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2+1=4, by quinoa (efavdb.com)
366 points by efavdb on July 3, 2020 | hide | past | favorite | 168 comments

This reminds me of how the Continental Congress ended up appointing a Baker General to serve with Washington during the Revolutionary War.

After the barrels had been transported by wagon out into the field and their contents distributed, soldiers devoid of ovens to make bread pooled their rations and made arrangements for those qualified bakers within their ranks to take the next step. They then went into the local community and used whatever cooking facilities were available, returning later to distribute one pound of bread for every pound of flour a soldier contributed. What they did not tell them was that for every 100 pounds of flour, some 130 one-pound loaves of bread could be produced simply because water was added. This allowed bakers to make a handsome thirty percent profit when they sold the extra loaves in the open market. For those soldiers deciding to keep their flour ration, they either transformed it into a very rough “fire cake” cooked in the coals of a nearby fire or traded it with the local country folk; many instances of straggling and plundering then ensued. There was clearly much room for improvement.


Q: Is the author saying that the straggling & plundering happened because of the annoyance at eating fire cake? That part wasn't clear to me. And is fire cake not made with water?

I think the firecake eaters had perhaps 30% more calories available to them (assuming their firecakes were cooked adequately), so they might not have been the ones straggling. But if a soldier traded his flour to the locals for booze, that would be a different story.

Fire cake is made with water so soldiers who went that route would get more than a pound of cake for their pound of flour.

After a brief search and glance at the citations, leading to "Supplying Washington's Army" by Erna Risch (written for the US Army Center of Military History), then to the original Washington Papers, here is the original letter from Knox to Washington: https://www.loc.gov/resource/mgw3f.003/?sp=2

It has been transcribed here: https://founders.archives.gov/documents/Washington/99-01-02-...

>Of the Articles of subsistence bread is the most essential, and yet of this we have been the most deficient, arising from the want of some general invariable system to govern the whole Army. In the field, all the troops receive flour of the Commissary. Some regiments have soldiers who are bakers and are permitted by the commanding officer to go to some neighbouring house, with other soldiers as their assistants, to bake for the regiment. These bakers receive the flour from the soldiers and return them a pound of bread for a pound of flour, by which means the bakers make a neat profit to themselves of 30 per cent in flour; and often times more, as they put as great a proportion of water as they please, there being no person whose duty it is to superintend them. This flour the bakers sell to the country people in the vicinity of the Camp, to the infinite damage of the public, or occupy public waggons, when the camp happens to move, to carry it away to a better market. Last year at Tappan, one or two soldiers who baked for part of one of the regiments of Artillery, consisting of not more than 250 or 300 men, saved such a stock on hand of the profits of baking for a short time, as to be able, on an Emergency to lend the Commissary of the Park, a sufficiency to issue one thousand rations for eight days.

>In other regiments the soldiers are permitted to carry their flour into the country and endeavour to exchange it for bread. This is always done to a disadvantage. besides, it is a pretence for straggling, and affords opportunities to plunder and maraud. Others again make a kind of bread which they bake on stones, this, besides being unpleasant is very unhealthy.

So the problem was not that soldiers were so annoyed at eating fire cake that they behaved poorly, but that allowing any soldier to his sell ration of flour gave frequent opportunity to leave camp and engage in distracted (or unscrupulous) countryside wandering.

I believe allthingsliberty.com made a mistake in their article. It seems to me that the cut bakers took in the "give 1 pound flour, get 1 pound bread" trade was understood by everyone as a form of payment. In other words, I presume a soldier could choose to make their own flatbread (time-consuming, poor quality, tedious), or they could give their flour ration to the baker and get back a smaller portion of higher-quality food for less trouble. I would be surprised if it was deception, as I cannot imagine mass theft and sale of flour going unpunished by commanders (and by fellow soldiers, particularly during lean times). Though it's possible there is some other primary source that indicate otherwise.

Knox's letter seems clear to me that he was complaining about theft by the bakers.

> and often times more, as they put as great a proportion of water as they please, there being no person whose duty it is to superintend them

The way I understood that passage, soldiers were expecting to lose around 30% of their flour in the deal, but some bakers figured out they could take a larger cut by adding more water. That doesn't necessarily mean the practice of taking a cut is forbidden, only that some bakers gave a worse deal than others.

> And is fire cake not made with water?

It is, why?

I worked in a company making warehouse management systems. After deployment on production for a new customer storing cheeses we found a lot of bugs (the system would say there should be 10 kg of some cheese at particular location but there was only 9.7 kg etc.)

Eventually we realized cheese is losing weight with time and we had to include that into all of our algorithms :)

Reminds me of the angel's share when you're aging whiskey:


Imagine a popcorn factory. Pre and post pop...

