Category Archives: science

The Octet Rule

The Octet Rule expresses the idea that atoms like to have eight electrons in their outermost shell, known as the valence shell. This provides something like an explanation for many chemical phenomena – for a start, the noble gases which make up the right-most column of the Periodic Table don’t usually bond with anything at all, because their outside shells are already full. The next column in, the halides, is extremely reactive because their valence shells have seven electrons, so they only need one more to bring them up to the magical number, eight. Over on the other side of the table we find the alkali metals, which are extremely reactive because in their electrically neutral form, they only have one electron in their outside shell, floating all on its own, and only weakly attracted to their nucleus – especially in the larger atoms, where the electrons are further out. If they manage to lose that electron, which doesn’t take much, they are immediately left with the eight electrons in the shell underneath, and the octet rule is satisfied.

The same thing happens when the alkaline earth metals, in the second column of the Periodic Table, lose two electrons, so they are also reactive but not so dramatically as their neighbours. Similarly, the elements in the sixth column can get a full shell by gaining two electrons. They can do that in two ways – either they acquire a pair of electrons and make off with them, allowing them to make compounds with metals by ionic bonding; or they share a pair of electrons with another non-metal, to form covalent bonds. If an oxygen atom shares two of its electrons with another atom, that effectively brings its total up to eight, which is why oxygen atoms often bond with two other atoms, as in water. With a carbon atom, it takes four electrons to fill up its valence shell, so every atom can bond with as many four other non-metal atoms, a property which makes possible the vast array of complex molecules required for life as we know it. On the other hand, it would take some doing for carbon to satisfy the octet rule by ionisation – it would pretty much need to gain or lose four electrons all at the same time, which is why carbon is not usually found in ionic compounds.

So far so neat, but if you haven’t studied so much chemistry that this stuff is already second nature to you, you may have a sense that this explanation is lacking a step or two. What on Earth is an ‘electron shell‘? Why would it want to have eight electrons in it anyway? And how much can we rely on this rule? Unfortunately there are no easy answers to any of these questions, so what follows are some quite difficult answers.

An electron shell is an abstraction – it refers to a collection of electrons in similarly-energetic ‘orbitals‘ around an atom. I put ‘orbitals’ in quotes there because it’s a technical term, with connotations that are misleading here. Electrons don’t exactly orbit atoms, because they’re not exactly particles – they’re more like waves that carry electrical charge. When they’re attached to an atom, they exist as standing waves around it. The fact we call them orbitals is a holdover from the ‘solar system’ model of the atom, proposed by Rutherford, which was superseded almost as soon as it was introduced, but which lives on in the popular imagination because it’s so much easier to imagine than the quantum mechanical truth.

When we talk about a full outside shell of electrons, we mean there’s one pair of electrons in a simple, spherical orbital (called an s orbital), and three more pairs of electrons in orbitals shaped more like hourglasses (p orbitals). Exactly three of those are physically possible, each pair being at right-angles to the other two.

So there’s an explanation for the shape of the orbitals, having to do with the fact that electrons exist as standing waves around atoms. That still calls for an explanation of what it means for them to get ‘full’, though. Why is there space for two electrons in each ‘s’ orbital, not just one, or more than two? This has to do with a property called spin, and the Pauli Exclusion Principle. Spin is a particularly abstract property for a thing to have, although it is related, somewhat obscurely, to the familiar observation that things sometimes spin around. If you imagine that every electron spins on the spot, and they can either spin clockwise or anti-clockwise, you won’t go far wrong, although scientists usually talk about ‘spin up’ and ‘spin down’ rather than ‘clockwise’ and ‘anti-clockwise’. The reason spin is important here is because the Pauli Exclusion Principle tells us that no two particles with the same quantum numbers can occupy the same space. Spin being a quantum number which can take one of two values, that means that exactly two electrons can occupy any given orbital. If you want an explanation that makes more sense than that, you’ll probably need at least one degree in physics, chemistry or preferably both. Sorry about that. One other thing to note here – when that valence shell is full, the atom is stable because, in a sense, it becomes inert. It’s left with the same electron configuration as one of the noble gases.

