You might think that Monday's discourse on thermodynamics in the Goldilocks story was the only children's story in which physics plays a role, but that's not true. Physics is everywhere in fairy tales.
Take, for example, the story of Rumpelstiltskin, in which a mysterious little man demands a terrible price for helping a miller's daughter spin straw into gold. This raises the obvious question of exactly how one would go about extracting gold from straw.
The use of the term "spin" might suggest the use of rotational motion-- if the straw were ground up very fine, and mixed with water, it might be possible to use a centrifuge to sift out the trace amounts of gold that might be present in the straw. This would perhaps explain the need for whole rooms full of straw-- the heavy metal content of most plants is minuscule, and so vast quantities of raw material would be required to produce a tiny amount of gold.
The sheer amount of wastage in this process, though, suggests that some alternate method must be employed. The next obvious choice would be to turn to nuclear reactions.
One might suspect that the mysterious little man was using some highly advanced nuclear reactions to convert the nuclei of the atoms in the straw into atoms of gold, perhaps through nuclear fusion. Straw is mostly carbon, and you might imagine a process whereby thirteen or so carbon nuclei were stuck together to produce a single atom of gold. This would still amount to a substantial reduction in the overall volume of material produced, requiring large rooms full of large material, but the gold yield would, in principle, be substantially higher.
This scheme, promising as it might seem, runs afoul of physics. As is well known to everybody but the people who write fairy tales, the nuclear binding energy curve reaches a maximum in the vicinity of iron. You cannot create elements heavier than iron through sustainable fusion reactions. While you might conceivably be able to fuse a few carbon nuclei into iron, getting from iron to gold would require a colossal amount of energy input, something well beyond the resources of a medieval-level society. The existing heavy elements in the universe are believed to have been produced in supernovae, which would tend to have a negative impact of the property values of any kingdom foolish enough to attempt this method of producing gold.
The peak of the binding energy curve does suggest a solution, though. While it would be impossible to fuse carbon into gold, you can use carbon nuclei to make iron and sulfur, and iron and sulfur are the main components of pyrite, also known as "fool's gold." Producing fool's gold from straw is only barely less impressive than producing real gold from straw, particularly in an agrarian society with low rates of scientific literacy. And passing off fool's gold as gold would be entirely consistent with the bad reputation of mysterious little men who make outrageous demands in fairy stories-- they are most emphatically not to be trusted, and their gold often turns out to be worthless trash.
So, there you have a physically consistent explanation of the Rumpelstiltskin tale: the mysterious little man is clearly an alien from a more technologically advanced species, using sophisticated control of nuclear reactions to convert carbon-based plant matter into pyrite, and passing it off as gold in an attempt to obtain human children for biological experimentation and possible cross-breeding.
It all makes sense, now...
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Even if the energy demands of trans-iron fusion are "well beyond the resources of a medieval-level society"... why should an alien like Rumplestiltskin have a problem with that? Bending space-time to travel interstellarly would require massive amounts of energy anyway, he probably uses some function of his ship's fusion drive to generate arbitrary amounts of gold, and the spinning thing is simply a ruse. The gold could be perfectly real, and for him cheap since he probably hails from a post-scarcity economy.
Thank you. I'd noticed that aspect of the story, and it bothered me (I can't say that about the thermodynamics of porridge :-). But, the explanation leaves me with 2 questions:
"the nuclear binding energy curve reaches a maximum in the vicinity of iron"
So that's why fairies hate the stuff!
Straw is mostly carbon, and you might imagine a process whereby thirteen or so carbon nuclei were stuck together to produce a single atom of gold.
Nitpick: you would need 17 carbon-12 nuclei to get one gold-197 (the only stable isotope of gold) nucleus plus some assorted nucleons. There are several isotopes with half-lives longer than a few hours (you would need that much for Rumpelstiltskin to be able to pass it off as real gold, but they all have atomic weights between 192 and 200.
Of course, there is also Asimov's short story "Pate de Foie Gras", in which a goose is able to lay golden eggs by converting oxygen-18 to gold-197 by nuclear reactions--it has iron-54 as an intermediate product, and gets the energy for the second step by capturing the energy from the first step with the help of enzymes and handwaving. There is some oxygen in straw, so maybe Rumpelstiltskin uses the same hypothetical reaction.
