Order makes finding easy
Why Do We Sort Things?
Sorting costs effort once, then saves effort every single time you look for something.
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Step 1 of 5
Sorting means putting things in an order.
By size, by colour, by letter, by number. You pick a rule, and then every item has a definite place relative to the others.
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Step 2 of 5
Finding things in a jumble is slow.
In an unsorted pile of 1,000 items you may have to check all 1,000. On average you check 500.
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Step 3 of 5
In sorted order you can halve the problem.
Open a dictionary in the middle. Your word is either before or after — so half the book is gone in one look. Repeat and 1,000 items take ten checks.
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Step 4 of 5
Sorting also reveals things.
Line up a class by height and the tallest, shortest and middle are instantly visible. Order exposes patterns invisible in a jumble.
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Step 5 of 5
It is worth it when you look more than once.
Sorting takes effort up front. If you only ever need one item, do not bother. If you will search a hundred times, sort first.
Sorting is one of the most studied problems in computing, precisely because so much depends on doing it well.
The short version
Unsorted, a pile of 1,000 costs 500 checks on average; sorted, halving the problem each look gets you there in ten. Order also exposes patterns a jumble hides. But it only pays if you are going to look more than once.
Try it yourself
Time yourself finding a word in a dictionary, then in a shuffled list of the same words. The difference is the value of order.