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  1. Path: sparky!uunet!spool.mu.edu!mixcom.com!ttyytt
  2. From: ttyytt@mixcom.com (Adam Costello)
  3. Newsgroups: sci.physics
  4. Subject: Re: ... an infinite mesh of 1ohm resistors ...
  5. Message-ID: <1992Jul28.000844.27051@mixcom.com>
  6. Date: 28 Jul 92 00:08:44 GMT
  7. Article-I.D.: mixcom.1992Jul28.000844.27051
  8. References: <1992Jul24.165217.16688@news.media.mit.edu> <1992Jul25.210947.12316@cs.yale.edu> <1992Jul27.210947.5820@fs7.ece.cmu.edu>
  9. Organization: Milwaukee Internet Xchange BBS, Milwaukee, WI U.S.A.
  10. Lines: 46
  11.  
  12. In article <1992Jul27.210947.5820@fs7.ece.cmu.edu> snyder@henry.ece.cmu.edu (John Snyder) writes:
  13. >
  14. >I believe that you are missing the point of the previous post here.
  15.  
  16. But I think you are missing the point of the second post.  The "solution"
  17. involved imagining that you could inject an amp of current into a network
  18. of resistors.  No capacitors!  Where is the charge supposed to go?
  19. Regardless of whether this can be done in the laboratory, there's still
  20. the question of whether it can be done in the mind.  Certainly, if the
  21. network were finite, it would make no sense.  Does the infinitude of the
  22. network allow a source with no sink?  We can argue that it does this way:
  23.  
  24. Consider this sequence of networks:
  25.  
  26. +-----+-----+     +-----+-----+-----+-----+
  27. |     |     |     |     |     |     |     |
  28. |     /     |     |     /     /     /     |
  29. |     \     |     |     \     \     \     |
  30. |     /     |     |     /     /     /     |
  31. |     |A    |     |     |     |     |     |
  32. +-/\/-+-/\/-+     +-/\/-+-/\/-+-/\/-+-/\/-+
  33. |     |     |     |     |     |     |     |
  34. |     /     |     |     /     /     /     |
  35. |     \     |     |     \     \     \     |
  36. |     /     |     |     /     /     /     |
  37. |     |     |B    |     |     |A    |     |
  38. +-----+-----+     +-/\/-+-/\/-+-/\/-+-/\/-+     And so on...
  39.                   |     |     |     |     |
  40.                   |     /     /     /     |
  41.                   |     \     \     \     |
  42.                   |     /     /     /     |
  43.                   |     |     |     |     |
  44.                   +-/\/-+-/\/-+-/\/-+-/\/-+
  45.                   |     |     |     |     |
  46.                   |     /     /     /     |
  47.                   |     \     \     \     |
  48.                   |     /     /     /     |
  49.                   |     |     |     |     |B
  50.                   +-----+-----+-----+-----+
  51.  
  52. In each network, connect a 1 amp current source from B to A.  In the
  53. limit, we have the infinite network with a source and no sink.  I'm
  54. still not convinced, because I'm not sure "limit" makes sense here.
  55. Any comments?
  56.  
  57. AMC
  58.