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So why exactly is the sky blue? SfD tries to investigate

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Canto: Well, Karl Kruszelnicki is one of our best science popularisers as you know, and therefore a hero of ours, but I have to say his explanation of the blueness of our daily sky in his book 50 Shades of Grey  left me scratching my head…

Jacinta: Not dumbed-down enough for you? Do you think we could form a Science for Dummies collaboration to do a better job?

Canto: Well that would really be the blind leading the blind, but at least we’d inch closer to understanding if we put everything in our own words… and that’s what I’m always telling my students to do.

Jacinta: So let’s get down to it. The day-sky is blue (or appears blue to we humans?) because…?

Canto: Well the very brief explanation given by Dr Karl is that it’s about Rayleigh scattering. Named for a J W Strutt, aka Lord Rayleigh, who first worked it out.

Jacinta: So let’s just call it scattering. What’s scattering?

Canto: Or we might call it light scattering. Our atmosphere is full of particles, which interfere with the light coming to us from the sun. Now while these particles are all more or less invisible to the naked eye, they vary greatly in size, and they’re also set at quite large distances from each other, relative to their size. The idea, broadly, is that light hits us from the sun, and that’s white light, which as we know from prisms and rainbows is made up of different wavelengths of light, which we see, in the spectrum that’s visible to us, as Roy G Biv, red orange yellow green blue indigo violet, though there’s more of some wavelengths or colours than others. Red light, because it has a longer wavelength than blue towards the other end of the spectrum, tends to come straight through from the sun without hitting too many of those atmospheric particles, whereas blue light hits a lot more particles and bounces off, often at right angles, and kind of spreads throughout the sky, and that’s what we mean by scattering. The blue light, or photons, bounce around the sky from particle to particle before hitting us in the eye so to speak, and so we see blue light everywhere up there. Now, do you find that a convincing explanation?

Jacinta: Well, partly, though it raises a lot of questions.

Canto: Excellent. That’s science for you.

Jacinta: You say there are lots of particles in the sky. Does the size of the particle matter? I mean, I would assume that the light, or the photons, would be more likely to hit large particles than small ones, but that would depend on just how many large particles there are compared to small ones. Surely our atmosphere is full of molecular nitrogen and oxygen, mostly, and they’d be vastly more numerous than large dust particles. Does size matter? And you say that blue light, or blue photons, tend to hit these particles because of their shorter wavelengths. I don’t quite get that. Why would something with a longer wavelength be more likely to miss? I think of, say, long arrows and short arrows. I see no reason why a longer arrow would tend to miss the target particles – not that they’re aiming for them – while shorter arrows hit and bounce off. And what makes them bounce off anyway?

Canto: OMG what a smart kid you are. And I think I can add more to those questions, such as why do we see different wavelengths of light as colours anyway, and why do we talk sometimes of waves and sometimes of particles called photons? But let’s start with the question of whether size matters. All I can say here is that it certainly does, but a fuller explanation would be beyond my capabilities. For a start, the particles hit by light are not only variable by size but by shape, and so potentially infinite in variability. Selected geometries of particles – for example spherical ones – can yield solutions as to light scattering based on the equations of Maxwell, but that doesn’t help much with random dust and ice particles. Rayleigh scattering deals with particles much smaller than the light’s wavelength but many particles are larger than the wavelength, and don’t forget light is a bunch of different wavelengths, striking a bunch of different sized and shaped particles.

Jacinta: Sounds horribly complex, and yet we get this clear blue sky. Are you ready to give up now?

Canto: Just about, but let me tackle this bouncing off thing. Of course this happens all the time, it’s called reflection. You see your reflection in the mirror because mirrors are designed as highly reflective surfaces.

Jacinta: Highly bounced-off. So what would a highly unreflective surface look like?

Canto: Well that would be something that lets all the light through without reflection or distortion, like the best pane of glass or pair of specs. You see the sky as blue because all these particles are absorbing and reflecting light at particular wavelengths. That’s how you see all colours. As to why things happen this way, OMG I’m getting a headache. The psychologist Thalma Lobel highlights the complexity of it all this way:

A physicist would tell you that colour has to do with the wavelength and frequency of the beams of light reflecting and scattering off a surface. An ophthalmologist would tell you that colour has to do with the anatomy of the perceiving eye and brain, that colour does not exist without a cornea for light to enter and colour-sensitive retinal cones for the light-waves to stimulate. A neurologist might tell you that colour is the electro-chemical result of nervous impulses processed in the occipital lobe in the rear of the brain and translated into optical information…

Jacinta: And none of these perspectives would contradict the others, it would all fit into the coherence theory of truth…

Canto: Not truth so much as explanation, which approaches truth maybe but never gets there, but the above quote gives a glimpse of how complex this matter of light and colour really is…

Jacinta: And just on the physics, I’ve looked at a few explanations online, and they don’t satisfy me.

Canto: Okay, I’m going to end with another quote, which I’m hoping may give you a little more satisfaction. This is from Live Science.

The blueness of the sky is the result of a particular type of scattering called Rayleigh scattering, which refers to the selective scattering of light off of particles that are no bigger than one-tenth the wavelength of the light.

Importantly, Rayleigh scattering is heavily dependent on the wavelength of light, with lower wavelength light being scattered most. In the lower atmosphere, tiny oxygen and nitrogen molecules scatter short-wavelength light, such as blue and violet light, to a far greater degree than long-wavelength light, such as red and yellow. In fact, the scattering of 400-nanometer light (violet) is 9.4 times greater than the scattering of 700-nm light (red).

Though the atmospheric particles scatter violet more than blue (450-nm light), the sky appears blue, because our eyes are more sensitive to blue light and because some of the violet light is absorbed in the upper atmosphere.

