Taking lessons from Goldacregate, I’ve removed all the rant and sarcasm from this post.
In this article in today’s Observer, we’re advised that this:
PA = gUG + min(k – g, (1 – g)(1 – r))
is an “intimidating” equation”. Only if we’re easily scared! It relates the profit gained from dynamically priced airline tickets to some variables. This equation really is a very straightforward it says:
“profit equals two things multiplied together plus the smallest of two other things”
Using a Greek letter (capital pi) with a superscript following is a bit of showmanship, P would have done perfectly well in this instance. You can read the paper from which it is drawn here. It is written in the style of a paper in pure mathematics, which might explain the intimidation of the journalists in question.
I wrote a little bit about maths a while back: maths is the language of much of the science I do, but its a convenient tool – it’s not an end in itself. The seed of “Goldacregate” was a query by a journalist as to how to read out an equation, the thing is that practitioners rarely speak equations out loud: they scribble them on the nearest available surface (often illegibly, and incorrectly) or fight endless battles with machines to get them into electronic documents. Furthermore there is a long and dishonourable history of public relations companies using essentially meaningless equations to promote products and services.
For non-users of equations they are simply a cloak, a cloud of chaff thrown up to hide the truth beneath. For users, they are a compact and exact way of writing down the truth.
The next time you see an equation, don’t be scared beneath it there is something simple which can be said.
Unexpurgated version: Ah, bless, the economists are playing at being scientists by using an equation and the journalists have got the vapours at the impossible complexity of it all. Nasty equation: please, don’t hurt me.
Category: Science
Science, usually research I have done or topics on which I have lectured
Aug 22 2010
“Intimidating equations”
Jul 28 2010
Spider silk
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| Photo by Fir0002/flagstaffotos (GFDL license) |
I’ve never worked on spider silk myself, but my work on synthetic polymers and biological physics took me to conferences where spider silk work was presented and it always struck me as a very interesting. Spider silk has a rather impressive set of material properties, yet it is produced rapidly at the back end of a spider under everyday conditions. This is a pretty electron micrograph of spider spinnarets from where the silk comes (warning: page includes creepy crawlies).
I introduced molecules, and proteins back in this post. Proteins are the key molecules used to make organisms, an organism’s DNA are the instructions to make a set of proteins. Spider silk is made from protein. A spider is able to produce a whole range of silks with different physical properties: dragline silk is used to make the outer-rim and spokes of a web and is strong and tough; capture-spiral silk is sticky, stretchy and tough; tubiliform silk is used for egg cases and is the stiffest; aciniform silk used for wrapping prey is the toughest; minor-ampullate silk used to make temporary scaffolding for building a web (it’s not as strong but very stretchy). From a technical point of view “strong” refers to how hard it is to stretch something, and “tough” refers to how hard it is to break something. Spider silk is similar to silkworm silk but it is stronger and more extensible.
The closest synthetic material to spider silk in terms of it’s strength per weight is Kevlar. Kevlar is processed using hot sulphuric acid under high pressure which as you might imagine is not very nice. Spider silk, on the other hand is made at room temperature and pressure from an aqueous solution of benign materials. Not only this, a spider can eat the silk it’s already made and use it to make more silk. As scientists, this makes us more than a little bit jealous.
Not only is spider silk interesting of itself, but from a material scientist point of view, it really isn’t fun to make and use new polymers (you need to build expensive plant to make them, you need to work out your ingredient supply chain, you need to check for safety and environmental problems). If, on the other hand, you can get the properties you want from one of your pre-existing polymers by changing the microstructure then life is much easier. Spider silk may provide hints as to how this might be done.
Scientists have done research on the effect of different drugs on web spinning, filmmakers have made some fun of this experiment* (warning: contains spiders). Other interesting biomaterials include, mollusc adhesive and slug slime and I’ve already written about why butterflies are blue.
Update: Curtesy of @happymouffetard, the evolutionary origin of spider-silk spinnarets appears to be hair follicles, according to this article.
*Thanks to Stephen Curry for pointing me to the “spiders on drugs” video.
