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The electron was discovered in 1897 by J.J. Thomson. It was the first sub-atomic particle to be discovered.

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As I mentioned in the first part of my series of blogs on the Analemma, understanding the vertical motion of the Sun at the same time each day is pretty easy, as we are all familiar with seeing the Sun higher in the sky in the summer than in the winter.

A solar analemma, showing the Sun at the same time each day over the course of a year. This analemma would have been taken at midday at several days throughout the year. We know it was taken at midday because the analemma is vertical.

This, of course, comes about because the axis of the Earth is tilted to the plane of orbit of the Earth about the Sun. The angle is 23.5^{\circ}. On the Spring Equinox the Sun crosses the Celestial Equator moving into the Northern sky, on the Summer Solstice it is overhead as seen by someone at the Tropic of Cancer, on the Autumn Equinox it crosses the Celestial Equator again going South, and on the Winter Solstice it is overhead as seen by someone on the Tropic of Capricorn.

This video shows the position of the Sun in the sky on these key dates.

But, what is more difficult to understand is the horizontal (East-West) motion in the analemma. Why is the Sun sometimes to the left of the vertical midpoint, and sometimes to the right? It turns out that the East-West motion in the analemma is due to two effects. One has to do with the same effect described above, the tilt of the Earth’s axis. This leads to the Sun moving against the background stars in a different way than if there were no tilt to our axis. The other part of the East-West motions is due to the shape of the Earth’s orbit about the Sun, which is elliptical and not circular.

I will explain the part due to the tilt of Earth’s axis first, and explain the part due to the shape of Earth’s orbit in part 3 on this subject, which I will post sometime in the next week.

As everyone knows, there are 24 hours in a day. But, how do we define a day? It turns out that, because the Earth moves in orbit about the Sun, that a day is not the time it takes the Earth to rotate 360^{\circ}. This is the sidereal day, the time it would take a given star to pass through a local meridian on two successive occasions (the local meridian is a line drawn from North to South across the sky. But the Earth has to rotate a little bit further for the Sun to cross the local meridian on two successive occasions because it has moved in its orbit about the Sun in the intervening time. The time between the Sun crossing the local meridian on two successive occasions is called the Solar Day.

The difference between the sidereal day (the time it takes the Earth to turn 360^{\circ} on its axis) and the Solar day (the time for the Sun to cross the local meridian)

Roughly speaking, the difference between the sidereal day and our Solar day is 4 minutes, which is why given stars rise approximately 4 minutes earlier each day. If the Earth’s axis were not tilted, and if the Earth’s orbit were circular, the length of the Solar Day would always be the same.

The average time it takes for the Sun to cross the local meridian on two successive occasions is called the mean solar day, and this is 24 hours. But, because of the two effects described above, the tilt of the Earth’s axis and the Earth’s path around the Sun during the year, the Sun does not always take 24 hours to do this. The diagram below shows the so called Equation of Time, which is how much the Sun varies from taking 24 hours to pass the meridian on two successive days.

The 2 components (dashed lines) and overall (red line) equation of time. The part due to the details of Earth’s orbit is the dark dash-dotted line, the part due to the inclination of the Earth’s axis is the dashed mauve line

If the Earth’s axis were not tilted to its plane of orbit about the Sun then there wouldn’t be any seasons and the vertical variation seen in the analemma would disappear. But, not only does the tilt produce the seasons, it also affects the way the Sun appears to move against the sky from day to day. Over the course of a year, the Sun appears to move against stars in the background. In fact, it moves through the 12 constellations which happen to be on the ecliptic, these are the so called constellations of the zodiac (or signs of the zodiac).

The Sun appears to move through 12 constellations (the constellations of the zodiac) at the Earth orbits it in the course of each year

If we plot the position of the Sun against the sky and the background stars on a chart which shows East-West on the x-axis and North-South in the sky on the y-axis (astronomers call this right ascension and declination respectively), the Sun follows a sinusoidal curve.

