user93703: I just started learning about Bitcoin, and something I can figure out is why miners have to use a random process (hashing a nonce) to get lower than the target. For example, if the target is
00000000000001ae00000000000000

why not just produce
000000000000000000000000000001

to become the winner? I have no practical experience mining, I'm guessing my ignorance lies in the requirements of how a hash is produced. If so, where can I find about those requirements? Thanks.

EDIT: For clarity, I mean this in the sense of what part of the technology requires me to use a hash function? Rather than in the sense of just constructing something that looks like a valid hash.

user208: Hash functions are unpredictable.
You can't simply find an input to the hash function that produces such an output. The only way to accomplish that is by trying lots and lots of candidate blocks as input. If the target is 1000 times smaller, it requires 1000 times as many tries.

user63872: 
EDIT: For clarity, I mean this in the sense of what part of the technology requires me to use a hash function? As opposed, to just constructing something that looks like a valid hash.

When determining whether or not a block is valid, each and every bitcoin node on the network will take the header of that block, and run it through a hashing algorithm to see what the output is. If the output is lower than the target value, then the block is valid (assuming that the rest of the block is also valid, of course). 
Notice something important: the hash value itself is not explicitly stored in the block. So you cannot just append some fabricated value that falls below the target value onto the block in lieu of a valid PoW. To create a valid block, you must construct it such that all other network nodes can independently verify it as being valid, and to do so, they use a hash function. 
As Pieter mentioned, hash functions are unpredictable 'one-way' functions. The only way to find a valid output is by trying a huge number of possible inputs, and 'getting lucky', so to speak. 

93703: <p>I just started learning about Bitcoin, and something I can figure out is why miners have to use a random process (hashing a nonce) to get lower than the target. For example, if the target is</p>

<pre><code>00000000000001ae00000000000000
</code></pre>

<p>why not just produce</p>

<pre><code>000000000000000000000000000001
</code></pre>

<p>to become the winner? I have no practical experience mining, I'm guessing my ignorance lies in the requirements of how a hash is produced. If so, where can I find about those requirements? Thanks.</p>

<hr>

<p><strong>EDIT:</strong> For clarity, I mean this in the sense of <em>what part of the technology requires me to use a hash function?</em> Rather than in the sense of just constructing something that looks like a valid hash.</p>
 208: <p>Hash functions are unpredictable.</p>

<p>You can't simply find an input to the hash function that produces such an output. The only way to accomplish that is by trying lots and lots of candidate blocks as input. If the target is 1000 times smaller, it requires 1000 times as many tries.</p>
 63872: <blockquote>
  <p>EDIT: For clarity, I mean this in the sense of what part of the technology requires me to use a hash function? As opposed, to just constructing something that looks like a valid hash.</p>
</blockquote>

<p>When determining whether or not a block is valid, each and every bitcoin node on the network will take the header of that block, and run it through a hashing algorithm to see what the output is. If the output is lower than the target value, then the block is valid (assuming that the rest of the block is also valid, of course). </p>

<p>Notice something important: <em>the hash value itself is not explicitly stored in the block</em>. So you cannot just append some fabricated value that falls below the target value onto the block in lieu of a valid PoW. To create a valid block, you must construct it such that all other network nodes can independently verify it as being valid, and to do so, they use a hash function. </p>

<p>As Pieter mentioned, hash functions are unpredictable 'one-way' functions. The only way to find a valid output is by trying a huge number of possible inputs, and 'getting lucky', so to speak. </p>