Jacinta: Yeah so that partially answers some of my questions… ‘selective scattering’, there’s something that needs unpacking for a start…

Canto: Well, keep asking questions, smart ones as well as dumb ones…

Jacinta: Hey, there are no dumb questions. Especially from me. Remember this is supposed to be science for dummies, not science by dummies

Canto: Okay then. So maybe we should quit now, before we’re found out…


‘Why is the sky blue?’, from 50 shades of grey matter, Karl Kruszelnicki, pp15-19

‘Blue skies smiling at me: why the sky is blue’, from Bad astronomy, Philip Plait, pp39-47

Written by stewart henderson

December 15, 2016 at 4:35 am

more on Einstein, black holes and other cosmic stuff

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Einstein in 1931 staring at a wee bit of the universe, with Edwin Hubble

Einstein at Mount Wilson in 1931, staring at a wee bit of the universe, with Edwin Hubble

Jacinta: Well Canto I’d like to get back to Einstein and space and time and the cosmos, just because it’s such a fascinating field to inhabit and explore.

Canto: Rather a big one.

Jacinta: I’ve read, or heard, that Einstein’s theory, or one of them, predicted black holes, though he didn’t necessarily think that such entities really existed, but now black holes are at the centre of everything, it seems.

Canto: Including our own galaxy, and most others.

Jacinta: Yes, and there appears to be a correlation between the mass of these supermassive black holes at the centres of galaxies and the mass of the galaxies themselves, indicating that they appear to be the generators of galaxies. Can you expand on that?

Canto: Well the universe seems to be able to expand on that better than I can, but I’ll try. Black holes were first so named in the 1960s, but Einstein’s theory of general relativity recast gravity as a distortion of space and time rather than as a Newtonian force, with the distortion being caused by massive objects. The greater the mass, the greater the distortion, or the ‘geodetic effect’, as it’s called. The more massive a particular object, given a fixed radius, the greater is the velocity required for an orbiting object to escape its orbit, what we call its escape velocity. That escape velocity will of course, approacher closer and closer to the speed of light, as the object being orbited becomes more massive. So what happens when it reaches the speed of light? Then there’s no escape, and that’s where we enter black hole territory.

Jacinta: So, let me get this. Einstein’s theory is about distortions of space-time (and I’m not going to pretend that I understand this), or geodetic effects, and so it has to account for extreme geodetic effects, where the distortion is so great that nothing, not even light, can escape, and everything kind of gets sucked in… But how do these massive, or super-massive objects come into being, and won’t they eventually swallow all matter, so that all is just one ginormous black hole?

Canto: Okay I don’t really get this either but shortly after Einstein published his theory it was worked out by an ingenious astrophysicist, Karl Schwarzschild – as a result of sorting out Einstein’s complex field equations –  that if matter is severely compressed it will have weird effects on gravity and energy. I was talking a minute ago about increasing the mass, but think instead of decreasing the radius while maintaining the mass as a constant…

Jacinta: The same effect?

Karl Schwarzschild

Karl Schwarzschild

Canto: Well, maybe, but you’ll again reach a point where there’s zero escape, so to speak. In fact, what you have is a singularity. Nothing can escape from the object’s surface, whether matter or radiation, but also you’ll have a kind of internal collapse, in which the forces that keep atoms and sub-atomic particles apart are overcome. It collapses into an infinitesimal point – a singularity. It was Schwarzschild too who described the ‘event horizon’, and provided a formula for it.

Jacinta: That’s a kind of boundary layer, isn’t it? A point of no return?

Canto: Yes, a spherical boundary that sort of defines the black hole.

Jacinta: So why haven’t I heard of this Schwarzschild guy?

Canto: He died in 1916, shortly after writing a paper which solved Einstein’s equations and considered the idea of ‘point mass’ – what we today would call a singularity. But both he and Einstein, together with anyone else in the know, would’ve considered this stuff entirely theoretical. It has only become significant, and very significant, in the last few decades.

Jacinta: And doesnt this pose a problem for Einstein’s theory? I recall reading that this issue of ‘point mass’, or a situation where gravity is kind of absolute, like with black holes and the big bang, or the ‘pre-big bang’ if that makes sense, is where everything breaks down, because it seems to bring in the mathematical impossibility of infinity, something that just can’t be dealt with mathematically. And Einstein wasn’t worried about it in his time because black holes were purely theoretical, and the universe was thought to be constant, not expanding or contracting, just there.

Canto: Well I’ve read – and I dont know if it’s true – that Einstein believed, at least for a time, that black holes couldn’t actually exist because of an upper limit imposed on the gravitational energy any mass can produce – preventing any kind of ‘infinity’ or singularity.

Jacinta: Well if that’s true he was surely wrong, as the existence of black holes has been thoroughly confirmed, as has the big bang, right?

Canto: Well of course knowledge was building about that in Einstein’s lifetime, as Edwin Hubble and others provided conclusive evidence that the universe was expanding in 1929, so if this expansion was uniform and extended back in time, it points to an early much-contracted universe, and ultimately a singularity. And in fact Einstein’s general relativity equations were telling him that the universe wasn’t static, but he chose to ignore them, apparently being influenced by the overwhelming thinking of the time – this was 1917 – and he introduced his infamous or famous cosmological constant, aka lambda.

Jacinta: And of course 1917 was an early day in the history of modern astronomy, we hardly knew anything beyond our own galaxy.

Canto: Or within it. One of the great astrophysicists of the era, Sir Arthur Eddington, believed at the time that the sun was at the centre of the universe, while admitting his calculations were ‘subject to large uncertainties’.

Jacinta: Reminds me of Lord Kelvin on the age of the Earth only a few generations before.

Canto: Yes, how quickly our best speculations can become obsolete, but that’s one of the thrills of science. And it’s worth noting that the work of Hubble and others on the expansion of the universe depended entirely on improved technology, namely the 100-inch Hooker telescope at Mount Wilson, California.

Jacinta: Just as the age of the Earth problem was solved through radiometric dating, which depended on all the early twentieth century work on molecular structure and isotopes and such.

Canto: Right, but now this lambda (λ) – which Einstein saw as a description of some binding force in gravity to counteract the expansion predicted by his equations – is very much back in the astrophysical frame. The surprising discovery made in 1998 that the universe’s expansion is accelerating rather than slowing has, for reasons I can’t possibly explain, brought Einstein’s lambda in from the cold as an explanatory factor in that discovery, which is also somehow linked to dark energy.