I should probably mention here that there are also electron shells with eighteen or thirty-two electrons in them, which is the main reason why the Periodic Table isn’t a rectangle, but they’re never the outermost shell; they have less energy, and hence smaller radii, than the s and p orbitals. The reasons for this, once again, are abstruse and quantum mechanical, and I won’t get into them here. The consequences bring us back to my fourth question above – how reliable is the octet rule? The answer is ‘not very’. It applies most of the time, especially for elements in the first couple of rows of the Periodic Table, but further down, when d and f orbitals start to become important, electrons from the lower shells can sometimes form bonds too, and things get significantly more complicated, with such weird chemicals as bromine pentafluoride. The Octet Rule is particularly useless for dealing with transition metals, which can typically lose one or more electrons, from different shells, and can sometimes gain extra ones too.

Chemistry, I find, is full of handy rules to which there are important exceptions; more than any other science, learning chemistry is like learning a language.



  1. How many electrons does iodine need to gain to get a full outside shell?
  2. How many covalent bonds can a carbon atom form before its outside shell is full up?
  3. Why is potassium even more reactive than sodium?
  4. Nitrogen gas is very stable, thanks to the number of bonds in every N2 molecule. How many bonds must that be, if each atom of nitrogen gets a full outside shell by sharing electrons?
  5. If oxygen forms ions by gaining two electrons, and aluminium forms ions by losing three, what must the formula of the ionic compound aluminium oxide be, in order for the charges on the oxygen ions and the aluminium ions to balance out?

Magnet Mushroom

At the end of 2013 Sonny Hallett and I invented a game. We’re calling it Magnet Mushroom, and you can play it too if you have an iron or steel tray, a bunch of magnets and some small pieces made of iron or steel. We used a baking tray, a pack of polished magnetite from a museum shop and the leftover metal bits from some Ikea bookshelves.

Here are the rules:

  1. Each player gets an equal set of magnets and metal bits.
  2. Take turns to place a magnet, with as many bits of metal as you like, on the tray, or on something which is already on the tray.
  3. If any magnet touches the tray during your turn, you lose. The last player to place a piece wins.
  4. At the end of a round, collect back all your pieces.
  5. The winner starts the next round.

Some Magnet MushroomsThe most basic move is a simple mushroom: a magnet stood on an upright metal piece. Because the metal becomes instantly magnetised, the magnet sits on it quite stably, however unlikely the configuration might look.

In fact, it is possible to make a mushroom two or three pieces tall and only moderately unstable. You can also support a magnet on two or three pieces, making it more stable, or attach more metal to the top or sides for added interest.

The challenge of the game comes mainly from the fact that every magnet is attracted or repelled by every other magnet – if you place one mushroom too close another, those forces will pull them down in an instant. There is a surprising amount of strategy involved in leaving the board in a stable enough configuration not to fall down, but unstable enough to make things difficult for the next player. Much of the fun of the game also comes from the creation of beautiful and wildly improbable-looking structures.

Some Magnet MushroomsThe simplest version of the game uses similar magnets and identical metal pieces, but if you want to mix things up a bit – or you run out of the pieces you started with – you can open it up by using  more different pieces. Experiment with it! Let me know what you come up with.

Extended Magnet Mushrooms

Project Wild Thing

Project Wild ThingNow free to view.

Kids in Britain don’t play outside so much these days. Where our parents were left to roam at will, and their parents wandered much further still, the children of the early twenty-first century are mostly kept indoors. It isn’t safe to go out – the traffic is dreadful, kids have terrible accidents, everyone knows that the streets are packed with paedophiles and murderers. Nobody knows their neighbours well enough to be sure they won’t eat their kids if they get half a chance.

What would kids do outdoors, anyway, even if they make it that far? Why would they want to play in the grass and shrubs, up and under the trees, when they can stay at home and spend their time playing on computers and smartphones?

This is a problem, if you believe that humans need time with nature to stay sane and physically healthy – and I think the evidence is strong. This is why David Bond appointed himself Marketing Director for nature, and made this film, Project Wild Thing. Marketing nature might be a faintly obnoxious concept, but it’s not hard to see where he’s coming from. The outside world, with its bugs and its plants and its dirt, has to compete for the attention of our children (and adults) against a vast array of highly profitable, heavily advertised consumer goods and activities. What chance does it have?

