SI at the RI

February 23, 2018


MdeP at the RI

On Monday 16th October 2017 I gave a talk at about the International System of Units (the SI) at the Royal Institution (the RI) in London.

It wasn’t a great talk, but it was at the RI. And I stood where Michael Faraday stood!

The RI have now processed the video and produced an edited version: enjoy ūüôā

The RI have tended to retain the video of me talking rather than showing the animated PowerPoint slides. If you would like the full multimedia experience, you can download the presentation using the link below.

On the day

I was nervous and arrived ridiculously early with a couple of glass Dewars containing triple point of water cells.

I waited outside the lecture theatre for Martin Davies from the RI to arrive.

When he arrived, he noticed the Dewars and without hesitation he turned to the wall and pointed out the painting above where I was standing, and said:

“What a coincidence: your standing by a picture of Sir James Dewar lecturing in this theatre!”

Henry Dewar at the RI

It’s hard to convey the historical significance¬†of Royal Institution without sounding trite. So I won’t try.

But it is a special place for chemists and physicists alike, and I feel honoured to have even had the chance to stand on that spot.


Thanks to Chris Brookes and Martin Davies for a memorable day.

Why is it so hard to lose weight?

February 21, 2018

After several years of looking, I think I have finally found the answer.

So if people follow a calorie-controlled diet based on government guidelines, almost everyone will put on weight.

Let me explain…

Mifflin St Jeor

The minimal basal metabolic requirements (BMR) of a human being have been the subject of scientific study for more than a century.

The best estimate of our requirements are the Mifflin St Jeor (MSJ) Equations which state that the calorific requirements for men and women are given by:

Men:     BMR = 10 × [Weight in kg] + 6.25 × [Height in cm] Р5 × [Age in years] Р5

Women:     BMR = 10 × [Weight in kg] + 6.25 × [Height in cm] Р5 × [Age in years] Р161

This is the amount of food (expressed as kiloCalories (kCal) per day) required to maintain a given weight and do nothing else: no exercise at all.

A sedentary male lifestyle

The MSJ equations are generally multiplied by a factor to reflect the amount of physical activity one undertakes during the day. And there is considerable uncertainty about which factor applies to any particular individual!

The factor 1.2 is commonly chosen to represent a “sedentary lifestyle”. In a moment I’ll come back to whether this factor is justified or not.

But based on this factor, the blue line on the graph below shows how the actual calorific requirements of a man of my weight and height vary with age. The equivalent graph for women is shown in the next section.

Calories versus Age

The most striking thing about this graph is that the actual amount of calories I need to maintain my weight (1860 kCal/day) is 25% less than the government recommend (2500 kCal/day).

The difference is not a rounding error – it amounts to 640 kCal/day which is a reasonably-sized meal!

A man of my age living a sedentary lifestyle and following government guidelines would put on weight at a rate of several kilograms per year.

The second striking feature of the graph is reduction in calorific requirements with age. The slope of the graphs is 50 kCal/day per decade.

This means that if I was maintaining my weight in my forties, then unless I changed either my eating habits or my exercise habits, I would slowly begin to put on weight.

Eating 50 kCal/day too much amounts to putting on weight at around 2 kg per year.

Is the sedentary lifestyle factor 1.2 appropriate?

One way to assess whether the factor 1.2 applied to the MSJ equations is appropriate is to consider the calorific equivalent of some exercise.

For a man of my weight and height, running 1 kilometre uses up about 74 kCal.

So if I were to run 25 km per week, then this would allow me to eat about another 260 kCal/day and still maintain my weight. This is shown as the red line on the graph above.

Most people would consider running 25 km per week to be quite serious exercise. Comparing this amount of exercise to the work done in a sedentary day makes me think that the factor 1.2 is probably about right.


The equivalent graph for women is shown below

Calories versus Age Women

It shows a similar disparity between government recommendations and actual metabolic requirements, but not quite as dramatically wrong as for men.

Government Guidelines

The reason I searched out the MSJ equations was because I know from experience that if I eat anything close to 2500 kCal per day I put on weight.

