Archive for January, 2018

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.

Wineglass

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.

IMG_6825

These waves have a very low speed – about 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 ε0 – 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 μ0 – 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:

image002

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:

image002

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 – about 0.02% of g.

And yet this weak field is sufficient to bind the Moon to the Earth with a force of 2 × 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.

Perspective

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.

So…

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.

 


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