Bond, the director and star of the film, talks to a range of marketing and branding consultants to brainstorm and market-test ideas on how to ‘sell’ nature to a generation that sometimes seems to have trouble seeing the point of it, and to parents who might think it’s a nice idea, but worry about the dangers of letting their children go wild. The conceit works, as something to hang a film off, and helps to generate some solid practical ideas, but it also underlies its main problems – the film is heavily dominated by upper-middle-class white men, often talking about branding. This is bound to make some viewers wince, understandably, and it’s not clear that it helps that many of the kids he talks to are brown-skinned and often female.

He also talks to a number of conservationists, naturalists and activists, including wildlife presenter Chris Packham and Jay Griffiths, the author of ‘Kith‘, as well as my brother Leo, who talks about outdoors play non-profit Monkey-Do. All make very good points about human nature and our relationships with risk, play and the outdoors, feeding into the strategies suggested for getting kids playing outside.

The film is informative, infuriating and really very entertaining, but I am glad to say it is just one result of the whole process. They also put together a simple, nicely designed app for smartphones, ‘WildTime‘, designed to provide a wealth of ideas about how to engage with the natural world, for anyone for whom it doesn’t seem obvious (and for many children, itisn’t obvious until they actually get out there). Perhaps most importantly, The Wild Network is a growing group of organisations concerned with connecting kids with nature, including the RSPB, the National Trust, the NHS Sustainable Development Unit and hundreds of others. Perhaps these trends can be reversed yet, both in Britain and around the world, but it’s going to take a lot of work yet.

Ionic Bonding

What Ionic Bonding Is

Ionic bonding is the type of chemical bonding that binds non-metals with metals, and occasionally other things*, forming ionic compounds. An ion is just an atom (or sometimes a molecule) with an overall electric charge – many atoms and molecules have exactly as many electrons as they have protons, so the charges cancel out; when that doesn’t hold true, we end up with ions.

Metals are prone to losing electrons from their outside shell, leaving them with a positive charge; non-metals often pick up additional electrons from somewhere, filling up their outside shell and leaving them with a negative charge. Opposite charges attract, so electric forces tend to cause these positive and negative ions to stick together. Since those forces radiate out in all directions, you don’t just get one positive ion (or cation) bonding with one negative ion (or anion) – any more ions that happen by get pulled in, too. There’s always a sweet spot where the pushing and pulling of the ions balances out, allowing new ions to slot neatly into any existing structure. That neatness gives a very regular lattice-like pattern to the solid – in other words, ionic compounds form crystals.

Ionic bonding illustrated
A crystallisation of some of these ideas by the brilliant Sonya Hallett

What Ionic Bonding Isn’t

It’s worth saying something about some common misconceptions about ionic bonding. If you have learned about it before, you may have been told that an ionic bond is what you get when a metal ion donates an electron to a non-metal. This description has a pleasing simplicity to it, but it is really very misleading. For one thing, ionic bonding typically holds together many atoms at once. This is in contrast to the covalent bonds** that hold non-metals together, where the bonding is down to each atom sharing electrons with its neighbours, which leads to the formation of well-defined molecules. Ionic compounds are not really made of molecules at all, just big crystalline structures.

The other thing wrong with the electron-donation picture is that the ions have usually gained or lost electrons long before they ever meet – for many elements, like sodium and the other alkali metals, it is rare to find them any other way on Earth. Less reactive metals may have been exposed to ionising radiation, or lost an electron or two in a collision. Reactive non-metals have a tendency to pick up any free electrons they bump into, whatever the source, because they fit nicely into the geometry of their outside shells.

Ionic Compounds

Ionic compounds are characteristically hard, usually with high melting points, and very brittle. The hardness and high melting points are down to their crystal structure; as long as the lattice holds, they are solid and quite strongly bonded. However, since the crystal is made of alternating positive and negative ions, a knock that causes one layer to get out of alignment with the next will often lead to cations lining up with cations, and anions with anions, producing a repulsive force that tears the crystal apart – hence the brittleness. Metals, which also have a crystalline structure, don’t suffer from this problem, which is why they are much more malleable.