It's everso slightly lighter after pop presumably (water content is lost), but a little oil would compensate that, presumably? I'm not sure what point you're making??

Volume ^^

My guess before reading is the resulting chow has more air in it.

Edit after reading: I think I am on the money. I don't think it is a completely sphere-packing phenomenon. Quinoa is fluffy when cooked, not soggy and laiden with completely with water. Packing might contribute but I am betting it's mostly air inside the Quinoa making that extra volume.

Trivially, you can also just cook some rice on the stove, verify that rice is not spherical, and also verify that it gets significantly bigger. (Like 3x bigger per dry rice unit of volume, and you don't (usually) cook water:rice 2:1 for most rices)

Whom among us has not overflown a rice pot on the stove?

2:1 is quite common, because it's simple, despite being not great, especially as amount cooked increases.

Rice isn't speherical, but it isn't a perfectly packed crystal either.

Unless you think air fills up inside each grain, the volume from "air" is the packing volume.

Except that the sphere-packing calculation does actually account for all the additional volume, so if there was some air-absorption too then that must mean that cooked quinoa packs more efficiently than uncooked quinoa.

Squishy things should pack more efficiently since they can deform to better fill the voids left. Not sure if this makes a significant difference here though. It's only the weight of the grains above that would cause the deformation to happen and cooked quinoa is only stacked up a few inches max I presume.

Yes, but boiling quinoa or rice doesn't pack it, it blows bubbles of steam through it.

Volume isn't conserved; only mass is conserved in physics, so your final pot can't have greater mass than what you put in it; it can only have less, considering steam is given off. But volume? All bets are off.

Even if it weren't a packing problem it's not obvious to me that a X mL single quinoa grain that absorbs Y mL water can occupy only X+Y mL. It could be much larger depending on the structure the resulting thing has.

Separately, I've always had to put more water in than the quinoa boxes say.

Indeed - plenty of cooking processes can produce gas bubbles that are trapped or escape leaving foam structures behind that take up considerably more space than the original material. Like bread, for example.

The volume of flour and water you put into a dough is considerably less than the volume of the loaves you'll produce - and a significant amount of the water you put in will have gone by the time they're cooked (also you'll have lost some of the carbohydrates from the flour which has been turned into CO2 and ethanol by the yeast, a bunch of which will also cook out of the loaf).

> It's not obvious to me that a X mL single quinoa grain that absorbs Y mL water can occupy only X+Y mL.

A pretty good example breaking that assumption would be popcorn. given some heat X mL popcorn + Y mL butter is going to end you up with a lot more than X+Y mL.

Exactly. This is also observable in baking, especially with yeast, where the end product is usually lighter because of the evaporation but larger.

I always liked this problem...

What packs more efficiently in a barrel; tennis balls, marbles, or a mixture of tennis balls and marbles?

It feels like the smaller marbles are denser but obviously they actually pack the same efficiency as the tennis balls or any other sphere, the mixture packs more efficiently.

> It feels like the smaller marbles are denser but obviously they actually pack the same efficiency as the tennis balls

That's not obvious to me. Won't the marbles pack more efficiently due to the edges of the container? As a limiting case, consider a container slightly smaller than 1 tennis ball: the packing efficiency of tennis balls will be 0%, while marbles will be something like 60-70%.

Packing efficiency is usually defined for an infinite space because finite containers don’t always favor the same size object.

Consider a marble with a diameter of 2inch and a tennis ball with diameter if 3 inches. A cube of length 9.01 inches now favors the tennis balls where one of 8.01 inches favors the marbles.

According to http://hydra.nat.uni-magdeburg.de/packing/scu/scu.html a cube of side 9.01 can fit 27 balls of diameter 3, but 100 balls of diameter 2. Since 27×3^3 = 729 and 8×2^3 = 800, the balls of diameter 2 are more efficient in this case.

In fact it seems that the diameter 3 balls are most efficient only for cubes of edge-length between 3 and 2+sqrt(2) = 3.414.... These are the sizes for which you can fit in 1 diameter 3 ball, but can't fit in 4 diameter 2 balls. Above that, diameter 2 balls are more efficient (except that a cube of edge-length 6 can fit in the same volume either way; 27 diameter 2 balls or 8 diameter 3 balls).

> Since 27×3^3 = 729 and 8×2^3 = 800

I think you mean 100 x 2^3 = 800. But, yer correct that’s what I get from using a half remembered example without checking.

A "barrel" though is way larger than a tennis ball, so we're not close to the limiting case.

The mixture seems like the intuitive answer to me. A single tennis ball packs the volume of a tennis ball more efficiently than the equivalent volume of marbles.

