·
When one figure goes up as another
goes down, math can help us look at problems from a new perspective.
By
June
18, 2020 11:55 am ET
As
the world begins to emerge from lockdown, some people are lamenting the
“quarantine 15,” extra pounds they gained by stress-eating or baking to pass
the time. Although I am typically very prone to comfort eating and baking, I
found a way to avoid this using some math.
Math
often involves equations showing a relationship between two quantities,
enabling us to understand one by means of the other. One familiar type of
relationship is when two quantities go up or down in proportion to each other.
For instance, since steak is sold by the pound, the more your steak weighs the
more you will pay for it (barring special offers). Likewise, if a certain proportion
of the population is infected by a virus, then a state with a higher population
is expected to have more cases than a state with a lower population.
With
proportional relationships, the ratio between the two numbers is constant. No
matter how large or small they get, if you divide one by the other the result
is the same. But there is another, less obvious type of relationship, called
inverse proportional or reciprocal, in which one number goes up while the other
comes down. In this case, it’s not the ratio that stays the same but the
product: multiplying them produces a constant result.
For
instance, if you drive faster you will get to your destination faster, because
when speed goes up the duration of a journey goes down. The constant product is
the distance, which remains the same regardless of how fast you drive. The word
“faster” obscures the fact that one quantity (speed) is going up while the
other quantity (journey time) is going down. We can use that relationship to
our advantage if we’re in a hurry.
MORE EVERYDAY MATH
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The Geometry of Dresses and Bodies May 7, 2020
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In
other situations, inverse proportional relationships work against us. Stepping
on a Lego brick is much more painful that stepping on a real brick, even though
you weigh the same in both cases, because with a Lego brick the weight is
distributed over a much smaller area, making the pressure larger.
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This
type of relationship is how I convinced myself not to overeat during lockdown.
Trying to eat less didn’t sound enticing to me, but with reciprocals I could
convert “less” into “more.” Instead of reducing the amount of food I ate, I
focused on increasing the time my supplies would last. Here the quantity that
is constant is the amount of food I bought. By eating less each day, I could
make my supplies last for more days.
Of
course, I could have just bought more food. By increasing my total supplies, I
could increase the amount I ate each day without reducing the number of days.
Our world of excess encourages us to buy more of everything all the time, but
during lockdown I was trying not to do that. Of course, those without easy
access to resources don’t have the option.
Inverse relationships are a version of a zero-sum game.
In such a game the sum of both players’ scores is fixed, whereas here the
product is fixed. But the idea is the same: to make one amount go up, you have
to make the other go down. Zero-sum games often have a negative connotation,
since they make it impossible for both sides to cooperate. But in this case I
used the concept to my advantage. I avoided gaining weight, and I avoided extra
trips to the grocery store. Math can seem fixed and rigid, but we can use it to
change our point of view in helpful ways.
https://www.wsj.com/amp/articles/relationships-where-more-means-less-11592495703
https://www.google.co.uk/amp/s/www.wsj.com/amp/articles/relationships-where-more-means-less-11592495703
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