48
$\begingroup$

Premise

The premise is an adept modern chemist is transported back in time and is to serve as the court alchemist to a wealthy prince in the late 16th century.

Assumptions:

  • "Transmuting" gold is the chief goal, but the prince would possibly consider allowing for a different output to be yielded from "transmutation," providing its worth the time and resources
  • During this time nobility/royalty of the utmost wealth are documented having many alchemists on the payroll, so let's assume the modern chemist is working alongside actual alchemists
  • The prince's knowledge is expert; he has executed many con-artist alchemists in the past.
  • The modern chemist has disguised his strange accent/language/culture and has learned the local language, so as to communicate without raising superficial suspicion (of course it won't be how he says it, but rather what he says)
  • Though he may have modern knowledge, he has no modern scientific instruments with him; he must improvise everything with the resources available at the time
  • The modern chemist cleverly used his knowledge to predict results of experiments no one else could, and has worked his way to the position of lead alchemist and is partially immune to social ostracization. This means that he must still be mindful of how he articulates his concepts, but he cannot be overtly ostracized because he is different

European history shows that being ostracized by society doesn't bode well for said individual, so the last assumption is particularly necessary. Given these assumptions, which are generous for the chemist, there is still the problem of actually transmuting gold. As far as known science goes, the closest thing the modern chemist can think of that can serve as his "philosopher's stone" is a particle accelerator. He's thinking back to the 1941 Harvard particle accelerator experiment that bombarded neutrons into 400 grams of mercury resulting in a small amount of gold.

Alas, in the 1500's there can be no such luxury (tempting as it may be to throw that into the assumptions too), the modern chemist must bring his expertise to bear in another way if he is to save his hide and not be executed as a con-artist by the expert prince. What the modern chemist also knows is this: the prince may be an expert, but that just means he's an expert within the context of his era. Before the advent of modern chemistry, whether or not a metal was considered gold was determined not by its atomic structure (obviously), but rather if it satisfied the right properties: luster, malleability, color and weight.

Question

Could an adept modern chemist lead a team of obedient alchemists to produce a material that is extremely gold-like in terms of its physical/chemical properties? If so, roughly, how would he go about it? (no chemical formulae is required, just a general description)

Quality Metric 1: The more gold-like the output the better. This way, when rival alchemists present their "transmuted gold" the modern chemist's output will seem far superior, and thus improve his standing in society. To reiterate, by gold-like we mean properties including but not limited to: luster, weight, hardness, ect.

Quality Metric 2: If you are vehemently opposed to the idea that the modern chemist can yield a material that has properties more similar to gold than the material the 1500's alchemists transmuted, then propose the next-best way to save his skin.

$\endgroup$
5
  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – L.Dutch
    Commented Nov 29, 2018 at 21:03
  • 1
    $\begingroup$ I'm 10 billion percent sure I saw a similar story somewhere... $\endgroup$
    – ANeves
    Commented Nov 30, 2018 at 13:03
  • 25
    $\begingroup$ After achieving the position of lead alchemist, only copper, silver and gold alchemist positions are left. $\endgroup$
    – npst
    Commented Nov 30, 2018 at 14:57
  • 2
    $\begingroup$ His knowledge is expert, he's executed con-artist alchemists. He wants to transmute substances into gold. What?! I don't think there is such a thing as a non-con-artist alchemist by this line of reasoning. $\endgroup$ Commented Nov 30, 2018 at 21:28
  • 1
    $\begingroup$ @Apollys I see your point, but Issac Newton, as clever a man as any, was in his youth an ardent alchemist. Alchemy has a certain connotation now, but it took centuries for alchemy to be totally discredited in the transmuting regard. So you're right in that it's not a clever thing to expect to be able to transmute substances into gold, but given their knowledge at the time, it was understandable. Even Newton dabbled. $\endgroup$ Commented Dec 1, 2018 at 4:28

12 Answers 12

107
$\begingroup$

Why struggling for gold, which any king and even merchant of the medieval world has, when you can go for Aluminum, which no king yet has?

  • Aluminum is shiny, like gold.
  • Aluminum is malleable in thin foils, like gold.
  • Aluminum, once passivated (i.e. covered by a thin layer of oxide), stops further oxidation. Gold is not oxidized at all, but no one will notice that subtle difference.

