Everyone makes mistakes

Somebody has made a terrible mistake. I live in fear of having made even a tiny mistake.

I do love reading about mistakes. At least I love reading about other people’s mistakes. As I read them I comfort myself with the thought that I haven’t yet messed up as badly as that.

I am particularly sensitive on the subject of mistakes at the moment because of my paper on the Boltzmann constant, claiming the most accurate measurement ever. This is a bold claim and if I have made a mistake I will look very stupid in front of my colleagues.

So as the date of publication approaches, I don’t feel proud, or relieved. I just feel sick with anxiety. I worry that I have forgotten something obvious. Or something not-so-obvious. I worry that some step in the logic that leads to the estimated value is weaker than I thought. In short, I worry that I have made a mistake.

To be sure, the work has been checked and re-checked, and my co-authors are pretty smart. But there are always errors. However, this type of work involves a different approach to measurement, one in which the actual value of the thing being measured barely matters. What counts is our estimate of how wrong our answer could be.

Our main result is an estimate of the speed of sound in argon gas in the limit of low pressure. And to get this we need to measure (amongst other things), pressure, the size of the container, and the frequencies of some acoustic resonances at different pressures.

And how do we know we are right? We don’t. But by measuring the pressure in two different ways we can estimate how wrong we could be. By measuring the size of the container in three different ways we can estimate how wrong we could be. And by estimating the speed of sound from six separate resonances we can estimate  how wrong we could be.

The fact that different estimates of a quantity are self-consistent does not mean they are necessarily correct. But it does make it harder for them to be wrong. And if the data are not self-consistent, then we know that something is definitely incorrect.

So the whole experiment has been designed and performed in a way that will allow us to estimate how wrong we could possibly be in a precise, numerical value. And our description of the experiment is written – as far as is possible – in a way which exposes our mistakes.

But in a primitive and superstitious manner I still feel the need to worry about it, even though there is now nothing I can do. So if I have made a mistake, then it is already too late and I will look silly in front of my colleagues. But as least I didn’t drive a train through a wall!

Arctic Sea Ice: Summer Update

Arctic Sea Ice Cover up to 14th June 2013. Picture from The National Snow and Ice Data Centre.

Arctic Sea Ice has become a news story. At least it is news in September when it reaches its annual minimum. But as the UK basks in a summer heatwave, it is nice to pop over occasionally to the National Snow and Ice Data Centre to check how the annual melt is progressing in the Arctic.

Last year was record minimum, and in large part that was due to an event which took place just at the start of June 2012. You can see the evidence of that on the graph above (click for larger figure). I have also enlarged the relevant detail in the graph below.

Arctic Sea Ice Detail. 2012 data is shown is as a dotted line.

The sudden fall at the start of last June was due to an unusually strong storm which broke up the sea ice, and dispersed it. Since the graph charts the area of the Arctic with at least 15% ice cover – just spreading the ice about resulted in a precipitous decline of about 1 million square kilometres in two weeks.

Now it might be argued that ‘this shouldn’t count’ as real sea ice loss because it was an ‘exceptional circumstance’. I disagree.

Firstly, no matter what the proximate cause, the ultimate cause was that the sea ice was thin and relatively fragile.

And secondly, no matter what the cause, it made the sea/ice surface darker and resulted in increased absorption of sunlight.

And although it would make a great ‘news story’ if there was another storm and another ‘record’ Arctic sea-ice minimum, for the planet’s sake we could we do with a few ‘no news’ years in the Arctic.

Me and the Media

A television programme about precision measurement? Yes!

Astute readers may have noticed that I haven’t posted anything for a month! This is because I have been working crazily hard and I still am. However, three things prompt me to post this now, all in a way connected with media.

The first and by far the most important is that my paper (with colleagues) on the measurement of the Boltzmann constant has been accepted for publication in Metrologia, the journal that concerns itself with precision measurement. Take a look at the pleasingly obscure contents this month. This is the culmination of 6 years work, and is the most accurate thermal measurement in human history. I will write more in the coming weeks, and when all the wrinkles have been ironed out I will post a  copy here.

The second is to point out (as the picture above shows) that there is a television series being broadcast about precision measurement! NPL played host to the team who filmed it and I spent many hours talking with the team about temperature. Let’s hope that something beautiful makes it to the screen: Radio Times have ‘featured’ the programme so that bodes well. I have been told I may actually feature on screen for few moments in the third episode on June 24th!

And the third is to mention that – slightly to my surprise – I have written a ‘feature’ that will appear in New Scientist magazine that will appear on June 22nd. It is about the journey towards the absolute zero of temperature  and – well — errr. That’s it.