Many ionic compounds are soluble in water. This is because water molecules are polar, in the sense that they have more positive charge on one side than the other. A negative ion will attract the positive ends of water molecules, and when it collects enough water molecules that way, their collective attraction can overcome its bonding with its ionic neighbours and carry the ion away. The positive ions dissolve much the same way. All these positive and negative ions allow a solution, to conduct electricity – distilled water is actually an electrical insulator, whereas salt water conducts extremely well. Molten salts and other ionic liquids conduct in the same way. There is a useful complication to the way ions in a liquid conduct electricity – because the charge is carried by two kinds of ions travelling through space, not just free-floating electrons like you get in a metal, they tend to separate over time – cations are attracted to cathodes, and anions to anodes. This process, known as electrolysis, makes it possible to extract the constituent elements of a salt; sodiumpotassiumcalcium and various other elements were first isolated in this way.

* Sometimes polyatomic cations, like ammonium, can play the part usually played by metal atoms.

**We should note here that there is not really a sharp distinction between covalent and ionic bonds. Many covalent bonds are polar, meaning that the electrons are shared unevenly between the atoms, so that one of the atoms acquires a positive charge, and the other a negative one – these bonds can be considered to be a bit ionic. Similarly, ionic bonds can be considered mildly covalent when electrons get shared between atoms, which they inevitably do. Metallic bonding is sometimes considered a form of covalent bonding, but sometimes not – the shared electrons are more like a sea than a set of pairs. Chemistry gets pretty messy when you look close enough.


This piece also appears on Everything2.

The Everyday Signs of Light Waves

Light, like all the basic constituents of our universe, seems to be made of waves. Waves that act a bit like particles, sometimes, but which spread out and interfere with each other just like other waves.

It’s about 200 years since physicists finally agreed that light behaves like a wave, after Poisson proved himself wrong with an ingenious experiment involving a surprising bright spot in the shadow of a disc. We could have come to that conclusion much sooner, if we had known what we were looking for, but nobody really thought about interference patterns very much in those days.

Francesco Maria Grimaldi coined the term ‘diffraction’ in the 1660s, to describe his observation that light spreads out when it passes through a small hole. If you put a piece of paper in the path of the light you see a bright disc surrounded by increasingly large and faint rings. It looks something like this (the outer rings are fainter in real life, though):

Those dark rings are where the light waves coming from one part of the hole interfere destructively with those coming from the other side – the peaks of one meet the troughs of the other. The bright areas are where the peaks meet and combine. Grimaldi didn’t quite figure all of that out, although he did come to something like a wave theory of light.

Hooke and Huygens both worked on mathematical theories of light waves around that time too, but Newton published a theory of optics based on light consisting of particles (or ‘corpuscles’). It more or less worked, and given the towering nature of Newton’s scientific achievements, it isn’t surprising that people just sort of went along with that until the early 19th century, when it was conclusively disproved.

Once we realise that light is wavy, it becomes possible to explain quite a few observations which are otherwise a bit mysterious. Here are some of the things you might have noticed in your life, which are all inexplicable if you don’t know that light is made of waves which can interfere with each other.


SlickThe colours that we see when oil floats on the surface of water come about because the film is thin enough, and close enough to a constant depth, that light reflected from the bottom interferes with light reflected from the top. Since different colours have different wavelengths, they interfere to different degrees depending on tiny variations in the thickness of the film, and the angle of the light. A related effect explains the iridescence of certain beetles and butterflies.

Supernumerary Rainbows

A sunset rainbow over LondonRainbows, and even double rainbows, can be explained by simple refraction – the light changing speed and direction as it passes through a medium, in this case water. That itself doesn’t prove that light isn’t a particle, but some rainbows have additional, narrower bands of colour inside the main bow – and those are entirely puzzling until you understand that they are caused by interference. The explanation is in the diffraction of light bouncing from fine raindrops, which creates a series of increasingly faint inner rings. The smaller the droplets, the bigger the spacing is between the rings, which is the general rule in all kinds of diffraction. This means that unless they are all much the same size, the effect gets smeared out with different rings overlapping, and we don’t see the supernumerary bows at all.


