Operation Search Equations


Thing ? = Other Thing


In the elementary schools, we are asked to solve equations with the assumption that operators are already given. For example: "4 + X = 5", or "6 - X = 9", etc., mostly with the already defined operators, like +, -, *,... etc. However, what's more useful in real life, is the creativity and operation search. So, instead of providing +, -, *, ÷, , ,... etc. as given, teach kids to do operation search to satisfy conditions defined by the equality sign.

For example, "4 ? = 5", meaning, -- what can we do with "4" to get "5". Or "6 ? = 9" -- what can we do with "6" to get "9"? Now, replace the numbers with real situations in kids' lives, and teaching operation search math can help them, fostering their creativity rather than life in one axiomatics of mathematics.

And, perhaps the question mark is not the best symbol here, as it is directional. Something like an infinite-dimensional circular question mark around one side of equation would be more appropriate.

Credits: Mindey of HalfBakery.

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// Can computers do this? Symbolic reasoning?

Depends on what is x and y in "x ? = y". If they are numbers or some low complexity objects, then computers can do this (it is sometimes called entity grounding). For example, it is easy to imagine how computers can do search for path, like technological method, in a similar way how it searches for driving directions.

However, if x and y are non-trivial (having vague features or vague value dependency on feature combinations (that can only be evaluated by a human looking at it and using one's value system to feel about it), or computationally complex, or not fitting into memory), then computers usually can't do it, unless you think of entire universe and humans as computers, which is probably not what you meant by "computers" :)

Can computers do this?

Symbolic reasoning?

That makes me think, that this is how internet search should work -- you specify what is your current condition, and what is your target conditions (what you're trying to achieve), and the ? -- is the driving directions, or sequence of hints, that the search engine should provide to get you there. To be able to do that, it actually does require to have information about your current situation. Most search engines do that automatically, as we use a plethora of their services (in case of Google). So, they know what situation each person is in. Now, the task is to figure out what each person actually wants to happen in their lives ^__^ and provide search results with that context in mind, to make it happen... What could possibly go wrong?

So I wonder: isn't the field of "operations research" - subconsciously already trying to apply math to finding such x-es? I wonder, how does the field formally define its problem domain...