Also, a lot of programs are really programs for making programs. Microsoft Excel is Turing complete, so (if the Church-Turing thesis is true) it can be used to solve any computable problem. The set of "problems that can be solved" and "problems that can be solved using Excel" completely intersects, at least in theory.
When you use Excel, you're really programming a solution to a real-world problem. You don't have to hope that someone has written a program to solve the "working out how much of the budget we'll have left at the end of Q2" problem, because Excel allows you to write it yourself.
Is "what should I do with the tinned sardines my dad gave me?" the kind of problem they can't solve? Because that's obviously fine.
This feels like some kind of false dichotomy. Sure, a computer can't cook me a dinner, but it can get me to a webpage where I could read a post about how to cook my own dinner.
They seem to be saying that since there are 'infinite' problems, but not infinite computers, that computers can't be relied on to solve problems? Seems like you could say the same thing about humans - we don't have infinite thought.
Like you say, context is important here, and the fact that computers exist solely to solve problems we tell them to sort of makes the observation pointless.
Logically, what is a 'problem'? We can conceive of solving a problem as deciding whether a string belongs to a specified set of strings.
Solving the problem 'is 6 is even?' means deciding whether '6' belongs to the set {'0', '2', '4', '6', '8', ...}.
A computer program can be expressed as a string of text but not all strings are computer programs. So the set of all possible computer programs is smaller than the set of all possible strings.
By the power set rule, the set of all possible sets of strings is greater than the set of all possible strings.
Therefore, there are more problems than programs to solve them.
>So why are computers so useful in the real world? The problems in the real world can't be random.
That is like asking so why is a hammer so good at knocking nails in even if that type of nail was invented afterwards. The tool was designed for that purpose.
Up until recently we have used computers to solve a very specific set of problems that they have been designed specifically to solve (abstract maths and logic) things had to be broken down by someone who would explain things to the computer in the most basic of ways for really quite narrow use it is only that the work of hundreds of thousands of people has been colabrative that it seems like they are more than an input output box.
It has only really started getting a bit freaky since we developed evolutionary programing, but even a school boy understanding of dawinism should make it immediately apparent why that works not that that makes it's potential power less frightening.
