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Steven,
We have three responses for you.
Think about doses of medicine. If a 98 pound woman were having chemotherapy for her cancer would her radiologist give her the same amount of medication as a 350 pound summa wrestler? In many instances the amount of medication required is proportional to body mass.
Go to the home page of Math Central and follow the link to Math Beyond School. Type the keyword proportion into the search window and at the bottom of the returned list you will find three articles that concern medicine and proportions. I also suggest that you type the word medicine into the search window to see some other topics in mathematics and their relationship to medicine.
Penny
A key issue in medicine is 'drug dose'.
You give a drug to a patient to achieve a certain 'level' of the drug in, for example, the blood stream. This is expressed parts per (e.g. million) - really a proportion of the blood which is the drug. This is the goal.
Now - how much of the drug do you give each person? This is where you really need to use ratios and proportions. If a person is 'twice the size' - how much more of the drug do you need to give?
Well it really depends on what 'size' you measured. You need something that stands in for the volume of blood, so twice the height will not work (volume of blood is probably 8 times for the person who is twice as tall, and twice as wide and twice ... ). Twice the weight is probably right, so you give a proportionally larger dose.
It turns out this use of 'proportion' is so important, that Nurses have their own practices for computing drug doses in order to make sure they get it right. You do not want to give people way too much drug or way to little. You need to work effectively with ratio and proportion to do this.
There are other places where ratio and proportion come up, in biology, medicine, etc.
Issues like - can a child or an adult hold their breath longer, without brain damage?
In fact, once you start looking around, ratio and proportion appear almost everywhere!
Walter Whiteley
Incidentally, Simpson's paradox finds its way into medical science:
Two medications against the same disease, Xpill and Ypill were tested in two different towns:
In town A, 100 patients were treated with and 80 of them were cured, and
200 patients were treated with Ypill and 140 of them were cured.
In town B, 200 patients were treated with and 40 of them were cured, and
100 patients were treated with Ypill and 10 of them were cured.
The doctors cannot make up their minds on what to make of this:
Doctor I says that overall, Xpill cured 40% of the patients who took it, and Ypill cured 50% of the patients who took it, so that Ypill is the better medicine.
Doctor II says that Xpill cured 80% of its patients in town A, which is better than the 70% cured by Ypill in the same town, and in town B, Xpill cured 20% of its patients, which is better than the 10% cured by Ypill. So, Xpill is better than Ypill both in town A and in town B, hence it is the better medicine.
Doctor III says that he never bothered to learn about ratios and proportions,
so that is all mumbo-jumbo to him.
Claude
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