Jacinta: So his concept, which he simply invented as a ‘fix-it’ sort of thing, might’ve had more utility than he knew?

Canto: Well the argument goes, among some, that Einstein was a scientist of such uncanny insight that even his mistakes have proved more fruitful than others’ discoveries. Maybe that’s hero worship, maybe not.

Jacinta: So how does lambda relate to dark energy, and how does dark energy relate to dark matter, if you please?

Canto: Well the standard model of cosmology (which is currently under great pressure, but let’s leave that aside) has been unsuccessful in trying to iron out inconsistent observations and finding with regard to the energy density of the universe, and so dark energy and what they call cold dark matter (CDM) have been posited as intellectual placeholders, so to speak, to make the observations and equations come out right.

Jacinta: Sounds a bit dodgy.

Canto: Well, time will tell how dodgy it is but I don’t think anyone’s trying to be dodgy, there’s a great deal of intense calculation and measurement involved, with so many astrophysicists looking at the issue from many angles and with different methods. Anyway, to quickly summarise CDM and dark energy, they together make up some 96% of the mass-energy density of our universe according to the most currently accepted calculations, with dark energy accounting for some 69% and CDM accounting for about 27%.

Jacinta: Duhh, that does sound like a headachey problem for the standard model. I mean, I know I’m only a dilettanty lay-person, but a model of universal mass-energy that only accounts for about 4% of the stuff, that doesn’t sound like much of a model.

Canto: Well I can assure they’re working on it…

Jacinta: Or working to replace it.

Canto: That too, but let me try to explain the difference between CDM and dark energy. Dark energy is associated with lambda, because it’s the ‘missing energy’ that accounts for the expansion of the universe, against the binding effects of gravity. As it happens, Einstein’s cosmological constant pretty well perfectly counters this expansive energy, so that if he hadn’t added it to his equations he would’ve been found to have predicted an expanding universe decades before this was confirmed by observation. That’s why it was only in the thirties that he came to regret what he called the greatest mistake of his career. Cold dark matter, on the other hand, has been introduced to account for a range of gravitational effects which require lots more matter than we find in the observed (rather than observable) universe. These effects include the flat shapes of galaxies, gravitational lensing and the tight clustering of galaxies. It’s described as cold because its velocity is considerably less than light-speed.


the lambda- cold dark matter model

Jacinta: Okay, so far so bad, but let’s get back to black holes. Why are they so central?

Canto: Well, that’s perhaps the story of supermassive black holes in particular, but I suppose I should try to tell the story of how astronomers found black holes to be real. As I’ve said, the term was first used in the sixties, 1967 to be precise, by John Wheeler, at a time when their actual existence was being considered increasingly likely, and the first more or less confirmed discovery was made in 1971 with Cygnus x-1. You can read all about it here. It’s very much a story of developing technology leading to increasingly precise observational data, largely in the detecting and measuring of X-ray emissions, stuff that was undetectable to us with just optical instruments.

Jacinta: Okay, go no further, I accept that there’s been a lot of data from a variety of sources that have pretty well thoroughly confirmed their existence, but what about these supermassive black holes? Could they actually be the creators of matter in the galaxies they’re central to? That’s what I’ve heard, but my reception was likely faulty.

Canto: Well astrophysicists have been struggling with the question of this relationship – there clearly is a relationship between supermassive black holes and their galaxies, but which came first? Now supermassive black holes can vary a lot – our own ‘local’ one is about 4 million solar masses, but we’ve discovered some with billions of solar masses. But it was found almost a decade ago that there is correlation between the mass of these beasties and the mass of the inner part of the galaxies that host them – what they call the galactic bulge. The ratio is always about 1 to 700. Obviously this is highly suggestive, but it requires more research. There are some very interesting examples of active super-feeding black holes emitting vast amounts of energy and radiation, which is both destructive and productive in a sense, creating an active galaxy. Our own Milky Way, or the black hole at its centre, is currently quiescent, which is just as well.

Jacinta: You mean if it starts suddenly feeding, we’re all gonna die?

Canto: No probably not, the hole’s effects are quite localised, relatively speaking, and we’re a long way from the centre.

Jacinta: Okay thanks for that, that’s about as much about black holes as I can stand for now.

Canto: Well I’m hoping that in some future posts we can focus on the technology, the ground-based and space-based telescopes and instruments like Hubble and Kepler and James Webb and so many others that have been enhancing our knowledge of black holes, other galaxies, exoplanets, all the stuff that makes astrophysics so rewarding these days.

Jacinta: You’re never out of work if you’re an astrophysicist nowadays, so I’ve heard. Halcyon days.

an x-ray burst from a supermassive black hole - artist's impression

an x-ray burst from a supermassive black hole – artist’s impression

Written by stewart henderson

December 19, 2015 at 9:02 pm

Einstein, science and the natural world: a rabid discourse

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Einstein around 1915

Einstein around 1915

Canto: Well, we’re celebrating this month what is surely the greatest achievement by a single person in the history of science, the general theory of relativity. I thought it might be a good time to reflect on that achievement, on science generally, and on the impetus that drives us to explore and understand as fully as possible the world around us.

Jacinta: The world that made us.

Canto: Précisément.

Jacinta: Well, first can I speak of Einstein as a political animal, because that has influenced me, or rather, his political views seem to chime with mine. He’s been described as a supra-nationalist, which to me is a kind of political humanism. We’re moving very gradually towards this supra-nationalism, with the European Union, the African Union, and various intergovernmental and international organisations whose goals are largely political. Einstein also saw the intellectual venture that is science as an international community venture, science as an international language, and an international community undertaking. And with the development of nuclear weapons, which clearly troubled him very deeply, he recognised more forcefully than ever the need for us to take international responsibility for our rapidly developing and potentially world-threatening technology. In his day it was nuclear weapons. Today, they’re still a threat – you’ll never get that genie back in the bottle – but there are so many other threats posed by a whole range of technologies, and we need to recognise them, inform ourselves about them, and co-operate to reduce the harm, and where possible find less destructive but still effective alternatives.

