Archive for February, 2019

Boltzmann’s Birthday

February 20, 2019

Ludwig Boltzmann, one the greatest scientists of the nineteenth century, was born on this day, 20th February, in 1844.

Boltzmann was a visionary who saw and clearly described the dynamic, atomic, view of the world that we now see as somehow ‘obvious’.

It is therefore puzzling in retrospect that at the age of 62, after a career of substantial achievement, this genius took his own life.

While on holiday at the breathtaking Castle Duino on the Adriatic, he hanged himself one afternoon, while his wife and daughter were out walking.

Of course, we can never know the reasons for his actions. But this tragedy can form a focus for reflections.

And the poem below, written by my brother, Sean, does just that.

Then and Now

My brother wrote the poem for me as a gift for my 59th birthday.

The subject matter – the suicide of a physicist just a few years older than myself – might seem odd to some.

And indeed, although I am no Boltzmann, I am sure the similarities of our situation were on my brother’s mind. We are men about sixty years of age, able to pass for ‘successful’, driven towards our studies but – euphemistically in both cases – ‘unhappy at work’.

But I do not consider the choice of topic odd or ill-judged. My brother simply recognises that although the canvas of my life is smaller than Boltzmann’s, the truths of physics and the pain of despair are both universal.

The poem is based around a structure of elegies written by Rainer Maria Rilke: the Duino Elegies, which he began while staying at the castle where Boltzmann later killed himself.

The poem reflects on the truth that awareness of the true nature of the world, does not of itself bring joy, and does not dispel inner desolation.

Now, as then, we still lack a theory of hope against despair.

I hope you enjoy the poem… It’s quite long, so take your time. Or if you prefer you can download it here (as a pdf) and read it off line.

Note: I hate to even mention this, but I am concerned that some kind friends reading this might worry for my state of mind. These last months have not been a happy time for me and I am indeed finding ‘things’ difficult. But please be assured I am a long way from Boltzmann’s plight.

Boltzmann at Duino – For Michael

By Sean de Podesta

22 December 2018

You hope for something non-theoretical,
Your daughter’s smile,
The sound of your wife’s voice,
Or how she would touch you affectionately
When you were younger;
But now no-one is with you.

On the parapet of a castle,
Atop a high cliff,
One can feel defended and secure –Secure enough to look out over the sea
And contemplate its near-infinity,
To celebrate the life-giving essence of the air
To speculate what forces move the wind;
You have done all these things.
You have contrived poetic expressions
Of your fine elevated feelings;
You have calculated experimentally verified equations

Or one can feel the vertiginous exhilaration
Of contemplating release.
You are an old man, but you could be leaping
Out, out there for a few seconds
(You can make the calculation in your head),
Experiencing the thrill of weightless flight,
Plummeting, Boltzmann, into the depths.
This is just one of many tantalizing
Reflections and temptations.

Like a harp tuned to the wind
Your intellect responds to every disturbance of the ether,
Alert to invisible undulations; you infer
The collisions of atoms and calculate
The long decay of the universe.
It is as if by discovering the laws
You are their creator
And the world is somehow yours.
A humorous conceit: If you were God, The Designer,
You would certainly have used these equations.

But, Boltzmann, this is too proud;
You value humility above pride.
You tune to the field, feel the interactions of atoms
Not out there but inside.
The tuning fork, the aerial, the physicists brain,
Are part of nature, points of awareness
In the universe of itself, and dispersing
(as the equations predict),
To some point of disappearance
With loss of awareness
That you are gone, in the act of thinking,
Till random processes lead to your re-emergence
At some point in eternity’s slow course.
Nature is true, but daunting.
You have studied philosophy
And have become stoic
Up to the limit of pain
And non-endurance

As a man, well-situated but
Suffering the pains of any sixty-year old,
You know that September is the sweetest month
To be on the coast.
Your hotel is comfortable.
You feel not an intellectual but an animal
And when you look over the glittering Adriatic
Under the pale azure sky,
The landscape, seascape, skyscape,
Are like a proxy for infinity
And you feel not just animal, but an animal with a soul.
And you want out of the numinous atmosphere
Something divine to coalesce –
Or semi-divine would suffice:
A beautiful youth who would steal the attention,
Not of your intellect but your heart.
Or better – an angel would emerge
From all the immanent potential in the air,
A guardian angel, who would touch your skin like the sun
Or the warm breeze in the evening, so tender
That you knew you were cherished
And that they were really there.
With an absolute certainty (though you had no equations to prove it).
You would know the universe was benign,
Like God, only requiring no worship,
Simply eliciting gratitude and appreciation.

But your body’s overshadowed as the sun goes down
And for all the opening of your heart
No angel comes.
You know so much, but know nothing.
You intuit the whole arc of the universe
But feel just unworthiness and pain
(Why are you unworthy? You cannot explain.)
And there is this fathomless emptiness within.
You cannot hear your wife’s voice.
When you go to your room without a guardian angel or hope
You are the finite atoms in the infinite vacuum
Looking for something to serve as a rope.

We ask now, too late, what might have brought you comfort?
Did you even want comfort?
Was comfort even possible for you?
Maybe something in you weighed it all
And balanced Boltzmann the man
And what was still possible for him
Against Boltzmann the sum of his particles
And chose to let yourself flow with the entropic stream?

