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In a book, I read:

Engineering is all about breaking down big problems into smaller ones and putting the solutions for those problems back together.

My generalized interpretation of this text is that, sometimes we start from the big end, sometimes from the smaller ends, and then we move towards the other end.

Do we have terms to describe these approaches? Like saying "president is a X-ist" to denote that he starts from small problems to get to bigger ones till he solves the biggest problems.

I tried to bring forward some examples. But I failed. I hope you have understood.

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"My generalized interpretation of this text is that, sometimes we start from the big end, sometimes from the smaller ends, and then we move towards the other end." I don't think this is right. It's saying that (in Engineering) one starts at the big end. When one gets to the small end one works back to the big one, but one always starts with the big. The first part, I'd probably call deconstruction. – Rupe Aug 6 '14 at 9:09
@Rupe, nice word "deconstruction". – Saeed Neamati Aug 6 '14 at 9:22

The terms I would employ for this are top down:-

2: proceeding by breaking large general aspects (as of a problem) into smaller more detailed constituents : working from the general to the specific [Merriam-Webster]

and bottom up:-

from the lowest level of a hierarchy or process to the top: a bottom-up approach to corporate decision-making [World English Dictionary]

These terms are particularly common in the software trade.

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top down and bottom up are used in many areas of engineering and other topics. +1 for most widely used answer. – KnightHawk Aug 6 '14 at 15:03

I upvoted @BrianHooper's answer, because I believe top-down and bottom-up are the terms used in a constructive context (I've seen it in software engineering, but also in the context of a marketing strategy, portfolio construction, and of building out a business).

But for the sake of having a variety of answers, and in case you come across a need to express these concepts in different contexts, here's a couple more sets of terms.

Scientific endeavors will often have a period of analysis (breaking down observations into their constituent elements) followed by a period of synthesis (identification of patterns found among those primitive elements).

Similarly, philosophers will often debate the relative merits and legitimacy of deductive (top-down) and inductive (bottom-up) reasoning.

Side note: weaker counterparts to these types of reasoning exist: abductive is deductive reasoning using facts known to be imperfect or incomplete (a "best guess", e.g. a medical diagnosis); conductive is inductive reasoning using supporting arguments (because you don't think the facts necessarily speak for themselves).

For these reasons, if you want to say "X is philosophically committed to taking a bottom-up approach", you might say "X is an inductionist" (or subscribes to inductionism). Similarly, if you want to say "X understands how things work by taking them apart", you might say "X is an analyst". Unfortunately, inductivist and deductivist are really only applicable to certain stances in the philosophy of science (note the suffix, -iVist, compared the the -iONist of inductionist; a subtle distinction that makes a big difference).

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In Descriptive Psychology, behaviors are top-down, called implementation; answers the question, "How can I do X?" Observations are bottom-up, called significance; answers the question, "What is P doing by doing that?"

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When you break down large problems into smaller problems in engineering, you're using a Divide and Conquer Algorithm.

A divide and conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same (or related) type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.

It's not quite the same as "sometimes we start from the big end, sometimes from the smaller ends, and then we move towards the other end." Rather, you always start from the big end to break up the problem into problems small enough to solve. Then, you work from the smaller ends to put the small answers together to form a big answer.

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