The problem is ambiguously stated. A "volume of X" isn't well-defined when the point of the problem is to reason about packing efficiency.

Yes. I really like the metallurgy version: An alloy can be denser than pure elements.

I was just talking to a friend about how 1 part water plus 1 part ethanol becomes 1.92 parts solution.

This raised a question for me that I have yet to research/answer. Maybe one of you knows... if the above solution is 50% ABV, what happens if I add one more part alcohol to the solution? Is it now 66.6% ABV? More? Less? How does ABV take into account the fact that this solution is packed together tighter than its constituent parts?

The wikipedia article has all the charts and formulas you need. https://en.wikipedia.org/wiki/Alcohol_by_volume

(To make the above solution 50% abv, btw, you need to keep adding water until it's 2 (liters, whatever) total volume.)

This is a common issue for people doing liquors at home: you mix 1l of alcohol which you used to extract some flavour with 1l of water and don't get back 2l.

Thank you for being the best of HN.

The muderation might be awful, but the users are sharp.

Learned something new, and I'm a chem grad.

Assuming the barrel is an infinite space, and the marbles are small enough to fit in the gaps from an optimal tennis-ball sphere packing:

Not just tennis balls, because after adding all the tennis balls you can, there's still room for marbles to fill in the gaps

Not just marbles, because the optimal sphere packing density is the same whether it's all marbles or all tennis balls. Since all tennis balls wasn't optimal, neither is all marbles.

I figure things get interesting once the ratio between the two spheres gets closer to 1.

(And checking my work, this argument is described in a fancier sciencey way by https://en.wikipedia.org/wiki/Sphere_packing#Unequal_sphere_... )

Define efficiency - marbles are more dense and will fill the barrel with more mass.

This is why baking instructions are done with weight, not volume.

Actually in the US they are still done by volume most of the time unless you're a fanatic or a foodie. All the recipes I've ever read uses use cups and teaspoons.

I can see why it would help though.

Weight helps for consistency, but it’s also much easier: you just put the bowl or pot on the and toss stuff in. Fewer measuring cups to clean, and you don’t have to wonder how much of the honey (etc) actually made it into the bowl.

You can even retare the scale between ingredients if you don’t want to do mental math.

Yeah. Measuring by volume is a nightmare. 3tbsp of unmelted butter? How am I supposed to measure that? 3tbsp of melted butter? So I just have to guess and then melt too much? A cup of brown sugar? Is it packed? To what extent? And now I have to clean that cup because I need it again for flour?

So many deficiencies.

Butter is labelled in tablespoons on the package. You just slice it at the about the right spot. Do an image search for a "stick of butter".

Counterpoint: The butter we often buy comes in tubs. So we measure by weight when possible, and approximate the volumetric conversions.

I've never seen butter in a tub before. We get weird "spreadable" vegetable-based butter substitutes in tubs. Some British people call it margarine but that's incorrect as margarine comes in solid blocks like butter (it's uncommon these days as it's no longer really needed).

In the US we have "whipped butter" which (according to Wikipedia) is made spreadable by aerating it with nitrogen. I recall hearing that it isn't suitable for situations that require measuring because the volume is not the same. (But it does works well on bread or for greasing a pan.)

Great comment. I think a word got missed :), "put the bowl or pot on the scale".

Yeah, they accidentally that word there.

(sorry, couldn't help myself)

Precisely: this is why foodies and fanatics in the US, in spite of the dominant cultural preference for volumetric measure, prefer - like most of the rest of the world - to measure food by weight, this being a great example of how volumetric measurement can be misleading.

Do recipes also say 200g of eggs, or just four eggs?

I saw a pasta recipe[0] the other day that said ~ Wet ingredients: “2 eggs, 3 yolks, plus water to bring it to 185g”

[0] https://youtu.be/m_fu5RaXMVk?t=246

Some recipes require only egg whites or only egg yolks — or a combination of both.

It depends. A normal recipe may say: 4 large eggs, where large is actually a regulated weight range. A baked recipe where the ratios are more important may ask you to weigh your eggs, then use that weight for the flour and sugar. Or... it may just say 4 eggs where it doesn’t really matter.

>a regulated weight range

Under a single region-bound regulatory body, making it useless internationally.

Most recipes are useless internationally anyway, the ingredients are often different locally or hard to source. If you're lucky and you have a kitchen in two different regions or, like me, you live in a non-English speaking country who still wants to cook dishes from home then it's going to affect you. That's a vanishingly small number of people.

Otherwise, most people will know how much an egg weighs, especially if they bake regularly.

Yes, this is a point that is usually neglected. People search for recipes online and assume they will all work. The flour is very different across the world. You can easily get Indian flours in the UK, but it's quite hard to find French and impossible to find American (it is considered not fit for human consumption due to the bleaching process).