Jul 22 2010
The Periodic Table
Understanding the Periodic Table is very much like making love to a beautiful woman, there’s no point rote-learning the location of the different elements if you don’t know what they do… langtry_girl*
The Periodic Table of the Elements is a presentation of the known elements which provides information on the relationships between those elements in terms of their chemical and physical properties. An element is a type of atom: iron, helium, sulphur, aluminium are all examples of elements. Elements cannot be broken down chemically into other elements, but elements can change. An atom is comprised of electrons, protons and neutrons.
This is all very nice, but if you look around you: at the wallpaper, the computer screen, the table – very little of what you see is made from pure elements. They’re made from molecules (pure elements joined together), and the molecules are arranged in different ways which may be completely invisible. So in a sense the periodic table represents the bottom of the tree of knowledge for people interested in materials, other scientists may be more interested in what makes up the elements.
As a design, shown above, the periodic table is a cultural icon which everyone knows. Even if they don’t understand what it means, they know what it stands for – it stands for science. How to make sure people know your scene is set in a lab or your character is a scientist? Bung in a periodic table. It has been purloined to organise other sorts of information, such as Crispian Jago’s rather fine “Periodic Table of Irrational Nonsense“, some more examples here. There is a song.
At various times in my life I’ve been able to name and correctly locate all the elements in the periodic table, normally takes a bit of effort and some mnemonics to help. Increasingly now, I can remember the mnemonics but not the elements they refer to.
Different parts of the periodic table are important to different sorts of scientists. To organic chemists carbon (C), hydrogen (H), oxygen (O), nitrogen (N) hold the majority of their interest with walk on parts for some of the transition metals (the pink ones in a block in the middle) which act as catalysts. Inorganic chemists are more wide ranging, only really forbidden from the Noble Gases (helium (He), neon(Ne), argon (Ar), krypton (Kr), xenon (Xe)) which refuse to react with anything. Semi-conductor physicists are after the odd “semi-metals”: silicon (Si), indium (In), gallium (Ga), germanium (Ge), arsenic (As). For magnets there’s iron (Fe), cobalt (Co), nickel (Ni) along with other transition metals and the Lanthanides. The actinides are for nuclear physicists, radiation scientists and atomic bomb makers. Hydrogen is for cosmologists. In this view, as a soft condensed matter physicist, I am closest to the organic chemists.
I’m rather fond the periodic table, it is the scientist’s badge, but I’m scared of fluorine.
*To be fair to langtry_girl, I pondered on twitter “Trying to finish the sentence: “Understanding the Periodic Table is very much like making love to a beautiful woman…” and I think hers was the best reply. It is, of course, a reference to Swiss Toni.
Jul 12 2010
How does a magnet work?
How does a magnet work? This question arose on “I’m a Scientist, Get me out of here“, a fine piece of science communication which involved putting scientists in contact with school children. This is my attempt at an answer, which says a bit more about science in general but is utterly untimely. The short answer to the question is that magnets are made from atoms which act like little magnets and in a proper magnet are all lined up, but as an answer this is somewhat unsatisfactory.
From a scientific point of view, what you’d commonly call magnets are just one group of magnetic materials – the ferromagnets. They are accompanied in early magnetism courses for aspiring physics students by paramagnetic and diamagnetic materials. A ferromagnetic material, like iron, is strongly attracted to a magnet, a paramagnetic material is weakly attracted and a diamagnetic material is very weakly repelled. Diamagnetism and paramagnetism are useful for scientific research but it is ferromagnetism where all the practical applications are found. Iron, cobolt and nickel are the only ferromagnetic elements.
At this point I am ashamed to admit I nearly missed out on a tortured analogy to explain magnetism but fortunately I caught myself in time! Imagine, if you will, a crowd bearing vuvuzelas. Individuals in this crowd can blow their vuvuzelas in any direction they please, however much we might wish they didn’t. In a ferromagnet groups of vuvuzela players spotting their neighbours spontaneously face the same direction to play their devilish instruments. The whole crowd may not be blowing them in the same direction but groups of them will. They can be marshalled to all blow their horns in the same direction by a band leader, and once pointing in the same direction they will continue to face that way, even in the absence of the band leader.
