Answers.Body: <p>No in general.</p>
  <p>Example: What values can x assume?</p>
  <pre><code>1. a * x^2 + b * x + c = 0, a,b,c are integer numbers.
  2. a = 44^2 + 347829 ^ 21 
  3. b = 39289238
  4. c = 999!
  </code></pre>
  <p>To know if you can answer this question you only need information 1. It is a quadratic equation, so yes you can find values for x. But to actually answer the question you need also 2,3,4.</p>
  <p>Yet there are questions in which knowing if we can answer a question requires answering the question. For instance consider a webpage with a lone password input field which only allows inputs with less than 10 characters. Can you login? Since the password field may be dummy (no input will allow you to login) and there is no indication of what the password may be you are forced to brute force all possible passwords until you either login or conclude that no login is possible.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-10-19T13:23:52.433Z
Answers.LastActivityDate: 2024-10-19T13:23:52.433Z
Answers.UserDisplayName: Rexcirus
Body: <p>I am reading <a href="http://bayes.cs.ucla.edu/WHY/" rel="nofollow noreferrer">The Book of Why: The New Science of Cause and Effect</a> by <a href="http://bayes.cs.ucla.edu/jp_home.html" rel="nofollow noreferrer">Judea Pearl</a>, and in <a href="http://bayes.cs.ucla.edu/WHY/why-intro.pdf#page=12" rel="nofollow noreferrer">page 12</a> I see the following diagram.</p>
  <p><a href="https://i.sstatic.net/qB1ns.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qB1ns.png" alt="Diagram from The Book of Why by Pearl, page 12" /></a></p>
  <p>The box on the right side of box 5 &quot;Can the query be answered?&quot; is located before box 6 and box 9 which are the processes to actually answer the question. I thought that means that telling if we can answer a question would be easier than actually answering it.</p>
  <h1>Questions</h1>
  <ol>
  <li>Do we need less information to tell if we can answer a problem (<strong>epistemic uncertainty</strong>) than actually answer it?</li>
  <li>Do we need to try to answer the problem and then realize that we cannot answer it?</li>
  <li>Do we answer the problem and at the same time provide an uncertainty estimation?</li>
  </ol>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-05-01T16:17:21.377Z
Comments.Text: This is more of a statistics question than an AI question. I suggest this be migrated to stats.stackexchange.
Comments.UserDisplayName: The Pointer
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-05-05T00:41:51.053Z
Comments.Text: @ThePointer As soon as I saw "Inference Engine" I was persuaded otherwise.  We love theoretical question such as this!  This also involves higher maths, specifically formal logic, which is a form of computing related to artificial intelligence (complexity classes, theorem solving, etc.)
Comments.UserDisplayName: DukeZhou
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-05-05T00:53:55.650Z
Comments.Text: @Lerner At a high level my sense is no—complexity classes tell us which problems can be solved and the degree of "hardness".  We can determine this by looking at the structure of the problem.  For instance, we can determine if a problem is solvable but intractable, or undecidable (a coinflip) merely by knowing the rules of the "game or puzzle".  I'll think about a formal answer
Comments.UserDisplayName: DukeZhou
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-10-13T15:23:46.773Z
Comments.Text: A concept in [Bloom's Taxonomy](https://www.coursemapguide.com/bloom-s-taxonomy) may be important in this issue: metacognitive. @DukeZhou
Comments.UserDisplayName: Lerner Zhang
Tags: <computational-complexity><causation><uncertainty-quantification><epistemic-uncertainty><philosophy-of-math>
Title: Do we need as much information to know if we can can answer a question as we need to actually answer the question?
UserDisplayName: Lerner Zhang
ThreadText: # Do we need as much information to know if we can can answer a question as we need to actually answer the question?
  
  (Asked by: username_0 on 2021-04-24)
  
  I am reading [The Book of Why: The New Science of Cause and Effect](http://bayes.cs.ucla.edu/WHY/) by [Judea Pearl](http://bayes.cs.ucla.edu/jp_home.html), and in [page 12](http://bayes.cs.ucla.edu/WHY/why-intro.pdf#page=12) I see the following diagram.
  
  [![Diagram from The Book of Why by Pearl, page 12](https://i.sstatic.net/qB1ns.png)](https://i.sstatic.net/qB1ns.png)
  
  The box on the right side of box 5 "Can the query be answered?" is located before box 6 and box 9 which are the processes to actually answer the question. I thought that means that telling if we can answer a question would be easier than actually answering it.
  
  # Questions
  
  1. Do we need less information to tell if we can answer a problem (**epistemic uncertainty**) than actually answer it?
  2. Do we need to try to answer the problem and then realize that we cannot answer it?
  3. Do we answer the problem and at the same time provide an uncertainty estimation?
  
  **Tags:** computational-complexity, causation, uncertainty-quantification, epistemic-uncertainty, philosophy-of-math
  
  > **Comments:**
  > **username_1**: This is more of a statistics question than an AI question. I suggest this be migrated to stats.stackexchange.  
  > **username_2**: @username_1 As soon as I saw "Inference Engine" I was persuaded otherwise.  We love theoretical question such as this!  This also involves higher maths, specifically formal logic, which is a form of computing related to artificial intelligence (complexity classes, theorem solving, etc.)  
  > **username_2**: @username_0 At a high level my sense is no—complexity classes tell us which problems can be solved and the degree of "hardness".  We can determine this by looking at the structure of the problem.  For instance, we can determine if a problem is solvable but intractable, or undecidable (a coinflip) merely by knowing the rules of the "game or puzzle".  I'll think about a formal answer  
  > **username_0**: A concept in [Bloom's Taxonomy](https://www.coursemapguide.com/bloom-s-taxonomy) may be important in this issue: metacognitive. @username_2  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_3 on 2024-10-19. Score: 1
  
  No in general.
  
  Example: What values can x assume?
  
  ```
  1. a * x^2 + b * x + c = 0, a,b,c are integer numbers.
  2. a = 44^2 + 347829 ^ 21 
  3. b = 39289238
  4. c = 999!
  
  ```
  
  To know if you can answer this question you only need information 1. It is a quadratic equation, so yes you can find values for x. But to actually answer the question you need also 2,3,4.
  
  Yet there are questions in which knowing if we can answer a question requires answering the question. For instance consider a webpage with a lone password input field which only allows inputs with less than 10 characters. Can you login? Since the password field may be dummy (no input will allow you to login) and there is no indication of what the password may be you are forced to brute force all possible passwords until you either login or conclude that no login is possible.
  
  
  ---
  
  