The path of the Sun against the background stars in the course of the year. The x-axis is Right Ascension (RA), the y-axis is Declination (dec)
Over the course of a year, the Sun appears to follow a sine curve against the background sky as seen from the Earth. It crosses the x-axis going up (North) on the Spring Equinox, reaches its maximum positive declination on the Summer Solstice, whereupon it starts moving South again. It crosses the x-axis going South on the Autumn Equinox, and reaches its maximum negative declination on the Winter Solstice.

In the diagram above, East is to the left and West is to the right, North is up and South is down. The Sun crosses the celestial equator heading north on the Spring Equinox, reaches a maximum declination of +23.5^{\circ}. If you look carefully at this diagram, you will see that the East-West motion of the Sun in the sky is going to be at its least at the times of the equinoxes, and at its greatest at the times of the solstices. We set our clocks so that the solar day at the time of the equinoxes is the correct length of the day, i.e. 24 hours. As the Sun moves into the northern part of the celestial sphere, away from the celestial equator, it moves more to the East (left) each day that it does at the time of the equinox. If the Sun moves to the East it will pass the meridian slightly later, so the Sun will appear to the East (left) of the meridian at midday. In the diagram of the equation of time, you can see that the dashed mauve curve (the part due to the tilt of the Earth’s axis) does indeed become positive after the Spring Equinox.

This effect reaches its greatest at the Summer Solstice, when all of the Sun’s motion on the celestial sphere is in an East-West direction, there is no North-South component. The maximum motion to the East is on the Summer Solstice, and this is when the dashed mauve curve reaches its maximum of

The detail of the change in RA when the Sun is crossing the Celestial Equator at the Equinox
Detail of the Right Ascension moved when the Sun is at its highest point in the North, the Summer Solstice
As seen from the Earth, the Sun moves in the sky as shown, not along the equator. As seen from the Earth, the Sun moves in the sky as shown, not along the equator.
The diagram on the right shows the Earth as seen from above. The angle the Sun moves through is less than the angle it would move through if it moved along the equator. The diagram on the left shows the Earth as seen from above. The angle the Sun moves through is different to the angle it would move through if it moved along the equator. The difference is denoted by \alpha. On the right is how this difference appears if one is looking at the Celestial Sphere from the Equator of the Earth.

Today I thought I would blog about another of my favourite Meic Stevens songs, “Dic Penderyn”. This song appears on his 1972 album Gwymon, and also on his compilation album Disgwyl Rhywbeth Gwell i Ddod.

The subject matter of this song is the Welsh labourer and coal miner Richard Lewis (1807-1831). He has become better known as Dic Penderyn, and he has gone down in Welsh history as being one of the heroes of the Merthyr Rising on 3 June 1831. This was a day of violence which capped many years of unrest amongst the working class people of Merthyr Tydfil in South Wales, after their wages had been cut and the unemployment rate had risen.

Dic Penderyn was charged with stabbing a soldier with a bayonet during the riot. Despite the people of Merthyr Tydfil doubting his guilt (they even signed a petition for his release), he was found guilty and hanged on 13 August 1831 outside Cardiff Castle.

Here is the YouTube video of Meic Stevens’ song about Dic Penderyn.

Here are the lyrics to this song.

Dic Penderyn, wyt ti’n foi

Ble est ti’n yfed was?

Lawr yn Merthyr oeddwn ddoe

O saith tan hanner nos.

Pwy sy’n gweithio yn y pwll?

Pwy sy’n yfed medd?

Mae’r Cymry’n bwyta bara sych,

Mae’n dywyll fel y bedd.


Dic Penderyn, redwch nawr

Mae’r milwyr ar dy ôl.

Cotiau coch a’u gynniau gwyllt

Saethu bobol ffôl.

Saethu bobol ffôl.

Pwy sy’n gweithio yn y pwll?

A pwy sy’n yfed medd?

Mae’r Cymry’n bwyta bara sych,

Mae’n dywyll fel y bedd.


Dic Penderyn, cuddiwch nawr

Mae plismyn yn ein stryd.

Dewch mâs yn gloi trwy drws y cefn

Rhowch ‘ goesau di yn rhydd

Ie, tra bo’ch goesau di yn rhydd.