> it is considered not fit for human consumption due to the bleaching process

Pretty far up there on "dumbest things I've ever heard/read"

Bleach is not generally considered OK to eat. The flour is naturally whitened by ageing and there are naturally softer flours so no need to chemically alter them.

The good news is that everyone puts their life story before you get to the recipe, so you'll know if they're American or not.

No different than US volume measure where you actually need to have the "measuring cups". Weight is still easier, as you can refer to the reference range of 'large' and reproduce it on a scale.

Eggs are usually uniform enough to not matter. The one exception is macarons, where you measure egg whites by precise weight. But perfect macarons are incredibly finicky.

Eggs are just... eggs, no matter how you write down your recipe. If you made a great cake and wanted to repeat the process, and it had three eggs in it, you'd... write down that you used three eggs. It's not really relevant to how you describe the quantities of the other ingredients you use.

But if you used 220g of flour, you're more likely to recreate the cake accurately next time if you write that down, than if you write down '1 3/4 cups flour'.

Eggs come in different sizes. There can be 100% size differences depending on the type of bird. Typical variation is usually a lot lower.

Yes, even from what you might call an ordinary chicken.

I know this because I have chickens. One hen lays eggs 50% bigger than the others. Another frequently does double yolks. This is far from uncommon.

But, like, I buy them in boxes, labeled 'Large', and... they're all pretty much the same, week after week. So... sure, I can get different sized eggs. But if I want to buy a lot of same sized eggs to cook with, I can do that.

Yeah I do the same. I also put "large egg" on those recipes. Sometimes it matters. Proportions of egg to flour can be significant for some recipes.

Yes (both are correct).

No, and this is a great reminder that any home cook who claims they cook by weight for precision and repeatability is full of it. It turns out that not all eggs are the same, not all flour had the same moisture, not all butter has the same amount of flavor, not all kitchens are at the same temperature.

I don’t know how many times I’ve seen someone in a video boast about measuring the flour by weight for their bread, only to add a completely unmeasured amount when flouring the working surface or their hands.

And there’s a reason most recipes use values that are straight conversions from volume rounded to a whole number. There’s a reason nobody says “the real trick to this recipe is the extra 10 grams of sugar”. Indeed, food preferences are largely based on our upbringings, so it’s no surprise that American tastes are built on recipes that can be measured in cups, tablespoons, etc.

Frankly, garbage. Serious bakers are capable of a lot more consistency than you realize.

> It turns out that not all eggs are the same.

You can weigh eggs, or more often it's actually sufficient to balance the liquid to offset the variation in eggs -- a lot of baking especially isn't just about taste - but about consistency and proper proportions to get repeatable texture and density. It is also generally speaking quite sufficient to deal with food liquids in volume as well since room temperature differences are controlled close enough such that it doesn't matter.

The difference in weight of a cup of water between 20 C and 25 C is negligible.

1 cup of flour on the other hand can vary in actual material by over 20% because of numerous variables from clumping to type of flour.

> I don’t know how many times I’ve seen someone in a video boast about measuring the flour by weight for their bread, only to add a completely unmeasured amount when flouring the working surface or their hands.

Basically bullshit again because: In most cases, the working surface flour won't amount to even 1% of the final product, however as stated volume vs. weight can make double-digit differences.

Your whole "10 gram" of sugar claim is a straw-man.

Baking and pastries tends to require a lot more precision then basic cooking to get repeatable edible results. It's the one reason why pre-made cake mixes and Bisquik are so popular, even with professional chefs.

Eggs are consistent enough that they generally contain the same amounts of the relevant chemicals as another, similar sized egg. As a result, you don't generally need to weigh or measure the volume of your egg to achieve consistency, so long as your eggs are consistent. But you do need to use approximately the proportionately correct amounts of the other chemicals in your recipe.

And you're just making your life easier if you measure those quantities in terms of mass, because it has all sorts of benefits:

1) You don't need to worry about packing - the same mass of table salt and coarse salt, sifted flour and packed flour, confectioners' sugar and granulated sugar; all will have the same amount of the active substance (but the form factor may of course have other effects on your recipe)

2) you can use a fine grained scale like grams, without having to introduce cumulative error (imagine if you tried to measure out 7/8 cup of flour by measuring 42 teaspoons - your error would be huge)

3) you can add it up across combinations of ingredients (100g of flour + 100g of milk weighs 200g; 1 cup of flour + 1 cup of milk has... who knows how much volume? That was, after all, the point of the original article at the top of this thread). This has huge benefits when adding mixed dry ingredients like mixtures of types of flour and cocoa, or mixed dried fruits, where you need to have a reasonably fixed total mass, but the ratios aren't as important. Just keep adding until you have the right total mass - something you can't do with volume.

