How does your hair know how long to grow?

In science it is important to check our work. Scientists are as interested in questions as answers. One important question scientists ask is: "Can I verify the answer the model gives me?"

One way to look at verification is "Did I do the arithmetic correctly?" Did I copy the right numbers. Did I add and subtract correctly. Did I follow the recipe correctly?

Use a calculator to verify the answers you got from the model.

A second way to verify the results is to compare the answers that the different models give for the same question. Are the answers the same? Pick a growth rate, anogen and telogen for a hair. Put these values into both the Excel and JavaScript models. If you get the same answer you have verified them.

After we have verified the model we need to validate it. Validation asks if the model's predictions match reality. If we observed real people's hair, would our observations equal the model's prediction?

Because of the months involved in growing hairs we can't directly check the model's validity. Outside of class you could check how fast your scalp hairs grow by measuring the length of hairs at several parts of your head. Then re-measure the hairs each week until you get a hair cut. Shaving our eyebrows and waiting for them to grow out wouldn't go over with most parents or students for that matter.

In a general sense we can say that the model can predict all of the hair lengths that we observe. We could even generalize the model to predict the hair growth of dogs, cats, horses or bears.

There are a few validation questions that we can ask. I showed these models to my class. One of my students said, "The model says that my eyebrows fall out and are bald after 4 months. My eyebrows always look the same. The model is WRONG!"

This is a good scientific answer. Remember that scientists love to ask questions. Answers are good if they allow us to ask new questions. I can ask, have I seen people who's hairs all fall out at the same time. People with Alopecia Areata lose their hair.

For most of us our hair doesn't all fall out one day. The model's predictions about hair growth may be accurate. My student identified a problem with the way the model predicts hair loss. Is the problem with the data we used? Is the problem with the theory? Or is the problem with the model? As scientists we can ask, "Can the model be fixed?" If so what should we change or add?

Let's revisit the data. The scientific literature says that everyday 40 to 100 scalp hairs fall out. We have about 100,000 scalp hairs. How long would it take for all of them to fall out?

Hairs fall out at the end of telogen and the beginning of anogen. This means that on average 40 - 100 hairs are entering anogen or the growth phase everyday.

To visualize this, think about the human population. Everyday babies are being born. Some children are in kindergarten, others are in High School. Other people are middle aged. Grandparents are old. Everyday some people die. We are all in the birth, life, death process. We are in different places in it. The same is true for our hairs. Some hairs are starting to grow. Some hairs are half way through the growth phase. Some hairs have stopped growing and are in telogen. A few hairs are falling out.

The question is how can we change the model to account for the staggered position of hairs within the cycle.

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