Pwy sy’n gweithio yn y pwll?

Pwy sy’n yfed medd?

Mae’r Cymry’n bwyta bara sych,

Mae’n dywyll fel y bedd.

O, mae’n dywyll fel y bedd.


Dic Penderyn, o rhy hwyr

Mae e’n hedfan dros y bryn.

Ar llawr y carchar mae o nawr

A’r ddial rownd pob glun.

O, a’r haearn rownd pob glun.

Pwy sy’n gweithio yn y pwll?

Pwy sy’n yfed medd?

Mae’r Cymry’n bwyta bara sych,

Mae’n dywyll fel y bedd.

O, mae’n dywyll fel y bedd.


Dic Penderyn, Cymro glân

Llofruddwr nawr wyt ti.

Wrth borth y castell yng Nghaerdydd

Rhaff y Sais gei di.

Ie, rhaff y Sais gei di.

Pwy sy’n gweithio yn y pwll?

Pwy sy’n yfed medd?

Mae’r Cymry’n bwyta bara sych,

Mae’n dywyll fel y bedd.

O, mae’n dywyll fel y bedd.

Ie, mae’n dywyll fel y bedd.

As usual, my translation is as accurate to the Welsh lyrics as I can make it, without any attempt to retain a rhythm or rhyme in the English words.

Dic Penderyn, you are a boy

Where did you go drinking son?

I was down in Merthyr yesterday

From seven until midnight.

Who works in the mine?

Who drinks mead?

The Welsh people eat dry bread,

It’s as dark as a grave.


Dic Penderyn, run now

The soldiers are after you.

Red coats and wild rifles

Shooting crazy people.

Shooting crazy people.

Who works in the mine?

Who drinks mead?

The Welsh people eat dry bread,

It’s as dark as a grave.


Dic Penderyn, hide now

The policemen are in our street.

Come out quickly through the back door

Let your legs be free

Yes, whilst your legs are free.

Who works in the mine?

Who drinks mead?

The Welsh people eat dry bread,

It’s as dark as a grave.

Oh, it’s as dark as a grave.


Dic Penderyn, oh it’s too late

He is flying over the hill.

On the floor of the jail he is now

With revenge around each hip.

Oh, with the iron around each hip.

Who works in the mine?

Who drinks mead?

The Welsh people eat dry bread,

It’s as dark as a grave.

Oh, it’s as dark as a grave.


Dic Penderyn, pure Welshman

You are now a murderer.

At the gates of Cardiff Castle

You’ll get the Englishman’s rope.

Yes, you’ll get the Englishman’s rope.

Who works in the mine?

Who drinks mead?

The Welsh people eat dry bread,

It’s as dark as a grave.

Oh, it’s as dark as a grave.

Yes, it’s as dark as a grave.

5. Simple Twist Of Fate (1975)

Dylan’s saddest song. As he sings of the last night of a couple together with weary despair, Dylan’s narrative unfolds in the third person, except for one devastating giveaway “I remember well”. Even the wheezy harmonica solo sounds emotionally shattered.

4. Jokerman (1983)

Many of Dylan’s most devoted fans were alienated by the preachiness of Dylan’s born again Christian phase. On Jokerman he released himself back into a beautiful ambiguity that more perfectly distils the mysteries of faith. The Jokerman is Jesus, “born with a snake in both of your fists while a hurricane was blowing.” With legendary Jamaican rhythm section Sly Dunbar and Robbie Shakespeare pulsing beneath Mark Knopfler’s silvery guitar, the track has a slipperiness that mirrors its audacious lyrical twists and turns.

3. A Hard Rain’s A Gonna Fall (1963)

Adapting the melody and refrain of traditional English folk song Lord Randall, Dylan lets loose the full force of his poetic imagination like an apocalyptic storm. This first recording is sparse, just strummed acoustic guitar and that barbed wire voice, but the cascade of imagery holds listeners in hypnotic thrall.

2. Blowin’ In the Wind (1963)

This song was released in 1962 by Dylan on his Freewheelin’ Bob Dylan album.

