user157: The Zen monk Hakuin said that 3 things are essential to practice

great faith, great doubt, and great resolve

I can see how faith and resolve would be essential but I don't see why doubt would be? Also wouldn't faith and doubt contradict each other unless they occur separately at different times.

user43: This doubt is a byproduct of really paying attention to details. As you pick up bits and pieces here and there, some of them don't fit together. So you put them aside and keep going. Then, later, some of them fit together, but others still don't. You have great faith in three jewels, and great resolve to walk the path. At the same time you have no choice but to suspend your judgement on some things that don't make sense. The further you go, the more this happens. But only if you really pay attention, and only if you don't get discouraged by logical inconsistencies, and only if you are determined to follow through. Somewhere along the way you get unwavering certainty on some points, even if they contradict other, equally authoritative points. Because you are certain about these things, you can give up some other things you would never have dreamt of giving up, even though your heart sinks as you do it. You keep doing it in the name of "no hope, no fear" until you lose all ground and fall through space. This is the great doubt, the flip side of your faith and determination. It's not the goal, it's a thing you have to go through. It's not something that can or should be induced artificially though. As Master Bankei said:

What’s worse, they [the false teachers] tell practitioners that unless they can raise a “great ball of doubt” and then break through it, there can’t be any progress in Zen.  Instead of teaching them to live by the unborn Buddha-mind, they start by forcing them to raise this ball of doubt any way they can.  People who don’t have a doubt are now saddled with one.  They’ve turned their Buddha-minds into “balls of doubt.”  It’s absolutely wrong.

So doubt must be natural to be real. That's why even though Master Hakuin is right in listing it as one of three essential things, I now say it is secondary to paying attention properly, taking note of facts and how they fit together or not.

user-1: In reverse order:
"wouldn't faith and doubt contradict each other unless they occur separately at different times"
...or unless they are directed to different things: Great faith [on the approach], great doubt [about Truth]. Great resolve: the act of persevering on the approach to penetrate the Truth.
"I can see how faith and resolve would be essential but I don't see why doubt would be?" 
Great doubt can be seen as the catalyzer that creates motivation to make one go through great lengths to reach something so hard to reach. It can also be seen as "The Doubt among the doubts", a fundamental, deep and honest question, greater than any other, that no superficial answer would satisfy it, settle it, or make it rest.

user16296: This has been explained by Yashutani Roshi in his 10th lecture. The relevance of doubt (Dai-gidan among faith aka dai-shinkon & strong resolution aka dai-funshi) has been explained by him as follows -

The second indispensable quality is a feeling of strong doubt. Not a simple doubt, mind you, but a "doubt-mass" and this inevitably stems from strong faith. It is a doubt as to why we and the world should appear so imperfect, so full of anxiety, strife, and
  suffering, when in fact our deep faith tells us exactly the opposite is
  true. It is a doubt which leaves us no rest. It is as though we knew
  perfectly well we were millionaires and yet inexplicably found ourselves
  in dire need without a penny in our pockets. Strong doubt, therefore, exists in proportion to strong faith.
  I can illustrate this state of mind with a simple example. Take a man
  who has been sitting smoking and suddenly finds that the pipe which
  was in his hand a moment before has disappeared. He begins to search
  for it in the complete certainty of finding it. It was there a moment
  ago, no one has been near, it cannot have disappeared. The longer
  he fails to find it, the greater the energy and determination with
  which he hunts for it. - Page 81, The three pillars of Zen.


157: <p>The Zen monk <a href="http://buddhism.about.com/od/whoswhoinbuddhism/a/hakuin.htm" rel="nofollow">Hakuin</a> said that 3 things are essential to practice</p>

<blockquote>
  <p>great faith, great doubt, and great resolve</p>
</blockquote>

<p>I can see how faith and resolve would be essential but I don't see why doubt would be? Also wouldn't faith and doubt contradict each other unless they occur separately at different times.</p>
 43: <p>This doubt is a byproduct of really paying attention to details. As you pick up bits and pieces here and there, some of them don't fit together. So you put them aside and keep going. Then, later, some of them fit together, but others still don't. You have <em>great faith</em> in three jewels, and <em>great resolve</em> to walk the path. At the same time you have no choice but to suspend your judgement on some things that don't make sense. The further you go, the more this happens. But only if you <em>really</em> pay attention, and only if you don't get discouraged by logical inconsistencies, and only if you are determined to follow through. Somewhere along the way you get unwavering certainty on some points, even if they contradict other, equally authoritative points. Because you are certain about these things, you can give up some other things you would never have dreamt of giving up, even though your heart sinks as you do it. You keep doing it in the name of "no hope, no fear" until you lose all ground and fall through space. This is the great doubt, the flip side of your faith and determination. It's not the goal, it's a thing you have to go through. It's not something that can or should be induced artificially though. As Master Bankei said:</p>

<blockquote>
  <p>What’s worse, they [the false teachers] tell practitioners that unless they can raise a “great ball of doubt” and then break through it, there can’t be any progress in Zen.  Instead of teaching them to live by the unborn Buddha-mind, they start by forcing them to raise this ball of doubt any way they can.  People who don’t have a doubt are now saddled with one.  They’ve turned their Buddha-minds into “balls of doubt.”  It’s absolutely wrong.</p>
</blockquote>

<p>So doubt must be natural to be real. That's why even though Master Hakuin is right in listing it as one of three essential things, I now say it is secondary to paying attention <em>properly</em>, taking note of facts and how they fit together or not.</p>
 -1: <p>In reverse order:</p>

<p><strong>"wouldn't faith and doubt contradict each other unless they occur separately at different times"</strong></p>

<p>...or unless they are directed to different things: Great faith [on the approach], great doubt [about Truth]. Great resolve: the act of persevering on the approach to penetrate the Truth.</p>

<p><strong>"I can see how faith and resolve would be essential but I don't see why doubt would be?"</strong> </p>

<p><em>Great doubt</em> can be seen as the catalyzer that creates motivation to make one go through great lengths to reach something so hard to reach. It can also be seen as "The Doubt among the doubts", a fundamental, deep and honest question, greater than any other, that no superficial answer would satisfy it, settle it, or make it rest.</p>
 16296: <p>This has been explained by Yashutani Roshi in his 10th lecture. The relevance of doubt (Dai-gidan among faith aka dai-shinkon &amp; strong resolution aka dai-funshi) has been explained by him as follows -</p>

<blockquote>
  <p>The second indispensable quality is a feeling of strong doubt. Not a simple doubt, mind you, but a "doubt-mass" and this inevitably stems from strong faith. It is a doubt as to why we and the world should appear so imperfect, so full of anxiety, strife, and
  suffering, when in fact our deep faith tells us exactly the opposite is
  true. It is a doubt which leaves us no rest. It is as though we knew
  perfectly well we were millionaires and yet inexplicably found ourselves
  in dire need without a penny in our pockets. Strong doubt, therefore, exists in proportion to strong faith.<br>
  I can illustrate this state of mind with a simple example. Take a man
  who has been sitting smoking and suddenly finds that the pipe which
  was in his hand a moment before has disappeared. He begins to search
  for it in the complete certainty of finding it. It was there a moment
  ago, no one has been near, it cannot have disappeared. The longer
  he fails to find it, the greater the energy and determination with
  which he hunts for it. - Page 81, The three pillars of Zen.</p>
</blockquote>
