A fine story. I've read it before, but it was good to read it again. If I were a school maths teacher, I'd love to give it to a class for a discussion.
Thanks for sharing that story. I read a lot of stories from Asimov before, but I didn't know that one. What I don't get, though, is that the people in the future see a benefit in having humans doing the computations that are made by the computers. It sure makes sens for the humans to gain as much understanding as they can of the computers, but multiplications are much faster done by computers. I am missing something here?
I think it's not just about time. Computers are way faster than humans for multiplications and elementary arithmetic, but it doesn't "think".
Computers are just doing some calculus, with less information on their environment than we get with our human brain.
Computed missile guidance will in most cases fail if its target fires the right countermeasure, when a human guiding the missile would more likely avoid it and reach the goal.
Also, I do think that basic understanding of mathematics seriously enhances human intuition, which then helps develop better strategy.
For the problem you describe - computer missile guidance - I could imagine a program that analyzes when the missile reaches its target and when it doesn't as a function of some external parameters (weather, temperature, obstacles, etc.). It could detect when the target fires a counter measure (e.g a counter missile) and act accordingly: by doing some tweaks on the missile trajectory and the number of missiles fired at the same time, an ML algorithm could learn how to avoid various counter measures...
So, while it would obviously benefit to have some human brains overseeing the process, such a program could run almost autonomously most of the time. So we let the computer do the "ground work" while we focus on "high level tasks". Today the ground work is the basic calculations, tomorrow it will be part of what is done by humans today, such as adapting the trajectory of a missile as I just described above, the point is that the computing power should allow humans to focus on higher level tasks.
So I don't see how the backward movement described by Asimov can help with anything. Did he just want to warn the mankind against forgetting how calculation works?
While I agree that a program could be made to build sort of counter-countermeasure, I think that we are still not conscious of all the information we get from our environment thanks to our brain.
And as we don't have this knowledge, we can't give it to our products, like this program.
Now, let's say that we have such a program, able to reach its target most of the time.
In that case, people would still have to focus on higher level tasks as you said, like global offensive strategy.
Even for this task, I think that a spirit forged with mathematics will certainly be more efficient, with better logics and intuition.
But my opinion might be influenced by the fact that in France, our best military schools do have high maths expectations for the entry exam.
Well, the example of AI applied to ballistic is a bit particular as the environment - the place you are trying to bomb - will adapt to what you are doing, and thus some human intervention will always be needed, but for a more standard problem where the environment is not adaptive, say, the exploration of an unknown region, I guess an AI could be left all by itself to do some specific tasks. I think it's more relevant in the context of space exploration where sending humans is both more expensive and very risky (note: I have no idea if Curiosity is controlled by an AI or not).
Off topic: I'm French as well, and yeah, Polytechnique has a high level of expectation in maths.
This also might be in the time where computers would normally take up an entire room, and cost insane amounts of money. No one really saw the miniaturization of the transistor as having the effect it did on computers. It's why a bunch of non-established players one the personal computing war (Apple, Intel, Microsoft) instead of someone like IBM.
I see it as a sort of mirror to the thinking of our time. They see a way to put a human in control of something that was computer-controlled, and think that it will be better, despite the fact that their human computation can only do a tiny amount of the computation a computer can do.
Nowadays, we see a way to automate something a person does, and think that it'd better that way, despite a human mind being capable of much more than what a computer is capable of. The point of the story as I read it is that the power of new technologies can be illusory.
