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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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...

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?

Can computers do this?

Symbolic reasoning?

// 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" :)

I had an idea for computers to work out how to perform an action based on representations.

So If you have an image it might not be in the right format for a crop code. so you need to convert it to pixels first.

First it would detect the image format is PNG and find a PNG decoder. Then it would find an operation that works on decoded PNG. Such as crop.


    : Mindey
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I think this idea is related to advice engine.

Life is a bit of a decision tree.

You can't just go to Harvard or Oxford or Cambridge an exclusive university at step 1. You need to do other things first.

I also had an idea for achieving guided browsing. Which is on half bakery. The idea is you go through a set of pages before concluding your search. Like a tutorial that is reactive to what you have done so far.


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    : Mindey
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This idea is also related to Automated API traversal - Program synthesis.

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    : Mindey
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This is also related to forward chaining and backward chaining logical inferences.

To calculate towards an end value you need a distance function and a direction.

While distance(current_value) greater than 0 {

For function in next_functions(function) (

 Candidate = Function(current_value)

 If distance(candidate) Less than distance(current_value) (


Current_value = Candidate





What is described here, is really not new: solving operation search equations can be shown to be equivalent to search for ground terms to solve truth equations made from truth functions, where symbol = is a requirement for both sides of it to be equal.

An "operation" then can be said to be a "ground term" or a "solution" to an operation search equation.

I think the novelty here is only in simplification of description to make it relevant to education systems to catch up in the levels of abstraction and pragmatics with the modern day thinking: i.e., instead of asking kids to regurgitate existing functions or operators to plug in to solve problems given to them, -- allowing them to imagine possible operators to apply to the resources to resolve a problem that they care about: for example:

  • writing a computer program is a kind of operator search, where the program written is the operator found,
  • making an instrument like a drill, is a kind of operator search, where the instrument (the drill) made is the operator found,


    : Ruta
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I assumed there was always multiple operators in the problem and they are applied in order.

This as you say is programming. We can have computers programming themselves if they can do operation search.

I dont know if sequence to sequence neural networks can help. They are used for translation problems and sentence trees.

You mentioned Github's OpenAI Codex on additive GUI page, I think that is relevant on this idea.

I want systems that programs themselves such as the following function -

F(database state 1, request) = (output HTML, database state 2, network calls)

The program can search for references for information used in the request to create the concatenated strings of HTML and database inserts. If you specify that order_number in the request corresponds to Orders table in database state 1 then the computer can probably work out what data needs pulling out into the output HTML.

[Mindey] , I wonder, how would this look like as a Lesson / Learning Experience? Can you give some example?

"Think ? = Other Thing" sounds like a framework for problem solving through creativity. Would a learner define the "other thing" or a teacher facilitating a lesson?

// Think ? = Other Thing" sounds like a framework for problem solving through creativity.

Yeah, well, replace "Other Thing" with 'Desired Thing' (Y), and the first "Thing" with current circumstances (F), and the question mark with "X", and you get essentially "F(X)=Y".