Archive for Newton

The Shadow of Newton

Posted in History, The Universe and Stuff with tags , , , , , , , on November 7, 2013 by telescoper

Yesterday I overheard some Electrodynamics students talking about the fact that all the famous names attached to pioneering laws or theorems in that subject seem to be either French (Biot-Savart, Laplace, Poisson..) or German (Gauss, Helmholtz…). Why are there no British names in this list?

Well, there was Faraday, of course. But Michael Faraday was primarily an experimentalist rather than a theorist, which sets him apart from the others already mentioned. So why is it that British theoretical was behind continental Europe in the early part of the 19th Century when all this important work on electricity and magnetism was being done.

There was also Maxwell, but he came along a bit later; he published his theory of electromagnetism in 1861/2. So why were the British so slow to enter this field?

Well, my theory of this is that it’s all the fault of Isaac Newton. I came to this conclusion when reading about the work of British mathematician and physicist George Green, who lived from 1793 until 1841, and who left a substantial legacy for modern theoretical physicists, in Green’s theorems and Green’s functions. George Green is also credited as being the first person to use the word “potential” in electrostatics. Green was the son of a Nottingham miller who, amazingly, taught himself mathematics and did most of his best work, especially his remarkable Essay on the Application of mathematical Analysis to the theories of Electricity and Magnetism (1828) before starting his studies as an undergraduate at the University of Cambridge (which he did at the age of 30, after his father died, and he leased out the mill he consequently inherited, to pay for his studies).

Extremely unusually for British mathematicians of his time, Green taught himself from books that were published in France. This gave him a huge advantage over his national contemporaries in that he learned the form of differential calculus that originated with Leibniz, which was far more elegant than that devised by Isaac Newton (which was called the method of fluxions).

Great scientist though he was, Newton’s influence on the development of physics in Britain was not entirely positive. Newton was held in such awe, especially in Cambridge, that his inferior mathematical approach was deemed to be the “right” way to do calculus and generations of scholars were forced to use it. This held back British science until the use of fluxions was phased out. Green himself was forced to learn fluxions when he went as an undergraduate to Cambridge despite having already learned the better method.

Unfortunately, Green’s great pre-Cambridge work on mathematical physics didn’t reach wide circulation in the United Kingdom until after his death. William Thomson, later Lord Kelvin, found a copy of Green’s Essay in 1845 and promoted it widely as a work of fundamental importance. This contributed to the eventual emergence of British theoretical physics from the shadow cast by Isaac Newton which reached one of its heights just a few years later with the publication a fully unified theory of electricity and magnetism by James Clerk Maxwell.

Hawking at 70

Posted in Books, Talks and Reviews, The Universe and Stuff with tags , , , , on January 8, 2012 by telescoper

Today is the 70th Birthday of renowned British theoretical physicist Stephen Hawking. His  immense contributions to physics, including but not restricted to cosmology, are remarkable in their own right, but  made even more emarkable that has done so much after having been stricken by such a debilitating disease when he was only in his twenties. Hawking’s is undoubtedly a brilliant and inspirational mind, but his courage and physical endurance in the face of difficulties that  others might have found unbearable provide inspiration far behond physics. I’d therefore like to add a genuine Many Happy Returns to Professor Stephen Hawking, and I hope he’s enjoying the celebratory conference and other events that have been laid on to mark this special occasion.

I have in the past gone on record, both on television and in print, as being not entirely positive about the “cult” that surrounds Stephen Hawking. I think a number of my colleagues find things I have said disrespectful and/or churlish. I do, however, stand by everything I’ve said. I do have enormous respect for Hawking the physicist, as well as deep admiration for his tenacity and fortitude, and have never said otherwise. I don’t, however, agree that Hawking is in the same category of revolutionary thinkers as Newton or Einstein, which is how he is often portrayed.

In fact  a poll of 100 theoretical physicists in 1999 came to exactly the same conclusion. The top ten in that list were:

  1.  Albert Einstein
  2. Isaac Newton
  3. James Clerk Maxwell
  4. Niels Bohr
  5. Werner Heisenberg
  6. Galileo Galilei
  7. Richard Feynman
  8. Paul Dirac
  9. Erwin Schrödinger
  10. Ernest Rutherford

The idea of a league table like this is of course a bit silly, but it does at least give some insight into the way physicists regard prominent figures in their subject. Hawking came way down the list, in fact, in 300th (equal) place. I don’t think it is disrespectful to Hawking to point this out. I’m not saying he isn’t a brilliant physicist. I’m just saying that there are a great many other brilliant physicists that no one outside physics has ever heard of.