CoronaWhen the moon shines through thin clouds, or a layer of fog, there is often a bright area around it, fringed by bands of colour. Again, this only happens when the droplets of the cloud are particularly consistent in size – if the size varies from one part of the cloud to another we get a patchwork of colours referred to as iridescent clouds. With sunlight these effects tend to happen where the light is too bright to make out the colours, while with the moon, the light is too faint for our colour vision to work at full capacity. The best way to see these beautiful effects in their full glory is to wear sunglasses, and look at the thin clouds around the sun while blocking the sun itself from your view.

Nacreous clouds

Nacreous Clouds 1Far rarer than the corona and a good deal more spectacular, nacreous clouds are also the result of diffraction. The difference is that rather than droplets of liquid water, the light of nacreous clouds are diffracted through stratospheric ice crystals. Usually the stratosphere is too dry to form clouds at all, and not quite cold enough, but when it drops below about 85°C, and especially when moist air is lifted up from the troposphere by gales down below, great wave-shaped clouds of fine ice crystals can form, with amazing colours that are often at their most vivid just before dawn and just after dusk.


Balloon glory atmospheric opticsSpeaking of glory, if you ever get to look down at your shadow (or your aeroplane’s shadow) in mist or clouds of the right consistency, you will see something called a glory, which looks very much like a corona surrounding your shadow in the mist. Your shadow, meanwhile, is likely to take on an eerie shape known as Brocken’s spectre.

Net curtains

When net curtains, or umbrellas, are made with sufficiently thin and uniform fabric, it is quite common to see diffraction fringes around light sources. The shape of these is characteristic of a square diffraction grating, and closely analogous to some of the patterns seen in x-ray crystallography.

Water drops

abstract yellowIf you get the chance to look through a drop of water at an unfocused point of light somewhere behind it – through a window or a pair of glasses, for example – you are likely to see a caustic projected on the back of your eyeball. Around the edges and cusps, where the light is bent back on itself, we can sometimes see quite rich and occasionally colourful interference fringes.

Water droplets

A different but related effect is sometimes seen through a fine mist of water on a glass pane, or an eye that is covered with the right kind of gunk. There is a hazy ring around light sources, and then the darker and lighter fringes that are characteristic of diffraction. Occasionally the same effect can be seen in a dusty mirror.


When we look at a bright, featureless area, it is common to see what look like translucent objects floating across our fields of vision. These are the shadows of loose cells and other tiny pieces of debris passing close to our retinas, and they are often on the right scale to show noticeable diffraction fringes around their edges.

Once you know what to look out for, the wave nature of light is easy to see. All these little oddities in the behaviour of light make perfect sense when you know that light – just like water waves and sound waves – bends when it passes from one medium to another, spreads out around barriers, and shows areas of greater and lesser intensity where waves reinforce or cancel each other out.

Iron Noder

This November I posted 30 finished pieces of writing on Everything2, on whatever I felt like writing about at the time. By doing so I completed the Iron Noder Challenge, which has been running every November since 2008. This was the first time I took part in earnest – making the effort to write and re-write for an hour or two almost every day, in order to average at least one post a day that I could be happy with. Continue reading Iron Noder

Reading about Thinking

This year I’ve found myself reading a bunch of books about the mind, the brain, and the nature of the self. For some reason I’m reading them all in parallel, picking one or the other depending on how I’m feeling on any given day, which is probably why I haven’t actually finished any of them yet. I’m loving them all, in different ways. I could probably do with spending more time talking to people about all this stuff, as well, which is one reason I’m posting this now rather than waiting till I’ve finished the books to write about them (although I will probably do that, too).

Here are a few words about what’s in the Mind/Brain section of the towering pile on my bedside table right now… Does anyone else have any thoughts about any of these, or interest in discussing them?

