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Feb. 22nd, 2004 01:40 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
andrewduckerDear Dr Phil. I sometimes find myself having conversations like this at 2am on a Sunday Morning. Is there something wrong with me?
b_ostrum_99: If I were to have a line segment AB, and I were to delete the midpoint C of that line segment, then the length of the sum of the line segments between AB would remain the same as if C had not been deleted. This is because C-A + B-C = B - A. I can continue to delete points in AB and this will remain true as long as I delete a finite number of points. Although the initial line segment length is finite, it contains an infinite number of points within it. What I am curious about and not convinced of is why I cannot delete an infinite number of points within the line segment successfully while still maintaining the full sum of line segments which add up to the initial line segment.
andrewducker: You can delete _some_ infinite numbers of points
andrewducker: For instance, all the odd numbered ones
andrewducker: Would leave all the even numbered ones
b_ostrum_99: That's exactly what i was trying to do!
b_ostrum_99: But somehow that doesn't work
andrewducker: Doesn't work in what sense?
b_ostrum_99: That was the way I thought about it too...about deleting every other point
andrewducker: Infinity isn't a number, it's a concept
andrewducker: There's a difference between "an infinite number of points" and "all the points"
b_ostrum_99: I don't know if that would be convincing...because the reason I can't delete an infinite number of points to begin with is because I would be deleting all the points and we need the line to still exist
b_ostrum_99: If I deleted all the odd points then I have deleted some length
b_ostrum_99: And that's a no no if I want to keep the line
andrewducker: The line isn't made of points
b_ostrum_99: Sure it is
andrewducker: If it was, then deleting "c" in the original would leave a shorter line
b_ostrum_99: The geometric definition of a line is a series of infinite points
b_ostrum_99: C is infinitely small
andrewducker: "C" is a positional indicator. Deleting it doesn't delete a bit of line, it just removes a note of a spot on the line
andrewducker: Which is to say that if you draw a line from point A to point B it passes through an infinite number of points.
andrewducker: But saying it's "made" of those points doesn't make any semantic sense
andrewducker: Points don't "exist" as anything more than notional indicators of location
b_ostrum_99: Suppose I were a human point on ice skates and the line segment was ice and I would fall in if there were any break in the ice that is at least the size of me. If I were to skate from A to B with its midpoint deleted, would I fall in?
andrewducker: Depends how much ice you removed and how the skates were
b_ostrum_99: I removed ice the size of the midpoint
andrewducker: geometry _isn't_ the real world. It's an abstract system that happens to be useful for solving some real-world problems
andrewducker: As soon as you start talking about things like "infinity" you've stopped talking about the real world at all
b_ostrum_99: Well, I'd like to make it true that I can pass a line through the earth and never hit anything solid
b_ostrum_99: And I can't get to that point without first resolving this
andrewducker: With an infintely thin line
b_ostrum_99: Yep, that's what lines are
andrewducker: Well, there you go then.
andrewducker: Neutrinos do this all the time
andrewducker: and they actually exist (or at least, so I'm assured)
b_ostrum_99: Yeah but it's the next step that isn't so convincing
andrewducker: atoms are made mostly of space, so if the line can go through the space between the electrons and the nucleus, you'll be fine
andrewducker: Anyway, it's 1:40am with me, and I have to be up in 7 hours.
b_ostrum_99: ah that is not how i want it to be approached though
andrewducker: And at some point you'll have to tell me how you found me and who you are
b_ostrum_99: The absence of free space must be solid space and solid space would have infinite density which would be a black hole and suck everyone in
andrewducker: If it's infinitely small there's no reason it couldn't miss everything, provided there was a straight path.
andrewducker: And on those scales you're talking about smeared quantum energy fields anyway.
andrewducker: I think
b_ostrum_99: I'll go further with this later if that's ok. Can I add you?
andrewducker: Sure thing
andrewducker: Night
b_ostrum_99: night
b_ostrum_99: If I were to have a line segment AB, and I were to delete the midpoint C of that line segment, then the length of the sum of the line segments between AB would remain the same as if C had not been deleted. This is because C-A + B-C = B - A. I can continue to delete points in AB and this will remain true as long as I delete a finite number of points. Although the initial line segment length is finite, it contains an infinite number of points within it. What I am curious about and not convinced of is why I cannot delete an infinite number of points within the line segment successfully while still maintaining the full sum of line segments which add up to the initial line segment.