It is interesting to speculate what would have happened if the list had been restricted to living physicists. I’d guess Hawking would be in the top ten, but I’m not at all sure where…

And before I get accused of jealousy about Stephen Hawking’s fame, let me make it absolutely clear that if Hawking is like a top Premiership footballer (which I think is an appropriate analogy), then I am definitely like someone kicking a ball around for a pub team on a Sunday morning (with a hangover). This gulf does not make me envious; it just makes me admire his ability all the more, just as trying to play football makes one realise exactly how good the top players really are.

Anyway, I had better wind this up because that sporting metaphor has just reminded me that there are some FA Cup ties on the TV this afternoon. I’ll therefore switch to a slightly different kind of hawking, i.e. trying to peddle a few copies of my book  Hawking and the Mind of God, which was published in 2000. Excuse the blatant self-promotion, but these are hard times!

Here is the jacket blurb:

Stephen Hawking has achieved a unique position in contemporary culture, combining eminence in the rarefied world of theoretical physics with the popular fame usually reserved for film stars and rock musicians. Yet Hawking’s technical work is so challenging, both in its conceptual scope and in its mathematical detail, that proper understanding of its significance lies beyond the grasp of all but a few specialists. How, then, did Hawking-the-scientist become Hawking-the-icon? Hawking’s theories often take him into the intellectual territory that has traditionally been the province of religion rather than science. He acknowledges this explicitly in the closing sentence of his bestseller, “A Brief History of Time”, where he says that his ultimate aim is the “know the Mind of God”. “Hawking and the Mind of God” examines the pseudo-religious connotations of some of the key themes in Hawking’s work, and how these shed light not only on the Hawking cult itself, but also on the wider issue of how scientists represent themselves in the media.

And you can take a peek at the inside here:

(Guest Post) What is Colour?

Posted in Art, The Universe and Stuff with tags , , , , , on February 7, 2010 by telescoper

As often happens on this blog, the comments following an item a few days ago went off in unexpected directions, one of which related to optics and vision. This led to my old friend, and regular commenter on this blog, Anthony Garrett (“Anton”), sending me an essay on the subject of colour perception and some very fine examples of abstract art. There thus appeared a perfect opportunity for another Guest Post, so for the rest of this item I’m handing over to Anton…

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Some years ago I was privileged to get to know, toward the end of her life, a retired teacher from Durham called Olive Chedburn. She made wonderful greeting cards which she sent to her friends, using a technique known as encaustic art. This employs heated beeswax with coloured pigment added, and a hot iron; you can read more about it at Wikipedia.

Here are the three pieces that she sent to me:

Although I am in general not a fan of abstract art, I think these are lovely. One friend said that they resembled underwater coral scenes. To me they look more like the inside of caves or chasms, perhaps with a waterfall. One of their beauties is that they definitely look like something – but you can never quite catch what.

Olive wrote a meditation on light and colour, in nature and in the Christian Bible, which I enjoyed reading very much. The main thing she left out was the science of light and colour, of which she had no knowledge. I wrote and sent her a complementary essay about this. Peter clearly likes her art and my essay, because he kindly offered to reproduce both on his blog, as you see. Olive died two years ago and her art now stands as her memorial. I hope you enjoy it as much as I did.

My essay now follows; if you want to look into the subject in greater depth then I recommend this website, which was designed to inform artists.

Colour perception is often said to be subjective. It is less clear what that means, however. The relevant scientific notion is wavelength. Light is a wave – although, remarkably, no physical medium oscillates (unlike sound waves in air, for instance); in the language of a century ago there is no ‘aether’.

Strictly speaking it would be better to talk about the frequency of light waves, because the wavelength changes with the density of the medium through which the light passes, but the frequency is unchanged. (The product of the wavelength and the frequency is the speed of light, which is a staggering 300,000 kilometers per second in empty space.) But the change in wavelength of light passing from a vacuum into air is so small that it can be ignored for present purposes. The change in wavelength (and in wave speed) is much greater when light passes into glass, or into the transparent fluids inside the eye, is much greater (25% reduction in water), since these media are much denser than air.

