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<div id="content">
<h1 class="title">Exercises Versus Problems</h1>
<div id="outline-container-orgf080eb7" class="outline-2">
<h2 id="orgf080eb7">Make a Distinction</h2>
<div class="outline-text-2" id="text-orgf080eb7">
<p>
This is a synopsis of the explanation Paul Zietz gives in Chapter 1 of his
book <a href="https://www.wiley.com/en-us/The+Art+and+Craft+of+Problem+Solving%2C+3rd+Edition-p-9781119094845">The Art and Craft of Problem Solving</a>, wherein he seeks to clearly answer
these and related questions:
</p>
<p>
What does problem solving mean?
</p>
<p>
Why should you study it?
</p>
<p>
What is the difference between exercises and problems?
</p>
<p>
<b>An exercise</b> is a mathematical question that you immediately know how to
answer. You may not answer it correctly, or it may be nearly impossible to
answer, but there is no doubt about how to proceed.
</p>
<p>
<b>A problem</b> is a question that you initially don’t know how to answer. One
person’s problem may be another person’s exercise. Problems require
investigation, using strategies and tactics.
</p>
<p>
Work on problems to develop mental discipline.
</p>
<p>
Brain exercises like crossword puzzles or Sudoku puzzles are not without
merit, but they miss a crucial aspect of your intellectual life. Our brains
can help us with open-ended experimentation, involving long wild goose chases
and hard-earned triumph. We need brain problems.
</p>
<p>
Exercisers are gym rats, problem solvers are mountaineers. Climbing a mountain
is a messier experience, but it is much more fun.
</p>
<p>
Exercise: Learning Italian from a book.
</p>
<p>
Problem: Learning Italian by immersion.
</p>
<p>
Problem solving should be a way of life.
</p>
<p>
There are psychological barriers to problem solving.
</p>
<p>
Learning to become a problem solver requires a change in mental attitudes.
</p>
<p>
Most of us are not used to thinking hard for a few seconds or a minute.
</p>
<p>
Work on increasing your levels.
</p>
</div>
<div id="outline-container-org03f683a" class="outline-3">
<h3 id="org03f683a">Levels in seconds (roughly)</h3>
<div class="outline-text-3" id="text-org03f683a">
<ul class="org-ul">
<li>10<sup>0</sup> Second</li>
<li>10<sup>1</sup> Minute</li>
<li>10<sup>3</sup> Hour</li>
<li>10<sup>5</sup> Day</li>
<li>10<sup>6</sup> Week</li>
<li>10<sup>7</sup> Year</li>
<li>10<sup>9</sup> Lifetime</li>
</ul>
<p>
We will fail in problem solving. We need to cultivate an attitude that
investigation is worthwhile even if it doesn’t lead to a solution.
</p>
<blockquote>
<p>
The explorer is the person who is lost. — Tim Cahill, <i>Jaguars Ripped My Flesh</i>
</p>
</blockquote>
</div>
</div>
<div id="outline-container-org1b0c908" class="outline-3">
<h3 id="org1b0c908">Art</h3>
<div class="outline-text-3" id="text-org1b0c908">
<p>
Folklore: Stories with morals
</p>
</div>
</div>
<div id="outline-container-org362948d" class="outline-3">
<h3 id="org362948d">Craft</h3>
<div class="outline-text-3" id="text-org362948d">
<p>
Strategies: broad
</p>
<p>
Tactics: narrow
</p>
</div>
</div>
<div id="outline-container-orgf638b28" class="outline-3">
<h3 id="orgf638b28">Strategies and Tactics</h3>
<div class="outline-text-3" id="text-orgf638b28">
<p>
Strategy: Wishful Thinking. Yay, I’ve solved the problem! Pretend you’ve got
a solution. This helps you learn the penultimate step.
</p>
<p>
Strategy: Get Your Hands Dirty (Concretize The Abstract)
</p>
<p>
Tactic: Symmetry.
</p>
<p>
A problem is a problem because we needed more information. When you
balance your problem, you get more information.
</p>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Rick Neff</p>
<p class="date">Created: 2018-09-26 Wed 12:24</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>