Canto: A great little speech Jas, suitable for the UN general assembly…

Jacinta: That great sinkhole of fine and fruitless speeches. So let’s get back to general relativity, what marks it off from special relativity?

Canto: Well I’m not a physicist, and I’m certainly no mathematician, but broadly speaking, general relativity is a theory of gravity. Basically, after developing special relativity, which dealt with the concepts of space and time, in 1905, he felt that he needed a more comprehensive relativistic theory incorporating gravity.

Jacinta: But hang on, was there really anything wrong with space and time before he got his hands on them? Why couldn’t he leave them alone?

Canto: OMG, you’re taking me right back to basics, aren’t you? If I had world enough, and time…

Jacinta: Actually the special theory was essentially an attempt – monumentally successful – to square Maxwell’s electromagnetism equations with the laws of Newton, a squaring up which involved enormous consequences for our understanding of space and time, which have ever since been connected in the concept – well, more than a concept, since it has been verified to the utmost – of the fourth, spacetime, dimension.

Canto: Well done, and there were other vital implications too, as expressed in E = mc², equivalating mass and energy.

Jacinta: Is that a word?

Canto: It is now.

Jacinta: So when can we stop pretending that we understand any of this shite?

Canto: Not for a while yet. The relevance of relativity goes back to Galileo and Newton. It all has to do with frames of reference. At the turn of the century, when Einstein was starting to really focus on this stuff, there was a lot of controversy about whether ‘ether’ existed – a postulated quasi-magical invisible medium through which electromagnetic and light waves propagated. This ether was supposed to provide an absolute frame of reference, but it had some contradictory properties, and seemed designed to explain away some intractable problems of physics. In any case, some important experimental work effectively quashed the ether hypothesis, and Einstein sought to reconcile the problems by deriving special relativity from two essential postulates, constant light speed and a ‘principle of relativity’, under which physical laws are the same regardless of the inertial frame of reference.

the general theory - get it?

the general theory – get it?

Jacinta: What do you mean, ‘the initial frame of reference’?

Canto: No, I said ‘the inertial frame of reference’. That’s one that describes all parameters homogenously, in such a way that any such frame is in a constant motion with respect to other such frames. But I won’t go into the mathematics of it all here.

Jacinta: As if you could.

Canto: Okay. Okay. I won’t go any further in trying to elucidate Einstein’s work, to myself, you or anyone else. At the end of it all I wanted to celebrate the heart of Einstein’s genius, which I think represents the best and most exciting element in our civilisation.

Jacinta: Drumroll. Now, expose this heart to us.

Canto: Well we’ve barely touched on the general theory, but what Einstein’s work on gravity teaches us is that by not leaving things well alone, as you put it, we can make enormous strides. Of course it took insight, hard work, and a full and deep understanding of the issues at stake, and of the work that had already been done to resolve those issues. And I don’t think Einstein was intending to be a revolutionary. He was simply exercised by the problems posed in trying to understand, dare I say, the very nature of reality. And he rose to that challenge and transformed our understanding of reality more than any other person in human history. It’s unlikely that anything so transformative will ever come again – from the mind of a single human being.

Jacinta: Yes it’s an interesting point, and it takes a particular development of culture to allow that kind of transformative thinking. It took Europe centuries to emerge from a sort of hegemony of dogmatism and orthodoxy. During the so-called dark ages, when warfare was an everyday phenomenon, and later too, right through to the Thirty Years War and beyond, one thing that could never be disputed amongst all that disputation was that the Bible was the word of God. Nowadays, few people believe that, and that’s a positive development in the evolution of culture. It frees us to look at morality from a broader, richer, extra-Biblical perspective..

Canto: Yes we no longer have to even pretend that our morality comes from such sources.

Jacinta: Yes and I’m thinking of other parts of the world that are locked in to this submissive way of thinking. A teaching colleague, an otherwise very liberal Moslem, told me the other day that he didn’t believe in gay marriage, because the Qu-ran laid down the law on homosexuals, and the Qu-ran, because written by God, is perfect. Of course I had to call BS on that, which made me quite sad, because I get on very well with him, on a professional and personal basis. It just highlights to me the crushing nature of culture, how it blinds even the best people to the nature of reality.

Canto: Not being capable of questioning, not even being aware of that incapability, that seems to me the most horrible blight, and yet as you say, it wasn’t so long ago that our forebears weren’t capable of questioning the legitimacy of Christianity’s ‘sacred texts’, in spite of interpreting those remarkably fluid texts in myriad ways.

Jacinta: And yet out of that bound-in world, modern science had its birth. Some modern atheists might claim the likes of Galileo and Francis Bacon as one of their own, but none of our scientific pioneers were atheists in the modern sense. Yet the principles they laid down led inevitably to the questioning of sacred texts and the gods described in them.

Canto: Of course, and the phenomenal success of the tightened epistemology that has produced the scientific and technological revolution we’re enjoying now, with exoplanets abounding, and the revelations of Homo floresiensis, Homo naledi and the Denisovan hominin, and our unique microbiome, and recent work on the interoreceptive tract leading to to the anterior insular cortex, and so on and on and on, and the constant shaking up of old certainties and opening up of new pathways, all happening at a giddying accelerating rate, all of this leaves the ‘certainty of faith’ looking embarrassingly silly and feeble.

Jacinta: And you know why ‘I fucking love science’, to steal someone else’s great line? It’s not because of science itself, that’s only a means. It’s what it reveals about our world that’s amazing. It’s the world of stuff – animate and inanimate – that’s amazing. The fact that this solid table we’re sitting at is made of mostly empty space – a solidity consisting entirely of electrochemical bonds, if that’s the right term, between particles we can’t see but whose existence has been proven a zillion times over, and the fact that as we sit here on a still, springtime day, with a slight breeze tickling our faces, we’re completely oblivious of the fact that we hurtling around on the surface of this earth, making a full circle every 24 hours, at a speed of nearly 1700 kms per hour. And at the same time we’re revolving around the sun at a far greater speed, 100,000 kms per hour. And not only that, we’re in a solar system that’s spinning around in the outer regions of our galaxy at around 800,000 kilometres an hour. And not only that… well, we don’t feel an effing thing. It’s the counter-intuitive facts about the natural world that our current methods of investigation reveal – these are just mind-blowing. And if your mind doesn’t get blown by it, then you haven’t a mind worth blowing.

