Tag: supersaturated vapour

Of liars, paradoxes, and vanity

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Keith S. Taber

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the song works wonderfully as a kind of paradox as in a sense
the song can only be about someone whom it is not about

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In a popular song of the early 1970s, singer-songwriter Carly Simon reflected on having had some "clouds in my coffee", which is an intriguing reference. If this was meant as an objective observation, then it seems to invite some interpretation. What kinds of things are clouds and coffee such that clouds can be observed in coffee?

Solutions, suspensions and supersaturation

In everyday life clouds are usually observed in the sky, and are due to myriad tiny water droplets. The air always naturally contains some water vapour, and the amount depends on the conditions – air just over a hot sea is likely to have a high 'moisture' content due to the rate of evaporation. If very moist air cools then it may become supersaturated with water vapour, in which case any suitable 'nuclei' will facilitate condensation. (These nuclei may be dust particles for example – but ions can also act as condensation nuclei.)

Today everyone is taught at school about the water cycle which is so essential for life on this planet, by which water is recycled through repeated evaporation/transpiration and condensation and precipitation. (Sadly, in Isaac Newton's day the school curriculum was mostly limited to learning maths and Latin, which was unfortunate – as if he had been taught about the water cycle he might not have felt the need to posit an extraterrestrial explanation for how the seas do not dry up with all that evaporation.)

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Clouds may occur on a smaller scale, such as in cloud chambers used to detect the traces left by alpha or beta radiation. Here, material soaked with a suitable volatile liquid, such as ethanol, is placed in a chamber so that the air becomes saturated, and then, where it cools, supersaturated. An alpha or beta source will emit fast moving particles that transfer momentum by colliding with molecules in the air, often ionising them. As the alpha or beta particle moves through the chamber it leaves behind it a 'trace' in terms of a trail of ions – in a cloud chamber the alcohol or other other supersaturated vapour condenses around these ions giving a visible trail – somewhat like the vapour trails left by jets that are often still visible when the plane is too far away to be seen.

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The atmosphere – nature's own cloud chamber

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So, what is coffee? I think that depends on how you make it. Assuming you take your coffee black, then if you serve it in a glass, and hold the glass up to the light, it may seem to be transparent. That is, it has a brown colour, but you can see through it to what is behind. If so, that is a solution with various substances in the coffee dissolved in the solvent (hot water). Perhaps you cannot see through your coffee, and if you try shining a torch or laser pen at it you see the beam lighting up its route through the coffee? If so, as well as dissolved material, it also contains suspended particles that are too large to be in solution. You can test this – as long as you do not mind not drinking your coffee. Given enough time, if the glass is undisturbed, the suspended particles will form a sediment at the bottom, and you will be left with a clear solution above. (But your coffee will now be cold.)

Coffee is made in various ways, and whether your coffee is a solution or has both dissolved solute and suspended particles will depend on how finely the coffee solids are filtered in preparing the drink. If you take milk or something similar in your coffee, then you definitely have some suspended particles of fat or oil in there.

So, how are we to understand how clouds can form in coffee? If one had hot coffee which was purely a solution (finely filtered), and was very strong coffee, then perhaps some of the solute would be saturated – the most that could be dissolved at that temperature. If the coffee cooled, then perhaps it would become a supersaturated solution, and, if suitable nuclei were present (so perhaps not too fine a filter, so allowing a few suspended particles?), 'clouds' of precipitating coffee solids would be seen in the solution?

Song-writing as representing a poetic truth

Now, dear reader, you are probably suspecting that I am being an over-literal scientist here, as clearly Carly Simon was writing a song and not making laboratory observations. Surely, it is obvious, that the clouds in her coffee were metaphorical clouds? She is representing how she felt – as she mused over her coffee – she was sad or melancholy or at least reflective.

When released as a single, the record, 'You're so vain', was a big hit in many parts of the world, no doubt in part because it was a very catchy song, but perhaps also in part because of ongoing speculation about WHOM it was Ms. Simon was accusing of vanity. Over the years she has suggested the song is about a composite of three men, and she has acknowledged one of them (the actor Warren Beatty) but speculation has continued. Perhaps if it was released today, a song that includes the line "You had me several years ago when I was still quite naive" might be viewed as reporting something darker than just a failed love affair? But what especially appeals to me about the song is its sense of paradox.