Calorific intake is notoriously difficult to estimate with an uncertainty better than about 10%,  but the MSJ figure of about 1860 kCal/day for a man of my age weight and height seems about right.

The UK Government guidelines are – frankly – nonsense, and given that the UK has something of a problem with obesity – not least with people of my age – it would seem a sensible first step to just get this simple factual message about right.

One important step would be to emphasise the reducing calorie requirements with age.

Government guides in the US such as this one are closer to reality, but if you want real information I recommend this helpful calculator.


February 18, 2018


After writing about ‘singing glasses’ previously, I was discussing the effect with my friend and colleague Andrew Hanson.

Have you done the mug thing?” he asked. And proceeded to hit the rim of a mug with a spoon.

As he moved the location at which he struck the mug, the pitch of the note changed.

And then he explained. Looking from the top, if the handle of the mug is at 12 O’clock, then:

  • Striking the mug at 3, 6, 9, or 12 produces one note – a lower note.
  • Striking¬†the mug between 1 & 2, between 4 & 5, between 7 & 8 and between 10 & 11 produced a second note – a higher note.

Mug Vibrations 01

Andrew said the explanation was that in a mug, there are two types of flexural oscillations, and the frequency of the oscillations depends on whether the handle moves or not.

I was fascinated. How had I never noticed that before? And why was the note that sounded when the mug was struck ‘on the quarter hours’ lower?

This is a very long article, and I apologise. But the physics of this phenomenon is complex and it took me a long time to get to the bottom of it.


I picked 5 mugs from our domestic collection which were as straight-sided as possible, and which had walls which were as thin as possible. I thought these choices would make the vibrational spectrum simple.

First I measured the mugs: their diameter and the wall thickness, and then I picked a wooden striker and started hitting the mugs. (Speadsheet)

The place where one strikes the mug produces an oscillation with the striking location as a local maximum of the oscillation.

For a glass, it wouldn’t matter where one struck¬†– any location on the rim is equivalent to any other. But for mugs, the striking position matters because of the handle.

Mug Vibrations 02

To see if I could understand what was going on I arranged the mugs in size order, from the smallest radius to the largest and struck each one three times at each location.

You can hear the sound here.

I also recorded the ‘spectrogram’ using the wonderful Spectrum View app for the iPhone. A screenshot from the app is shown below together with the mugs which made the noise.Mug Vibrations 03.png

A spectrogram shows:

  • time along the horizontal axis
  • frequency along the vertical axis
  • and the loudness of a sound at a particular frequency and time is shown by the colour: blue is quiet and yellow and red are loud.

On the spectrogram above one can see vertical lines which result from the ‘impulse’ sound of me hitting the mugs. This dies away quickly and one is just left with the ‘ringing’ of the mugs which I have¬†outlined with dotted lines.

One can see that each mug rings at two closely-spaced frequencies. The two notes differ in frequency by between 5% and 15%.

Hitting the rim at either location produces mainly one mode of oscillation, but also a little of the other.

Let’s get numerical!

I used the app to locate the frequency of each note and plotted it on a graph of the frequency versus the mug diameter. I plotted each ringing note as a red dot, and their average as a black dot.


There was a general trend to lower frequency for the larger mugs, but the Toronto mug didn’t fit that trend.

I noticed that the walls of the Toronto mug were much thicker than the other mugs. So I wondered whether I could compensate for this by dividing the frequency by the thickness of the wall.

I did this based on the idea that the speed of the wave would be proportional to the¬† rigidity of the mug wall against bending. And that rigidity might be roughly proportional to the wall thickness. This seemed to be confirmed because the¬†formerly ‘anomalous’ mug frequency now sat quite sweetly on a smooth trend.

Mug Vibrations 05

Now that the data seemed to fit a trend, I felt I was getting a handle on this problem. Could I understand the dependence of the resonance frequency on diameter?


All waves obey the wave formula¬†v = f őĽ. That¬†is, the speed of the wave, v, is the product of the frequency of the wave, f, and its wavelength¬† őĽ.