Measuring volumes is harder, less effective, and more error prone. That would all be the case even if you used a sensible volume measure like milliliters, but it's even worse if you insist on using a volume measure system made of arbitrarily named units like tablespoons and cups where you have to memorize a dozen conversion factors and work in fractions the whole time.

I'm guessing you don't do much cooking.

The vast majority of cooking is done by sight, feel, smell and taste. The key to repeatability is to adjust based on experience. 'Hmm, this doesn't taste right, i think it needs a little more vinegar/sugar/whatever to bring it together'. That's the art in cooking.

Now there is science as well, and this tends to come into play with techniques and ingredients which change considerably when cooked, so things like baking, or bread making (there are lots of examples, but these are a good place to start). You'll find plenty of cooks who say they can't make great cakes, and generally it's because they aren't good at measuring. Bread making is a little bit of both. With the starting point you do tend to adjust as you go along. After a first rise when you knock the bread back you get a feel for how the dough is behaving, and add a little more flour (typically) to bring things under control. Yeast is a live ingredient so you get batch to batch variations you need to correct for.

I'm not convinced by your argument about America and cups - you'll not find that in American restaurants, and I can't remember Americans complaining about how restaurant food 'just doesn't taste right' or something like that!

You don't weigh your eggs?

You don’t have to be a fanatic, you just have to care about getting a consistent result. A cup of dry flour can vary in weight by more than 20%, depending on how you scoop it, the humidity, etc. That’s such a large variance that you would see the difference in the result. Bake a cake with 20% more flour than you should and it’s going to be dry.

assuming the volume of flour changes with humidity because it contains more moisture, wouldn't it also increase the weight?

Not an expert by any means though, so correct me if I'm wrong

When flour gets wet, it sticks together to form dough. Dough can have large air pockets in it. Dry flour with a bit of humidity can also form these air pockets, albeit typically on a much smaller scale.

Whether you pack flour down or sift it through a sieve into your measuring cup can make a huge difference in the weight.

No, not at all. Volume ≠ Weight.

Another example: Some books use paper with bigger volume (so it looks thicker) but of course they are not twice as heavy suddenly.

We use various spoons here in the UK in cooking but not cups (tea spoon, dessert spoon, table spoon). I think it's 2 tea spoons to a dessert spoon, 3 to a table spoon.

These tend to get used for liquids (so you tend to see 1/2 teaspoon of vanilla extract, or something like that).

For solids there's still a fair amount of recipes floating about with oz rather than grams but these tend to be the ones handed down from the 70s!

The USA still uses miles and inches... I'm not surprised that their baking recipe protocols are 230 years out of date as well.

Well, it's really a mixed system.

For examples, we do use parking meters!

There's a difference between accuracy and precision, and there's also a difference between consistency and convenience.

It's the reason I might choose Ruby over C (convenience - Ruby was designed to be centred around the human, like many Imperial measures, and non-decimal currency btw), or use feet instead of metres (because I have feet that are, astonishingly, close to a foot long) or any other number of examples where metric is not the best or a better choice.

I'll leave you to divide 100 by 3 or 12 so I can buy 1 or 4 of those dozen eggs you're selling with £1 while this Victorian street urchin who's had little to no schooling beats you at it because they're using a non-decimal currency with more factors…

tl;dr People in the past weren't stupid, they just had less access to the technology required to maintain a metric or decimal system in a widespread number of contexts. The existence of such technology does not obviate their usefulness.

I wasn't calling Americans stupid. I was simply pointing out that their ways of doing things are a bit dated.

The imperial system isn’t what we use instead of the metric system — we use it in addition to.

Yet, with our “outdated” systems, we seem to have still done alright with regards to our tech, Michelin starred restaurants, etc.

Your Michelin starred restaurants are doing alright compared to which country? Many countries are doing better than the US there, both per capita and even absolute.

Power of 2 volumetric measures are actually quite nice.

Can you be specific as to what they are nice for?

It explicitly means that dividing by anything other than a power of 2 is hard. One third of a quart is... quick, how many cups? Okay, now what's that in ounces?

And that's just dividing by three, which is a pretty normal thing to want your measure system to handle.

Base 10 measures are directly compatible with the number system. Even though metric doesn't admit factors other than 2 and 5, because it's decimal I can still confidently and quickly tell you that 1/3 of a liter is 333ml. Or that 1/7 of a liter is 142ml - and if I want to check that I can just type 1000/7 into a calculator and read off the result. How many ounces in 1/7 of a quart?

How do you expect to use a calculator with dough on your hands?

> How many ounces in 1/7 of a quart?