The gold and the straw were as golden as her her locks. A blonde will believe pretty much anything.
Summed straight fibers in tension are no stronger than the sum of the individual fibers' tensile strengths and rapidly cascade to failure. If you spin carded (parallel) fibers into helices, behold! When the helices are put into tension their pitch lengths increase and their diameters decrease. They seize one another in compression and the composite is stronger than the summed individual fibers for tension is directed off at an angle. Local failure is grabbed and distributed with dilution. The composite is resistant to sporadic failure causing global failure.
Kevlar thread is useless as an overhand knot. OTOH, if you try to snap the thred in tension you lose fingers.
Uncle Al, you turn up in the darndest places! I need to use Nomex in an application where it will be under tremendous tension, tremendous aerodynamic heating, and a long, thin rod of it must reflex efficiently when bent completely around on itself. I am going with a honeycomb pattern of construction, but is that best?
Anyhow, if I wanted gold I would work on an unobtrusive dredge to work the ocean floor off the mouths of major rivers like the Yukon, the Sacrimento, and all the Siberian rivers. Work the deepest muck you can find, but don't let government know what you are up to or they will make your caper impossible and then demand nearly all your profit.
I have a more prosaic, less fantastical, theory...
One expensive textile product available in the middle ages were brocaded bands made with metallic gold thread as the brocade. This wasn't just gold wire, but rather a flat, narrow ribbon of gold wrapped around a core of silk or flax.
The method of manufacture of this gold-wrapped thread was a closely guarded secret of guilds and guild equivalents. Today, we don't know exactly how it was made, although there are theories.
It isn't hard to imagine calling flax "straw", especially in translation long after the story was originally told. I can very easily see the manufacture of gold-wrapped flax fibers being referred to as "spinning straw/flax into gold".
A claim by the heroine of the story that she can make this thread would be enough to attract the attention of the local nobility, even without the belief that she could transmute straw into metallic gold.
So my theory is that the spinning straw into gold was not so much about transmutation of organic material into gold, but rather about claims of a highly prized and normally cloistered skill in making a real, marketable, and expensive commodity.
Blaise Pascal is close, but not prosaic enough.
Flax culture was developed in Europe in the late middle ages. To make cloth, you wet the flax, then dried it in the fields, a process called retting. When ready to spin, it looked like straw. Most of the spinning was done by young women earning money, usually in the form of gold, towards the expenses of setting up their households when they got married. (Women who didn't get married kept spinning as spinsters.) It does not take a great deal of metaphoric extension to recognize that these young women were indeed spinning straw into gold.
They tended to work in small factories with many other young women. Needless to say, the young men of the day picked up on this, and dropping by to chat a bit was irresistible. In some quarters, at least, this factory system was considered morally suspect. If nothing else, it combined sex, gold, flax and the prospect of children.
Rumpelstiltskin was based on one of those forest throwbacks, not yet in the cash economy that was engulfing Europe. The entire story was a cautionary moral tale warning against daughters joining the burgeoning flax for gold economy. I'm surprised we haven't had an updated version, except the modern girl is text messaging some boy she met online while working at a 7-11. Then again, maybe they have done an updated version or twenty. From a feminist perspective, it's the same old, no sex, no money, no flax, no fun.
Flax culture had a pretty serious impact on Europe in its day. The era is often accounted the first industrial revolution. Just as it is hard to have a contemporary love story without cell phones, flax appeared in other stories from that era. For example, in the story of Sleeping Beauty, another young spinner, it was a sliver of flax that poked through her finger that put her to sleep. (Right, flax, sure.) Pulling it out revived her. Europe back then was full of stories with lots of sex, flax and gold when you come down to it.
Aha, I found my copy. I'll cite Rumpelstiltskin's Bargain: Folklore and Merchant Capitalist Intensification of Linen Manufacture in Early Modern Europe by Jane Schneider as published in Cloth and Human Experience, Smithsonian Institution Press, 1989.