For the waves on these mugs, the¬†wavelength of the wave which runs around the rim of the cup is just half the perimeter i.e.¬† őĽ =¬†ŌÄ D/ 2 where¬†D is the diameter of the mug.

  • So if all the waves travel with the same speed, then the resonance frequency should vary with diameter as f = 2 v /¬†(ŌÄ D) i.e. inversely proportional to the diameter.
  • However, for flexural waves, the material supporting the wave becomes floppier at longer wavelengths, and the speed of a flexural wave should fall with increasing wavelength. If this were the case we would expect the resonance frequency to vary inversely as the diameter squared.

Which of the above cases described the data best? I have plotted the two predictions on the graph below.

Mug Vibrations 06

I adjusted the speeds of the waves to match the data for large mugs and then calculated how it should vary for smaller diameter mugs.

Overall I think it is the theory in which the  speed of the flexural wave changes with wavelength that matches the data best.


So now I had a theory that the speed of a flexural wave that runs around the rim of a mug is:

  • Proportional to the wall thickness
  • Inversely proportional to the diameter
    • So the resonance frequencies are inversely proportional to the diameter squared.

After I had finished all these measurements I came across another mug that I could have included in the study – my wife’s ‘Do more of what makes you happy‘ mug.

I decided to see if I could predict its resonant frequency from measurements of its wall thickness and diameter.

I have plotted data on this mug as crosses (√ó) on the graphs above and I think that overall it fits the trends rather well.

The two notes

If you belong to the minority who have read this far, then well done. It is only you who get to understand the final point about why the ‘quarter hour’ notes are lower.

What is the role of the handle? There are two possibilities.

  • Does it act as an extra mass which slows down the wave?
  • Or does it provide extra stiffness, which would speed up the wave?

Since the quarter hour notes are lower, it seems that it is the extra mass which appears to dominate in the mugs I have examined.


Wonder and Science

January 31, 2018

Recipes for Wonder

My good friend Alom Shaha has a new book out!

And discussing it over dinner the other evening I was struck by an analogy.

Talking and listening and reading and writing 

Children have no problem learning to understand and speak their mother tongue.

All they require is to be exposed to people speaking and they will learn to speak

But this ability does not make them ‘good at languages’.

In contrast with the ease with which children learn to speak, is the great difficulty they have in learning to read and write.

A web search tells me that 15% of the UK population are ‘functionally illiterate’ – a figure which I think has not changed much in recent years.

Reading and writing are hard: they take practice:

  • learning letter shapes.
  • learning the relationship between shapes and sounds.

And it can be a long time before all this becomes automatic and there is a payback on the effort expended.

Nonetheless, widespread literacy is considered essential for a functioning democracy.

And most people who have been taught to read and write are happy with the extra possibilities their new skills enable.

Wonder and Science

Similarly, I think children have an intrinsic sense of wonder.

Or at least they can acquire the sense with ease if they are exposed to adults who express interest in the world around them.

But going beyond the simple pleasure of “Wow!” is hard work.

However, it is that step – from ‘Wow!” to “How?” that is the step from wonder into science.

Why is it hard?

Firstly, imagine how well parents would teach their children to read and write if they were themselves illiterate.

Similarly, scientifically illiterate parents – or more commonly parents lacking confidence in their own abilities – can find teaching science hard.

And secondly, everything is complicated. So it is easy to spread confusion rather than enlightenment.

Consider a ‘simple’ experiment¬†– the kind of activity that people recommend for kids – such as making a wine glass ‘sing’.

Just managing to make this happen is pleasurable – it is intriguing and surprising to hear. It is, literally, wonder-ful.

But when one begins to ‘step beyond’ wonder, it all becomes difficult. I have just spent a happy thirty minutes with my wife investigating. And even with two PhDs, an iPhone equipped with a slow motion camera, and spectrogram software¬†we found it difficult!

For example:

  • Is it the glass or the air in the glass which is vibrating?
  • Why can one see very fine waves running on the surface of water in the glass?

If you search for clues as to what is happening you will find a dearth of answers on the web.