Since you are not aiming for mass production, sized on the needs of modern days, but you need to produce only small batches, you can set up a small electrolytic process to separate Aluminum from Bauxite.

Before the invention of the Hall–Héroult process, Aluminum cost was higher than gold, and considering its low density it will be appreciated also the lower burden of its transportation.

You will also have 0 risks of some competitor unmasking you, because nobody except you knows the technology and you are actually doing no trick.

$\endgroup$
16
  • 32
    $\begingroup$ I think it was Napoleon who had an Aluminium cutlery set for really important guests. The rest would use silver. $\endgroup$
    – Windlepon
    Commented Nov 28, 2018 at 13:38
  • 4
    $\begingroup$ The cap of the Washington Monument was originally made out of Aluminum. $\endgroup$ Commented Nov 28, 2018 at 19:13
  • 3
    $\begingroup$ Clean aluminum is not strong(and making duraluminum is hard) and gets scratches easily. Also it has low density which makes it unlike gold/silver. $\endgroup$
    – Vashu
    Commented Nov 29, 2018 at 0:00
  • 5
    $\begingroup$ If your chemist is historically inclined, they'll know how to separate aluminum by reaction with sodium, which doesn't require electricity. (It does require a pretty good furnace to reduce soda ash to metallic sodium.) $\endgroup$
    – Mark
    Commented Nov 29, 2018 at 8:03
  • 10
    $\begingroup$ Also, at the time aluminium was more valuable than gold - theatlantic.com/technology/archive/2014/11/… $\endgroup$ Commented Nov 29, 2018 at 14:29
103
$\begingroup$

Gold is one of the densest metals in existence. Only a few metals and alloys are heavier, but they are not much easier to obtain, like iridium, osmium, neptunium and plutonium (!). If you use any lighter metal and try to make it look like gold, you will be discovered and beheaded—a method of determining the density of alloys pretending to be gold was discovered by Archimedes around 200 BC: https://en.wikipedia.org/wiki/Eureka_(word)

Luckily for you, and contrary to popular belief, alchemists were not tasked with transmuting common metals to gold. At least not by smart princes. If you think about it, why would a magician who can produce gold out of common elements even need an employer? To take all the gold from him? That's the opposite of what most smart people look for in employment :)

Alchemists, at least those in princely courts, were very educated people. They were doing something much more useful than transmutation: they were improving the quality of gun alloys and gunpowder. We're talking about an era when artillery becomes a common and important element of war, and handguns are improving to be actually somewhat useful too.

The stories of alchemists dealings with Satan are rumours originating in the smell of sulfur and mysterious fires coming from their workshops as misunderstood by the less educated courtiers, and also probably used as cover stories by princes who wanted to keep their real interests secret from their cousins in other courts.

In conclusion: don't bother with gold. Learn how to make really good gunpowder and maybe some alloys, and the prince will give you gold instead of waiting for you to make it from dirt.

$\endgroup$
7
  • 32
    $\begingroup$ One hundred times this. Nobody was looking seriously into transmuting lead into gold, and nobody was paying for such research. (OK, almost nobody; there were from time to time crooked alchemists and foolish princes, but such examples are rare and everybody at the time recognized them as crooks and fools.) The modern chemist only has to demonstrate how to make guncotton and his carreer is safe. $\endgroup$
    – AlexP
    Commented Nov 28, 2018 at 11:10
  • 4
    $\begingroup$ There are many other valuable things a modern chemist would be able to teach 16th century craftsmen to make, as well. For instance, much of what we know about organic chemistry today was discovered during the 19th and early 20th century quest for cheap, safe, bright, durable fabric dyes. The modern industrial processes might be a little too dependent on petroleum and electricity, but that just gives your character a chance to demonstrate their ingenuity. $\endgroup$
    – zwol
    Commented Nov 28, 2018 at 13:24
  • $\begingroup$ @AlexP Nobody was into chrysopoeia? Nobody?...not even people who were Emperor for 35 years? This is literally the exact person the OP is describing.... $\endgroup$
    – kingledion
    Commented Nov 28, 2018 at 14:09
  • 8
    $\begingroup$ @kingledion: Emperor Rudolf II had a lot of extra-curricular interests, and he spent a lot of money on all kinds of women, all kinds of art, all kinds of books, all kinds of scientists and pseudo-scientists, and all kinds of clairvoyants and would-be magicians. However, his extra-curricular expenditures remained under control and did not jeopardise the treasury, unlike his military efforts, which did -- and, eventually, resulted in rather dire consequences. Had he been more interested in extra-curricular activities and less interested in imperial stuff the empire would have fared much better. $\endgroup$
    – AlexP
    Commented Nov 28, 2018 at 14:32
  • 6
    $\begingroup$ Also, modern chemist is pretty certain no other alchemist is going to come up with gold, fake or real, so now and then saying “I still didn't manage to make gold, but I came up with this alternative to gunpowder that makes less smoke… this beautiful dye… this way of making stronger steel…” will still make him the best of the bunch by far and thus great career. $\endgroup$
    – Jan Hudec
    Commented Nov 29, 2018 at 21:03
36
$\begingroup$

