Treebeard's Stumper Answer
98.6 in the Shade
It's hard to dress right for school in the fall. Mornings are usually cold and foggy, but it gets warm. A week ago it was hot, good for local vintners, but too much for me. Normal body temperature is 98.6° F. Why is it that when the air is that warm, it's too hot? Shouldn't that be just right? Even more confusing, that's not hot enough for a good hot tub, which we like about 105° F. Finally, why is that familiar 98.6 so exact? Real body temperature varies by the hour! (Bonus: Connect this with the loss of the NASA Mars Climate Orbiter spacecraft!)
Humans are warm-blooded. We produce heat like a car engine, and we need active cooling from air and sweat. In very hot (and humid) weather, we can't lose our extra heat, so we begin to warm up inside, sometimes dangerously. A hot tub feels great for a while, but only for a while. The number 98.6 °F (3 digits) is a kind of round-off error using the formula °F = (9/5) °C + 32 to convert Carl Wunderlich's original 37 °C (only 2 digits). NASA apparently lost the Mars Climate Orbiter spacecraft due to another problem converting units.
Graybear emailed just what I was going to add about fall weather:My problem is that I wear a jacket to work in the morning, and then forget to bring it home in the evening. I end up with five jackets at work and then have to swing by the office on Sunday morning so I have something to wear to church.Here in California, I have the added problem that I often go home from school in my swim suit after PE, and then I forget to bring it back to school in the morning. I end up with all my swim suits at home and all my jackets at school. I'm still wearing shorts to school. It's a major decision when to switch to long pants!
Graybear also corrected me on my choice of words: "As my mother says, 'Horses sweat, men perspire, women glisten.'" Whatever you call it, we are mostly cooled by water evaporating from our skin. Dip your finger in alcohol or acetone to really feel the cooling effect of evaporation. 98.6 is our normal temperature with efficient water cooling. But when the air is that hot we can't do it. He goes on:We sweat (or rather perspire) to eliminate wastes from our body and to regulate temperature. The low 70's are ideal for this process, much lower and the perspiration evaporates too fast and we feel chilly. At 98.6 F, the opposite happens and we get 'sweaty'.
We take measurement units for granted as long as we don't have to convert to some other system. But converting units is always trouble. NASA apparently lost the Mars Climate Orbiter spacecraft because of a problem converting units. One research team used English/American units while others used Metric (SI) units. Pounds and newtons are not even close. This is a project management issue that shouldn't have happened, and probably won't happen again. The familiar but over-exact 98.6 °F body temperature is also a units problem caused by preserving too many digits after converting.
The German physician Carl Reinhold August Wunderlich (1815 - 1877) made the original study of normal body temperature in the 1800s by doing a statistical study of thousands of people in Europe. He was one of the first to describe fever as a symptom, not a disease by itself. He averaged his results to 37° Celsius, rounded to the nearest degree. But +/- 0.5 °C, is nearly a full degree Fahrenheit after converting by the formula °F = (9/5) °C + 32. I remember Yossarian in Catch-22 who "was comfortable in the hospital [rather than flying bombing missions in WWII] because he always ran a temperature of 101." We're all different.
The recent JAMA article " A critical appraisal of 98.6 degrees F, the upper limit of the normal body temperature, and other legacies of Carl Reinhold August Wunderlich" (1992) concludes that normal body temperature is in fact a bit lower:36.8 degrees C (98.2 degrees F) rather than 37.0 degrees C (98.6 degrees F) was the mean oral temperature of our subjects... CONCLUSIONS--Thirty-seven degrees centigrade (98.6 degrees F) should be abandoned as a concept relevant to clinical thermometry; 37.2 degrees C (98.9 degrees F) in the early morning and 37.7 degrees C (99.9 degrees F) overall should be regarded as the upper limit of the normal oral temperature range in healthy adults aged 40 years or younger, and several of Wunderlich's other cherished dictums should be revised.