You can keep track of progress towards the Royal Society Summer Science Exhibition by following this other blog!

Watching Earth Breathe

Daily carbon dioxide concentration measurements for the year to May 2013. Daily measurements are shown as black dots, weekly averages as red lines, and monthly averages as blue lines. On May 9th 2013, the daily value exceeded 400 ppm. Click for larger graph: Graphic is from NOAA Mauna Loa Observatory

On May 9th 2013, the observatory at Mauna Loa in Hawaii recorded a single daily reading of carbon dioxide concentration of 400.3 parts per million (ppm) – the highest value since human beings have existed as a distinct species.

This is a bit depressing for reasons we are all familiar with, but on the bright side, the annual average won’t exceed 400 ppm until 2015

I took the opportunity to look at the Mauna Loa data again – it is freely available – because I found the annual cycle rather curious. The graph at the head of the page shows the Earth ‘breathing’ – absorbing CO2 from May to October (Northern hemisphere summer) and then emitting it again from November to May.

The daily variations are interesting showing lots of systematic increases and decreases, presumably reflecting imperfect mixing of CO2 in the weather in the central Pacific ocean

You can see that the concentration from May 2012 to May 2013 has increased by around 3 ppm – that’s our carbon dioxide emissions – but I wondered if the annual cycle of  ’breathing’ had changed over the years. After a little bit of Excel jiggery -pokery I found to my relief and surprise that there was no evidence of this. I think this means that Earth is still ‘breathing’ OK.

The annual cycle of carbon dioxide measurements at Mauna Loa plotted with the trend subtracted against month of the year. The data is colour-coded and stupidly I have used the same colour for the 2010′s as the 1970s (Doh!). But even so it looks to me like this cycle is unchanged

However the rate at which we are emitting CO2 is increasing. No news here

The annual increase in annually averaged CO2 concentration. Back in the 1970s the annual increase about 1.5 ppm per year. Now it is more typically 2 ppm per year and above. The rate of acceleration is around 0.23 ppm per year per decade.

Getting ready for the Royal Society Summer Science Exhibition

Why did I buy six insanely-loud supporters horns today? That’s right – I am getting ready for the Royal Society Summer Science Exhibition

You may have noticed that the frequency of my postings has gone down lately. Sorry: I have just been too busy.

I find this distressing because writing this blog is my way of clarifying what I feel and think about the torrent of ‘science news’ that flows through our collective consciousness. The lack of time to distill my thoughts adds to my sense of permanent and irretrievable ‘backlog’.

Work is overwhelming at the moment and on top of the normal tasks, I am organising an exhibit at the Royal Society Summer Science Exhibition. In fact I am organising two exhibits.

Their common theme concerns the likely redefinition of the units of measurement for mass and temperature: the kilogram and the kelvin.

Getting the stands ‘right’ is challenging. My aim is to avoid prolonged ‘monologued’ explanations. Instead I am trying have demonstrations which can seed conversations – because taking part in a dialogue feels so much better than being either the source or the target of a monologue.

The challenge is to have demonstrations that are meaningful to Fellows of the Royal Society, normal people, and school children. The demonstrations need to be simple enough to understand, but in some way surprising or delightful.

At the moment I am feeling enthusiastic about all parts of the stand, and this weekend I went shopping for bits for the demonstrations. I bought four types of sand, a candle lantern, a steam generator, and six insanely-loud supporters horns: it will all makes sense in the end!

You can follow the build up to the exhibition by following:

• my ‘event blog’ at boltzmannplanck.tumblr.com 
• twitter stories with the hashtag @summerscience

And of course, do feel free to come along to the exhibition itself (1st July until the 7th July 2013). If you do come, please look me up and say “hello”.

Even though it is held at the Royal Society – possibly the poshest place in London – normal people are welcome. So if you are even in the slightest bit interested in science, you will find a building full of scientists who would love to talk with you about their work.

All in all – its a pretty amazing event.

Copy this!

A GIANT Jelly Baby Wave Machine at Protons for Breakfast together with some of its constructors!

At school we are told ‘not to copy’. But in real life, learning to copy from people who do things well is an essential skill. But it is important to give credit to the people from whom you copy!

For example, five or six years ago I took one look at the Jelly Baby Wave Machine  and fell in love. If you are prepared to register you can see a slightly longer demonstration here. At Protons for Breakfast we make a bigger version – about 12 metres long – and everyone loves it!

And then a few years ago I saw a beautifully simple demo of a motor – which I thought had been invented by Alom Shaha – and I immediately made a short film.