The individuals in this group are atoms in a material, and the vuvuzelas represent the magnetic field of a single atom. Groups of players facing in the same direction represent magnetic domains and the band leader represents an applied magnetic field. The point about ferromagnets is they massively enhance an a magnetic field applied by something like a coil of wire with a current flowing through it – this is how you make an electromagnet. The difference between a “magnet” and any old bit of ferromagnet is that in a “magnet” all the domains have been lined up to face the same way.
In paramagnetic materials vuvuzelas players ignore their neighbours and play away in random directions, they respond in a somewhat feeble fashion to the directions of the band leader.
In diamagnetic materials the crowd have no vuvuzelas but use their hands as a substitute, rather petulantly they face the opposite direction to that proposed by the band leader. In scientific language the hands represent induced magnetic dipole moments.
But why is an atom magnetic? An atom could be magnetic because the electron orbiting the nucleus acts like a little current loop, which gives it a magnetic field like a little bar magnet (posh name for “little bar magnet” is “magnetic dipole moment”) but actually the majority of the magnetic dipole moment of an atom comes from the intrinsic magnetic dipole moment of individual electrons.
We really don’t know why the electron acts as a magnetic dipole, it is ascribed to a property known as ‘spin’ but it can’t be spin as we normally define it since electrons are, as far as we can tell, point-like – nobody has every managed to measure the diameter of an electron. Therefore how can we meaningfully describe it as spinning? In a sense the origin of the electron magnetic dipole moment is not important, it exists, we know what it is and we can use the measured value in our calculations for designing magnetic materials. This question of the “why” of fundamental properties of sub-atomic particles is what string theory seeks to address. For most scientists the answer is unimportant for practical applications, but for physicists in particular it is a nagging unpleasantness that we don’t know why.
Magnetism and electricity have been known since antiquity but as two very separate phenomena, and unsurprisingly really. Magnetism is a property of some funny rocks (lodestone) whilst electricity is a property of rubbed materials, and lemons. The connection between the two is far from obvious, the link was made in the early part of the 19th century. This is a recurring theme in science, we blithely teach that such and such is true, implying that it’s truth is pretty much self-evident and elide the fact that for most of history we have not believed these things and that it has taken the painstaking work of a number of very great minds to reveal these self-evident truths. I must admit to being a little unsure of the history in this area, taught in England the key figures were Michael Faraday who did much of the experimental work in linking electricity and magnetism followed by James Clerk Maxwell who formulated a mathematical theory. In the experimental area in particular there were many other participants in the story, I suspect who takes centre stage depends on where you are taught.
So there you have it: magnets work because the vuvuzela players copy each other and play in the same direction.
Jun 24 2010
Book review: Botany of Desire by Michael Pollan
Yet another in my erratic series of book reviews cum notes. This time I’m reading “The Botany of Desire:A Plant’s-eye View of the World” by Michael Pollan.
The introduction lays out the land of the book, sections on apples, tulips, marijuana and potatoes and the central thesis: that it’s a useful idea to consider that not only do we domesticate plants but that in a sense plants naturalise us. As stated in the introduction this thesis felt a bit hardline, grating a little for my taste but once into the reading this feeling receded since the illustrative stories are enticing and nicely written.
First up, are is the story of apples in American and the folk hero, Johnny Appleseed, who travelled the mid-West, setting up ad hoc orchards from seeds, a little way in front of the settler-wave, and sold them trees as they moved into the area.
The point about apples is that they don’t grow true from seed, take a fine apple and plant its seed and what you get is a lucky dip. This is a recurring theme, plants amenable to domestication appear quite often to be those amenable to quickly producing a wide variety. To grow “true” from an apple you need to graft from the parent onto a root stock. It’s always struck me as something of a miracle that grafting works and that people managed to discover it.
Apples were significant to the early settlers since they offered sweetness (sugar would not have been very available), a sense of order when planted in neat orchards and cider. It seems cider played a big part in the popularity of Johnny Appleseed during his life, since the apples grown from seed were most often best suited to cider-making rather than eating. After he died the temperance movement gained strength in the US, and this aspect of apple cultivation was pushed into the background.