The song that really announced Dylan, a troubadour for a generation, old beyond his years. He was just 21 when he wrote it but cautiously held it back from his debut album of folk covers. It sounds like a song that has been blowing around for 1000 years and has a quality of simple, universal, mysterious truth that will keep it relevant for a thousand more.

1. Tangled Up In Blue (1975)

The most dazzling lyric ever written, an abstract narrative of relationships told in an amorphous blend of first and third person, rolling past, present and future together, spilling out in tripping cadences and audacious internal rhymes, ripe with sharply turned images and observations and filled with a painfully desperate longing. “I wanted to defy time” according to Dylan. “When you look at a painting, you can see any part of it altogether. I wanted that song to be like a painting.”

In this blogpost here, I derived the Lorentz transformations from first principles. The derivation uses a simple thought experiment; two reference frames S \text{ and } S^{\prime} are moving relative to each other with a speed v. The origins of S \text{ and } S^{\prime} coincide spatially at time t=t^{\prime}=0. At this moment, a flash of light is created at their origins, and expands as a sphere.


The radius of this sphere of light will be r \text{ and } r^{\prime} in S \text{ and } S^{\prime} respectively. So, we can write

x^{2} + y^{2} + z^{2} = r^{2} \text{ in } S \text{ (1) }
and
x^{\prime}{^2} + y^{\prime}{^2} +z^{\prime}{^2} = r^{\prime}{^2} \text{ in } S^{\prime} \text{ (2) }

But, in reference frame S, the distance r that light travels in time t is related to the speed of light c, as c = r/t, so for S we can write that

r = ct

We can do the same thing for reference frame S^{\prime}. The distance r^{\prime} that light travels in time t^{\prime} in S^{\prime} is related to the speed of light c^{\prime} in S^{\prime}, c^{\prime} = r^{\prime} / t^{\prime}, so for S^{\prime} we can write

r^{\prime} = c^{\prime} t^{\prime}.

However, crucially, Einstein said that the speed of light c is the same for all inertial observers. This is the most important principle which underpins special relativity. It means that c^{\prime} = c, and so we can write

r^{\prime} = c t^{\prime}

which allows us to write Equations (1) and (2) as

x^{2} + y^{2} + z^{2} -c^{2}t^{2} = 0 \text{ in } S \text{ (3) }

and

x^{\prime}{^2} + y^{\prime}{^2} + z^{\prime}{^2} - c^{2}t^{\prime}{^2} = 0 \text{ in } S^{\prime} \text{ (4) }

Using the Galilean Transformations, which can be written as


we can substitute xfor x^{\prime} (=x - vt), y^{\prime}=y, z^{\prime}=z and t^{\prime} =t in Equ. (4) to give us

(x-vt)^{2} + y^{2} + z^{2} - c^{2}t^{2} = x^{2} - 2vxt +v^{2}t^{2} + y^{2} + z^{2} - c^{2}t^{2}

which is the same  as Equ. (3), except for the two extra terms -2vxt \text{ and } v^{2}t^{2}. This shows that Equations (3) and (4) are not equal under a Galilean transformation, even though the two equations should be equal (as both are equal to zero).

Let us now show that Equations (3) and (4) are equal using the Lorentz transformations. These can be written as


where \gamma is the Lorentz factor, and is defined as

\gamma = \frac{ 1 }{ \sqrt { \left( 1 - v^{2}/c^{2} \right) } }

We will substitute these expressions for x^{\prime},y^{\prime},z^{\prime} and t^{\prime} into Equ. (4). When we do this, we have

\left( \gamma (x-vt) \right)^{2} + y^{2} + z^{2} - c^{2} \left( \gamma (t - vx/c^{2}) \right)^{2}

Multiplying this out, and dropping the y^{2} and z^{2} terms, we get

\gamma^{2}(x^{2} -2vxt +v^{2}t^{2}) -c^{2}\gamma^{2}\left(t^{2} - \frac{2vxt}{c^{2}} + \frac{v^{2}x^{2}}{c^{4}}\right)

