Poll on *Really* Wide Angle Lenses

Discussion in 'Digital Photography' started by BC, Aug 5, 2005.

  1. BC

    Nostrobino Guest

    Yes, but if tangents were drawn at those points *they* would be parallel,
    which seems a reasonable basis for calling the points parallel.

    N.
     
    Nostrobino, Aug 22, 2005
    1. Advertisements

  2. Plagiarise, plagiarise, plagiarise!
    You can't have a "moon" in a Rieman 2-space. The universe consists only
    of the spherical surface, nothing else exists.
    See above. I guess parallel lines in this world are only parallel at one
    (or two) points, though I've never gone into it in detail.

    David
     
    David Littlewood, Aug 22, 2005
    1. Advertisements

  3. Only if you accept that "parallelism" is a concept which can be applied
    to non-straight lines, which it can't, at least in the world of
    mathematics.

    David
     
    David Littlewood, Aug 22, 2005
  4. At least in part, I think. It's all so far back I've almost lost the
    will to live.

    David
     
    David Littlewood, Aug 22, 2005
  5. BC

    Nostrobino Guest

    It may have been related to Chris's idea (if I understood him correctly)
    that the rules of spherical projection must strictly apply to the retina,
    since that is (approximately) hemispherical. That is what I question, since
    we don't know (or at least I don't) how accurately the lens of the eye
    manages spherical projection. It does not appear to be, and doesn't need to
    be, very accurately at all as soon as you move away from the axis.

    Yes, definitely.

    N.
     
    Nostrobino, Aug 22, 2005
  6. BC

    Nostrobino Guest

    Well, he said, "Because you are receiving light reflected from four times as
    much wall
    area." I wouldn't take that to mean "from the whole wall," only that any
    point on the negative receives light from four times as many points on the
    wall (as it did at half the distance). In fact, if "the whole wall" were
    meant that would be wrong, unless the wall filled the frame vertically as
    well as horizontally of course. I doubt he meant that.

    N.
     
    Nostrobino, Aug 22, 2005
  7. BC

    Neil Ellwood Guest

    Points cannot be either diverging or converging.
     
    Neil Ellwood, Aug 22, 2005
  8. BC

    Nostrobino Guest

    Rectilinear, not necessarily wide angle (doesn't matter), wall and film
    parallel, lens axis perpendicular to both. On- or near-axis part of the wall
    should be presumed, I think, since otherwise moving back from it would
    change everything.

    N.
     
    Nostrobino, Aug 22, 2005
  9. BC

    Prometheus Guest

    I remember my calculus (just, it was a long time ago), hence my comment
    about the function. But does knowing what happens when d -> 0 let you
    distinguish Euclid, Rieman and Lobachevsky space? Of course the point
    of the rail in contact with the wheel can be said to be parallel
    (ignoring deformities) or it can be said to be a tangent; neither view
    is incorrect but which is more useful depends on rather more. Of course
    the rim of the wheel is NOT parallel as can be shown if you consider
    more than one point (not the diametrically opposed point), more work for
    your calculus, whereas the set of points defining two non-crossing
    Euclidean lines can be shown to be parallel for any closest pair.
    Actually thinking about it I am not sure that the points where the wheel
    touches the rail can be said to be parallel since they reduce to one
    point.
     
    Prometheus, Aug 22, 2005
  10. BC

    Prometheus Guest

    Nor can they be parallel, but a series of points can be diverging or
    converging.
     
    Prometheus, Aug 22, 2005
  11. BC

    ASAAR Guest

    I was well aware of the "real world" problem cause by deformities,
    since I first started to describe the concept using a car's tire on
    a road. Even steel is elastic, but I hoped that it would allow the
    question of deformities (which don't change what the concept I was
    trying to illustrate) to be sidestepped. :)

    That's correct, points have no direction. But a purely
    mathematical wheel (unlike a steel, or any other real wheel) would
    touch at only one point. And as one looks at a vanishingly small
    section of the rim containing the single point that touches the
    rail, one would see what appears to be an increasingly straight line
    which does have a direction, and which would be parallel to the
    rail. Those that don't see this (not referring to you) probably
    have non-mathematical reasons for their lack of vision. :)
     
    ASAAR, Aug 22, 2005
  12. BC

    ASAAR Guest

    My friend's 10 inch disc was the first one I came across, but my
    own copies were all standard 12" LPs. I may have an old 10" Benny
    Goodman record from my father's collection buried away somewhere.
    There are only a few performances that I can say that I recall
    precisely where I was when I first heard them. One was hearing Tom
    Lerher's record. Another was Stravinsky's "Rites of Spring", heard
    on a radio broadcast. The last was Carla Bley's "Blunt Object",
    heard live.
     
    ASAAR, Aug 22, 2005
  13. BC

    ASAAR Guest

    A moon isn't necessary. Would a spherical, infinitesimally thin
    shell be acceptable in Rieman's 2-space? Real world objects are
    only used to try to make it easier to visualize concepts. I also
    thought of describing an orange, cut into slices (the cuts being
    great circles) but remaining intact.
     
    ASAAR, Aug 22, 2005
  14. BC

    ASAAR Guest

    I never said or implied that the entire line or curve was
    parallel. Just that a vanishingly small part of it could be
    considered to be parallel. That's always been a part of the
    mathematics I was taught. But as someone else mentioned here,
    tangent surfaces are usually described instead.
     
    ASAAR, Aug 22, 2005
  15. BC

    ASAAR Guest

    Hang in there David Littlewill. We'd miss your points if you
    vanished. :)
     
    ASAAR, Aug 22, 2005
  16. Indeed, tangents (which are by definition straight lines) can be
    parallel.

    David
     
    David Littlewood, Aug 22, 2005
  17. Yes; it would of course be a point....
     
    David Littlewood, Aug 22, 2005
  18. BC

    Nostrobino Guest

    Though I haven't listened to that Lehrer record for many years (in fact,
    don't know where it is now and haven't even owned a turntable to play it on
    for many years), I can still clearly recall the tunes and that inimitable
    voice of his in at least some of the songs. That Lobachevsky piece for one,
    The Boy Scouts' Marching Song, The Old Dope Peddler, and odd fragments of
    others. I wish I had made a digital version..

    N.
     
    Nostrobino, Aug 22, 2005
  19. BC

    Nostrobino Guest

    <guffaw!>
    I know what you mean! Glad I'm not the only one.

    N.
     
    Nostrobino, Aug 22, 2005
  20. Sorry, I think I misunderstood; I read as infinitesimal rather than
    infinitesimally thin. What you say is in fact a description of the space
    itself. Another such space adjacent to it makes as much sense as a
    parallel 3D universe lying alongside ours but not touching it.
     
    David Littlewood, Aug 23, 2005
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.