Alom’s book?

As I understand it,¬† Alom’s aim in writing his ‘recipes for wonder’ is to hold hands with parents and children so that their first steps beyond wonder into science are beguiling and delightful rather than bewildering and demoralising.

Such a book is sorely needed. I hope it does well.

By the way, if you would like to hear Alom talk, he will be appearing at the Royal Institution on March 8th .

P.S. What is happening with the ‘singing’ glass?

I am afraid, the physics is too complicated to explain in full, so here is a summary.

Firstly, the fundamental mode of vibration being excited is a ‘flexural’ oscillation of the glass rim and bowl.


Normally if one calculated the resonant frequency of a sound wave in a glass object of similar dimensions to a wine glass, one might expect a resonance at a very high frequency – perhaps 10 kHz or higher.

This is because the speed of sound in glass is over 4000 metres per second‚ more than 10 times higher than the speed of sound in air.

However, when a material is formed into a ring, it¬†has a ‘soft’ mode of flexing illustrated in the animation above. (The bowl of the glass is not quite a ring, but the upper part of the bowl is ‘almost’ a ring.)

Even if the speed of sound in the material is very high, as the material of the ring becomes thinner, then it becomes easier to flex, and the restoring force pulling the ring back into shape becomes weaker.

This causes the speed a flexural wave in a glass ring to be much lower than the speed of a sound wave in glass. Thus the resonant frequency falls as well.

Once the vibration is established, it vibrates the air around the glass which is what we hear.

But note that this is not a resonance of the air in the glass. If it were, then adding water to the glass would reduce the size of the resonant cavity and cause an increase in the resonant frequency. In fact adding water lowers the resonant frequency.

A spectrogram showing how the frequency of a singing glass is lowered by adding water. Note, the application was paused at 3.8 seconds and then re-started with water in the glass.

A spectrogram showing how the frequency of a singing glass is lowered by adding water. Note, the application was paused at 3.8 seconds and then re-started with water in the glass.

Note also that the gravity capillary waves that can be observed on the surface of the water are also a red herring.


These waves have a very low speed Рabout 30 centimetres a second, and so at few hundred hertz, they have a wavelength of much less than 1 millimetre.

Finally, there is also a connection between the noise made by a glass and that made by a xylophone. Xylophone

The vibrations excited by hitting the xylophone keys are not sound waves in the metal but flexural waves.

The speed of flexural waves falls in long thin (floppy) bars –¬†getting less and less for longer bars. So¬†for¬†thin materials, the flexural wave can have a low speed leading to a low resonance frequency.

The fact that a xylophone uses flexural waves explains the relative sizes of the keys.

To make a key for a note one octave lower (i.e. half the frequency) of the top key, one does not have to double the length of the key. In fact one only needs to lengthen the bar by a factor of the square root of two (i.e. make about 41% longer).

Like I said: everything is complicated!





Gravity: one more thing

January 28, 2018

I am a great admirer of James Clerk Maxwell.

And amongst his greatest achievements was the prediction that waves in electric and magnetic fields should travel at the speed of light.

He arrived at his prediction by considering the observed strength of static electric magnetic fields.

  • For example, studies had established the strength of the force from a given amount of electric charge at a given distance.
  • This electrical force was characterised by a constant called (for historical reasons) the permittivity of free space. It was given the symbol¬†őĶ0 – the greek letter ‘epsilon’ with a subscript of zero. It was considered to represent in some way how ‘disturbed’ the space was around an electric charge.
  • Similarly, studies had established the strength of the magnetic force from a given electric current at a given distance.
  • This magnetic force was characterised by a constant called (for historical reasons) the permeability of free space. It was given the symbol őľ0 – the greek letter ‘mu’ with a subscript of zero. It was considered to represent in some way how ‘disturbed’ the space was around an electric current.

Maxwell analysed these static experiments and predicted that there should be coupled waves in the electric and magnetic fields and that they would travel with a speed of:


And when Maxwell calculated this number he arrived at a number very close to the previously measured speed of light.

