For the HN population, translating this into security can be useful.<p>Here is a Sorites argument for AES key strength.<p>A key of length 1 bit is not secure<p>A key of length 2 bit is not secure<p>A key of length 3 bit is not secure<p>------------------------------------<p>A key of length 1024 bits is not secure<p>We would consider the conclusion absurd. Why?<p>Because we have a definition of security as such: The expense of breaking the key is not worth the value of the secret it protects.<p>For 1 bit, the expense of breaking the key is so low, it is very easy to come up with secrets that are greater than the value.<p>For 256 bits, the expense of breaking the key is so (literally) astronomically high, that it would be very hard to come up with secrets that have greater value than the expense of breaking the key.<p>In addition, note that for a given secret 1 bit can make the difference between secure and not secure.<p>Notice as we increase the key length bit by bit, more and more secrets are having values that are less than the expense of breaking the key.<p>Now let us look at a heap. First let us come up with a working definition. Let us say that we define a heap as an amount of grain that is larger than can be held in a closed fist.<p>Notice how this varies from person to person. Also notice for a given person, there can easily be the case where 1 extra grain makes the difference between heap and not.<p>Also notice, that as we increase the number of grains by one, more and more people would consider the collection of grains a heap.