Your modern chemist would be foolish to even try to make or fake gold. Instead, you make something that will cause other people to willingly give you THEIR gold. For instance, look the commercial possibilities in the aniline dyes, which should be easy for a modern chemist, and from which fortunes were made in our own history: https://library.si.edu/exhibition/color-in-a-new-light/making

$\endgroup$
1
  • 18
    $\begingroup$ This. Aspirin, penicillin, and other medicines, gun powder and other explosives (how about some C4?), smokeless powder, better metallurgy or "new" metals like the aluminum mentioned in another answer, or knowledge of the world - 1500s still had plenty of "undiscovered" land and routes... Heck, if real gold is a must, lead an expedition to sail east from China (China/Japan were known then...) and "discover" the west coast of America, which will include California and you can have a little private gold rush 250 years early. $\endgroup$
    – ivanivan
    Commented Nov 28, 2018 at 18:59
20
$\begingroup$

The only answer is platinum

Many other answers have pointed out the density problem. Since Archimedes was able to determine the difference between pure gold and electrum (gold alloyed with silver) using density, this should be a reasonably well known process for an 'expert' king. If you really want to trick the king into thinking he has gold, the only element that has most of gold's physical attributes (malleable, ductile, non-reactive, and very very dense) is platinum.

However, there is still one significant difference: melting point. Pure platinum would not be meltable with 1500s technology, you can't get a fire hot enough until the coke ovens of the later Industrial Revolution. A wise proto-chemist will know this isn't exactly gold. But, I'd hardly say that is disqualifying. If gold is valuable, how valuable is unmeltable gold (you can call it aurum indissolubilis in Latin)?

How to get some platinum

There are two basic ways you can separate platinum.

First, from nickel based ores, you can try to separate it magnetically. Platinum is paramagnetic, unlike ferro-magnetic nickel and iron. If you run an electromagnet over ground up ore, you could separate out the platinum. This won't be cheap or easy, but with some obedient apprentices, some copper wire, and a watermill, you could build both an ore grinder and a basic dynamo.

Second, you can electro-refine a copper ore. You basically make unrefined copper ore into a battery in a sulfuric acid bath (sulfuric acid was known as 'oil of vitriol' at the time, so you could get your hands on it). The majority copper will be dissolved into the acid bath, while the less reactive (or 'noble') elements like gold, silver, and platinum will end up in the sludge at the bottom.

So the real challenge is then finding ore with platinum in it. There, I can't really help you, I'm not sure how to identify those ores. But, hopefully, the chemist going back in time has some time to prepare, and get some mining maps or something.

Conclusion

If the goal is to simulate creating gold, the best way to do it is to separate platinum from various ores, using one of the two listed methods. This is about as close as you will get to the Philosopher's stone without a nuclear reactor to help you out.

