概念: 科学:数学教育

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...

これにより、インターネット検索はこのように機能するはずだと思います。現在の条件は何か、ターゲットの条件は何ですか(達成しようとしていること)を指定し、? -は、そこに到達するために検索エンジンが提供する必要がある運転ルートまたは一連のヒントです。それを行うには、実際には現在の状況に関する情報が必要です。多くの検索エンジンは、Googleの場合に大量のサービスを使用しているため、自動的にこれを実行します。だから、彼らはそれぞれの人がどのような状況にあるかを知っています。今の仕事は、それぞれの人が実際に何をしたいのかを理解し、そのコンテキストを念頭に置いて検索結果を提供し、それを実現することです...おそらく失敗する可能性がありますか?

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?


"x?= y"のxとyに依存します。それらが数値またはいくつかの複雑度の低いオブジェクトである場合、コンピューターはこれを行うことができます([エンティティグラウンディング](https://web.archive.org/web/20141130194155/http://tedsider.org/teaching/ground)と呼ばれることもあります/HO_entity_grounding_and_truthmaking.pdf))。たとえば、[技術的方法](https://www.halfbakery.com/idea/Technology_20Maps_20_99)のように、コンピューターが経路を検索するのと同じように、コンピューターが経路を検索する方法を想像するのは簡単です。


// 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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Current_value =候補





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





ここで説明することは、実際には新しいことではありません。操作検索方程式を解くことは、truthを検索してtruth関数。ここで、記号 =は、その両側が等しくなるための要件です。



-コンピュータプログラムを書くことは一種の演算子検索であり、書かれたプログラムは見つかった演算子であり、 -ドリルのような器具を作ることは一種のオペレーター検索であり、作られた器具(ドリル)はオペレーターが見つけたものです、


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.


「Think?= Other Thing」は、創造性による問題解決の枠組みのように聞こえます。学習者は「他のこと」を定義しますか、それとも教師はレッスンを促進しますか?

[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?

// 考え ? =その他のこと」は、創造性による問題解決の枠組みのように聞こえます。

そうですね、「OtherThing」を「DesiredThing」(Y)に、最初の「Thing」を現在の状況(F)に、疑問符を「X」に置き換えると、基本的に「F(X)=」になります。 Y」。

// 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".