Despite the focus on Johnny Appleseed (and comparisons to Dionysus) the thing that will remain with me from this section is the descriptions of the wild apple forests around Alma-ata in Kazakhstan. You can get a flavour of the place from the fabulous images here, in an article in Orion Magazine and here, on the BBC website. These wild trees are important because they represent massive genetic diversity. The drawback of grafted plants is that they are genetically identical to their parents, so over time they become more and more susceptible to pests and diseases which evolve freely to take advantage of their stasis.
After the apples come the tulips, and Tulip Mania amongst the unlikeliest of enthusiasts: the Dutch. Tulips are a relatively recent addition to the pantheon of flowers, unlike the rose and the lily which appear in the Bible, tulips appear to have been introduced to Europe from Turkey in around 1550.
Interesting thought from this section: flowers became beautiful before there were ever humans to appreciate them – in a sense flowers are the result of the aesthetic decisions of bees (and other pollinating insects).
Tulip Mania was a speculative bubble in the Netherlands slightly before the middle of the 17th century wherein the prices paid for tulip bulbs skyrocketed, a single bulb fetching the equivalent of a acres of land or a fine townhouse, only to crash thereafter.
The flower in the picture to the left is Semper Augustus, emblematic of the most valued of the tulips during tulip mania. The interesting thing is that the most prized of these flowers – those that had “broken” – were actually suffering the effects of a virus from which their line would eventually weaken and die. “Broken” refers to the variegated appearance with a dark colour, appearing in streaks on a lighter background. The modern Rembrandt tulips are similar in colouring but, according to Pollan, less impressive than the best of the virus “broken”.
A common theme through all these stories is the large variability of the species from which the domesticated cultivars are drawn and the vulnerability of the much more uniform varieties once domesticated.
The third section is devoted to marijuana, clearly a plant for which the author has some fondness. Marijuana has long been cultivated for two reasons: one for fibre as hemp, and one for drugs. Since the early 80’s and the American “War on drugs” marijuana production has been pushed underground, or rather indoors. Pollan recounts the story of the recent cultivation of marijuana by Dutch and American growers. The plant has undergone fairly rapid change in the last few years with the crossing of the large, traditional cannabis sativa and the more compact, frost resistant cannabis indicas. A substantial amount of work and horticultural ingenuity has gone into this process, leading to plants that can produce high yields of the active material in small, indoor spaces. The prize being the $13,000 that a hundred plants grown on a 6 foot square table can yield in a couple of months.
For Pollan there is an element of horticultural challenge in this process, he clearly grows a wide range of plants in his own gardens (from each of the sections of this book) valuing the challenge and the diversity. The garden at SomeBeans Towers is similar: more a plantswoman’s garden than a designer’s garden.
He digresses at length on purpose of intoxication and whether drug taking really does open the doors of perception, or just lead to inane blithering, falling eventually for the former. There’s an interesting section on the neuroscience of cannabis.
The book finishes with a chapter on potatoes, in particular on a genetically modified potato called NewLeaf which was developed by Monsanto to express the pesticide from the Bacillus thuringiensis bacteria (Bt). Organic certification schemes allow the limited ‘manual’ application of the Bt pesticide. In this chapter he visits various potato growers, spanning the ultra-technological to the organic. He highlights the dilemma that he finds GM potatoes more palatable than the non-organic equivalent when presented with the choice, in large part because the level of inputs, in particular fungicides and insecticides, to conventionally grown potatoes is very high. His visit to an organic highlights something from the organic movement in which I’m in favour: which is a willingness to explore different methods of cultivation (and a wider range of cultivars), where I part company is where they say “There must be no X” where X is a somewhat arbitrarily drawn list, enforced with religious fervour.
The section also covers the history of the cultivation of the potato, from the wide variety in the mountain gardens of its native Peru, to its introduction into Europe as a favoured staple crop. Prior to the introduction of the potato bread was the staple food in Europe; wheat is somewhat fussy in its growing conditions particularly in Northern Europe and getting bread from wheat is quite an involved process. Potatoes, on the other hand, are less fussy on growing conditions and exceedingly simple to prepare for eating (stick in fire and wait, or if feeling extravagant: boil in water).
Overall I enjoyed this book, each section seemed to divide into two unlabelled parts one largely factual and one rather more philosophical – I preferred the more factual sections but appreciated the philosophical too.