Mathematician John Allen Paulos (quoted in Science, August 18, 1995, page 992) explains:"Consider a precise number that is well known to generations of parents and doctors: the normal human body temperature of 98.6 Fahrenheit. Recent investigations involving millions of measurements reveal that this number is wrong; normal human body temperature is actually 98.2 Farenheit. The fault, however, lies not with Dr. Wunderlich's original measurements - they were averaged and sensibly rounded to the nearest degree: 37 Celsius. When this temperature was converted to Fahrenheit, however, the rounding was forgotten and 98.6 was taken to be accurate to the nearest tenth of a degree. Had the original interval between 36.5 and 37.5 Celsius been translated, the equivalent Fahrenheit temperatures would have ranged from 97.7 to 99.5. Apparently, discalculia can even cause fevers."
Novelists can also fall into this trap. The Dark Design (1977) is the third volume in Philip Jose Farmer's classic sci-fi Riverworld series. It is full of passages like this (italics mine):"Beyond the hills of the valley were the mountains, inclined at an angle of forty-five degrees for the first thousand feet or 305 meters or so, then ascending straight up, smooth as a mirror, for 10,000 feet or about 3048 meters. During his first years here, Burton had estimated the mountains to be about 20,000 feet or 6096 meters high. He was not the only one to make that error when only the eye was available for calculation."In fact the author (or more likely an over-zealous editor with a computer acting on a suggestion) made a different error! About 10,000 feet is about 3,000 meters, not 3,048! I found the book almost unreadable because of such writing. This quote is from page 23 of the original July 1978 Berkley paperback. I hope they changed it in later editions.
Different systems of units are so human, and so subject to human error. All modern temperature scales are based on measuring two points on a scale and extrapolating the rest. Consider the sources:
The great Danish astronomer and instrument maker Ole Rømer (also written "Roemer") made one of the the first modern thermometers. (He was also the first to measure the speed of light; see my stumper Seeing the Light from Jupiter.) Looking at these very different scales, we have to wonder what their creators had in mind. You can find the answer on the Web, but I think I'll save it for a future stumper.
Generalities aside, comfort is a complicated topic. I still wonder why Julie always leaves the shower set too hot for me, but I always want the hot tub hotter!
I found lots of information about body temperature by searching the Web. Here are a few starting links for more research:
- New research on the range of average body temperature is summarized in " A critical appraisal of 98.6 degrees F, the upper limit of the normal body temperature, and other legacies of Carl Reinhold August Wunderlich" by Mackowiak PA, Wasserman SS, and Levine MM (JAMA 1992 Sep 23-30;268(12):1578-80). I remember Science News ran a cover story about the findings, but I can't find the issue.
- Lena Wong's Temperature of a Healthy Human has a useful page of different authorities on "normal body temperature" that suggests how variable it really is.
- Paul Cox' Glossary of Mathematical Mistakes uses the 37/98.6 conversion as an example of Dramadigits, "the reporting of a number with more significant digits than what can be reasonably expected." He tells a good math joke from John Allen Paulos:A visitor at a natural history museum asks a guard how old the dinosaur skeleton is. The guard responds that it is 90,000,006 years old. He explains, "They told me it was 90,000,000 years old when I started working here, and that was six years ago."
- Here are a few sites that discuss heat stress and comfort levels:
- Grounds Maintenance Magazine report on The Basics of Heat Stress.
- The FDA has an article on When Summertime Gets Too Hot to Handle.
- Innova Air Tech Instruments' Thermal Comfort is a rather technical article on human comfort with cute illustrations and pages of hairy equations. Glancing at the math is enough to appreciate the difficulties.
- Here are a few sites that discuss temperature and the history of thermometers:
- Theres's an on-line Temperature Conversion Calculator for converting between different units.
- About Temperature is an introduction for middle school math/science teachers.
- Marshall Brain's How Thermometers Work shows how to make your own thermometer. Now I can measure temperature in treebeards!
- What Marilyn omitted about the Fahrenheit Thermometer has interesting discussion on the history of thermometers. This is part of Herb Weiner's Marilyn is Wrong! site dedicated to the "Ask Marilyn" columns in Parade Magazine by the less-than-modest Marilyn vos Savant.
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