Canto: And we have two metres of DNA packed into each nucleus of the trillions of cells in our body. Who’d’ve thunkit?



Written by stewart henderson

November 23, 2015 at 11:33 pm

Boyle’s law

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I think it would be amusing – for me anyway – if my blog posts were connected by threads, one leading to another. For example, the last post on aerosinusitis resulted from comments on my previous one about my recent air travel, and this one results from comments about pressure differentials in the last one, and so on and on.

Well, anyway, Boyle’s law.

Boyle’s law describes how the pressure of a gas increases as its volume decreases.

Take a set amount of gas – that’s to say, a certain mass of gas – and decrease its volume. Then the pressure it exerts increases in proportion. That’s to say, the relationship between volume and pressure is inversely proportional, given a constant temperature and mass. This relationship can be expressed in the formula PV = k, where k is a constant. In ‘word’ terms, the product of pressure and volume is constant, controlling for the other factors. If the pressure is calculated as 6, and the volume 2, then if the volume is doubled to 4, then the pressure will be halved to 3, with, on both occasions, the constant being 12. Another way of expressing this relationship is P1V1 = P2V2.

The English chemist/physicist, or ‘natural scientist’, Robert Boyle, first published the relational law in 1662, though he wasn’t the first to notice a relationship between pressure and volume. Nor did he fully understand the reason for the relationship, because gases were not then seen as molecular, with the molecules in kinetic relationship to each other. However, Boyle’s thinking was moving in the right direction, as he theorised that air – the gas on which he experimented – was ‘a fluid of particles at rest in between invisible springs’. Edme Mariotte of France independently formulated the law a little over a decade after Boyle.

The best physical explanation for the law emerged more than two centuries later, with work on the kinetic theory of gases by James Clerk Maxwell and Ludwig Boltzmann. This theory explains pressure within a container as  a result of atoms or molecules colliding with the container at various rates and velocities. It provides a molecular, microscopic accounting of such macroscopic measurements as pressure, volume and temperature. Einstein’s work on Brownian motion, the motion of dust or pollen particles as seen under a microscope, helped confirm the theory, on a level kind of in between the molecular and the macroscopic. Interestingly, the idea that macroscopic conditions might be the result of microscopic bodies in collision was put forward by Lucretius nearly 2000 years ago.

Boyle’s law treats of an ideal gas, something not known or considered at the time because gases under standard conditions of temperature and pressure behave essentially like ideal gases. Other ideal gas laws include Charles’ law, which is a law of volumes, Gay-Lussac’s law, which treats pressure, and Avogadro’s law, which covers the proportional relationship between volume and the number of moles present (molar volume). As always, improvements in technology led to the observation of a wider range of conditions requiring new hypotheses, the confirmation of which led to new knowledge – in this case, the kinetic theory.

Written by stewart henderson

May 18, 2014 at 9:03 am

Posted in history, physics, science

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it's all about Boyle's Law, apparently (P1V1 = P2V2)

it’s all about Boyle’s Law, apparently (P1V1 = P2V2)

Aerosinusitis, also called barosinusitis, sinus squeeze or sinus barotrauma is a painful inflammation and sometimes bleeding of the membrane of the paranasal sinus cavities, normally the frontal sinus. It is caused by a difference in air pressures inside and outside the cavities.

The above quote is from Wikipedia, and it describes something I experienced on two flights recently (see previous post), though I experienced it, or felt I experienced it, in the ears (I’ve learned not to trust my own perceptions). On the first flight, I experienced a build-up of pressure until a sudden change as of a bubble bursting in some inner cavity, and then everything was fine. I’ve had similar, but less intense, experiences in a car when driving up into the hills near my home. In fact, they’ve been so mild that I’ve often looked forward to them as a physical sensation, and I know it’s common because people would ask around – have your ears popped yet? On my second flight, the pressure built up again on the descent, and I fully expected the bubble to burst as it always did. But the pain just increased, to an excruciating level, so that my face was all scrunched up and I was gasping, squealing and whimpering like a pup. By the time we landed, though, the worst of the pain was gone, and it gradually got better over the next hour or so, and although I could still ‘feel’ it 24 hours later, it was more a memory of a feeling than the thing itself. I don’t know whether my pain was severe or relatively mild as I’ve never felt other people’s pain. This was one of the first things I had ‘deep’ thoughts about as a child. When I was nine or ten years old I fell, while running, and bashed my shin against the edge of our front porch, and I still think that was the most extreme pain I’ve ever felt in my life. I screamed and screamed, and amongst the comforting remarks came the inevitable ‘come on now, stop squealing, it’s not that bad’. Of course this made me angry and resentful but it also raised the questions, ‘am I over-reacting? Would others react like this in the same circumstances? Would they feel the same pain? How could we ever know?’ And along with those questions was one that always ate at me, and probably still does – can I control my pain, can I obliterate it with the power of my mind? I’d sell my soul, FWIW, for total control. But that’s a rather too large side-issue for this post. The Wikipedia article, though, does classify aerosinusitis in terms of pain, along with other more measurable symptoms:

Grade I includes cases with mild transient sinus discomfort without changes visible on X-ray. Grade II is characterized by severe pain for up to 24 h, with some mucosal thickening on X-ray. Patients with grade III have severe pain lasting for more than 24 h and X-ray shows severe mucosal thickening or opacification of the affected sinus; epistaxis or subsequent sinusitis may be observed.