But in fact both these demonstrations were invented by Science Communication maestro, Jonathan Sanderson (This hub has links to all Jonathan’s web personas). 

Jonathan’s talents extend from classy cinematography and photography, to insightful story-telling, both of which are informed by a delight in science and human ingenuity.

Anyway, the other day I received a tweet – or a ping back – or a something – that indicated that Jonathan felt slightly peeved that his invention of these demonstrations had not been properly credited. Ooops.

Jonathan: If I have failed to give you full credit for your inventions – I apologise. And I hope this sets things out clearly. And Oh Yes, Thanks:-)

A piano from a plane

What happens if you throw a piano from a plane? Would it be dangerous?

I think we should ban people throwing pianos out of planes!

Exactly, what would happen if you threw a piano out of a plane? Are you sure it would be dangerous?

Well, you say it’s obvious, but let me ask you some questions and then let’s see if you are so sure.

• How long will it take to fall? Will it be 10 seconds? One minute? Two minutes? Oh! you need to know how high the plane was flying before you can tell me how long it will take to fall? What what range of times will it take? What if the plane is only just above the ground – would that be dangerous?
• Will it break apart as it falls? Pianos are not known for their aerodynamic efficiency. So could the wind actually tear it apart? Well yes, it might. It could easily loose a lid, and some internal parts.
• How dangerous would a falling piano be? Very dangerous? Well doesn’t that depend on where it fell? And in how many pieces. And the range of speeds of those pieces. And of course, there are many types of piano.

So based on this we conclude that you want a blanket ban, but you don’t know exactly how long it would take to fall – that would need further research. And low altitude falls -from  say 1 metre would probably not be dangerous. You don’t know how many pieces it would break into – that too would need research. And you don’t know exactly how fast each part would be travelling when it hit the ground. And you would need to know where the piano exited the plane in order assess the likelihood of damage.

So without further research you can’t be sure that de-planing of pianos would definitely be dangerous. And yet you want a complete ban?

Is a blanket ban appropriate? Yes! Because despite the detailed uncertainty, we all know that one way or another the piano will hit the ground and damage whatever it happens to hit.

And it’s the same with putting 35 billion of tonnes of  carbon dioxide in the atmosphere every year. Lots of the details are uncertain, and much of the argument against actually doing something exploits this uncertainty. But the end result is simple to calculate.

As surely as a piano thrown from a plane will hit the Earth, carbon dioxide emissions will warm it.

Just my cup of tea

Using two thermometers to estimate the temperature of my cup of tea. Which of them is right?

I was in my office this weekend trying to finish off some work for the European Space Agency. So naturally I made a cup of tea to help me concentrate. But before I could drink it, I obviously needed to measure its temperature. So I reached for the two thermometers I happened to have lying around in the office.

One was a Fluke 62Max+, a thermometer that works my detecting the infrared light emitted by all objects. In the picture you can see two red dots on the surface of my tea. Most of the infrared radiation the device measures comes from a circle on which those dots would be on opposite sides.

The other was a thermocouple thermometer, a device which works by measuring the small voltage produced between the ends of two pieces of metal wire joined together in the middle. If the midpoint of the wire is heated – the junction – then a tiny voltage appears across the ends of the wire. It is only 40 microvolts for every degree temperature difference – or  40 millivolts for a 1000 °C temperature difference.

As you can see the infra red thermometer read 57.5 °C and the thermocouple thermometer read 59.8 °C, a difference of 2.3 °C. The question then arises of which thermometer I should believe?

Now I know you don’t care, and neither did I. But in a small way this experiment summarised exactly the kind of question I face every day. There is a temperature that someone wants to know, and uncertainty about the answer is bugging them, or costing them money. And a difference this large could easily be significant.

Answering such questions requires a fair amount of experience, an understanding of typical errors encountered with each type of thermometer, and an appreciation of the physical processes that can affect the answer. A neurotically-anxious personality coupled with some basic physical and mathematical training helps too.

In this case, there is the cooling of the liquid by the metal thermocouple probe, the infrared emission properties of hot water, and the temperature gradients within the water. And then there is the calibration of each device against national measurement standards.

And as I reflected on all the levels of complexity required to get the ‘right answer’, I had a moment of personal insight. For all my anxiety about my work, and for all my being behind on almost every project I am working on, I am well-suited to my work. In fact, it is just my cup of tea.

Accuracy and Uncertainty

A target-based visual metaphor for accuracy and precision. Accuracy is about ‘arrows’ being centred on the target – the true answer. Precision is about arrows being close to each other. However in reality one never knows what the target is or whether one has hit it. One never gets to look up the ‘true answer’. This is where the concept of uncertainty helps.