Why are you trying to divide volumetric measures by weight? You need to measure the liquid's weight and divide that by 7. Liquids differ in weight per unit volume.

:-) There are volumetric and weight-based ozs. There are 128 ozs in a gallon. That is 16 cups to a gallon with 8 ozs per cup.

The problems that the poster one-higher stated are trivial. 128/3 = 42 2/3 ozs. 1/7 of a gallon in ozs is 8/7 * 16 in ozs = just over 18 ozs. 1/7 of a quart is just that answer divided by 4, 4.6 as an off the cuff calculation.

> There are volumetric and weight-based ozs

That's a good point, the good old fluid ounce or "floz" as I would read it as a child. I did used to wonder who Floz was and what she'd done to deserve having her name in so many recipe books :)

That's funny! I just did an image search to see if anyone had ever drawn a picture of her. The first three images on google for floz were a shot glass measuring out 2 ozs of bourbon, Cetaphil, and a container of clear edible glue!

32/7 oz. Was this a trick question?

You seem to be hung up on converting between place values. When you say, quick, how many cups in a pint" it's like asking "quick, how many grams in a kilogram!" You'd look at the person funny.

What? "How many cups in a pint?" is a perfectly normal question. Even if you use both measures you might not know the conversion factor.

"How many grams in a kilogram?" is a strange question because the answer is self-evident.

It's only self evident because you know the answer. How is knowing kilo = 1000 that much different than pint = 2 cups = 16 oz? They're just powers of 2 instead of 10.

Because a kilogram is still just "grams"; the relation between kilo-, milli-, etc. is linear. Metric units allow you translate, for example, 1 liter to milliliters in just one jump. And it's not like there are that many prefixes to remember.

The relationship isn't linear, it's logerithmic, just as the us volumetric measures are.

There are more steps in the power-of-two measures, but hardly anything unreasonable.

The real usability of the metric system, which I think you're getting at is that those prefixes are reüsable between all units, whereas in the us customary system it's no holds barred and everything outside the volumetric is arbitrary.

That said, with length, it is nice having units that break apart evenly at 2, 3, 4, and 6; but I don't think that's quite enough to redeem it.

It must surely be a trick question because you have to ask "which country's pint and cup" to answer it?

It doesn't matter, since the material is singular and specified. A cup of flour (typical in the US) or 120g flour (everywhere else) is the same amount of flour.

edit: It's the case that in the US recipes are commonly specified by volume, with default packing conditions assumed or specified. Here's the top hit for 'cake recipe' on Google for me, where every ingredient but eggs is specified in volume:


edit 2: There are multiple assumptions baked into conventional references. A cup of flour does not mean a cup of sifted flour unless it says so. Similarly, 120g of flour means under one Earth gravity at sea level and not on the surface of a neutron star unless it says so.

If I scooped 8 cups of flour I'll bet I would get 8 different weights. They'd probably all be within some margin of error, but not all the same.

I bake with whole meal, high grade, tipo 00, zentrofan flour and straight gluten flour. If I do it by volume it gets all messed up. Zentrofan and gluten are very fine and seem to pack down much tighter.

I need surprisingly different sized containers to store the same weight of wheat and rye flour. That shows how off volumetric measurement is.

Depends on how well sifted or otherwise packed the flour is and how precisely the cup was filled.

And yet recipes are usually specified in volume in the US. This means packing properties are assumed to be in some default range so that can be neglected:


I use volumetric measures for dry goods all the time. I'm not saying it doesn't work, I'm just saying that it's not as precise as a weight would be. Whether or not that matters is a different story. I would say "not really".

Sifted vs. packed flour disagrees.

Agreed, so recipes call for a cup of sifted flour or to sift a cup of (unsifted) flour, i.e. specifying the approximate packing property.

Or you could just weigh out 120g?

You could. Many or most places do that. But US recipes typically don't, and work out fine. So I guess volumetric measurements that assume default packing conditions often work out OK in practice, though @lostlogin above reports a corner case that doesn't work.

Most people don't sift out the chaff or rocks today, but sifting performs important functions of making flour lighter for certain "light & airy" recipes that cannot be properly performed only by weighing.

And... then you can weigh out 120g of it, right?

Your prior point was that you don't need to sift flour but only weigh it. That is false, as sifting flour changes the properties of the final baked product. You now changed that to, in essence, say that weighing tells you the weight of flour. Yes, weighing tells you the weight of what is being weighed.

My point was that ‘120g of sifted flour’ is a declarative statement. It describes a quantity of an ingredient.

‘Sift one cup of flour’ or ‘measure 1 cup of sifted flour’ are procedural statements. They describe a process to acquire a quantity of an ingredient.

And that, in general, the declarative form is better.