Light that consists of a single wavelength is called monochromatic light. Monochromatic light is not divided (further) by a prism, or by anything else that is done to it – a fact discovered by Isaac Newton in the 17th century. (Newton also reassembled the various colours back into white light.) One may superimpose differing amounts (intensities) of light of various wavelengths and look at the result. ‘White light’ is a superposition having roughly the same intensity in each colour band, as we confirm by putting it through a prism. (A prism splits light, because differing wavelengths of light entering the prism are shortened by differing amounts. The same effect creates rainbows as light passes through water droplets in the atmosphere.) In analysing colour, physics deals only the notion of how much light of each wavelength reaches the eye – the ‘spectrum’ (formally, the spectral density function) of the light. The distribution of the light across the retina – the screen at the back of the eye – also counts; a single object may appear to be coloured somewhat differently when viewed against differing backgrounds. Light has further characteristics (such as coherence, which is significant in lasers), but they make no difference to the perception of colour. A property of light known as its polarisation may change upon reflection from – or transmission through – a medium, but polarisation of light is not itself detected by the eye. (This raises the question: Are we interested in the object we are looking upon, or the light entering our eye?)

Wavelength is precisely defined, but colours – such as ‘blue’ – relate to a (fairly narrow) band of wavelengths, such that any monochromatic beam within that band will be perceived as blue. Moreover, if I add a low intensity of white light into blue, the result will still be perceived as blue. And if, in a spectrum that is generally agreed to be white, I make a small change in the amount of one particular wavelength, the result will still generally be agreed to be white. Only black is unambiguous: it is the absence of any light, of any wavelength. (Even then, it is the perceived absence, for light that is below the sensitivity threshold of the eye does not count; we shall consider perception below.)

We perceive some objects because they emit light into our eyes, such as a LED (light-emitting diode). Light of a particular frequency/wavelength/colour is emitted is when a (negatively charged) electron within an atom falls from one orbit around the positively charged atomic nucleus to another orbit around it; quantum theory tells us that only certain orbits are possible. (The difference in energy between the two orbits goes into the light that is emitted when the electron shifts orbit, and is proportional to the frequency of the light.) We see non-emitting objects because they reflect some of the light that falls on them, into our eyes. The colour that we say such an object is depends on the light that passes from the object to our eyes. This depends in turn on two factors: the combination of wavelengths falling on it; and how much of each particular wavelength the object reflects. (All light that is not reflected is absorbed, warming the object in the same way as sunbathing.) Intrinsic to the object is not its ‘colour’ but the proportion of each wavelength hitting it that it reflects. ‘Red paint’ means paint containing pigment that reflects only red light and absorbs all other colours (likewise for blue paint, etc); so that if ‘red paint’ is illuminated by a uniform mixture of light colours (i.e., white light) then only the red bounces back off it, and it looks red. But if the same object is illuminated by blue light, it absorbs the blue light so that (virtually) nothing comes off by way of reflection, and the object is perceived as black. We say that objects ‘are’ a particular colour because we generally view them in daylight or artificial white light, which contains all colours. ‘White paint’ is paint that reflects all colours and absorbs none. It looks whatever colour is shone at it – red in red light, blue in blue light, white in white light, and so on. Black paint absorbs all colours, and (uniquely) looks the same in any light.

A ‘red filter’ is something designed to let only red wavelengths through (and similarly for other filters). Something that lets all wavelengths through – the analogue of ‘white paint’ – is called transparent. (Air is virtually transparent, although it lets slightly more blue light through than other wavelengths – that is why the sky, which is lit by the many wavelengths emitted by the sun, looks blue.) Something that lets no light through – the analogue of black paint – is called a barrier. On its far side from the light source it looks black.

Also important is the texture of a surface. A perfectly reflecting material is colloquially called a white surface if it is rough enough to disperse incoming light in all directions, but if it is smooth on the scale of the incoming wavelengths then it is called a mirror. Texture is also responsible for the difference between matt and gloss paint. As for the scales involved, wavelengths of light visible to humans vary from red, which is around wavelength 0.7 micrometers (a micrometer is one thousandth of a millimetre) to blue/violet, which is about half that wavelength. In contrast, radio waves, which are of the same family and speed as light, have wavelengths of hundreds of metres.

Biological science can translate the physical specification of what lands on the retina into a specific pattern of nerve impulses passing from the eye to the visual cortex. That can in turn be correlated with the person saying “it’s green” or “it’s red” (or whatever). The names of colours are learned by tradition. As a child, each of us shared with an adult the experience of perceiving light of a particular wavelength; the adult named the colour and we learned the name. If children were not taught the names of colours then a consensus would emerge among them of what to call the colours, based on the similarity of their experiences. This consensus arises in turn from the common features of their perceptive systems (eye plus visual cortex).

