# Milk and wine

The US uses a mix of imperial and metric units of measure. Some people, almost all outside the US, are quite agitated by this. In practice, the two systems coexist peacefully.

Americans buy milk by the gallon and wine by the milliliter. Milk typically comes in gallon jugs, and wine typically comes in 750 milliliter bottles. The inconsistency is curious but harmless.

For practical purposes, milk is sold in units of jugs, not gallons. And wine is sold in units of bottles, not milliliters. When I go to the store to buy a jug of milk or a bottle of wine, I’m not that aware of the units. If overnight the size of a milk jug changed from one gallon to four liters, or if wine went from 750 milliliter bottles to 25 fluid ounce bottles, no one would know.

If you went to a store determined to buy exactly equal volumes of milk and wine, you couldn’t do it. You’d need to buy more containers of each than any store could possibly sell [1]. But nobody ever does this.

And if for some bizarre reason you really did want to buy equal volumes of milk and wine, the biggest problem would not be gallons versus milliliters but rather the uncertainty in both. A jug of milk isn’t exactly one gallon, nor is a bottle of wine exactly 750 milliliters.

Related post: In defense of complicated measurement systems

[1] A US gallon is 231 cubic inches, and an inch is 2.54 centimeters. From this can work out that 31,250,000 milk jugs contain the same volume as 157,725,491 wine bottles.

## 9 thoughts on “Milk and wine”

1. SteveBrooklineMA

It’s surprising how little that wine bottle holds. Just over three cups, while the milk jug next to it holds 16!

2. mpledger

You said:
Some people, almost all outside the US, are quite agitated by this.

When you start losing multi-billion dollar space objects because someone used the wrong system of measurements then you ought to be a little agitated.

3. During an employment lull, I spent the first half of this year tutoring algebra full-time with “at-risk” high school students, all of whom had failed algebra at least once, and most of whom had failed entire years of school (many were over 18).

I was bombarded with the usual questions: “What is it good for, and when will I ever use it?”

Looking for some concrete applications, sure enough, the text had a few problems involving unit conversion, rates, and the beginnings of dimensional analysis (stuffed in among some truly horrible “fake” word problems). I was amazed to find that while the students could learn the math, they had a terribly poor grasp of units!

Over 2/3 of the students didn’t know how many feet were in a mile, and over half didn’t know how many ounces were in a gallon. Nearly half of the students had trouble using Google to find the conversion factors! Only the few students who actually cooked meals had a real clue. Some adamantly insisted a quarter-mile was measured in seconds, not feet. Sigh.

Is there a word in metrology that is equivalent to math’s “innumerate”? Whatever it’s called, I had an epidemic of it.

On one hand, this supports John’s assertion of package-oriented units (“jug”, “bottle”) being the fundamental units of daily life: These students functioned well enough in their daily world. On the other hand, its scared the heck out of me. And it also frustrated me, as my brain went blank trying to find starting points for them.

I finally did find a lever to “make units matter”: Money. These students could readily approximate value comparisons in their heads that they struggled with on paper: They knew how to stretch a dollar and make use of a sale. So I gave them some increasingly difficult pricing, percentage sale, two-fer, metric/imperial and other similar purchase choice complications, and they were routinely able to solve them with minimal assistance (though in highly variable time). I even added different currencies to the mix.

This soon devolved into a raucous contest, where teams of students took ads from local supermarkets and kept score based on who had the best prices for each general kind of goods: Liquid dish soap, frozen broccoli, and so on. Though most often they focused on candy, deserts, and energy drinks.

With only a little nudging, they went on to compare the lifetime costs of different cars, including purchase price and gasoline/electricity consumption. Then they repeated it for some used cars. Then they added simple-interest loans to the mix.

A few of the students who wanted muscle cars soon added a second economy car to their wish-list, then decided to get the economy car first. I let them know they had just proved that algebra can save lives! But the motorcycle folks literally didn’t buy it.

We didn’t get as far in algebra that week as we needed to, but at least the “Why” questions stopped. Completely.

4. SteveBrooklineMA

Very nice story BobC!

5. Stefano

I’ve noticed the jug of milk I bought is leaking, but fear not! I have plenty of empty wine bottles I can use. How many do I need to fetch?

I added 3 jugs of milk to the shopping bag, so it now wights at least… it’s heavier!

Using easily interchangable units for different concepts does have practical advantages. Furthermore, even for, let’s say milk, it is not uncommon that a recipe will say you need 250ml of milk, but the shop sells it by the pint. Is half a pint enough?

6. Tomas Singliar

What is the notion for “least common multiple up-to”?

To buy the exact same amount, just get a jug of milk and about 6 wine bottles. Then drink a bit less then a bottle of wine and voila! You could drink the milk too but the former option is more canonical.

7. Ah John, you’re not usually wrong, but you’re wrong here.

Buying milk is easy. Maths is supposed to help with things that are not obvious.

You are in the supermarket. The recipe calls for 1 cup of milk for one cake, and you are making 20 cakes for the bake sale. How many gallons? 1 x 20 / 19. By comparison: the recipe calls for 250ml of milk for one cake, and you’re making 20 cakes, how many litres? 0.25 x 20. In gallons you’d guess 1.5 to be safe, in litres you know it’s 5 exactly.

There is a tenet of Perl to make easy things easy, and hard things possible. Adding non-trivial unit conversion makes offhand calculations like this impossible without a calculator; it pushes a lot of this into ‘impossible’.

Although imperial units make it marginally easier to understand normal things in normal amounts (cups of flour, fluid ounces of baby milk), it makes it much harder to relate heterogeneous sets of things; I have storage containers in gallons, how many cups of flour can I fit in them? I can lift 50 lb, can I carry this plastic box if I fill it with water?

Everyday life is heterogeneous, varied, complicated. Specialised units make easy things easier, but hard things impossible.

8. Job Eagleton

What about tyres! Over here, Ireland, mm for the width and inches for the diameter.

9. Roger Alberque

The imperial system functions like a folkloric mashup of ancient units. In ancient times, it may have been sufficient to measure length in elbows, and that there is a difference between the Egyptian Ell and the Greek Ell.

Sure, there is a US gallon, which differs from the British gallon. But there is also a US dry gallon. How did one get to 231 in^3 for 1 gal? And then 128 fl oz for 1 gal, making a wonderful conversion from in^3 to fl oz. The pound force and pound mass issue is also very confusing, even to US engineers. Feel free to continue using those units, and make mistakes. The rest of the world has moved on.

Actually, the US has moved on as well. Nearly all imperial units are defined as derivatives of exact SI units. One gallon is defined as *exactly* 3.785411784 dm^3. So much for doing your own thing.