You intuit something
And you want what you intuit –
That’s part of the intuition –
But you don’t know what it is,
And in any case feel unworthy of it.
How is this possible?
It is the x in the equation,
The unknown, generalized,
So that the solution confirms
You are unworthy of everything,
Of anything.
You can claim nothing
In the domain of hope.

This is so unfair, Boltzmann.
Intuitions are true, or feel true
But we cannot quantify or predict them:
And when the reality is statistical,
What we expect may never happen
And seeming miracles can occur
Or, more likely, not occur.
And any particular thing does not matter.
So you feel the angel,
But the angel does not come.
That is what you deserve
Or what you don’t deserve.
In either case, it is certain
Desolation, and it hurts.

If only, Boltzmann, there were
Where things are so beautiful
A proper theory of hope against despair.

Global Oxygen Depletion

February 4, 2019

While browsing over at the two degrees institute, I came across this figure for atmospheric oxygen concentrations measured at a station at the South Pole.

Graph 1

The graph shows the change in:

  • the ratio of oxygen to nitrogen molecules in samples of air taken at a particular date


  • the ratio of oxygen to nitrogen molecules in samples of air taken in the 1980’s.

The sentence above is complicated, but it can be interpreted without too many caveats as simply the change in oxygen concentration in air measured at the South Pole.

We see an annual variation – the Earth ‘breathing’- but more worryingly we see that:

  • The amount of oxygen in the atmosphere is declining.

It’s a small effect, and will only reach a 0.1% decline – 1000 parts per million – in 2035 or so. So it won’t affect our ability to breathe. Phewww. But it is nonetheless interesting.

Averaging the data from the South pole over the years since 2010, the oxygen concentration appears to be declining at roughly 25 parts per million per year.


The reason for the decline in oxygen concentration is that we are burning carbon to make carbon dioxide…

C + O2 = CO2

…and as we burn carbon, we consume oxygen.

I wondered if I could use the measured rate of decline in oxygen concentration to estimate the rate of emission of carbon dioxide.

How much carbon is that?

First I needed to know how much oxygen there was in the atmosphere. I considered a number of ways to calculate that, but it being Sunday, I just looked it up in Wikipedia. There I learned that the atmosphere has a mass of about 5.15×1018 kg.

I also learned the molar fractional concentration of the key gases:

  • nitrogen (molecular weight 28): 78.08%
  • oxygen (molecular weight 32): 20.95%
  • argon (molecular weight 40):0.93%

From this I estimated that the mass of 1 mole of the atmosphere was 0.02896 kg/mol. And so the mass of the atmosphere corresponded to…

5.15×1018 /0.02896 = 1.78×1020

…moles of atmosphere. This would correspond to roughly…

1.78×1020 × 0.02095 =3.73×1019

…moles of oxygen molecules. This is the number that appears to be declining by 25 parts per million per year i.e.

3.73×1019× 0.000 025= 9.32×1014

…moles of oxygen molecules are being consumed per year. From the chemical equation, this must correspond to exactly the same number of moles of carbon: 9.32×1014. Since 1 mole of carbon weighs 12 g, this corresponds to…

  • 1.12×1016 g of C,
  • 1.12×1013 kg of C
  • 1.12×1010 tonnes of C
  • 11.2 gigatonnes (Gt) of C

Looking up the sources of sources, I obtained the following estimate for global carbon emissions which indicates that currently emissions are running at about 10 Gt of carbon per year

Carbon Emissions


So Wikipedia tells me that humanity emits roughly 10 Gt of carbon per year, but based on measurements at the South pole, we infer that 11.2 Gt of carbon per year is being emitted and consuming the concomitant amount of oxygen. Mmmmm.

First of all, we notice that these figures actually agree within roughly 10%. Which is pleasing.

  • But what is the origin the disagreement?
  • Could it be that the data from the South Pole is not representative?

I downloaded data from the Scripps Institute for a number of sites and the graph below shows recent data from Barrow in Alaska alongside the South Pole data. These locations are roughly half a world – about 20,000 km – apart.

Graph 2

Fascinatingly, the ‘breathing’ parts of the data are out of phase! Presumably this arises from the phasing of summer and winter in the northern and southern hemispheres.

But significantly the slopes of the trend lines differ by only 1%.  So global variability doesn’t seem to able to explain the 10% difference between the rate of carbon burning predicted from the decline of atmospheric oxygen (11.2 Gt C per year) , and the number I got off Wikipedia (10 Gt C per year).

Wikipedia’s number was obtained from the Carbon Dioxide Information and Analysis Centre (CDIAC) which bases their estimate on statistics from countries around the world based on stated oil, gas and coal consumption.

My guess is that there is considerable uncertainty – on the order of a few percent –  on both the CDIAC estimate, and also on the Scripps Institute estimates. So agreement at the level of about 10% is actually – in the context of a blog article – acceptable.


My conclusion is that – as they say so clearly over at the two degrees project – we are in deep trouble. Oxygen depletion is actually just an interesting diversion.

The most troubling graph they present shows

  • the change in CO2 concentration over the last 800,000  years, shown against the left-hand axis,


  • the estimated change in Earth’s temperature over the last 800,000  years, shown  along the right-hand axis.

The correlation between the two quantities is staggering, and the conclusion is terrifying. chart

We’re cooked…


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