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Tiny ideas to encourage girls to explore mathematics and physics - 4: Example: "A thing to care of"

Let's amuse a bit!

Do you remember your first contact with geophysics?

Mine was through meteorology, on the fourth high school year.

I remember quite a little, apart the subject seemed to me “difficult” and wide at the time.

It had something to do with large air masses who develop somewhere to then meet (why?) and clash producing so many effects...

Curiously enough, in high school textbooks air masses having different properties do always “clash”. They have no special intention and, would even they do, they are not that solid after all. They "clash", however! Instead of interacting in the extremely complicate and contextual manner they actually do, while maintaining their individuality over many days.

I'm totally indifferent t wrestling, so the idea of air masses clashing didn't made them interesting subjects. But in addition, the idea of “clashing” also conveyed the sense of a sudden, short-lived dramatic event: a misleading idea, so far from what really happens!

But, did you arrive to realize these fine details on your high school student time?

Sincerely, I didn't – much before the teacher used the word “clash” my mind was irreversibly somewhere else, writing some futility on my personal diary, exchanging messages on tiny paper sheets with my next classmate or (more dreadful) desperately trying my best to not fall asleep.

Sure I didn't feel so involved, despite the teacher's passion (which, guaranteed, was outstanding).

May this same material be presented more attractively? Sure so...

In the last couple years I began experimenting with a bit different approach (I'm part of a nice non-profit association whose main objective is diffusing scientific knowledge among the general public, and there it sometimes happens to me trying to tell what meteorology is to children or adults).

I try to explain it to you, as just an example. I hope you find interesting, and hope even more to know what you envisioned in your fields (without any obligation).

Now. The atmosphere, dealing with air masses, looks big, huge, almost infinite. But: have you ever considered how thin and tiny is it?

In fact (that's commonsense) pressure decreases with height. That because (also commonsense) as you climb a mountain there is less air loading its weight on you. As you remain close enough to the Earth surface (say, some ten kilometers) pressure decreases following a simple (for you, the teacher) negative exponential law, waning away progressively.

We know that beyond Earth atmosphere there is "outer space". Where this "outer space" begins, then?

As I said, pressure diminishes progressively, so a precise level is hard to find based on our senses or instruments.

However, below some pressure air becomes so thin you may imagine you are in “the vacuum” (of course, the “vacuum” does not exist so close to the Sun as our Earth is). We have (unfortunately) to use a convention, and give a not-too-unreasonable number.

Although consensus is not universal on this value, space may be imagined to begin at 100km from the Earth surface. This is a concept again not so easy to grasp. But we are on a possibly right way. To make things more involving, we may remind students how rich and complicate the atmosphere below the limit of space is, with thunderstorms, clear sky, turbulence, clouds, rain and snow falling, wind, lightnings, electrical tempests, and anything you can see over your head.

So: how thick the atmosphere would be, would Earth is shrinked to a dimension you can conceive? Say, a ball?

The Earth, we may explain, is not a perfect sphere, but it looks much alike. Its radius has been measured quite accurately and is 6368 km (having a bit of time and Internet access, you may let them some minutes to find the answer on their own, advising where to look at – Wikipedia has a very nice article). If this is the radius, then diameter is something like 12800 km, isn't it?

Now: imagine to get this almost-sphere 12800 km wide, and reduce it to 20 cm. What the magnitude of the atmosphere thickness would be?

“Dear, this isn't that difficult, it's a proportion the kind you already know” That is,
12800 : 100 = 0.20 : X
You may solve it together with the students, calmly, passage after passage. And you get a number:
X = 0.0016 m
That is, one millimeter and half. (Good occasion to refresh equivalences and conversions - so many people find them not intuitive).

This is something you may easily visualize. Looks thin, isn't it?

Now, where clouds are? Most “visible” phenomena we see in the atmosphere occurs in the troposphere, and most within the first 10 km. One tenths of the whole atmosphere's. That is, on your ball-sized Earth, less than two tenths of a millimeter: a sheet of paper!

Back to something visual, now. The NASA has placed into the public domain many wonderful pictures showing Earth from space. In some of them you can actually see the thickness of atmosphere. In some others, tropical cyclones spiraling over half an ocean. A good place where to find beautiful images is

And now imagine! All the shiny clouds you see, in your ball-sized world would occur in a layer as thin as a sheet of paper!

Presented this way, the atmosphere appears in an entirely different (and less boring) manner. Not as something incommensurably large and uninteresting, but as a sort of tiny delicate creature, so immensely important to our life, yet possibly unstable.

A subject, a living being, someone you may imagine to interact with.

If you want, you may even do one step more. Some IR-band satellite images taken on daytime over Central Europe, the US or China show the smoke plumes from wildfires, ships, big industrial plants, and other sources of pollution. If you're lucky, you may even find some erupting volcano. These images are really compelling, as plumes tend to remain visible for a long time after emission.

As you have created a context of “the atmosphere, a tiny creature”, the last image evokes a feeling of vulnerability, under attack.

In my view, this pattern may be repeated on any kind of concept, even the most apparently far. The key "trick" is encouraging students to "empathize" with supposedly inanimate "objects". I've seen this comes quite natural to girls, on average.

I feel this way of doing is interesting in many ways.

First, it fosters further curiosity. It's hard to decide investing time and emotional involvement into something you feel indifferent or worthless - but if you have some real deep interest, then no difficulty seems insuperable.

And also, it encourages a caring attention, a sense of "reciprocal belonging" which may endure an entire life. This can only be for good, as after all we humans have the power of (not) damaging environment.

It may be developed further, too. Encouraging discussion, and allowing people to aggregate spontaneously in groups to share-and-test, you may also trigger a wider-angle exploration of the subject...

Personally, I've always believed in the possibility of an intimate relation with nature and natural objects. It's quite natural to me imagining "objects" like a special case of "persons telling stories". I am so deeply identified and intertwined with this view that I get a lot of positive energy from my wandering in nature. But this also elicits some words of caution. In a sense, I devised an explain line "I would have found warmly involving, had someone cared to use with me": a bias! ("Language is never neutral", as Luce Irigaray advised so many years ago).

And in fact, as far as I've seen, not all people like to be deeply involved in a personal "individual-to-individual" relationship with nature (something resembling friendship/love), and prefer a more distant approach. As they retreat scared, you risk losing them forever. This kind of failure has sad consequences, as unjust and arbitrary it is. A "B plan" is clearly needed in these cases (but, in all honesty, I don't know it yet - I'm confident someone of you will give me some advice).

"That's all, folks!"
For now...

I'm thinking to the next section, dealing with big explorations we may do in very little material space.

See you soon...


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