Annoyingly, my own intense but transitory experience doesn’t fit into any of those grades. I also find that this extremely technical article makes no mention at all of ear pain. Much of the focus is on the frontal sinuses, situated behind the brows and connected to the nose or nasal meatus, which naturally makes me uncertain about where my pain was located. Interestingly, the frontal sinuses still haven’t come into existence at birth, and aren’t fully developed until adolescence, and some 5% of people don’t even have them, which just complicates matters for me. As is mentioned above, the frontal sinuses are part of a whole labyrinth of hollows, bones, cartilaginous membranes and passageways known as the paranasal cavities. I’m hoping that the inner ear, or more accurately the middle ear cavity – technically called the tympanic cavity, is also part of that.

Though ‘ear-popping’ seems to be commonplace, aerosinusitis usually occurs in people who have head colds, or as the article puts it, it’s ‘typically preceded by an upper respiratory tract infection or allergy’. Of course, with my bronchiectasis, I’m effectively in a more or less permanent state of infection, so this may be a problem for me every time I fly.

So, what remedy? Well, the problem for me seems to be with the tympanic cavity or eustachian tube on one side. When I was eight, I perforated my ear drum and had to have an operation. I was told afterwards that I should never hold my nose tight while blowing it, as people do (making that horrible honking nose), as this might damage my eardrum. I remember being fascinated by this connection between the nose and the ears, and of course I’ve always followed the doctor’s advice. I didn’t want to blow my brains out of my ears.

Wikipedia suggests using decongestants or painkillers for mild forms of barotrauma, as does this useful site, which deals more with popping ears. First and foremost, though, it suggests gargling with warm salt water, which was my mother’s advice for many medical problems (she was a nurse).

I’m resisting any description of what I went through as ‘mild’.

Working the eustachian tube or tympanic cavity seems to be a good idea, for example by regular swallowing, chewing gum, sucking sweets, yawning, etc.

Sudafed is highly recommended. I’ll bear that in mind next time.

Written by stewart henderson

May 12, 2014 at 11:50 pm

Stephen Jay Gould, NOMA and a couple of popes

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I’ve been making my way through my second collection of Stephen Jay Gould essays, Leonardo’s mountain of clams and the Diet of Worms, published in 1998, having read his 1993 collection, Eight little piggies, a couple of years ago, and I was surprised to come across ‘Non-overlapping magisteria’ as number 14 in the collection. I read it today. I’d heard that he promulgated his famous – or infamous, depending on your perspective – thesis on NOMA in a book called Rocks of Ages, so I wasn’t expecting such a treat, if I can put it that way, when I turned over the page to that essay.

As it turns out, Rocks of Ages, subtitled Science and religion in the fullness of life, was published in 1999, immediately after the collection I’m reading, and it presumably constitutes an elaboration and refinement of the earlier NOMA essay. So maybe one day I’ll get to that, but meanwhile I’m itching to get my teeth into this first ‘attempt’ – reminding myself of the original meaning of the term essai, in the hands of Montaigne.

Gould begins his essay with a story of a conversation he has, in the Vatican – half his luck – with a group of Jesuit priests who also happened to be professional scientists. The Jesuits are concerned with the talk of ‘Creation Science’ coming out of the US. One of them asks Gould:

‘Is evolution really in some kind of trouble, and if so what could such trouble be? I have always been taught that no doctrinal conflict exists between evolution and catholic faith, and the evidence for evolution seems both utterly satisfying and entirely overwhelming. Have I missed something?’

Gould assures them that this development, though big in the US due to the peculiarities of evangelical protestantism there, is quite localized and without intellectual substance. He wonders, in the essay, at the weirdness of an agnostic Jew ‘trying to reassure a group of priests that evolution remained both true and entirely consistent with religious belief.’

This was the first point at which my (highly primed) sceptical sense was roused. First, the priest had been taught, or told, that no doctrinal conflict existed between Catholicism and evolution. One hardly gets the impression that he’s nutted this out for himself. What about the doctrine of the human soul? What about the absolutely central Judeo-Christian idea that humans were specially created in their god’s image? Can anybody honestly say that evolution casts no doubt upon these notions? To me, making such a claim would defy credibility. I mean, isn’t that precisely why so many Christians, of every denomination, have such difficulty with evolution? Second, Gould tells us that he was able to reassure the priests that evolution wasn’t under threat (fine, as far as it goes), and that it was ‘entirely consistent with religious belief’. Eh what? Did he show them or just tell them? Of course we get no detail on that.

Gould gives other examples of his fatherly reassurance, e.g. to Christian students, of the complete compatibility of Christian belief with evolution, which he tells us he ‘sincerely believes in’, but still without providing an argument. Finally he claims that, notwithstanding fundamentalism and biblical literalism, Christians by and large treat the Bible metaphorically. He seems to feel that this smooths away all incompatibilities. The six days of creation, ensoulment, original sin, humans in god’s image, salvation from sin through Jesus, his resurrection, his virgin birth, his miracles, etc etc, these are just stories. Is that what most Christians believe? Or just that some of them are stories, some of the time, for some believers? This question of literalism and metaphor is in fact a great can of worms that Gould doesn’t even glance into. It’s important, for isn’t literal truth also empirical truth, and doesn’t science have something to say about that?

In any case, having ‘established’, to his satisfaction, all this compatibility, Gould moves on to his central thesis:

The lack of conflict between science and religion arises from a lack of overlap between their respective domains of professional expertise – science in the empirical constitution of the universe, and religion in the search for proper ethical values and the spiritual meaning of our lives. The attainment of wisdom in a full life requires extensive attention to both domains – for a great book tells us both that the truth can make us free, and that we will live in optimal harmony when we learn to do justly, love mercy, and walk humbly.

This is NOMA in a nutshell, together with some unobjectionable remarks about harmony, justice, mercy and humility, all vaguely associated with religion. Yet I’ve read a lot of history, and this has made me sceptical of the role of religion in promoting such values. If you examine sermons and priestly speeches through the centuries, you’ll find them very much parroting the ethics of  their time – with a certain lag, given the inherent conservatism of most religious institutions. The Bible, that multifarious set of texts, is ideal for quote-mining for every Zeitgeist and Weltanschauung, but really we don’t need history to inform us that our ethical values don’t come from religion, a point made by many philosophers, anthropologists and cognitive psychologists. Religion is essentially about protection, hope and human specialness, all emanating from a non-worldly source, and all of these elements have been profoundly buffeted by the scientific developments of the last few centuries, precisely because the domains of scientific exploration and religious conviction overlap massively, if not completely. As Gould writes in another essay in this collection:

‘Sigmund Freud argued that scientific revolutions reach completion not when people accept the physical reconstruction of reality thus implied, but when they also own the consequences of this radically revised universe for a demoted view of human status. Freud claimed that all important scientific revolutions share the ironic property of deposing humans from one pedestal after another of previous self-assurance about our exalted cosmic status.’