\gamma^{2}x^{2} -2\gamma^{2}vxt + \gamma^{2}v^{2}t^{2} - c^{2}\gamma^{2}t^{2} +2\gamma^{2}vxt - (\gamma^{2}v^{2}x^{2})/c^{2}

The two terms 2\gamma^{2} vxt disappear and, gathering terms in x^{2} and t^{2} together, we can write

\gamma^{2}x^{2} - \left( \frac{ (\gamma^{2}v^{2}) }{ c^{2} } \right) x^{2} + \gamma^{2}v^{2}t^{2} - \gamma^{2}c^{2}t^{2}

\gamma^{2}x^{2} (1 - v^{2}/c^{2}) + \gamma^{2}t^{2}(v^{2}-c^{2})

Remembering that \gamma^{2} = \frac{ 1 }{ ( 1 - v^{2}/c^{2} ) }, and changing the sign of the t^{2} term, we can write

\frac{ 1 }{ (1 - v^{2}/c^{2} ) } \cdot (1 - v^{2}/c^{2}) \cdot x^{2} - \frac{ 1 }{ (1 - v^{2}/c^{2} ) } \cdot (c^{2} - v^{2}) \cdot t^{2}

which is

x^{2} - \frac{ 1 }{ (1 - v^{2}/c^{2} ) } \cdot c^{2}(1 - v^{2}/c^{2}) \cdot t^{2}

which is

x^{2} - c^{2}t^{2}, exactly as in Equ. (3).

We have therefore shown that Equations (3) and (4) are equal if we use the Lorentz transformations.

Yesterday I introduced Paul Dirac, number 10 in “The Guardian’s” list of the 10 best physicists. I mentioned that his main contributions to physics were (i) predicting antimatter, which he did in 1928, and (ii) producing an equation (now called the Dirac equation) which describes the behaviour of a sub-atomic particle such as an electron travelling at close to the speed of light (a so-called relativistic theory). This equation was also published in 1928.

The Dirac Equation

In 1928 Dirac wrote a paper in which he published what we now call the Dirac Equation.

The equation now known as the Dirac Equation describes the behaviour of an electron when travelling close to the speed of light. The equation now known as the Dirac Equation describes the behaviour of an electron when travelling close to the speed of light.

This is a relativistic form of Schrödinger’s wave equation for an electron. The wave equation was published by Erwin Schrödinger two years earlier in 1926, and describes how the quantum state of a physical system changes with time.

The Schrödinger eqation

The time dependent Schrödinger equation which describes the motion of an electron The time dependent Schrödinger equation which describes the motion of an electron

The various terms in this equation need some explaining. Starting with the terms to the left of the equality, and going from left to right, we have i is the imaginary number, remember i = \sqrt{-1}. The next term \hbar is just Planck’s constant divided by two times pi, i.e. \hbar = h/2\pi. The next term \partial/\partial t \text{ } \psi(\vec{r},t) is the partial derivative with respect to time of the wave function \psi(\vec{r},t).

Now, moving to the right hand side of the equality, we have
m which is the mass of the particle, V is its potential energy, \nabla^{2} is the Laplacian. The Laplacian, \nabla^{2} \psi(\vec{r},t) is simply the divergence of the gradient of the wave function, \nabla \cdot \nabla \psi(\vec{r},t).

In plain language, what the Schrödinger equation means “total energy equals kinetic energy plus potential energy”, but the terms take unfamiliar forms for reasons explained below.

Today (January 30th) marks the 50th anniversary of the last time The Beatles played live together, in the infamous “rooftop” concert in 1969. Although they would go on to make one more studio album, Abbey Road in the summer of 1969; due to contractual and legal wranglings the rooftop concert, which was meant to be the conclusion to the movie they were shooting, would not come out until 1970 in the movie Let it Be.

It is also true to say that some of the songs on Abbey Road were performed “live” in the studio with very little overdubbing (as opposed to separate instrument parts being recorded separately as was done on e.g. Sgt. Pepper). But, the rooftop concert was the last time the greatest band in history were seen playing together, and has gone down in infamy. It has been copied by many, including the Irish band U2 who did a similar thing to record the video for their single “Where the Streets Have no Name” in 1987 in Los Angeles.