The picture above presents a well-known visual metaphor for accuracy and precision. The idea is that firing an arrow at a target is like making a measurement. And  accuracy is a qualitative measure of how close a measurement is to the centre of the target – ‘the true answer’.

However in any real-world measurement, one can never know the “true answer”! If we did know the ‘true answer’, then there would have been no need to make the measurement!

In the real world, we fire our arrows i.e. we make our measurements – and that is it! We would like to know how far away our arrows fell from the target – but that is not possible! There is no way to compare them with the ‘true answer’.

So in the real world, what interests us is the answer to the question “How far from the target could our arrows have fallen?” or equivalently we need to ask “How wrong could we have been?”. We can work out an answer to this latter question without knowing the mystical ‘true value’.

Assessing the uncertainty of measurement is hard. It involves looking at all the factors that go into a measurement and asking how each factor could have affected the final estimate of the answer. We can then work out how wrong we could possibly have been.

However “how wrong we could possibly have been” is unlikely to be a useful number. To work out that answer we have to assume that ‘everything went wrong’ i.e. we have to assume that all the factors which affected the measurement were all – by chance – at the limit of what they could have been in a way that moved our estimate furthest away from the ‘true answer’.

What we really want to know is how wrong are we likely to have been?.

The answer to  “How wrong are we likely to have been?” is called the measurement uncertainty, and this is the most useful assessment of how far our estimate lies from the mystical and unknowable ‘true answer’.

A representation of what a measurement tells us. The shading represents the results of an analysis of the likely uncertainty of measurement i.e. how wrong our measurements are likely to have been?

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This is the 400^th post on this blog, which as I write has had around 140,000 ‘page impressions’, corresponding to around 200 visitors each day. If you are reading this then I would just like to say ‘Thank you’. Writing these articles helps me stay sane – and the thought that anyone reads them makes staying sane seem like a worthwhile activity.

See you at 500.

Kind regards

Michael

BAD THING WILL HAPPEN, say scientists

Annual Global Temperature anomalies compared with 1950 to 1980 base line. The data are colour coded with red indicating an El nino event. We can characterise these events, but we can’t predict them. Graph from Wikipedia

I worry a lot. It’s deep rooted, and I can’t help it. But there you have it, I worry.

And reading about  the things that climate change “is going to cause” worries me a great deal. Not because I am worried about the things in the themselves. Bad as they are, we will face them when they happen – as we have done with events throughout history. What worries me is the consequences of them not happening.

For example today the Guardian reports that

MILLIONS FACE STARVATION AS EARTH WARMS, say scientists .

And last week I read that

CLIMATE CHANGE WILL LEAD TO BUMPIER FLIGHTS, say scientists. 

Please understand, I don’t want either of these things to happen – I am against mass starvation. But these stories worry me for another reason.

• Firstly, they fit the general formula which media of all kinds love. They are a chance to use the headline BAD THING WILL HAPPEN, say scientists. The ‘say scientists’ tag absolves the reporting organ from editorial responsibility. And from their perspective, the bigger and badder the ‘bad thing’ the better.
• Secondly, they are both based on models of Earth’s climate. And impressive as these models are, Climate Models cannot yet predict some very basic features of our climate – such as the timing of an El Nino event. An El Nino event is a periodic oscillation linking ocean and atmospheric circulation across the Pacific Ocean, and affecting climate world-wide – see the graph at the head of the page – El Nino years are globally hotter. To the best of my knowledge, we simply do not know if Climate Change will cause more of these events, or less, or none, or something else. But whether an El Nino event happens or doesn’t happen will affect the details of almost any climate prediction.
• Thirdly both of these predictions are about the future. Human beings are spectacularly bad at predicting the future. And when a particular prediction doesn’t come true then the credibility of all predictions is affected.

So together these three features worry me. I am worried that people will just grow weary of hearing about bad its going to be. And this will cause them to take the fundamental issue less seriously. And if specific prediction X doesn’t happen this will only be reinforced.

The actual message is so much simpler. Putting carbon dioxide into the atmosphere will inevitably warm the Earth’s surface for really simple reasons.  And as a result, ice will melt, sea levels will rise, some places will get wetter and some will get drier. There is no doubt about any of these predictions. And none of super Climate Models actually predict anything very different.

What the models do is attempt to say how quickly things will change, which places will get wetter, and by how much. And these details are – in honesty – still uncertain. Like a weather forecast they will often be right – but also commonly wrong. And like a weather forecast, climate models are useful – but never certain.

These are worrying times.