Another, simpler way of putting this is that science – which after all is only the pursuit of reliable, verifiable knowledge – is perennially confronting us with our own contingency, while religions, and most particularly the Abrahamic monotheistic religions, seek desperately to keep us attached to a sense of our necessity, our centrality in God’s plan. It’s hard to imagine two activities on a more complete collision course.

Gould’s first essay on NOMA was apparently triggered by an announcement of Pope John Paul II to the effect that his Church endorsed evolutionary theory and found it compatible with Catholic dogma. This was much hyped in the media, and Gould considered it much ado about nothing, as it merely repeated, or so he thought, an earlier papal proclamation:

I knew that Pope Pius XII…. had made the primary statement in a 1950 encyclical entitled Humani Generis. I knew the main thrust of his message: Catholics could believe whatever science determined about the evolution of the human body, so long as they accepted that, at some time  of his choosing, God had infused the soul into such a creature. I also knew that I had no problem with this argument – for, whatever my private beliefs about souls, science cannot touch such a subject and therefore cannot be threatened by any theological position on such a legitimately and intrinsically religious issue.

Now, it seems to me, and to many others, that this question of a soul, possessed only by humans, is an empirical question, unless the soul is to be treated as entirely metaphorical. If empirical, all our understanding of humans and other mammals, derived from evolution but also from zoology in general, tells against the existence of such an entity. We see clearly, and can map, through neurophysiology, genetics and other disciplines, the continuity of humans with other mammals, and with earlier hominids, and there is no trace of, or place for, a Homo sapiens soul. If metaphorical, the religious implications are enormous, for if the soul, which supposedly lives on after the body’s demise, were metaphorical, wouldn’t that make heaven, hell and the afterlife also metaphorical?

This is a real problem for the believers in such an entity, and a source of some amusement for non-believers. In a debate with Richard Dawkins a while back, George Pell, the Catholic archbishop of Sydney was apparently challenged on the exclusivity of the human soul and came up with the view that souls inhabit all living things but that the human soul was ‘infinitely more complex’ than those of other organisms. So now we know that white ants do indeed have souls, as well as blue-green algae and amoebae.  This sounded like a physiological claim to me, and I wondered how well synchronised it was with official Catholic doctrine on the matter – or is that non-matter? It seemed much more likely that the good archbishop was making it up as he went along, just as Dawkins accuses such authorities of doing.

Gould, though, congratulates Pius XII, because he ‘had properly acknowledged and respected the separate domains of science and theology’. We get here a whiff of the authoritarian arrogance of Gould, which grates from time to time. He presents separate domains as virtually an established fact and ‘proper’, and so takes on the role of chiding those who don’t subscribe to it, because he himself has ‘great respect for religion’. He also claims, but without any evidence, that the majority of scientists think like him. It was a questionable claim in 1998, and is even more so in 2013.

Still, Gould recognises that there’s a problem, because, according to him, the two non-overlapping domains are not widely separated, like the USA and Australia, but share a troubled border, a la Pakistan and Afghanistan. This seems a concession, but it goes nowhere near far enough. Gould himself uncovers the problem while probing the detail of Pius’s Humani Generis, and finding that the fifties pope was rather less well-disposed towards evolution than he’d thought. What’s more, Pius seems aware of the conflict Gould is so keen to avoid, as he writes of ‘those questions which, although they pertain to the positive sciences, are nevertheless connected with the truths of the Christian faith.’ Pius elaborates on these questions by castigating claims, in particular as regards evolution, that might not be in keeping with ‘divine revelation’, which naturally he regards as some kind of truth. One of these truths is that ‘souls are immediately created by God’, which contradicts the evolutionary idea that all that is human is derived, through incremental moderation, from previously existing creatures. Gould provides a gloss on this by essentially claiming that Pius is patrolling the border between science and religion, intent on preserving the integrity of religious territory. I’m not convinced.

Gould then turns to the more recent statement on evolution by John Paul II. John Paul makes the point that in the 50 years or so since Human Generis, the strength of evolution as an explanatory theory has grown to the point that it’s pretty well unassailable. So he seems to have none of the qualms of Pius, yet still he makes empirical claims about matters ‘spiritual’ while claiming them not to be empirical, something which Gould prefers to obscure with a lot of self-congratulatory language about respect for ‘that other great magisterium’. Here is a slab of John Paul’s argument:

‘With man, then, we find ourselves in the presence of an ontological difference, an ontological leap, one could say. However, does not the posing of such ontological discontinuity run counter to that physical continuity which seems to be the main thread of research into evolution in the field of physics and chemistry?  Consideration of the method used in the various branches of knowledge makes it possible to reconcile two points of view which would seem irreconcilable. The sciences of observation describe and measure the multiple manifestations of life with increasing precision and correlate them with the time line.  The moment of transition to the spiritual cannot be the object of this kind of observation.’

It’s a nice try, but the ontological difference described here is ‘just saying’.  But the ‘just saying’ has a lot of religious energy behind it, because so much of monotheistic religion is tied up with human specialness, and even necessity. We are in the creator-god’s image, we’re the ultimate end-point of the universe, and other hubristic clap-trap. What John Paul is trying to ‘say into being’ is the spiritual realm, no less. The ‘spiritual transition’, the emergence of soul-stuff, is real but beyond scientific observation. Thus it is both empirical and non-empirical, which is impossible.

