Immovable giants

I’m often amused by the way small children who are learning to walk will use an adult’s leg for support just as readily as a piece of furniture. To a young child’s eyes, we grown-up giants must seem so strong and immovable that, if we are doing what they want, it’s because they’ve convinced us to do so of our own volition, not because they’ve forced us.

equalopposite1
Equal and opposite forces
equalopposite2
These are still the actions of equal and opposite forces, but the more massive blue object moves less than the light red object.

This attitude is understandable: while Newton’s third law tells us that every force exerted by one object on another is also exerted in the reverse direction—to pull themselves up, children pull down on you with the same force—his second law says under the same force, acceleration is inversely proportional to mass. All together, this means that if you pull on something bigger than yourself, it moves less than you do. Children quickly learn the approximation “I have no control over the motion of large objects,” hence their pulling on adults to stand up or cruise, and their climbing on dressers and bookcases without thinking that they might tip over.

Adults have a better sense of physics, but even we don’t always think about how every step we take makes the earth turn a little in the other direction like a treadmill. More generally, if the consequences to our actions are small and spread out enough, it’s easy to assume they don’t exist.

For example, when I buy eggs at the grocery store, I usually sigh over the expensive, naturally-nested egg cartons and go with the cheaper store brand. If I could pay the one dollar price difference to give those dozen chickens a better life, I would, but the effect I have is so concentrated for me and so diffuse for the egg industry that it’s hard to feel like I’d be making any difference beyond the one to my bank account. Besides, those eggs are already laid, and I can’t do anything about how they got there, right?

Similarly, was it right for Clara and me to buy a used vertical dresser instead of an IKEA horizontal one, thereby slightly increasing the demand for tall furniture and raising the expected number of tip-over injuries? This sounds like a difficult calculation, certainly not one that I can do for every purchase. How can I do a better job incorporating small spread-out consequences into my decision making on a gut level?

The solution is the same as the one to the parking paradox from last week: imagine if everybody in your situation made the change, and then see what the difference is per person. For the question of whether or not it’s worth it to pave an extra parking spot on your front lawn, instead of calculating the revenue it would get you and comparing it to the slight decrease in property values across your slightly-uglier neighborhood, imagine that each of you on your street paves a spot and consider whether you’d be better off.

For the real-life egg situation, the two “forces” from my choice to buy cheaper eggs look something like this. How can I tell whether that’s a net positive or net negative?

imbalanced
The blue boost to my bank account from buying cheaper eggs, compared to the spread out red effect of higher demand for caged chickens

But if everyone buying eggs made the same choice, there’d be no more demand for natural nesting, and all the eggs sold would be conventionally farmed:

imbalanced2
Everyone saves $1 by buying conventional eggs, but all the chickens are now conventionally farmed.

So what is the result for one person, say, me? I save a dollar, and the chickens who lay the eggs I buy are farmed in a battery. That’s exactly the comparison I made at the beginning of this post, where I said giving up the dollar savings was worth it, only now it’s the real consequences of my actions concentrated into a picture my brain can understand.

imbalanced3
In this picture, it’s much easier to see that the negative effects outweigh the positive.

In conclusion, the giant world is a lot less immovable than it seems. Make those responsible purchases, those phone calls to your congressman, those kind gestures that feel futile in the face of an unkind world. Not just because if everyone did, there might be some real change, but because you acting alone already makes a difference.


4 thoughts on “Immovable giants

  1. “Every step we take makes the earth turn a little in the opposite direction”
    I never heard of, or thought about, this before! If everyone on the planet coordinated their walking efforts in the same direction, theoretically, we could stop the earth from rotating?

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    1. Good question! If we say that all 7 billion people with an average body weight of 60 kg congregate at a spot on the earth’s equator and walk east at 1.5 meters per second, that’s a total momentum of (60 kg)(1.5 m/s)(7 · 109) = 6.3 · 1011 kg m/s. Since we’re talking about counteracting the earth’s spin, we should calculate the angular momentum they impart to the earth, which includes a factor of the earth’s radius, 6300 kilometers. (This is the same reason it’s easier to turn a bolt with a long wrench than a short one: the same force gives a greater change in angular momentum if applied with a longer lever arm.) So that’s a total of (6.3 · 1011 kg m/s)(6.3 · 109 m) ≈ 4 · 1021 kg m2 / s.

      In contrast, the total angular momentum of the earth is about 7 · 1033 kg m2 / s, over 12 orders of magnitude larger. So we’d need to multiply the population of the earth by over one trillion (who will be the lucky 7 sextillionth baby?) to carry out your dastardly earth-stopping scheme. 🙂

      I love these sorts of thought experiments! Do you know the What If? blog at xkcd? He answers this kind of hypothetical question all the time, and with such a great sense of humor.

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