In this case, the forms of the statement are identical. "One cup of sifted flour" is semantically identical with "sift one cup of flour."

The difference is the method of measurement, whether by volume or by weight. Then, it is important to either understand the rules of recipe specification, especially with baking, or to have the recipe specify as to whether there are implicit steps.

.2+.33=8, by popcorn

It’s winter here - I’m pretty sure that firewood bought by “thrown” volume uses the same maths. You stack it and it all vanished.

It's an interesting observation. Can you add some close up photos of the quinoa grains before and after cooking? (With something that does not change of size, for scale.)

thanks for your comment and suggestion. unfortunately we ate it all, but I'll try to add such a picture next time. The truth is that they aren't exactly spherical, but squished in on one side.

Eating ones own workings is a new take on “the dog ate my homework”.

... and that cute little germ/bran tail that automatically pops out and tells you when it's done cooking.

This seems reasonable if the final product also contains something else, like air, or the water is less efficiently packed inside the quinoa. It's easy to pack water less efficiently then it will normally be as a liquid. Freezing it into ice causes it to expand and have a lower density as well.

The crux of this is that volume is not the same as mass.

That’s what the black hole said!

When cooking rice a good rule of thumb is to use equal parts water and rice because a given volume of rice is able to absorb the same volume of water. I imagine the rice or quinoa is expanding as it cooks and absorbs water.

For most types of rice, you'll always use a ratio of 1 cup rice to 2 cups water. When the water is gone the rice is done. Some rice like arborio for risotto take even more.

A lot of people have strong views on the right ratio of water to rice (and I will admit this post is a bit hypocritical given how long it is), but ignore that while their ratio may work when cooking X cups of rice it often doesn't work when cooking 2X cups of rice. Meaning that such ratios don't fulfil their purpose as ratios, they're just an unscaleable recipe for a fixed amount of rice.

For instance, I'm sure a ratio of 2:1 works fine for you if you're cooking 1 or 2 cups of rice, but if you're cooking 4 cups of rice are you going to add 8 cups of water? I hope not, because I can guarantee you will get porridge. Why? Because there are two processes going on which use the water you've added (absorption by the rice and evaporation). The vast majority of rice absorbs about the same volume of water when cooked properly, but you need some extra water to account for the evaporation while the water is hot for the dozen minutes it takes to cook rice. But the rate of evaporation isn't dependent on how much water or rice you have, it's the surface area exposed to the air (which is the same for most rice cooking vessels). So using a simple ratio is incorrect -- one of the processes depleting the water during cooking does not scale with the amount of water.

In fact, your comment about risotto confirms this view through your own experience -- you have to add more water because a pan (which is what most risotto is cooked in) is wider than a pot and evaporates water more quickly (if you don't believe me, compare how long it takes to thicken sauces or evaporate a fixed amount of water between pots and pans). If you try cooking risotto rice the same way as normal rice you'll find it absorbs a similar (though possibly slightly more) amount of water.

This is why most people from Asian households will tell you that they don't use ratios to calculate how much water they need. They fill up the water to the level of the rice and then add enough water such that when they put their index finger vertically and touch the rice the waterline reaches the last knuckle on their finger (about 2cm). If you something more like a ratio, it's about a 1:1 ratio plus an extra cup of water -- but the amount will somewhat depend on the diameter of your cooking vessel.

At least around here rice is typically cooked in a covered vessel so the effect of evaporation should be fairly minor.

Rice cookers are also covered vessels (though they have a small vent), so even if you are cooking rice on the stove evaporation would have a similar impact.

One way to check might be to try to cook the same mass of water as though it were rice and see how much water you've lost through evaporation. 250mL (1 cup) of water really isn't that much liquid to lose in ~20 minutes during cooking -- if you've cooked soups before you may recall that uncovered soups will lose far more than 1 cup of liquid in ~20 minutes.

Before theoretically trying to explain it, why not test it experimentally first. It might be a misprint.

Another similar food for thought: How does a car transform 1 l of gas into 3kg of emissions?

Answer: your car won’t work in space :)

Your car doesn't carry its own onboard oxygen tanks for combustion? Time to go off grid pal! ;)

Actually, I'm not sure if my car would run in space or not! However, it's about as "on the grid" as it gets ;)

This experiment should have been done in an airtight container.

gently triggered by someone having a PhD in stat mech and not having to do the grueling proofs of this sort of stuff that at least I did in materials science.

I wonder if the mass stays roughly the same.

It loses a little mass due to water boiling off, but other than that the mass has to stay exactly the same (barring nuclear reactions, which typically don't make for good quinoa).

Hot quinoa is slightly heavier than cold quinoa.


Heat is energy, so hot quinoa has more energy, which means more mass. All internal energy of a system contributes to its rest mass.