$\endgroup$
6
  • 4
    $\begingroup$ Platinum was so common in some New World ores that the Spanish literally just threw it out because it seemed to have no practical use. In fact, it was first described in 1557 - people of the time knew it existed, but working it would still be a valuable secret that they wouldn't figure out for another 200 years. $\endgroup$
    – Cadence
    Commented Nov 28, 2018 at 14:01
  • $\begingroup$ @Cadence Indeed, it was described as a peculiar gold "which no fire nor any Spanish artifice has yet been able to liquefy." Something like... aurum indissolubilis maybe? Where do you think I got that name :) $\endgroup$
    – kingledion
    Commented Nov 28, 2018 at 14:02
  • 2
    $\begingroup$ Sorry, but no go. The attribute that you left off the gold list is softness, which was very well-known. And platinum is very hard. $\endgroup$ Commented Nov 28, 2018 at 18:29
  • $\begingroup$ @WhatRoughBeast Platinum's Mohs/Vickers hardness is 3.5, gold is 2.5. Copper is 3.0. Different...but not that different. $\endgroup$
    – kingledion
    Commented Nov 28, 2018 at 19:05
  • 2
    $\begingroup$ @WhatRoughBeast What are you going on about? Malleability is on the list in my answer. Hardness is represented by ductility, a more unique property of gold, related to its softness. Also, this is a modern chemist, so he wouldn't be limited by the knowledge of the day, and I include two feasible methods of purifying platinum. I get the impression you didn't read the question or answer thoroughly. $\endgroup$
    – kingledion
    Commented Nov 28, 2018 at 19:34
11
$\begingroup$

Forget gold. You can't do it. You can't even come close. If your prince wants riches, how about synthetic gemstones?

You might be able to produce diamonds through the chemical vapor deposition process, but the stones produced will be tiny, and prior to De Beers' marketing push, they were considered a fairly boring gemstone.

You could put together a suitable oxyhydrogen torch, and fuse alumina into synthetic rubies and sapphires. Alumina is pretty ubiquitous, and you can vary the color by adding trace amounts of iron, copper, chromium, and other metals to the mix.

Synthetic emeralds are probably not an option, since the techniques for making them are still mostly trade secrets, and appear to involve materials or material purities that would be unavailable in the 1500s.

The last of the cardinal gemstones, amethyst, requires high-pressure conditions for synthesis, though the main ingredient, silica, is even more common than alumina. You could try making it, but the metallurgy of the time means you're more likely to blow up your lab than produce gemstones.

$\endgroup$
5
  • 1
    $\begingroup$ I don't see how you could do CVD in pre-industrial revolution. $\endgroup$
    – tox123
    Commented Nov 28, 2018 at 23:14
  • $\begingroup$ @tox123, diamond's a special case for CVD: you only need a vacuum, methane, hydrogen, and heat. Getting the vacuum is borderline (the guy's a chemist, not an engineer), which is why I've listed it as a "maybe". $\endgroup$
    – Mark
    Commented Nov 28, 2018 at 23:18
  • $\begingroup$ High pressure + poor metalurgy just means you need to build your press larger and thicker. Or make some good-quality steel first. That would get the prince's attention on its own. $\endgroup$
    – Perkins
    Commented Nov 30, 2018 at 17:17
  • 1
    $\begingroup$ @Perkins "Sorry, I can't make you gold. But I can make you better swords, so you can go take that other Prince's gold instead?" $\endgroup$ Commented Dec 1, 2018 at 14:46
  • $\begingroup$ @Mark Vacuum is easy. He just needs to know a glassblower and the history of his own profession. Getting the mercury needed should be easy since alchemists loved to experiment with that stuff. And, on the plus side, he knows how to handle mercury safely so he won't poison himself like they usually did. youtube.com/watch?v=viJ3T-1KZqY $\endgroup$
    – Perkins
    Commented Dec 3, 2018 at 17:01
9
$\begingroup$

Gold is nice and shiny, but you can not eat it and it does not give you any power to protect the gold you do have. But troops are nice. There are only a few problems with them.

They need feeding. So increasing food production by inventing synthetic fertilization is Huge. You need less people to grow food, you need less land for the same army production.

Another problem is logistic of army march. So you invent some basic food preservatives. Any of the simple ones will do. And you can transport much more food on longer routes. So no war of attrition against your lord.

And as for the troops equipment, steel is nice but tricky to produce.... if you don't have the right knowledge. And good steel can make your small army strong as a big one.

Conclusion

So going for something petty like producing few grams of gold-like substance is not as useful as providing your lord with the means to rob all his neighbors of the real stuff.

Afterthought

If still in a pickle, just destille some fungi juice and make him really happy

Or if you really want something with only value, then produce something like a purple dye that was in the time much more valuable then gold.