The Beatles were trying to think of a way to finish the movie that they had been shooting throughout January of 1969. They had discussed doing a live performance in all kinds of places; including on a boat, in the Roundhouse in London, and even in an amphitheatre in Greece. Finally, a few days before January 30th 1969, the idea of playing on the roof of their central-London offices was discussed. Whilst Paul and Ringo were in favour of this idea, and John was neutral, George was against it.

The decision to go ahead with playing on the roof was not made until the actual day. They took their equipment up onto the roof of their London offices at 3, Saville Row, and just start playing. No announcement was made, only The Beatles and their inner circle knew about the impromptu concert.

The concert consisted of the following songs :

  1. “Get Back” (take one)
  2. “Get Back” (take two)
  3. “Don’t Let Me Down” (take one)
  4. “I’ve Got a Feeling” (take one)
  5. “One After 909”
  6. “Dig a Pony”
  7. “I’ve Got a Feeling” (take two)
  8. “Don’t Let Me Down” (take two)
  9. “Get Back” (take three)

People in the streets below initially had no idea what the music (“noise”) coming from the top of the building was, but of course younger people knew the building was the Beatles’ offices. However, they would not have recognised any of the songs, as these were not to come out for many more months. After the third song “Don’t Let Me Down”, the Police were called and came to shut the concert down. The band managed nine songs (five different songs, with three takes of “Get Back”, two takes of “Don’t Let Me Down”, and two takes of “I’ve Got a Feeling”) before the Police stopped them. Ringo Starr later said that he wanted to be dragged away from his drums by the Police, but no such dramatic ending happened.

At the end of the set John said

I’d like to thank you on behalf of the group and ourselves, and I hope we’ve passed the audition.

You can read more about the rooftop concert here.

Here is a YouTube video of “Get Back” (which may get taken down at any moment)

 

 

and here is a video on the Daily Motion website of the whole rooftop concert (again, it may get taken down at any moment).

 

 

Enjoy watching the greatest band ever perform live for the very last time!

In late October 2017, astronomers announced the first ever discovery of an asteroid (or comet?) coming into our Solar System from another stellar system. The object was first spotted on 19 October by the University of Hawaii’s Pan-STARRS telescope, during its nightly search for near-earth objects. Based on its extreme orbit and its rapid speed, it was soon determined that the object has come into our Solar System from somewhere else, and this makes it the first ever asteroid/comet with an extra-solar origin to have been discovered. Originally given the designation A/2017 U1, the International Astronomical Union (IAU) have now renamed it 1I/2017 U1, with the I standing for “interstellar”. 

SafariScreenSnapz005

The object, given the designation A/2017 U1, was deemed to be extra-solar in origin from an analysis of its motion.

In addition to its strange trajectory, observations suggest that the object also has quite an unusual shape. It is very elongated, being ten times longer than it is wide. It is thought to be at least 400 metres long but only about 40 metres wide. This was determined by the rapid and dramatic changes in its brightness, which can only be explained by an elongated object tumbling rapidly.

The object has also been given the name Oumuamua (pronounced oh MOO-uh MOO-uh), although this is not its official name (yet).  This means “a messenger from afar arriving first” in Hawaiian. In other respects, it seems to be very much like asteroids found in our own Solar System, and is the confirmation of what astronomers have long suspected, that small objects which formed around other stars can end up wandering through space, not attached to any particular stellar system.

To read more about this fascinating object, follow this link.

A couple of weeks ago I was in New York City. Although I have been to NYC many times since I first visited it in October 1985, this was the first time I had spent the night in Manhattan.

On the evening of Saturday 17th November I booked a ticket to go up the Empire State Building to take night-time photos. The cost of a ticket to the 80th floor is US$32, and I’d say that it’s good value. But, what is not is the extra $20 to go up to the 102nd floor. I had forgotten from my last time that this is not worth the extra money. Hopefully I’ll remember next time.

