Generally, I have been very satisfied with the stack exchanges, but on occasion I run into a problem like this. I am trying to understand the significance of the transition functions of a manifold being differentiable. The answers give a very nice explanation for what the transition functions represent, but they all end with a very informal reason for showing that a differentiable transition function implies a derivative can be defined. They appeal to intuition that just does not convince me of the result.

Here are some things I could do (and where they could go wrong):

  1. Try to rephrase the question so it is not identical. (Seems vulnerable to being related enough that it would be flagged as a duplicate.)
  2. Ask on the chat room. (Tried it. No one answered.)
  3. Repeat option 2 until I get an answer. (I suppose if there is a nonzero probability of getting an answer for a given attempt, as the number of tries approaches infinity I am guaranteed an answer eventually.)
  4. Leave a comment on one of the answers to where the original question is posted. (The question was last active 11 months ago so it seems unlikely that anyone would respond.)
  5. Abandon hope. It was asked and answered. Try to find another site.

What would you recommend I do in this situation?

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Well, my answer would be «just carry on». With time, you'll see yourself what's the significance of transition functions being differentiable. The fun thing is, to carry on you do not need any über-deep understanding of that significance, just a working knowledge of the needed definitions. Asking for «understanding», «significance» and so on is usually not successful (at this level), as those things are very, very, VERY difficult to convey, as opposed to concrete knowledge. –  Mariano Suárez-Alvarez Jan 19 '13 at 5:57
    
Bill Thruston asked on MO a while ago something related here; it may help. –  Mariano Suárez-Alvarez Jan 19 '13 at 6:00
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A comment on an answer would generate a notification for the answerer, no matter how old the post is. They may or may not be able and willing to add more. // But for this particular question I agree with Mariano: understanding is more likely to come from using the definition than from meditating upon it. –  user53153 Jan 19 '13 at 6:20
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Once you have enough reputation you can also offer a bounty on the question and hope this gives new answers. –  Julian Kuelshammer Jan 19 '13 at 13:32

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