$\endgroup$
2
  • 7
    $\begingroup$ "increasing food production by inventing fertilization" is not actually a thing. The necessity and desirability of fertilization was well-known. I suspect you mean inventing nitrogen fertilizer, with the classic being the Haber ammonia process. Of course, this will be a challenge, since a) you must separate nitrogen from oxygen, b) generate hydrogen, and c) react the two, typically at 450 C and 200 atmospheres. Oh yes, and d) you have to do this on an industrial scale. Like, in ton lots. And did I mention that ammonia is extremely toxic? Or that hydrogen and hydrogen - Hindenburg! $\endgroup$ Commented Nov 28, 2018 at 18:37
  • 1
    $\begingroup$ Preservatives were also known -- salt being the most common. The problem, like that of fertilizer, is synthesis in sufficient quantity. A chemist and a chemical engineer have very different skillsets. $\endgroup$
    – Mark
    Commented Nov 29, 2018 at 7:44
4
$\begingroup$

Most of the great questions of alchemy, like transmuting lead into gold and elixirs of eternal life, have not only failed to materialize but turned out to be impossible in any practical sense. So I don't think you have much potential there. As you remark, one could make counterfeit gold, but why bother when there are other much more valuable legitimate things you can make?

  • Many dyes were extremely valuable, because they could only be produced through laborious processes in tiny amounts. This is why royalty wore purple, for example, it used to be very hard to make the dye and only kings could afford it.
  • Aluminum used to be more valuable than gold. Many other metals were expensive because efficient production methods did not exist.
  • Better steels and other alloys can be used for making very high quality weapons.
  • Chemical fertilizers could greatly improve agriculture, which had a huge influence on the economy back then.
  • Various methods of preserving food could provide enormous strategic advantage in war and trade.
  • Electricity could be discovered centuries early. Chemical batteries are not hard to make, even modern generators are pretty straightforward if you have access to a King's craftsmen.
  • Gunpowder and other explosives are very useful for military purposes, mining and construction.
$\endgroup$
2
$\begingroup$

Brew poisonous chemicals & create bombs etc.

A prince may be interested in Gold, in order to gain money and power. But why ? He wants to win against his enemies: other kingdoms.

Also, the more Gold floods the market, the cheaper it becomes.

So, propose him some poisonous stuff. It helps him to reach his goals, allowing him to easily assassinate leaders causing chaos in the other kingdoms.

Also, many poisons are easy to create and show great effect. And even more of them could be of great use in battles ! Think of grenades and other explosives, or even guns.

To make sure your chemist isn't killed, make him keep all the formulas secret, stored only in his head. That way, if the prince kills him, he looses his advantages in combat and against other kingdoms.

PS : One example for a family that made their way to power using poison would be the Borgias.


Also, think of some other nice modern chemicals you could present him : sleeping gas(chloroform) etc.


Totally different attempt : cook some meth/other drugs. Make the prince addicted. And then he'll neeever let you be killed. He'll protect you to the end of his life.


TL;DR

Forget the Gold. Basically, with modern knowledge and basic education, you could easily become his new leading scientiest and thus hardly replaceable. By keeping some key formulas etc. secret you can also make sure that you'll always be needed.

Also, I can think of tons of extremely useful chemicals for all purposes. Others already mentioned fertilizers.

$\endgroup$
12
  • $\begingroup$ While equally valid an answer as the others, I question the morality of the modern chemist becoming the producer of highly-addictive synthetic drugs or dangerous chemical WMDs just to gain some acclaim. There are plenty of ways for the chemist to distinguish himself to his 16th century peers without also needing to be a sociopath. $\endgroup$
    – Abion47
    Commented Nov 29, 2018 at 21:55
  • $\begingroup$ @Abion47 Drugs are just the safest way. The prince appears to be a "not-so-nice" guy. You can't trust him. That's why you have to control him. If you produce anything else, he may decide to kill you, just because of the risk that you may change sites. If he's under drugs, the decision isn't up to him anymore. $\endgroup$
    – Luatic
    Commented Nov 30, 2018 at 13:51
  • 1
    $\begingroup$ Because devoted addicts of highly-dangerous and controlled substances have historically been capable of making logical and predictable decisions both while under their effects and while in withdrawal. $\endgroup$
    – Abion47
    Commented Nov 30, 2018 at 17:20
  • $\begingroup$ Also I have to disagree. Using drugs to manipulate the prince into keeping you around by hooking him on drugs is far from a safe course of action. Nobility/royalty of the time seek power via control and have not been keen on te idea of being controlled. Once he realizes what you are doing, he will have you put to death, with the only question being if he plants spies in your laboratory to learn your process first in order to reinforce the point that he doesn't need you, only your drug. $\endgroup$
    – Abion47
    Commented Nov 30, 2018 at 17:23
  • $\begingroup$ The only thing that can put you in his good graces long term is to give him what he really wants - a means to control. This can be through military conquests by supplying him with efficient gunpowder or other explosive substances or economically with synthetic gemstones, dyes, or other precious commodities that are difficult and expensive to make with 16th century means but trivial to a modern chemist. Not to mention I imagine that any given person would be much happier making these things than hard drugs and mustard gas. $\endgroup$
    – Abion47
    Commented Nov 30, 2018 at 17:26
1
$\begingroup$