I was on the observation deck of the Empire State (86th floor) for about 2 hours taking photos and videos. I’ll post some of them over the next few weeks. Then, at about 11:30pm I walked to Time Square. I stopped to get a coffee and warm up a bit so got to Time Square at about 12:30am. The place was heaving, hundreds of people were milling around and many of the shops were open.

At about 1:30am I caught the subway to Brooklyn as I wanted to get a photo of Manhattan with the Brooklyn Bridge in the foreground. I took my photos from the Brooklyn Bridge Park, then walked back to Manhattan over the Brooklyn Bridge.

By this time it was lashing it down with rain and I was soaked. The rain had seeped through my winter coat and my sweater and trousers were pretty much wet through. But, as I walked over the bridge I caught sight of the Statue of Liberty illuminated (it was about 3am by this time). So I decided to walk to Battery Park to take photos of her at night.

When I got to Battery Park and set up my camera I discovered that my camera battery was dead from all the long exposure photos I’d been taking. So I got my spare battery out of my backpack, only to find that it too was dead. So, I didn’t get any photos of Lady Liberty at night. It was now 4am.

I then walked back to my hotel which was in the Little Italy part of Manhattan. The rain was still lashing it down, and by now my phone was getting damp leading to Google maps misbehaving. The app kept on going haywire every minute or two, so I couldn’t use it to guide me back from Battery Park to Little Italy. Instead I just tried to figure it out, and it took me two hours!

I collapsed into my bed at 6am, having spent nearly 12 hours wandering around nighttime Manhattan taking photos.

When I was walking across the Brooklyn Bridge at about 3am this great Simon & Garfunkel song kept playing in my head.

The Only Living Boy in New York

This song appears on Simon & Garfunkel’s last album Bridge Over Troubled Water. Written, of course, by Paul Simon, the “Tom” in the lyrics refers to Art Garfunkel. When they were teenagers in Queens they released a single and briefly called themselves”Tom & Jerry”.

By 1970 Simon and Garfunkel were arguing and about to go their separate ways. Garfunkel decided to have a go at acting, he appears in the movie Catch 22. Simon is wishing him the best for his part in the movie Garfunkel is filming in Mexico.

As is usual with Paul Simon, the song’s lyrics are exquisite.

Tom, get your plane right on time
I know your part’ll go fine
Fly down to Mexico
Da-n-da-da-n-da-n-da-da a
And here I am
The only living boy in New York

I get the news I need on the weather report
Oh, I can gather all the news I need on the weather report
Hey, I’ve got nothing to do today but smile
Da-n-do-da-n-do-da-n-do
Here I am
The only living boy in New York

Half of the time we’re gone but we don’t know where
And we don’t know where
Here I am
Half of the time we’re gone, but we don’t know where
And we don’t know where

Tom, get your plane right on time
I know that you’ve been eager to fly now
Hey, let your honesty shine, shine, shine
Like it shines on me
The only living boy in New York
The only living boy in New York

Here is a video of this beautiful song. Enjoy!

A couple of weeks ago this fascinating version of the periodic table of the elements was the NASA Astronomy Picture of the Day (APOD). Most people have seen the periodic table of the elements, it is shown on the wall of most high school chemistry classrooms. But, what is totally fascinating to me about this version is it shows the origin of each element.

It has been a long process of several decades to understand the origin of the elements. In fact, we have not totally finished understanding the processes yet. But, we do know the story for most elements. All the hydrogen in the Universe was formed in the big bang. This is true for nearly all the helium too. A small amount of the 25% or so of helium in the Universe has been created within stars through the conversion of hydrogen into helium. But, not much has been created this way because most of that helium is further converted to carbon.

The only other element to be formed in the big bang is lithium. About 20% of the lithium in the Universe was formed in the big bang, the rest has been formed since,

Together, hydrogen and helium comprise 99% of the elements in the Universe by number (not by mass).

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Where Your Elements Came From – from the NASA Astronomy Picture Of the Day (APOD) 24 October 2017.

I have decided to use this fascinating table as the basis for a series of blogs over the next few weeks to explain each of the 6 processes in these six boxes