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The liar paradox

There is a famous paradox which was said to have bemused and puzzled some ancients. Imagine meeting someone who tells you:

All Cretans are liars.
I am a Cretan.

I mean no disrespect to the people of Crete, but this is how I understand the paradox was originally framed. We could substitute Venusians or politicians or whatever. A modern version could be

All members of the Bullingdon Club are liars.
I am a member of the Bullingdon Club

This is supposed to present a paradox. Either the first statement is true, in which case the second is not. Or the second is true, in which case the first is not.

If (and see below) we accept this is a paradox then it has a simple solution. As well as saying things they think are true, and things they think are false, people are also capable of saying things that do not make sense – even to themselves! Not all texts can be considered to have truth value. There is then no paradox, just a lack of consistency!

After all, we can say all kinds of things that do not relate to possible situations

• Gas sample A contains 2g of hydrogen at a lower temperature and higher pressure than gas sample B
• Gas sample B contains 2g of hydrogen that occupies a smaller volume than gas sample A

Oh, how much easier (if less interesting) life would be if there was a law of nature that meant we could not say or write things that were not true or not physically possible! Scholars would simply need to sit down and start writing. Anything they were able to produce would be true and we would not need the expense of CERN and all those other laboratories!

Applying hermeneutics

Now, even though what people say or write need not make good sense, one should be careful dismissing an apparently non-sensical statement too easily. I know from working with science students who may have various alternative conceptions and alternative conceptual frameworks that often they say things that do not seem to make sense. Certainly, sometimes, this may be because they are confused or are guessing an answer to a teacher's question without fully thinking it through.

But sometimes what they say makes good sense from their perspective. We only find this out by engaging them in conversation when it may transpire from the wider context of their talk that they are using a term in a somewhat non-canonical way, or have a different way of dividing up the world, or they limit certain principles to a too restricted set of contexts (or apply principles beyond their valid range of application), et cetera. That is, we apply a hermeneutic approach to seeking sense by seeking to understand a statement in terms of the wider 'text'.

Whilst, from a canonical scientific perspective, the student has still got some of the science wrong, it is much more likely a teacher can shift their thinking towards the target knowledge in the curriculum if she recognises it has coherence for the student and understands and if she engages with the student's way of thinking (for example exploring limitations, pointing out it has absurd or clearly incorrect implications), than if she simply dismisses it as 'wrong'. This, of course, is the basis of the constructivist approach to science teaching.

Read about constructivist pedagogy

Liars, and effective lairs

However, even if we take the Cretan's couplet as a paradox, it is not very convincing. A liar is someone who tells lies – not someone who only ever tells lies. A 'good liar' (if that is not an oxymoron – I mean someone good at lying), that is someone able to use lying to their advantage, presumably does this by being truthful enough of the time that people do not suspect when they are lying. Someone who announced themselves on the telephone with…

"Hi, I'm John. I am a fish. I eat oak trees for breakfast. I am four thousands years old. I used to be Napoleon Bonaparte. I can hold my breath for months at a time. I levitate when I sleep. I am England's greatest goalscorer, even though, as a fish, I do not have any feet. I am phoning from your bank because we are concerned about some suspicious activity on your account, so would like to just check with you on some recent transactions to make sure you authorised them. First of all, because we take customer privacy and security very seriously, I need to be sure who I am talking to, so would you mind giving me your full name, postcode, account number and password."

A very unconvincing scammer

…would be unlikely to be believed. Much better to start with something that is clearly true if you want to sneak in a lie without it being noticed. (The recent demise of a UK Prime Minister perhaps offers an example of how, when you already have a reputation for not telling the truth, people are more likely to suspect, scrutinise and check your claims, and, so, detect dishonest statements.)

Reductio ad absurdum

So, an improvement on the Cretan liar paradox is the card which has a statement on each side:

• the statement on the other side of this card is true
• the statement on the other side of this card is a lie

This corrects for the need to understand 'liar' as someone who only tells lies.

If the statement on the first side is correct, then the statement on the other side is true, which means the statement on the first side was a lie, so not correct.

But if the statement on the first side is a indeed a lie (as we are informed by the statement on the other side) then the statement the second side is not true, which means the statement on the first side was not a lie, and is true…

Either way, whichever statement we begin by accepting we find is contradicted later. This reflects the method of 'reductio ad absurdum' which is a technique used to demonstrate false arguments.