andrewducker: You can delete _some_ infinite numbers of points
andrewducker: For instance, all the odd numbered ones
andrewducker: Would leave all the even numbered ones
b_ostrum_99: That's exactly what i was trying to do!
b_ostrum_99: But somehow that doesn't work
andrewducker: Doesn't work in what sense?
b_ostrum_99: That was the way I thought about it too...about deleting every other point
andrewducker: Infinity isn't a number, it's a concept
andrewducker: There's a difference between "an infinite number of points" and "all the points"
b_ostrum_99: I don't know if that would be convincing...because the reason I can't delete an infinite number of points to begin with is because I would be deleting all the points and we need the line to still exist
b_ostrum_99: If I deleted all the odd points then I have deleted some length
b_ostrum_99: And that's a no no if I want to keep the line
andrewducker: The line isn't made of points
b_ostrum_99: Sure it is
andrewducker: If it was, then deleting "c" in the original would leave a shorter line
b_ostrum_99: The geometric definition of a line is a series of infinite points
b_ostrum_99: C is infinitely small
andrewducker: "C" is a positional indicator. Deleting it doesn't delete a bit of line, it just removes a note of a spot on the line
andrewducker: Which is to say that if you draw a line from point A to point B it passes through an infinite number of points.
andrewducker: But saying it's "made" of those points doesn't make any semantic sense
andrewducker: Points don't "exist" as anything more than notional indicators of location
b_ostrum_99: Suppose I were a human point on ice skates and the line segment was ice and I would fall in if there were any break in the ice that is at least the size of me. If I were to skate from A to B with its midpoint deleted, would I fall in?
andrewducker: Depends how much ice you removed and how the skates were
b_ostrum_99: I removed ice the size of the midpoint
andrewducker: geometry _isn't_ the real world. It's an abstract system that happens to be useful for solving some real-world problems
andrewducker: As soon as you start talking about things like "infinity" you've stopped talking about the real world at all
b_ostrum_99: Well, I'd like to make it true that I can pass a line through the earth and never hit anything solid
b_ostrum_99: And I can't get to that point without first resolving this
andrewducker: With an infintely thin line
b_ostrum_99: Yep, that's what lines are
andrewducker: Well, there you go then.
andrewducker: Neutrinos do this all the time
andrewducker: and they actually exist (or at least, so I'm assured)
b_ostrum_99: Yeah but it's the next step that isn't so convincing
andrewducker: atoms are made mostly of space, so if the line can go through the space between the electrons and the nucleus, you'll be fine
andrewducker: Anyway, it's 1:40am with me, and I have to be up in 7 hours.
b_ostrum_99: ah that is not how i want it to be approached though
andrewducker: And at some point you'll have to tell me how you found me and who you are
b_ostrum_99: The absence of free space must be solid space and solid space would have infinite density which would be a black hole and suck everyone in
andrewducker: If it's infinitely small there's no reason it couldn't miss everything, provided there was a straight path.
andrewducker: And on those scales you're talking about smeared quantum energy fields anyway.
andrewducker: I think
b_ostrum_99: I'll go further with this later if that's ok. Can I add you?
andrewducker: Sure thing
andrewducker: Night
b_ostrum_99: night
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no subject
Date: 2004-02-21 05:50 pm (UTC)don't explain it.
i'm probably better off not knowing.
no subject
Date: 2004-02-21 06:00 pm (UTC)Re:
Date: 2004-02-21 06:28 pm (UTC)no subject
Date: 2004-02-21 06:47 pm (UTC)I wouldn't worry too much, though. I've heard several conversations like that at cons, and not always late at night either. (Yes, I do hang around with techies on occasion.)
no subject
Date: 2004-02-21 08:58 pm (UTC)andrewducker: And at some point you'll have to tell me how you found me and who you are
So, you not only do you have these conversations after 1am, but with complete strangers LOL...
no subject
Date: 2004-02-22 01:31 pm (UTC)