Method default argument whose type is the class not yet defined

Discussion in 'Python' started by Jennie, Nov 10, 2012.

  1. Jennie

    Jennie Guest

    What is the best solution to solve the following problem in Python 3.3?

    import math
    >>> class Point:

    .... def __init__(self, x=0, y=0):
    .... self.x = x
    .... self.y = y
    .... def __sub__(self, other):
    .... return Point(self.x - other.x, self.y - other.y)
    .... def distance(self, point=Point()):
    .... """Return the distance from `point`."""
    .... return math.sqrt((self - point).x ** 2 + (self - point).y ** 2)
    ....
    Traceback (most recent call last):
    File "<stdin>", line 1, in <module>
    File "<stdin>", line 5, in Point
    NameError: name 'Point' is not defined

    I propose three solutions. The first one:

    >>> class Point:

    .... def __init__(self, x=0, y=0):
    .... self.x = x
    .... self.y = y
    .... def __sub__(self, other):
    .... return Point(self.x - other.x, self.y - other.y)
    .... def distance(self, point=None):
    .... p = point if point else Point()
    .... return math.sqrt((self - p).x ** 2 + (self - p).y ** 2)
    ....
    >>> p = Point()
    >>> p.distance()

    0.0
    >>> p.distance(Point(3, 4))

    5.0

    The second one:

    >>> class Point:

    .... def __init__(self, x=0, y=0):
    .... self.x = x
    .... self.y = y
    .... def __sub__(self, other):
    .... return Point(self.x - other.x, self.y - other.y)
    ....
    >>> def distance(self, point=Point()):

    .... return math.sqrt((self - point).x ** 2 + (self - point).y ** 2)
    ....
    >>> Point.distance = distance
    >>> p = Point()
    >>> p.distance(Point(3, 4))

    5.0

    The last one:

    >>> class Point:

    .... def __init__(self, x=0, y=0):
    .... self.x = x
    .... self.y = y
    .... Point.distance = distance
    .... def __sub__(self, other):
    .... return Point(self.x - other.x, self.y - other.y)
    ....
    >>> def distance(self, point=Point()):

    .... return math.sqrt((self - point).x ** 2 + (self - point).y ** 2)
    ....
    >>> p = Point()
    >>> p.distance(Point(3, 4))

    5.0

    Is there a better solution?
    --
    Jennie
     
    Jennie, Nov 10, 2012
    #1
    1. Advertising

  2. On Sun, Nov 11, 2012 at 6:33 AM, Jennie <> wrote:
    > ... def distance(self, point=None):
    > ... p = point if point else Point()


    I'd go with this one. Definitely not the third one, which mutates the
    class according to a current global every time a Point is instantiated
    - could be *extremely* confusing if the name distance were ever
    rebound. You could also fiddle with the default args:

    >>> class Point:

    def __init__(self, x=0, y=0):
    self.x = x
    self.y = y
    def __sub__(self, other):
    return Point(self.x - other.x, self.y - other.y)
    def distance(self, point="Point()"):
    return math.sqrt((self - p).x ** 2 + (self - p).y ** 2)

    >>> Point.distance.__defaults__=Point(), # has to be a tuple


    ChrisA
     
    Chris Angelico, Nov 10, 2012
    #2
    1. Advertising

  3. Jennie

    Terry Reedy Guest

    On 11/10/2012 2:33 PM, Jennie wrote:
    > What is the best solution to solve the following problem in Python 3.3?
    >
    > import math
    > >>> class Point:

    > ... def __init__(self, x=0, y=0):
    > ... self.x = x
    > ... self.y = y
    > ... def __sub__(self, other):
    > ... return Point(self.x - other.x, self.y - other.y)
    > ... def distance(self, point=Point()):
    > ... """Return the distance from `point`."""
    > ... return math.sqrt((self - point).x ** 2 + (self - point).y ** 2)
    > ...
    > Traceback (most recent call last):
    > File "<stdin>", line 1, in <module>
    > File "<stdin>", line 5, in Point
    > NameError: name 'Point' is not defined
    >
    > I propose three solutions. The first one:
    >
    > >>> class Point:

    > ... def __init__(self, x=0, y=0):
    > ... self.x = x
    > ... self.y = y
    > ... def __sub__(self, other):
    > ... return Point(self.x - other.x, self.y - other.y)
    > ... def distance(self, point=None):
    > ... p = point if point else Point()
    > ... return math.sqrt((self - p).x ** 2 + (self - p).y ** 2)
    > ...
    > >>> p = Point()
    > >>> p.distance()

    > 0.0
    > >>> p.distance(Point(3, 4))

    > 5.0


    What I do not like about this one is that it creates a new 0 point each
    time one is needed. Two solutions:

    change Point() to point0 in the distance function and create
    point0 = Point()
    after the class.