Imagine we wanted to demonstrate that atoms can be divided. Let us posit that atoms are indivisible. This would lead us to conclude there are not discrete subatomic particles. Yet electrons, alpha particles, neutron, protons have all been shown to be subatomic particles. Therefore our premise (atoms are indivisible) must be false.

An even simpler version of the liar paradox is the statement:

• this statement is a lie

The statement claims to be a lie, but if it is a lie that means the truth is contrary to what it claims. So (as it claims to be a lie) it is true. But if it is true, then the statement must be correct. So if it is correct, as it claims to be a lie, it is a lie. So, if true it is a lie. But then if it is a lie…

Clearly we have self-contradiction. Again, there is no real mystery here – it is simply a clever statement that is neither true nor false but lacks coherent sense. What is a mystery, is who 'is so vain'?

Do the vain think themselves vain?

The hook of the song is the chorus

You're so vain
You probably think this song is about you
You're so vain (you're so vain)
I bet you think this song is about you
Don't you don't you?

This seems a nice reflection of the Cretan paradox. Carly's ex-lover would have to be very vain to think she would be so obsessed with him that she would write a song about him. So, if he thinks the song is about him, he is indeed 'so vain'.

Except of course, the song may actually be about him. If an ex-lover whom the song is about thinks it is about him then is that vanity? Surely, not. It is not vanity for someone to acknowledge, say, being a Nobel prize winner, if she is indeed a Nobel laureate. Vanity is thinking you should have won the Nobel that was given to someone else!

The song contains some specific biographic details, such as

Well I hear you went up to Saratoga
And your horse naturally won
Then you flew your Lear jet up to Nova Scotia
To see the total eclipse of the sun

So, someone hearing the song who had been a lover of Ms. Simon several years earlier, and had been up to Saratoga to watch a horse race where his own horse had won the race, and had flown himself to Nova Scotia in his own Leah jet to see the total eclipse, surely would have good grounds for feeling this could well be him.

In particular, we might think, if they recognised themselves as being vain! But this is what makes the song delicious lyrically, as surely a vain person does not recognise themselves as vain?

So, if someone thinks the song is about them, when it is not, they are vain enough to think an ex-lover would write a song about them. BUT that is not someone the song is actually about, so not whom is being accused of being 'so vain'.

If the person whom is being written about does not think it is them, then they are presumably not so vain. If they do recognise themselves, then they are justified in doing so, so that is not really evidence of vanity, either!

So, the song works wonderfully as a kind of paradox as in a sense the song can only be about someone whom it is not about! Did Carly Simon realise that when she wrote the song. I assume so. Does this contribute to its continuing popularity? Perhaps, if you, dear reader, know this song, do you too appreciate this aspect of it? Or, perhaps most people just sing along with the catchy tune and let the lyrics flow? They are poetry after all, not formal knowledge claims.

Explaining the clouds in the coffee

So, were the clouds in the coffee just meant as a metaphor for how Carly was feeling about the plans she had had during her time with her ex-lover?

Well you said that we made such a pretty pair and that you would never leave
But you gave away the things you loved
And one of them was me
I had some dreams they were clouds in my coffee clouds in my coffee and
You're so vain
You probably think this song is about you

On a number of websites Ms. Simon is quoted as explaining (in 2001) that

"'Clouds in my coffee' are the confusing aspects of life and love. That which you can't see through, and yet seems alluring…until. Like a mirage that turns into a dry patch. Perhaps there is something in the bottom of the coffee cup that you could read if you could (like tea leaves or coffee grinds)"

Carly Simon quoted on a range of websites

However, Carly has also explained she took the line from a comment her friend and pianist Billy Mernit made when they were served coffee on a plane – "As I got my coffee, there were clouds outside the window of the airplane and you could see the reflection in the cup of coffee. Billy said to me, 'Look at the clouds in your coffee.  That's like a Truffaut shot!'."

Mermet recalls on his blog that he had actually compared the image to a scene from a Godard film: "what I had talked about was a Godard shot, namely the overhead close-up of a coffee cup from [the film] 2 or 3 Things I Know About Her.

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Clearly Carly [sic] may have been in a reflective mood, but the clouds that appeared to be in her coffee were due to a different kind of reflection. So, it seems there was a sound physical interpretation, after all.