There’s a good reason why Gould’s claim about NOMA is bogus. All we have to do is look at what he claims these ‘magisteria’ cover. To quote Gould:

‘The net of science covers the empirical realm: what is the universe made of (fact) and why does it work this way (theory). The net of religion extends over questions of moral meaning and value.’

That the second sentence in this quote is false should be obvious to everyone after only a moment’s reflection. The central thesis in all monotheistic religions is surely that their one and only god exists and is real. We can’t possibly be talking in metaphorical terms here. Thus, an empirical claim lies at the very heart of Christianity, Judaism and Islam, and there’s just no way of arguing yourself out of this. The fact that this empirical claim appears to be unprovable doesn’t make it any less of an empirical claim. The statement ‘Unicorns exist’ is also an empirical claim that is essentially unprovable. We can be pretty certain that unicorns don’t exist on our planet, but how can we prove that a creature fitting that description has no existence in the whole universe, or the multiverse, if there is a multiverse?

What’s more, religion is much more about empiricism than it is about ‘moral meaning and value’, because what is absolutely central to the monotheisms is that moral meaning and value derive from that real and existent being, and as such are themselves real and existent. That’s certainly the point that William Lane Craig bangs on about in all his debates – the empirical reality of his god, and of the values this male being espouses and somehow bequeaths to us.

In fact, on reflection, the statement that ‘God exists’ is not quite of the same type as ‘Unicorns exist’. It’s much closer to the statement ‘Dark matter exists’.  Unicorns can only be contingent entities – they may exist in some corner of the universe, but if they suddenly went extinct on the planet Gallifrey it would make little difference. However, dark matter is necessary, as far as I’m aware, to the standard model of the universe and its mass. That’s why the search is on, big-time, to find it, to identify it, to learn more about it. To the religious, their god is also necessary, and it becomes a matter of urgency to ‘find God’, to know him, to understand him, etc. That’s why proof of their god’s existence is important, and always will be. Of course, the religious obviously believe they already have the proof, but an increasing percentage of inhabitants of our western world are unimpressed with such claims.

how to debate William Lane Craig, or not – part 5, the fine-tuning argument

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gee thanks, goddie - and can you help me win my soccer game on saturday?

gee thanks, goddie – and can you help me win my soccer game on saturday?

Dr Craig’s fifth argument is the well-known fine-tuning argument. Once again I should point out that when Dr Craig brings up these science-related topics it isn’t from a fascination with science itself – indeed Dr Craig likes to use the term ‘scientism’ when he refers to science other than when he’s using it to support his obsession. He uses science solely to mine and manipulate it to convince himself and others that there’s a warrant for a supernatural agent who has a personal love for him. So you should always consider his use of science with that in mind. And you should ask yourself, too, why is it that the physicists and cosmologists and mathematicians of the world, the people who work on a daily basis with the so-called laws of nature and the physical constraints of the universe, are by and large so completely lacking in belief in a personal deity? This is a sub-population that is more atheistic than any other sub-group on the planet. How does Dr Craig account for this? Madness, badness, indoctrination? How is it that the greatest physicist, by general acclaim, of the twentieth century, Einstein, regularly described belief in a personal god as a form of childishness? Why is it that Bertrand Russell, one of the greatest mathematicians and logicians of all time, wrote, ‘I am as firmly convinced that religions do harm as I am that they are untrue’? What is it with the Richard Feynmans, the Stephen Weinbergs, the Stephen Hawkings of this world that they’ve been so indifferent or hostile to the claims of religion? Perhaps Dr Craig should consider launching a wholesale attack on these disciplines, since they seem such a breeding ground for views so completely out of synch with his obsessions. How can they not know that all their researches and discoveries converge on the screamingly obvious fact that a loving human-focused supernatural being designed everything. What a bunch of blind fools.

The fine-tuning argument has been around for a long time despite its seeming ultra-modernity, though of course it gets updated in terms of constants and constraints. It’s of course, a rubbish argument like all the others. This universe wasn’t fine-tuned for anything. There was no tuner, as far as we know, and it would be impossible to predict what possibilities could emerge from the hugely complex and almost entirely unknown preconditions of the universe’s existence. Our universe will provide us with many many surprises long into the future, and I would not be surprised if those surprises include forms of life hitherto thought impossible, due to the ‘laws of nature’. Dr Craig claims that the various constraints and quantities that he talks about are independent of the laws of nature, which is a nonsense, as it’s only through our application of physical laws that we’ve been able to determine these quantities. So I don’t know what to make of his claim that these constraints aren’t physically necessary. The constraints exist as an essential part of the physical nature of this universe. The question of necessity or chance just doesn’t arise. These are the constraints we have to work with, and we find that, within these constraints, intelligent life is clearly possible, though perhaps very rare, though perhaps not so very rare as we once thought. I think we must all agree that we live in exciting times in the search for extra-terrestrial intelligence and extra-terrestrial life more generally. We’re homing in on the zones elsewhere that meet all the conditions for the emergence of life, and I believe we will find that life in time. Intelligent life, by our standards, will no doubt take longer.

Dr Craig says the odds of this universe being life-permitting are astronomically small. Some cosmologists agree, but they don’t then make any leaps to a supernatural cosmic designer. And I mean none of them do. It’s interesting that the cosmologist Alan Guth, to whom Dr Craig has already referred, believes that humans will one day be able to design new universes, no doubt with the help of quantum computers, and there are others who suggest that this may be how our universe came into being. All highly speculative stuff, and not particularly mainstream, but good fun, and worthy of reflection. Others, such as Stephen Hawking, have proposed a superposition of possible initial conditions for the universe which provides for an ‘inevitability’ of us finding ourselves in just this kind of life-sustaining universe at a later stage. It’s all to do with the manipulation of time-perception apparently. This hypothesis eliminates the need to posit a multiverse. There are many other hypotheses too, of course, including the multiverse, the bubble universe and others. It’s an exciting time for cosmology. Tough, but exciting, and far more interesting and rewarding than theology, I can promise you that. As students, I hope you continue to follow this stuff, for its own sake, not to mine it as confirmation for preconceived ideas.

Written by stewart henderson

March 18, 2013 at 3:24 pm