Gold is thought to have been produced in supernova nucleosynthesis, and from the collision of neutron stars,[47] and to have been present in the dust from which the Solar System formed.[

Wikipedia https://en.wikipedia.org/wiki/Gold#Origins

The reason they think that is the maths show that all the gold on earth couldn't have been produced in the previous two generations of supernova the earth and sun was made from.

Making Gold cannot be done with chemistry. It requires fusion and I suspect it is endothermic. Iron is the last exothermic fusion in a sun.

As a rough rule of thumb, atomic is two magnitudes of order stronger than chemistry, and sub atomic two orders again.

Think common chemicals that have been around for a while. Like gunpowder. One big invention (that saved a lot of towns) was to make it while wet. Dry it. Smash it up with wooden hammers then sieve it. This gave quality control over grain size and thus predictable burning. And the neighbours didn't have to die.

$\endgroup$
1
$\begingroup$

Other people who were asked to turn lead into gold did instead turn clay into china. Well, at least one did. If you can figure out how to create china you will make your prince very happy.

$\endgroup$
1
$\begingroup$

when faced with the issue of making gold why not respond with "but your majesty certainly that would not be considered wandering into the realms of magic?" in those superstitious times were magic was feared just the mention of gold and magic should be enough to put the prince off. if this does not deter him recommend that he seeks out a witch, as magic is not something a meagre alchemist could ever perform. both situations ensure your survival and the upkeep of your reputation. instead offer him other valuable metals like steel for weapons which is certainly something that would catch his interest. tell him that it would make weapons and armour far superior to all other major powers in the world. this would be more than enough to avert his focus from gold if the previous plan fails. also if you were able to find some common medicinal plants or fungi some basic medicines could be created which would make you very popular with the army.

$\endgroup$
1
$\begingroup$

Hide the gold in solution

During the German occupation of Denmark, the gold Nobel Prize medals of two Jewish scientists were hidden as a solution on a high shelf of a laboratory, and were never stolen. If a gold solution or salt can be surreptitiously introduced into the alchemical reaction, real gold can be produced, confirming the alchemist's power.

This solution comes with some major issues, however. First, aqua regia had been known for roughly three centuries already. Alchemists with gold fever will recognize the smell of the reagent and the color of gold (III) dissolved in it. (It is possible modern scientists might not have recognized the solution on the shelf in Copenhagen ... more possible that they simply did not care to comment about it to their armed visitors, I think) Ordinary legerdemain may be tricky - solid tetrachloroauric acid will surely be recognizable, and according to Wikipedia at least, colloidal gold was known in the 16th century, even if it was rediscovered in the 1800s. Nonetheless, if the alchemist can disappear some gold into aqua regia while unobserved, precipitate it as some salt or colloid that he mixes with other strongly colored components such as cinnabar or vitriol and slips into the reaction under the noses of his examiners, and introduces this into a very lengthy process of mumblewinknudgification, he can eventually wring out the gold.

If another alchemist spots the deception anyway, he still might not rat out our protagonist, because odds are he has done the same thing himself before. And it is not healthy to convince the King that alchemists are just flim-flam men. Basically, the trick has to be good enough to convince one alchemist watching that another alchemist watching would believe he honestly might not have noticed.

The process need not be very efficient - should not be very efficient, because our protagonist certainly doesn't want to be told to do it again. Instead, he should be convincing about how his talents are so much better put to use making precious aluminum or stainless steel, or any of the alternatives suggested in the other answers.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .