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A brewing puzzle: solution

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Kudos to Clayton, mantis, and MannekinPis, who were on the right track about how to make beer in 17th century Germany. The trick to exactly hitting arbitrary temperatures without a thermometer lies in the fact that boiling water is always 212 ?F.
Ice is not relevant here, though. For one thing, ice does not have a single fixed temperature, and can be much colder than freezing point. For another, Hans does not have a freezer, electricity, or any other way to make ice!
A traditional brewing technique is:

  • Take 10 gallons of water from the well. Underground temperatures are extremely steady throughout the year, so this will not vary by more than a degree or two. Hans must learn by trial and error what temperature his particular well happens to produce. Let's say this is 50 ?F.

  • Measure out 6.3 gallons, and bring it to a boil.

  • Mix everything back together. 3.7 gallons at 50 ?F plus 6.3 gallons at 212 ?F = the desired 152 ?F.

    There is no need to worry about heat loss once the mash is at the desired temperature. Five or ten gallons of hot liquid has a lot of thermal inertia, and can sit long enough for the enzymes to do their work without cooling too much.
    More complex mashes (used to make various kinds of beer) require a series of different temperatures, which can be achieved by repeatedly boiling the appropriate portion of the liquid and then mixing back together. The measurement could be done by weight, but volume was more often used. It's trivial to do this by ratio ("1 scoop into the small kettle, 2 into the big... 1 in the small, 2 in the big...") without needing any dedicated measuring equipment at all. And having counted out the scoops once, future batches can hit the exact same temperatures just by remembering how close to the top each kettle was filled.
    I think it's pretty amazing that, armed with nothing more than two kettles, a ladle, and a fire, uneducated farmers were able to follow complex mashing schedules such as:

    • 20 minutes at 109 ?F (acid rest: phytase enzymes alter pH while beta-glucanase breaks down gums)
    • 20 minutes at 122 ?F (protein rest: proteolytic enzymes split up the longer protein chains)
    • 30 minutes at 149 ?F (saccharification rest: beta-amylase enzymes convert starch to sugar)
    • 30 minutes at 158 ?F (saccharification rest: alpha-amylase enzymes convert starch to sugar)
    • 10 minutes at 168 ?F (mash out: denatures all enzymes, freezing the mash chemistry in its current form)

      and consistently get within a few degrees of each target temperature.
      But what really blows my mind is how anyone managed to figure out the right temperatures to make great beer, long before we understood enzymes or starch molecules! Those medieval monks must have had a LOT of spare time to experiment :-)aggbug.aspx?PostID=10374543

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