I'm not sure if special relativity applies in the context of quinoa. No scale is going to show a difference in the mass of quinoa caused by relativistic effects of heat differences.

No weighing scale ... sounds like a challenge!

I don't want to be extremely pedantic. But even regular chemical reactions change mass just as nuclear reactions.

It's very small, but it's there. Any change in internal energy will cause a mass change, regardless of the specific fields that are affected.


This is also a great of example of how really smart people with deep knowledge in one domain can totally fail real-world skills.

Anyone who cooks a lot has a gut feel for how different foods increase in volume when baked (breads, like popovers), fried (crispy rice noodles), fluffed (rice) or sifted (macrons!), even if they don't understand packing volumes or programming...

Experience actually does matter.

I don't think the author was expressing surprise that quinoa expands in volume when cooked, but rather at the fun reason why this is the case.

>This is also a great of example of how really smart people with deep knowledge in one domain can totally fail real-world skills.

This is a common sentiment, but what I think isn't so common is to observe that the "real world" is a euphemism for domains where people do not share and preserve accurate information in an easily digestible fashion. It's not really more "real", it's defined in my opinion by being more hostile to copying as mis/disinformation protects social roles.

My opinion is foremost in my mind from spending a lot of time practicing cooking rice, browning meat, and working on my car since "social distancing" has been a thing.

If you're curious enough to read a 900 page book containing very accurate information about the specific processes that occur when preparing most foods then On Food and Cooking by Harold McGee[0] is the book for you. It's not for everyone but I give you my guarantee as an internet stranger that you'll love it.

[0] https://www.amazon.com/Food-Cooking-Science-Lore-Kitchen/dp/...

Thanks, I may.

I have "Ratio: The Simple Codes Behind the Craft of Everyday Cooking" and was unimpressed. The idea of thinking in ratios is useful, but not the oversimplification to a few prototypes. You could look at a recipe as something with a whole bunch of ratios and valid ranges, and document the effects of variation and so on. It would be a much bigger book and not "this little volume contains all the secrets to everything".

Edit: by the way, what is with the Amazon pricing? Hardcover is $25; "mass market paperback", new is $901! Not to mention, the featured hardcover price is noticeably more than the specific new hardcover price of $20.

Amazon sellers use a lot of automated bots which automatically adjust their prices in apparent competition with each other [1]. You can find used copies of rare books that are priced at thousands of dollars. In this particular case, you're looking at a Chinese edition, which is presumably out of print.

On Food and Cooking is a fantastic book, by the way. A real classic that every food enthusiast should have on their shelf. I recommend the hardcover version.

[1] https://www.nytimes.com/2018/07/15/technology/amazon-used-pa...

I wasn't quite as unimpressed with ratio as you seem to have been, but I do think that there is really enough information there for a pamphlet not a complete book. Being able to think of doughs and batters as a state-space of flour/fat/liquid is conceptually useful. In general you might pick up on this from experience cooking, but it's rarely elucidated.

> "real world" is a euphemism

True. I think it is easy to fall into that trap, which after consideration is what I've sort of done.

That's an interesting view about it being hostile to copying. I suppose it often is because it needs practical experience. I often hear that "real world" term used to prop up the status of uneducated people by making their knowledge seem superior and inaccessible to educated people since they can't compete on conventional valuable knowledge such as scientific, engineering, or business.

I think OP approach is very interesting. It's not surprising that particles of food grow as they absorb water. What OP made me realize is that not only particles grow but gaps between them grow too which makes portion of food increase in volume even more.

I initially found this curious too - of course the quinoa increases in volume, why am I reading a blog on this?

But if the quinoa absorbed all the water you'd get 3 cups total, not 4, so where is the extra volume coming from? (In this case the theory is gaps of air).

The 1 cup of quinoa that you added to the start contributes the final missing cup (its packing ratio does not change much, it's just the water that changes its packing ratio).

No, the difference is that at the beginning there is water between the packed dry quinoa grains, while at the end there is air between the packed cooked quinoa grains. That air is the missing cup.

Actually that can't work, the cup of quinoa has air between balls as well. It does have less air because the volume of the balls increases, but the math has to be done from scratch.

It's 1 cup quinoa, 2 cups water, making 4 cups boiled quinoa. So there must be something else going on besides just mechanical absorption.

You gave 4 examples, none of which correspond to the problem in the OP which OP didn't fail in any way.

Is this another edition of "falsehoods programmers believe about quinoa"?

Contrary to popular belief, some quinoas actually have no middle name

I cooked some quinea and got what I started with.

See whatcha did

Willard be damned!

Myth 2. It is pronounced "Qwin-oh-wa"

Is quinoa partition tolerant?

Artificial Intelligence ?

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