He observed that this was unlikely to be a coincidence and concluded that light was a wave in the electromagnetic field.

I can still remember how I felt when – aged 19 – I followed Maxwell’s footsteps and ‘discovered’ this connection: I was gob-struck!

Other waves

This type of formula is typical of expressions for the speed of waves. For example, the speed of a wave on a stretched wire or string is given by:


where T is the tension in the string and m is the mass per unit length of the string.  So a wave will travel quickly when the string is taut and low mass.

And in general we expect the speed of waves to reflect how the medium in which the waves travel responds to a disturbance.

Gravity waves

And that is why last years’ announcement¬†(LIGO, Popular Report) that gravity waves travel at the speed of light is so profoundly important.

This discovery implies that there is a connection between:

  • electricity and magnetism – responsible for just about all the phenomena we experience around us – and…
  • gravity – which is associated with space and time and mass.

Alternatively, it could indicate a connection between them both and something else we don’t know about.

But the experimental fact of this connection astounds me as much if not more than the connection that Maxwell made.

And it makes me wonder just what he would have to say about the discovery.

Now I know this connection is not ‘new’:¬†I can remember being told that gravity waves would travel at the speed of light many years ago.

But the discovery of the experimental fact of the speeds of light and gravity being equal seems to me to be more profound than the mere expectation that it should be so.

You can see more about the discovery in the LIGO video below


Perspectives on Gravity

January 9, 2018

Gravity is such a familiar force that its utterly mysterious nature can sometimes go unnoticed.

Looking at the picture of Earth and Moon bound together in the solitude of the Universe, it is strange to think that all that holds them together is this apparently weak force.

In this article I will do a couple of calculations using Newton’s law of Universal Gravitation. If you know the maths, please check my calculations, and if you don’t, please trust me.

Not so weak

Many people are familiar with the fact that the average gravitational field strength at the surface of the Earth is approximately 9.8 newtons of force for every kilogram of mass. This is sometimes called one ‘g‘.

(This is sometime expressed as 9.8 metres per second per second, but I don’t think that formulation is as clear in¬†this context.)

But what is the gravitational field strength due to the Earth at the Moon? A simple calculation shows it to be just 0.0027 newtons per kilogram Рabout 0.02% of g.

And yet this weak field is sufficient to bind the Moon to the Earth with a force of 2 √ó 1020 newtons.

If gravity disappeared (!) and we applied that force to the Moon with a tensile steel cable, it would need to be 1000 km in diameter and would require about half the mass of the Earth to manufacture!

So weak

Many people are familiar with the fact that the tides on Earth are affected by the Moon.

We can work out the gravitational field strength on the side of the Earth nearest the Moon – where the Moon’s gravity opposes the Earth’s gravity: 9.8134727 newtons per kilogram.

Compare this with the gravitational field strength on the side of the Earth farthest from the Moon – where the Moon’s gravity acts with the Earth’s gravity: 9.8134749 newtons per kilogram.

The gravitational field strengths differ by just 0.2 parts in a million. And yet this difference is sufficient to affect the tides!

So very weak

Many people are familiar with the fact that the Earth is bound to the Sun by gravity. And that the Sun is bound to the Centre of the Milky Way Galaxy by gravity.

We can work out the gravitational field strength at the Earth due to the Sun. It is just 0.0059 newtons per kilogram or about 0.06% of g.

And the gravitational field strength at the Sun due to the Galaxy is a breathtakingly small¬†0.000000002135¬†newtons per kilogram or just¬†0.2 parts per billion of the gravitational field strength at the Earth’s surface.

And the lesson is?

There is no lesson here – it is just surprising to me how weak gravitational fields – billions of times weaker than the fields we are familiar with on Earth – can bind stars into galaxies. That’s all.

Good night.


January 8, 2018

Image courtesy fo NASA

The image above shows the Earth on the left and the Moon on the right.

It was acquired by a spacecraftOsiris Rex – a couple of months ago, 10 days after it had just been ‘slingshot’ into an orbit where it will eventually meet up with an asteroid.

