What Are Variables For?

Date: 02/09/2001 at 04:54:54
From: Cindy
Subject: Variables

Hi!

I just wanted to ask, why is it important to be able to figure out the 
values of variables? We've been doing that in our math class for 
more than half a year and I was just wondering.

Cindy

Date: 02/09/2001 at 13:24:58
From: Doctor Ian
Subject: Re: Variables

Hi Cindy,

This is a very perceptive question.  

Variables are important for a couple of reasons, which we might call
'planning' and 'analysis'. 

Think about planning a dinner party. You know that you'll need one 
half of a chicken for each adult, and one quarter of a chicken for 
each child; you'll need one bottle of wine for every three adults, and 
one bottle of soda for every five children; you'll need a half pound 
of potatos for each chicken that you have to cook; you'll need one pie 
for each six adults, and one bowl of jello for each child; and so on. 

But you don't yet know how many people you're going to invite. 
Variables let you set up a description of the situation (i.e., an 
equation) such that you can plug in two numbers (the number of adults, 
and the number of children) and get back other numbers that you'll 
find useful: how many chickens to buy, how much the total cost will 
be, and so on. If you decide at the last minute that you want to add 
another three guests, you don't have to start your calculations from 
scratch - you just change the values coming in, and the equations will 
tell you how to change the values at the other end. 

This, by the way, is why they are called 'variables' - they tell you 
how some quantities vary in response to changes in other quantities.  

Note that a dinner party isn't all that complicated, so it's almost 
not worth the effort of setting up equations to solve the problems.  
The same is true of a lot of the problems that you'd see in a math 
class, which is one of the things that can make math (as it's taught 
in schools) seem kind of pointless. 

But when you get to something more complicated - like trying to plan a
flight, or run an entire airline - it becomes absolutely necessary to 
make use of the kinds of techniques that you learn in your math 
classes. A big part of running any business is being able to figure 
out your potential costs in any situation, because that tells you how 
much you need to charge for goods and services in order to make enough 
money to stay in business.  

So, that's planning. What about analysis? Well, analysis is just 
planning in reverse. If you know how many people to invite, you can 
figure out how much money you'll have to spend. That's planning. If 
you know how much money you spent, you can figure out how many people 
you invited. That's analysis. The beauty of variables is that in most 
cases, you can use the same equations to go in either direction - to 
predict what's going to happen, or to understand what already 
happened.  

The planning aspect tends to be more useful in things like business, 
or construction, or engineering, where you have to decide what's going 
to happen. The analysis aspect tends to be more useful in science, 
where you don't get to decide what happens (the world behaves the way 
it behaves, whether you like it or not), but would like to understand 
it anyway, whether just from curiosity, or because you'd like to use 
that understanding to make your planning more accurate.

I hope this helps.  Please write back if you'd like to talk about this 
more, or if you have any other questions. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/