I think, we've reached this situation, where huge numbers of people, across different professions, need to manipulate data.

For the last 10/20 years, the dominant paradigm for data manipulation, was probably the spreadsheet. Spreadsheets give an enormous amount of power, for relatively little investment. So, now, a wide range of professionals - business analysts, geologists, even engineers, use spreadsheets as their standard data manipulation tools.

But I think we've entered a world where data manipulation is so central, that spreadsheets just aren't a powerful enough paradigm for these jobs.

At the moment, I feel that the best way for manipulating data, is probably a general purpose programming language, like Python. I would advise people starting a career in information work ( anyone that does advanced data processing and analysis - which is a great many people, these days), to try and learn to program. I see a lot of merit to the argument that programming is becoming a basic professional skill, like literacy did.

(I would advise something like Python, over something like R, or even Matlab; I think its just semantically more consistent, and cleaner. This is completely a personal opinion, but I think R, in its present form, will ultimately be considered a failure, as a data manipulation tool.)

Given this worldview, it'd make a lot of sense to _currently_ be teaching binary search, in school, rather than long division.

Now, programming languages are probably the best general purpose data manipulation tools we have currently, but, for all their power, I suspect that future generations will look back on what we use now, as we look back on writing machine code - a painstaking, and primitive exercise. There's plenty of people trying to build more powerful general data manipulation tools, at present, but I've yet to see something thats a convincing advance over both the spreadsheet, and the general purpose programming language.

But, even if we do have better data manipulation paradigms in future, where the binary search is completely abstracted away from the data manipulator, then I would still guess that it might make more sense to teach school kids binary search rather than long division.

I don't accept the argument that long division is in some sense more primitive, or more 'bare minimum', than binary search is. It is, in the order we currently teach things; but I don't see that order as at all fundamental. I think from an algorithmic worldview, binary search is a pretty fundamental operation. You can do a lot of algorithms before you need to divide anything - why not have them come first?

I'm not saying this is the definitive world view to have, and 'binary search' is just an example here; but I am saying that I don't see why we have to be so focused on the arithmetic-centred view of things; and I would hope that 'in the future' we'd have moved beyond that. Fewer and fewer people are going to have any experience with complex arithmetic, but more and more of them are going to have to manipulate data.

I don't think we give a lot of importance to childrens time at the moment; I think they are sent to spend time doing long division because thats what they've always been sent to do; but I think that this might all be about to change, as education is coming into line for some massive disruption.