On jumping to conclusions and historical data.

In discussions that refer to data about historical topics, the non-math folk often fall for the correlation - causation error, as well as misinterpreting their evidence.

It is generally accepted that height actually declined somewhat in late period and early modern times (see, for example, preserved sites like Williamsburg or Jamestown, where door frames and hallways are significantly smaller than nowadays), the reason having to do with more widespread malnutrition and chronic health problems emerging in the 14th century and continuing on until the 18th century. (from a mailing list focusing on medieval history.)

Average is a really tough thing to deal with here and there are a bunch of problems with this statement.

Let's deal with averages first. It's pretty easy to find the average height of modern people. They're alive and measurable. You call together twenty folks at the mall and ask them their height. Convenience sample leads to selection bias, so you retry with a cluster sampling. That's better, but did you happen upon the community of immigrants who are shorter? SO you expand your search and try a more systematic approach. In the end, you have a sense of the average height.

Now try that for the 14th century. Your sources are whichever bones you've been able to find and measure and a few written claims. Not much for numbers there.

Second issue is that pre-19th century doors, hallways and buildings weren't built for standard-sized people. They were built for the occupants and those occupants had different needs. Stating that door frames and hallways are smaller than currently because of a lesser average height is a conclusion that doesn't necessarily follow.

Your average tells you about the group but not much about individuals, so your building codes are set for the 99.8% who are shorter than +3 standard deviations from the mean so that no one is inconvenienced. But what is the average height? That's easier to tell now, but not so much for earlier demographics.

Room size does not correlate to occupant height either. My classroom ceiling, for instance, is nearly twelve feet high. Can we really conclude anything from that? On the other hand, all of the occupants for the last twenty years have been shorter than 6'5" and half of them were averaging 5'4" (the girls). All classrooms built in the last twenty years have 8' or 9' ceilings, becuse of changes in the building code, not because people kept hitting their heads.

The windows are huge, nearly 3' by 8', but that speaks to the need for free light and air rather than a race of giants.  Need and purpose are better indicators of door size in pre-code days.


The typical pre-1850 house has low ceilings and doors I want to crouch for (but that are still taller than I am), for a couple of reasons.

A room with a low ceiling is easier to heat, less difficult to build, and uses less wood in the building process. A 7' ceiling is not a problem for anyone who was going to use it - the builders were making houses for themselves and they didn't feel the need to give themselves 2' of headroom.

Sure, it's shorter than today, but only relatively. We notice because the standards have changed and it FEELS lower, not because we need to duck.

The same is true for the door. It's shorter. It was custom-made and of varying heights. Often it wasn't "square" but rather built to fit the space rather than the other way around. It might have a corner cut off to fit under the eaves or clear a stair. In any case, the door was built for the prospective occupants, not the rare fraction who needed a 6'8" door. Andre the Giant could bloody well duck.

Likewise hallways. What's the need for a wide hallway? It's just wasted space. Your big furniture was on the main floor or was carried up in pieces and assembled in place. There were no ADA-type requirements. Again, we feel constricted, but the person of that time would consider our modern requirements to be ostentatious displays of wealth. The typical house of the 15th century was maybe half the square footage of 20th century houses, and that is being dwarfed by 21st century ones. This correlation is with wealth, not height.

Other factors chime in: the cost or taxes assessed on road (or canal in this case) frontage might dictate your building style. For an extreme example of this, check out houses in Amsterdam: narrow, almost useless staircases and a hoist mechanism outside for lifting pianos and furniture to the second or third floor.


The takeaway for math teachers is to stress that we need more than correlations to justify cause. I might state the original paragraph and have the kids try to punch holes in it. Critical thinking and all that. I'd be looking for points like those above and:

• If the claim is that people were taller before the Templars' suppression at the hands of Philip the Fair, became shorter during the 14-17th centuries and then started getting taller again in the 18th, then your doors should show the same trends for the same time periods, in the same types of houses and at the same socio-economic levels. If the doors to churches showed the same decrease and increases, that would be a good sign.
• How could the builder know the average height of 15th century mankind? Communications were difficult and slow, the size of the foot varied by region among other factors. Besides, even if he did know, why would he care? He's building for the man in front of him, not some mythical beast. Is there evidence that builders knew the average?
• Is the rural house different from that in the city?  See the Amsterdam note above.
• What are other reasons for the differences do you see? 

• War.  Make your attackers duck as they enter. Some Indian adobes have four foot doors for this reason. This picture is from Doune castle.
• Security. A smaller door is easier to bolt closed.
• Religion. Make your visitors bow in humility as they enter.
• Practical. They wanted to reach the ceiling beams for storage hooks.
• Sexism.  Only women used this door so who cared about it being more than 6'? 
• This was where the children slept.  There was plenty of room under the eaves.
• Mathematical considerations:
• Can the average height be measured?  Is that number meaningful here? Should the anthropologist use median or mode instead?  What was the builder using?
• What kind of sampling would work best for ascertaining that measure?
• Historical considerations:
• How do we know that people did get shorter? Did they or is this a myth?
• If they were, was it due to nutritional deficiencies? Were chronic health problems all that widespread in just those four centuries or merely the Black Death taking all the headlines? Was the 9th century healthier?  How about NYCity in the 1800s tenements?  London's Soho at the time of cholera epidemics?
• Were the doors shorter during the time period in question? What was he looking at when he measured?
• What would the students do as step two to confirm or deny these theories? Why haven't they started?

I love math.