The mission is fascinating: it will rendezvous with an asteroid, take a sample from it – and in September 2023, return it to Earth for analysis.

But for me, this picture is worth the project in itself. I find it haunting and surprising.

Most significant is the tiny fraction of the image taken up by the Earth and the Moon. I find it chilling to see this against the blackness of space.

Next is the sense of perspective. The figure below shows where the spacecraft was when it took the image.

Image courtesy of NASA

From my perspective on Earth, the Moon looms large, and its true distance is unimaginable.

In the image the Moon seems less significant than I would have expected, and yet it still drives our tides.


If I place in one hand my anxiety about work, an anxiety which poisons so much of my life.

And in my other hand I place this image of my home in the cosmos.

Then I feel sure that if I could just gain the right perspective, and balance these two realities, then my anxiety would seem smaller and less significant.

And if I could manage that, then the view from a spacecraft deep in space would have meaningfully changed life back here on Earth. Mmmmm.



My Weight: Good News or Bad News?

January 5, 2018

I spent most of 2017 feeling bad about my weight.

But as I review the data now I realise I can say positive things about my weight which – if I could believe my own words – would leaving me feeling good about my weight.

Alternatively, I could say negative things which would leave me feeling bad about my weight.

In either case the data would be the same. So which view should I take?

The data

The graph below shows my weight determined first thing in the morning for almost every day throughout the last two years.

Weight 2016-2017

2016 was a good year. I lost about 14 kg and felt enormously better. And in 2017 I initially managed to lose another couple of kilos,

Weight 2017

But then, as work became a nightmare, my weight drifted back up at just 10 g per day – a weight gain equivalent to a biscuit or a glass of wine per day.

By the end of the year I managed to catch my breath enough to slowly lose some weight. And that is pretty much where I am at now.

Postive or Negative?

So how should I feel about this data? What story should I tell myself?

Should I say:

“Well done! You managed to keep control of your weight through a difficult year. And your weight is only 1 kg more than it was at the start of 2017. And still 13 kg lower than it was at the start of 2016”?

Or should I say:

“What a mess! You put on 3 kg through the year!

In either case, the data are the same.¬†So actually I think I will just keep the graphs and refrain from telling myself any story at all. Indeed, the real¬†storyline won’t become clear until¬†I find out what happens next.

I will keep you informed.

2018: Here we come!

January 4, 2018

Top Cat Guide to Life

2017 was a difficult year for me, by far the worst of my 17 years at NPL.

But after a break in which I have managed to breathe, become 58 years old, spend time with my family, and read some books, I have resolved to try to focus on the positive.

At first I thought I would follow advice from the ¬†‘indisputable leader of the gang’, Mr. Top Cat, from New York City, who has published his ‘Guide to Life‘.

But in fact after reading¬†Mr. Cat’s advice,¬†I can inform you that it is not so much feline, as asinine.

However, his positivity and self-assuredness are enviable, if somewhat (respectively) mysterious and misplaced.

My plan is to reflect on the positive – of which there is plenty – while not ignoring the negative. It’s a tough balance, but nobody said life would be easy.

In any case, if you are reading this, I wish you all the best for the remaining 98.9% of 2018.


Candles at Christmas Revisited

December 21, 2017

Last week I gave a presentation at NPL on the physics of candles.

Above is a video of the slightly chaotic 32 minute presentation and if you are so inclined, you can download the PowerPoint file here.

I have spoken before about the wonderful physics of candles. But in revisiting the subject I learned that wax is basically not flammable and I felt obliged to mention this inconvenient truth!

The highlight of the talk is using a candle to power a thermo-electric generator, which in turn powers a USB port, which in turn powers a torch, which is brighter than the candle.


Sadly, in the rush at the end of the talk I forgot to actually measure the brightness of the torch!

Next time!

And by the way, here is the slow-motion candle-relighting movie that is embedded in the PowerPoint but which doesn’t show up well in the lecture theatre view.

Thanks to Brian Madzima for the videography and editing, and Nikita Mezhnyakov for the photograph.

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