.

Einstein’s “happiest thought”

In 1907 Einstein was still working in obscurity in the Patent Office in Bern. Although his special theory of relativity had been published two years before, it was yet to have received much attention. It wasn’t until 1908 that he would get his first academic appointment. In his largely boring patent clark job, Einstein had allowed his mind to wander just as he had done leading up to his miraculous year of 1905. This time, it was in pondering how he could fit Newton’s theory of gravity into his own special relativity. One day he had what he would later refer to as the “happiest thought of my life”. In a lecture on the origins of general relativity which he gave at Glasgow University in June 1933 (“The Origins of the General Theory of Relativity”), he expressed this 1907 thought as


If a person falls freely he will not feel his own weight



Very few of us have experienced free-fall, but most of us have been in a lift (elevator). Right at the start, when the lift starts moving, we temporarily feel heavier and our stomach may feel as if it is sinking. When we slow down at the top of the lift’s travel we temporarily experience the opposite, we feel lighter and our stomach may feel as if it is about to hit our diaphragm!

What Einstein realised is that, if a person were in a lift and the cable were to snap so that the lift fell freely towards the Earth, that person would feel weightless whilst the lift was falling. Their feet would come away from the floor of the lift, and if they took e.g. coins out of their pocket, those coins would not fall towards the floor of the lift but instead would appear to “float” next to the person.



Einstein's "principle of equivalence" states that being in a lift (elevator) which is falling freely feels the same as being in empty space - you would feel weightless

Einstein realised in 1907 that being in a lift (elevator) which is falling freely would feel the same as being in empty space – you would feel weightless.



Einstein next illustrated his absolute genius – he went from this idea, which is fairly specific, to the much more general principle of equivalence – which states that:


there is no experiment you can do to distinguish between the effects of a uniform gravitional field and that of uniform acceleration




Einstein's "happiest thought", his principle of equivalence, simply states that being in a uniform gravitational field feels the same as accelerating in empty space. The consequences of this idea are far reaching.

Einstein’s “happiest thought” led to his principle of equivalence, which simply states that being in a uniform gravitational field feels the same as accelerating in empty space. They cannot be distinguished from each other. The consequences of this idea are profound and far reaching.



The first mention of what would become “General Relativity”

Einstein was under pressure from his German editor to write up a review of his principle of special relativity, and so in late 1907 he wrote an article entitled “Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen”
(On the Relativity Principle and the Conclusions Drawn from It) which appeared on the 4th of December 1907 in the journal Jahrbuch der Radioaktivität. In a section of this review article he included some ideas as to what would happen if he were to generalise his special theory of relativity to include the effects of gravity. He noted a few consequences (without going into the details as he had yet to work them out) – gravity would alter the speed of light and hence cause clocks to run more slowly (i.e. gravity would slow down time). He even postulated that generalising special relativity to include gravity may explain the drift in the perihelion of Mercury’s orbit, something which had been confusing astronomers for several decades.

Gravity bends light

One of the more celebrated predictions of Einstein’s general theory of relativity is that gravity should bend light. As I mentioned above, in 1919 this was shown to be the case by England’s foremost theoretical astrophysicist of the day, Arthur Eddington. I will go into the details of what he measured in another blog in this series on general relativity, but to finish this part one I will explain how gravity bends light in Einstein’s model.

To understand how this happens, we have to go back to the principle of equivalence. Remember, this states that whatever is true inside a lift which is accelerating in empty space is also going to be true for a lift which is stationary in a uniform gravitational field.

Imagine that a beam of light enters the lift horizontally on the left hand side of the lift. Because the lift is accelerating, rather than follow a straight path across the lift, it will appear to follow a curve (actually a parabola), and it will exit at a lower point on the right hand side than where it entered (this is exactly the same kind of path as a ball would follow if it is projected horizontally from a platform e.g. 200m above the Earth’s surface).

Through the principle of equivalence, if a beam of light crossing an accelerating lift will follow a curve, so will a beam of light crossing a stationary lift which is in a gravitational field. So, gravity should bend light!



Light traversing a lift which is accelerating will appear to bend (in fact it will follow a parabolic path). Because of the principle of equivalence, light should be similarly affected by gravity.

Light traversing a lift which is accelerating will appear to bend (in fact it will follow a parabolic path). Because of the principle of equivalence, light should be similarly affected by gravity.



As Einstein developed the mathematics of his general theory he was able to work out precisely how much a given gravitational field should bend light, and his predicted amount was found to be true for the Sun in a celebrated experiment in 1919 by Arthur Eddington.

In part two of this blog I will discuss some of the mathematical obstacles Einstein faced in bringing his general theory of relativity to fruition.

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