Every colour to which humans give a name corresponds to a characteristic shape of the spectrum of wavelengths entering the eye. Lodged in the human retina are different types of colour receptor cells, known as cones. Each type of cone contains a different light-sensitive pigment, which absorbs and reacts most strongly to light of a particular wavelength. If you fire monochromatic light at a particular cone cell and then gradually decrease the wavelength (starting from red), the cell will transmit an increasingly strong signal to the brain until its own wavelength of peak sensitivity is reached; after that the signal will fall away on the other side the peak. Humans have three working types of cone cell, having distinct wavelengths of peak sensitivity. (The three sensitivity curves overlap to some extent.) This is why we can reasonably accurately simulate all colours that humans perceive by mixing just three colours, known as the primary colours.

People who are said to be colour-blind may have only two types of working cone, rather than three. They perceive the world differently, although they learn this only by observing that their reactions to certain wavelengths of light differ from the reactions of the majority. A man who was not colour-blind and whose cones of one particular type were suddenly switched off would see the world tinted, but a colour-blind man whose retinal cells had identical firing responses would say that things looked normal – because his brain would have trained itself from birth to regard this as the norm. Some species of animals have sensitivity spectra very different from the normal human one. Some animals see in black-and-white only (like humans at low light levels – see below); others have cone combinations with a less or a more uniform response than humans to light that is equally intense across the visual spectrum.

The mixing of primary colours of light to generate any colour known to human experience is a conceptually different problem from mixing paints to do the same. When you mix (‘add’) together light beams of the primary colours (Red, Green, Blue, roughly corresponding to the responses of the differing pigments in the three types of cone cells), you get white light. (Colour monitors and televisions have a multitude of ‘RGB’ dots.) These three are known as the ‘additive primary colours’. If you mix pigments of the three primary colours then the result is black paint, since each primary reflects only one colour, which the other primary pigments in the mixture suppress. Colour printers in fact mix cyan (which is blueish), yellow and magenta (pink-purple) in order to create all the colours known to man when the printer output is viewed in white light. These are the ‘subtractive’ primary colours, so named because if we subtract one of the additive primary colours from white light, leaving a mixture of the other two, we obtain the three subtractive primary colours. Whereas the mixing of light to obtain a desired colour is systematic, the mixing of pigment to do likewise is based on a library of knowledge gained by trial and error. Similarly, prediction of the colour of light that passes through consecutive glass jars of coloured translucent liquid (i.e., filters) is systematic, but the result of mixing the fluids is not.

Photography is conceptually more complicated than painting. What you see depends on further factors: the light that originally hit the photosensitive recorder; the response of the photosensitive recorder; the printing of the photograph (which may compensate for deficiencies in the response); and the light that the photograph is viewed in. Furthermore, negative film followed by printing and viewing; slide film viewing; digital photography viewed onscreen; and viewing a printout of a digital photograph each provide distinct re-creations at the eye of the light coming into the viewfinder.

Human perception of colour is actually more complex than I have stated. There are other cells in the retina called rods. These are more sensitive to light than cones but do not distinguish between colours. They come into their own at low levels of illumination; as a result, human vision under dimly lit conditions is essentially black-and-white. When the light intensity increases, beginning from darkness, the cones ‘kick in’ roughly when the rods become ‘saturated’ and send out no stronger signal as the brightness increases further. The brain also appears to take into account differences between the signals coming from the three types of cone, and differences between these and the rods.

A century after Newton, Goethe wrote on colour in an apparently opposing (and highly critical) way. Although what Newton had said was correct, hindsight makes it clear that Goethe was more concerned with the perception of colour than with the physics of light. We glimpse here two different philosophies: the ‘modern’ view espoused by the Enlightenment (no pun is intended on the name) that a world exists ‘out there’ to be explained (Newton), and the ‘post-modern’ view that our sensory impressions are all we have, and are therefore the most fundamental (Goethe). Goethe took the view that colour arises from the interplay between light and dark. Nowadays we have learned that humans perceive colours when they look at a spinning disc with a particular black-and-white pattern printed on it, for instance – presenting a challenge to theories of colour perception. Although Goethe’s explanations have been superseded, he was an acute observer of colour phenomena more complex than those analysed by Newton. There is still plenty to learn about the perception of colour.

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