A question regarding "Who is born earlier in time"

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Discussion Overview

The discussion revolves around the question of determining who is born earlier in time between a grandson and a great-grandson, with considerations of definitions and assumptions affecting the clarity of the question. Participants explore the implications of various scenarios, including the "one child policy," and the assumptions necessary to arrive at an answer.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants argue that the question is insufficiently defined to provide a clear answer, suggesting that it lacks necessary criteria.
  • Others propose that the "one child policy" assumption simplifies the question, making it trivial under certain conditions.
  • A few participants challenge the assumption that all births occur at the same age, arguing that different ages could lead to varying conclusions.
  • Some suggest that the question could be reformulated to focus on counting generations rather than determining who is born earlier.
  • There are claims that the original question implies a specific family structure that may not account for multiple interpretations.
  • Participants note that even with a narrow interpretation, the question remains poorly posed, as exemplified by various family trees presented in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus; multiple competing views remain regarding the sufficiency of the question's definition and the assumptions required to answer it.

Contextual Notes

Limitations include the lack of clarity in the original question, dependence on assumptions about generational distances and birth ages, and the potential for multiple interpretations based on the family structure described.

simplex1
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http://math.stackexchange.com/questions/1625487/who-is-born-earlier-in-time-the-great-grandson-of-the-grandson-or-the-grandson
 
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How would you go about figuring this out (hint: it's trivial)
 
Actually, there is insufficient information. There's no way to tell which one was born earlier.

I sure hope this isn't a homework question...
 
I have found the question here: http://math.stackexchange.com/questions/1625487/who-is-born-earlier-in-time-the-great-grandson-of-the-grandson-or-the-grandson a place where the moderators considered it ill-defined, quote: "You need to study the theory of definite descriptions to help you avoid posing ill-defined questions."

In my opinion the problem has at least a nice solution.
 
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Yup. It is insufficiently defined to provide an answer.

phinds has egg on his face. He thought the answer was trivial. but right about now, he's realizing he went off half-cocked. :smile:
 
Just propose an answer, a solution, for a particular case of your choice.
 
Since the question cannot be answered as it stands, how is one supposed to answer it?

The only correct answer is: I don't know, and neither do you.
 
Take the case "one child policy".
 
simplex1 said:
Take the case "one child policy".

There you go! That must be specified in the question.

And now the question is trivial.
 
  • #10
DaveC426913 said:
Yup. It is insufficiently defined to provide an answer.

phinds has egg on his face. He thought the answer was trivial. but right about now, he's realizing he went off half-cocked. :smile:
No, I made a simplifying assumption that the ages at which everyone had their so was the same. That makes it trivial. The point is to simply count generations. A better-formed question would be "how many generations is that" and that is trivial.
 
  • #11
DaveC426913 said:
There you go! That must be specified in the question.

And now the question is trivial.
No, not YOU have egg on your face, at least to the same extent that I did. You have made the same simplifying assumption I did.
 
  • #12
phinds said:
No, I made a simplifying assumption that the ages at which everyone had their so was the same. That makes it trivial. The point is to simply count generations. A better-formed question would be "how many generations is that" and that is trivial.
Why have you
a] made an unfounded assumption, and
b] completely reformulated the question,
c] without stating your case-reducing assumption in the answer (necessary to make it correct)?
 
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  • #13
phinds said:
No, not YOU have egg on your face, at least to the same extent that I did. You have made the same simplifying assumption I did.
No I didn't.

The OP provided the missing criterion in post 8. 'One child policy' means that the answer is so trivial it is degenerate (Which is younger: Person A or the same person?) I'm not sure why you think I made any simplifying assumptions.
 
  • #14
DaveC426913 said:
No I didn't.

The OP provided the missing criterion in post 8. 'One child policy' means that the answer is so trivial it is degenerate (Which is younger: Person A or the same person?) I'm not sure why you think I made any simplifying assumptions.
But the one child criterion does not make for a unique answer. You have to make the simplifying assumption of same age births. Think it through, you'll get it. Assume all births are after a different number of years. Clearly you don't end up w/ the same answer (necessarily).
 
  • #15
phinds said:
But the one child criterion does not make for a unique answer.
Yes it does.

You are comparing the age of a person to themselves. They are the same person.

I think you might have overlooked the last criterion in the OP: the ancestor is the same person in both scenarios.
 
  • #16
DaveC426913 said:
Yes it does.

You are comparing the age of a person to themselves. They are the same person.
You're missing the point. Write it out, using different ages for each person when their son is born. You get different answers and which path leads to a younger person will vary depending on those ages.
 
  • #17
See post 15.
 
  • #18
DaveC426913 said:
See post 15.
Yeah, you're right. I goofed. Definitely egg on my face, not yours. Thanks. o:)
 
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  • #19
It's a really tricky one!
 
