概念: 科學:數學教育

操作搜索方程

+4  

事物?=其他事物

YAML 想法

在小學校,要求我們在已經給出運算符的前提下解方程。 例如:"4 + X = 5""6 - X = 9",等等。大多使用已經定義的運算符,例如+, -, *,...等。然而在現實生活中更有用的是創造力和操作搜索。 因此,與其提供給定的+, -, *, ÷, , ,...等,不如教孩子進行操作搜索以滿足等號定義的條件。

例如,"4 ? = 5",意思是用"4"做什麼可以得到"5"。或是"6 ? = 9"——用"6"怎麼得到"9"?現在,將數字替換爲孩子們生活中的真實情境,操作搜索數學教學可以幫助他們,培養他們的創造力,而不是生活在數學公理中。

而且,問號可能不是這裏的最佳符號,因爲它是有方向性的。像在等式一側的無限維圓形問號之類的東西會更合適。

最初由Mindey發佈在 HalfBakery





(別通知) (可選) 請,登錄

所以我想知道:“運籌學”領域不是在潛意識裏已經在試圖將數學應用於發現這樣的x-es嗎?我想知道,該領域如何正式定義其問題領域...

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...


這讓我認爲,這就是互聯網搜索的工作方式-您指定當前的條件,目標條件(您要達到的目標)以及? -是搜索引擎應提供的行車路線或提示順序,以幫助您到達目的地。爲了做到這一點,它實際上確實需要掌握有關您當前情況的信息。大多數搜索引擎會自動執行此操作,因爲我們使用了大量的服務(對於Google而言)。因此,他們知道每個人所處的情況。現在,任務是弄清楚每個人在生活中實際想要發生的事情^ __ ^,並在考慮到這種情況的情況下提供搜索結果,以使其成爲現實。可能會出問題?

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?


電腦可以這樣做嗎?

象徵推理?

Can computers do this?

Symbolic reasoning?


//電腦可以這樣做嗎?象徵推理?

取決於“ x?= y”中的x和y是什麼。如果它們是數字或一些低複雜度的對象,則計算機可以執行此操作(有時稱爲[實體接地](https://web.archive.org/web/20141130194155/http://tedsider.org/teaching/ground /HO_entity_grounding_and_truthmaking.pdf))。例如,很容易想象計算機可以如何搜索路徑,例如[技術方法](https://www.halfbakery.com/idea/Technology_20Maps_20_99),就像搜索道路的方式一樣。

但是,如果x和y是非平凡的(對特徵組合具有模糊的特徵或模糊的值依賴性(只能由人對其進行評估並使用自己的價值體系來對其進行評估),或者在計算上是否複雜放入內存),那麼計算機通常無法做到這一點,除非您將整個宇宙和人類視爲計算機,這可能不是您所說的“計算機”的意思:)

// 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.

https://github.com/samsquire/ideas#11-representational-computing



    : Mindey
    :  -- 
    :  -- 
    

chronological,

我認爲這個想法與建議引擎有關。

生活有點像決策樹。

你不能只在第一步就去哈佛、牛津或劍橋這樣的專屬大學。你需要先做其他事情。

我也有一個實現引導瀏覽的想法。這是半面包店。這個想法是您在結束搜索之前瀏覽一組頁面。就像一個對你到目前爲止所做的事情有反應的教程。

https://www.halfbakery.com/idea/Guided_20web_20browsing

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.

https://www.halfbakery.com/idea/Guided_20web_20browsing



    :  -- 
    : Mindey
    :  -- 
    

chronological,

這個想法也和自動化API遍歷——程序合成有關。

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



    :  -- 
    : Mindey
    :  -- 
    

chronological,

這也與正向鏈接和反向鏈接邏輯推理有關。

要計算最終值,您需要一個距離函數和一個方向。

而 distance(current_value) 大於 0 {

對於 next_functions(function) 中的函數 (

 候選人 = 函數(current_value)

 如果距離(候選)小於距離(當前值)(

 Directions.append(函數)

Current_value = 候選人

 休息

)

)

)

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) (

 Directions.append(function)

Current_value = Candidate

 Break

)

)

)


這裏所描述的其實並不新鮮:求解操作搜索方程可以被證明等效於搜索 ground term 來求解由 truth函數,其中符號 = 是要求它的兩邊相等。

一個“操作”可以說是一個“基本項”或一個操作搜索方程的“解”。

我認爲這裏的新穎之處僅在於簡化了描述,使其與教育系統相關,以趕上現代思維的抽象和實用水平:即,而不是讓孩子們反芻現有的功能或操作符來插入解決給他們的問題,——讓他們想象可能的操作符應用於資源來解決他們關心的問題:例如:

  • 編寫計算機程序是一種運算符搜索,其中編寫的程序是找到的運算符,
  • 製造像鑽頭一樣的儀器,是一種操作員搜索,其中製造的儀器(鑽頭)是操作員找到的,

等等。

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,

etc.



    : Ruta
    :  -- 
    :  -- 
    

Mindey,

我假設問題中總是有多個運算符,並且它們是按順序應用的。

這正如你所說的編程。如果計算機可以進行操作搜索,我們就可以讓計算機自己編程。

我不知道序列到序列神經網絡是否可以提供幫助。它們用於翻譯問題和句子樹。

您在附加 GUI 頁面上提到了 Github 的 OpenAI Codex,我認爲這與這個想法有關。

我想要自己編程的系統,例如以下功能 -

F(數據庫狀態1,請求)=(輸出HTML,數據庫狀態2,網絡調用)

該程序可以搜索請求中使用的信息的引用,以創建 HTML 和數據庫插入的串聯字符串。如果您在請求中指定 order_number 對應於數據庫狀態 1 中的 Orders 表,那麼計算機可能會計算出需要將哪些數據提取到輸出 HTML 中。

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] ,我想知道,作爲課程/學習體驗,這會是什麼樣子?你能舉一些例子嗎?

“Think ? = Other Thing”聽起來像是通過創造力解決問題的框架。學習者會定義“其他事物”還是教師促進課程?

[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?


// 思考 ? = Other Thing”聽起來像是通過創造力解決問題的框架。

是的,好吧,用“想要的東西”(Y)替換“其他東西”,用當前情況(F)替換第一個“東西”,用“X”替換問號,你基本上得到“F(X)=於”。

// 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".


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