> Another possibility is that by pressing slightly harder, you cross the threshold of the paper's strength and wind up with an ugly hole.
As you press harder, the paper gets more and more compressed. You can't go directly from 1mm thickness to hole.
> In the digital world, if I change the low-order bit of a single number in a single calculation, the result will be only slightly inaccurate.
If your single number represents a boolean variable, then it will be completely innacurate.
And the behaviour of a program can be completely different depending on the value of that single variable: exit instead of resuming; change the value of $bank_account_amount instead of waiting for the lock; dereference an invalid pointer, etc. Note that these aren't especially crafted examples. They could happen with existing programs, and actually do every day.
Of course you could come up with real examples of small changes in an analog system resulting in big changes, but Dijkstra's point is not that such things do not exist, only that it is not the rule in analog systems we're used to dealing with.
As you press harder, the paper gets more and more compressed. You can't go directly from 1mm thickness to hole.
> In the digital world, if I change the low-order bit of a single number in a single calculation, the result will be only slightly inaccurate.
If your single number represents a boolean variable, then it will be completely innacurate.
And the behaviour of a program can be completely different depending on the value of that single variable: exit instead of resuming; change the value of $bank_account_amount instead of waiting for the lock; dereference an invalid pointer, etc. Note that these aren't especially crafted examples. They could happen with existing programs, and actually do every day.
Of course you could come up with real examples of small changes in an analog system resulting in big changes, but Dijkstra's point is not that such things do not exist, only that it is not the rule in analog systems we're used to dealing with.