
2+1=4, by quinoa - efavdb
https://www.efavdb.com/quinoa%20packing
======
ddlatham
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._

[https://allthingsliberty.com/2015/05/george-washingtons-
bake...](https://allthingsliberty.com/2015/05/george-washingtons-baker-
master/)

~~~
themodelplumber
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?

~~~
jml7c5
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](https://www.loc.gov/resource/mgw3f.003/?sp=2)

It has been transcribed here:
[https://founders.archives.gov/documents/Washington/99-01-02-...](https://founders.archives.gov/documents/Washington/99-01-02-05193)

>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.

~~~
sukilot
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

~~~
jml7c5
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.

------
ajuc
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 :)

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

~~~
pbhjpbhj
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??

~~~
5Qn8mNbc2FNCiVV
Volume ^^

------
quickthrower2
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.

~~~
dmoy
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)

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

------
dheera
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.

~~~
jameshart
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).

------
JoeSmithson
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.

~~~
kens
> 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%.

~~~
Retric
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.

~~~
OscarCunningham
According to [http://hydra.nat.uni-
magdeburg.de/packing/scu/scu.html](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.

~~~
OscarCunningham
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).

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

~~~
djhaskin987
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.

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recipe protocols are 230 years out of date as well.

~~~
brigandish
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.

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

------
hirundo
.2+.33=8, by popcorn

~~~
lostlogin
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.

------
gus_massa
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.)

~~~
efavdb
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.

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

------
fredophile
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.

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

~~~
quickthrower2
That’s what the black hole said!

------
reedlaw
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.

~~~
kwelstr
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.

~~~
cyphar
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.

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

~~~
cyphar
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.

------
andi999
Before theoretically trying to explain it, why not test it experimentally
first. It might be a misprint.

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

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

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

~~~
saagarjha
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 ;)

------
amelius
This experiment should have been done in an airtight container.

------
nutate
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.

------
PopeDotNinja
I wonder if the mass stays roughly the same.

~~~
brianberns
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).

~~~
davrosthedalek
Hot quinoa is slightly heavier than cold quinoa.

~~~
gowld
why?

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

~~~
judofyr
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.

~~~
pbhjpbhj
No weighing scale ... sounds like a challenge!

------
tigerbelt
No

------
staycoolboy
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.

~~~
perl4ever
>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.

~~~
bhntr3
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/...](https://www.amazon.com/Food-Cooking-Science-Lore-
Kitchen/dp/0684800012)

~~~
perl4ever
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.

~~~
atombender
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...](https://www.nytimes.com/2018/07/15/technology/amazon-used-paperback-
book-pricing.html)

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

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

~~~
eurasiantiger
I cooked some quinea and got what I started with.

~~~
quickthrower2
See whatcha did

------
known
Artificial Intelligence ?