  1. Consciousness Explained, by Daniel Dennett
    I don’t know why it’s taken me so long to get round to tackling this book; I’ve known for a long time that Dennett is a very compelling, interesting writer and thinker. I had the feeling that his thoughts about how the mind works have a lot of overlap with my own, but until this year I’d only ever read a few of the essays from his collection ‘Brainstorms’, which is excellent if somewhat repetitious. What surprised me when I finally picked this up was what an entertaining writer he is.
  2. I am a Strange Loop, by Douglas Hofstadter
    I first met Hofstadter’s magnum opus, Gödel, Escher, Bach, when I was a kid – I was probably about twelve years old. I was enchanted, and I it may well have had a more profound influence on my thinking than any other single book, but in spite of that I could never finish it. It’s so much fun to dip into, especially the dialogues; but then its mathematical excursions are so involved, it can be hard to stay with it to the next flight of fancy without feeling like you’re either breaking your head or skimming too much. His later book covers much of the same ground – about the meaning of meaning, and how such a thing could possibly emerge from constituents that seem to obey the mathematical rules of physics – while avoiding most of those pitfalls. It’s dense, but never overwhelmingly so, and it’s just whimsical enough to make you smile without getting waylaid.
  3. The Feeling of What Happens, by Antonio Damasio
    Damasio is a medical doctor and neurologist by training, and more than any of the other books I have been reading, this one is grounded in science, particularly the study of the human brain. His approach to thinking rightly takes in the whole body, though – he is very concerned with the importance of looking at the whole organism if we want to understand thought, the nature of the self, and particularly emotions. What I find odd is that he has essentially written a whole book about embodied cognition in a book which doesn’t list that term or embodiment in its index; he does briefly name-check Francesco Varela and Maturana, but rather a lot of the time he seems to be writing as if he hasn’t noticed that anybody has ever had similar ideas. His science is impeccable, but I’m thrown by his lack of engagement with existing philosophy. Then again, this is a short book – much the shortest of these four – and I know that some people switch off the moment they see the word ‘phenomenology’.
  4. Mind in Life, by Evan Thompson
    This is probably the least accessible of the books in my stack, but still, the writing is lucid and uses no more jargon than it needs. This book was conceived as a follow-up to Thompson’s book with Varela and Eleanor Rosch, ‘The Embodied Mind: Cognitive Science and Human Experience’, which I haven’t read. Thompson is rounding up relevant thoughts from all over science and philosophy, in order to put together a strong case for thinking about the mind as something arising from life; not something unique to the human brain, but a process naturally arising from and involving any organism – and also, in some sense, extending beyond it. It’s a grand project, and my sense is that it’s a very worthwhile one. This is a pretty fat book, though, written very clearly but without a great deal of levity, so I’m relying on sheer fascination value to carry me through. I think it will.

The Rain in Carballo

Carballo at night

I’ve been a little slow to start going through my photos from this Summer’s two-month trip around the Iberian peninsula.

I stayed for about two weeks in the town of Carballo, which is 35km from A Coruña, 45km from Santiago de Compostela and 10km from the nearest beach. It’s a small, quiet town full of empty buildings, half-finished or abandoned, slapped together with an obvious disregard for any kind of building code. Most of the bars are mostly empty most of the time, and presumably they couldn’t stay open at all if they had to pay the kind of rent you have to pay for premises in places where people want to live. There is life and music if you know where to look, though, and it’s an easy enough journey to the beautiful beaches.

A clear stream runs through Carballo, past the bus station. close to where I was staying, with fish and bats and dragonflies. It leads quickly out of the bricks and concrete, into the woods, like an artery. The air is fresh, and the hazelnuts you can pluck from the trees in late summer are like a taste of heaven.

The last night I was there, I was woken by a mighty rainstorm battering against the thin roof of my attic flat. It’s the rain, above all, that makes Galicia so gorgeous, once you get outside of its depressed not-quite-seaside towns – the rain that feeds its lush forests and sustains its wide green fields. The countryside throughout northern Iberia is stunning; you might miss the sunshine, but it’s worth getting wet for.

Climate Camp

The towerClimate Camp (or the Camp for Climate Action, in full) is a reaction to the failures of our governments to take anything like the steps that science tells us will be necessary to avert catastrophic climate change, and to the failures of our democratic system to represent dissenting voices. When even majority opinions are readily ignored if they conflict with the plans of the ruling powers, people are encouraged to take politics into their own hands.
Continue reading Climate Camp