(no subject)

[andrewducker]

Dear 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

Comments

[biscuitware.livejournal.com]

i read it. it didn't make sense too me.
don't explain it.
i'm probably better off not knowing.