  • #20
DaveC426913 said:
It's a really tricky one!
Doesn't seem all that tricky if you think it through properly, which I did not at first.
 
  • #21
- If the distance between generations is considered the same, the one child policy assumption is not necessary.
- If the one child policy criterion is assumed then the distance in time between generations does not have to be constant.
Anyway the question already suggests that the reference person has only one grandson who has, in his turn, only one great grandson and the same person has only one great grandson who has also a single grandson. It is not "a great grandson of a grandson" is "the great grandson of the grandson".

- Father
- Sons + daughters (the number does not matter as long as only one grandson exists)
- Grandson
- Great grandson
- Great great grandsons + Great great granddaughters (the number does not matter as long as only one grandson of the great grandson exists)
-The grandson of the great grandson = The great grandson of the grandson

There could be multiple solutions but as it is the question is quite restrictive.
 
  • #22
simplex1 said:
- If the distance between generations is considered the same, the one child policy assumption is not necessary.
Not true.
Michael Collins is my grandfather's great-great-grandfather. He is also my brother's grandfather's great-great-grandfather.
Which of us was born earlier?

simplex1 said:
Anyway the question already suggests that the reference person has only one grandson who has, in his turn, only one great grandson and the same person has only one great grandson who has also a single grandson. It is not "a great grandson of a grandson" is "the great grandson of the grandson".
Flawed logic. I am the son of my father. That does not mean I have no brothers. You certainly can't assume that in the question.

simplex1 said:
There could be multiple solutions but as it is the question is quite restrictive.
Nope. Again, the initial question is insufficiently-defined to result in a unique answer.

You must include the 'one child' criterion (or some other, unspecified criterion).
 
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  • #23
simplex1 said:
Anyway the question already suggests that the reference person has only one grandson who has, in his turn, only one great grandson and the same person has only one great grandson who has also a single grandson. It is not "a great grandson of a grandson" is "the great grandson of the grandson".
Even with that narrow interpretation the question is still not well posed. Consider the following family tree:
Code: 
  A1
  |
  A2
  |
  --
 |  |
F1  M3
 |  |
M4  F2
 |  |
A3  A4
 |  |
M5  M6
A1 has only one grandson (M3) who has only one great grandson (M6), and A1 has only one great-grandson (M4) who has only one grandson (M5), but M6 and M5 are not the same person.
 
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  • #24
MrAnchovy, yes you have found an interesting solution where the two are not the same person also only one grandson and great grandson are assumed to exist. I am looking for other possible cases.
 
  • #25
If the distance between generations is considered the same, the one child policy assumption is not necessary.
DaveC426913 said:
Not true.
Michael Collins is my grandfather's great-great-grandfather. He is also my brother's grandfather's great-great-grandfather.
Which of us was born earlier?

You were both born exactly in the same time (which is impossible).
 
  • #26
simplex1 said:
You were both born exactly in the same time (which is impossible).
Why do you insist on this? We were not born at the same time, yet we still meet the criteria of the question as-stated in the OP.Is it possible that, by this:
If the distance between generations is considered the same
you mean every generation is some arbitrary yet fixed length of time?

That's fine, but you must state it as a criterion in the question. It would be folly to assume such a thing.
 
  • #27
simplex1 said:
MrAnchovy, yes you have found an interesting solution where the two are not the same person also only one grandson and great grandson are assumed to exist. I am looking for other possible cases.
What about the incestuous case in which the grandson and the great grandson of the original person are, in fact, one and the same person.

Code: 
A1
|
M1
| \
|  F1 -- Not a grandson
| /
M2 (by F1 and M1) -- "the" grandson and also "the" great-grandson
|
F2 -- Not a great-grandson
|
M3 -- The grandson of the great-grandson
|
M4 -- The great-grandson of the grandson

Edit -- or the less incestuous case in which the grandson is the son of the great-grandson.

Code: 
   A1
   | \
   A2 \
   |   \
   F2   F3 (F2 is not the grandson)
   |   /
   M1 /    (M1 is the great-grandson)
 / | /
F4 M2      (M2 is the grandson)
|  |
M3 F4      (M3 is the grandson of the great-grandson)
   |
   A3
   |
   M4      (M4 is the great-grandson of the grandson)
 
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  • #28
This thread is just getting too weird :smile:
 
  • #29
Dave - Phinds... would it be wrong of me to suggest "get a room"? I feel like I've just read a transcript of an argument with my wife! Although to be honest that transcript would have been much more one sided... In the words of the Bard; "me and the wife had words; I just didn't get to use any of mine"
 
  • #30
mgkii said:
Dave - Phinds... would it be wrong of me to suggest "get a room"
Yes. Nothing obliges you to read these posts.
 

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