    -or-
    instead of p = line,
    px,py = point.x, point.y if point else 0.0, 0.0


    > The second one:
    >
    > >>> class Point:

    > ... def __init__(self, x=0, y=0):
    > ... self.x = x
    > ... self.y = y
    > ... def __sub__(self, other):
    > ... return Point(self.x - other.x, self.y - other.y)
    > ...
    > >>> def distance(self, point=Point()):

    > ... return math.sqrt((self - point).x ** 2 + (self - point).y ** 2)
    > ...
    > >>> Point.distance = distance
    > >>> p = Point()
    > >>> p.distance(Point(3, 4))

    > 5.0


    my first thought


    > The last one:
    >
    > >>> class Point:

    > ... def __init__(self, x=0, y=0):
    > ... self.x = x
    > ... self.y = y
    > ... Point.distance = distance
    > ... def __sub__(self, other):
    > ... return Point(self.x - other.x, self.y - other.y)
    > ...
    > >>> def distance(self, point=Point()):

    > ... return math.sqrt((self - point).x ** 2 + (self - point).y ** 2)
    > ...
    > >>> p = Point()
    > >>> p.distance(Point(3, 4))

    > 5.0
    >
    > Is there a better solution?



    --
    Terry Jan Reedy
     
    Terry Reedy, Nov 10, 2012
    #3
  4. Jennie

    Jennie Guest

    On 11/10/2012 09:29 PM, Terry Reedy wrote:

    > On 11/10/2012 2:33 PM, Jennie wrote:
    >>
    >> I propose three solutions. The first one:
    >>
    >> >>> class Point:

    >> ... def __init__(self, x=0, y=0):
    >> ... self.x = x
    >> ... self.y = y
    >> ... def __sub__(self, other):
    >> ... return Point(self.x - other.x, self.y - other.y)
    >> ... def distance(self, point=None):
    >> ... p = point if point else Point()
    >> ... return math.sqrt((self - p).x ** 2 + (self - p).y ** 2)


    > What I do not like about this one is that it creates a new 0 point each
    > time one is needed. Two solutions:
    >
    > change Point() to point0 in the distance function and create
    > point0 = Point()
    > after the class.
    >
    > -or-
    > instead of p = line,
    > px,py = point.x, point.y if point else 0.0, 0.0


    Thanks, I like the second one :)

    --
    Jennie
     
    Jennie, Nov 10, 2012
    #4
  5. Jennie

    Jennie Guest

    On 11/10/2012 09:29 PM, Terry Reedy wrote:

    > On 11/10/2012 2:33 PM, Jennie wrote:
    >>
    >> I propose three solutions. The first one:
    >>
    >> >>> class Point:

    >> ... def __init__(self, x=0, y=0):
    >> ... self.x = x
    >> ... self.y = y
    >> ... def __sub__(self, other):
    >> ... return Point(self.x - other.x, self.y - other.y)
    >> ... def distance(self, point=None):
    >> ... p = point if point else Point()
    >> ... return math.sqrt((self - p).x ** 2 + (self - p).y ** 2)


    > What I do not like about this one is that it creates a new 0 point each
    > time one is needed. Two solutions:
    >
    > change Point() to point0 in the distance function and create
    > point0 = Point()
    > after the class.
    >
    > -or-
    > instead of p = line,
    > px,py = point.x, point.y if point else 0.0, 0.0


    Thanks, I like the second one :)

    --
    Jennie
     
    Jennie, Nov 10, 2012
    #5
  6. Jennie

    Dave Angel Guest

    On 11/10/2012 03:51 PM, Jennie wrote:
    > On 11/10/2012 09:29 PM, Terry Reedy wrote:
    >
    >> On 11/10/2012 2:33 PM, Jennie wrote:
    >>>
    >>> I propose three solutions. The first one:
    >>>
    >>> >>> class Point:
    >>> ... def __init__(self, x=0, y=0):
    >>> ... self.x = x
    >>> ... self.y = y
    >>> ... def __sub__(self, other):
    >>> ... return Point(self.x - other.x, self.y - other.y)
    >>> ... def distance(self, point=None):
    >>> ... p = point if point else Point()
    >>> ... return math.sqrt((self - p).x ** 2 + (self - p).y ** 2)

    >
    >> What I do not like about this one is that it creates a new 0 point each
    >> time one is needed. Two solutions:
    >>
    >> change Point() to point0 in the distance function and create
    >> point0 = Point()
    >> after the class.
    >>
    >> -or-
    >> instead of p = line,
    >> px,py = point.x, point.y if point else 0.0, 0.0

    >
    > Thanks, I like the second one :)
    >

    I like the first, once you fix the minor inefficiency in it; add the
    qualifier "is None"


    .... def distance(self, point=None):
    .... p = point if point is None else Point()
    .... return math.sqrt((self - p).x ** 2 + (self - p).y ** 2)

    The advantage it then has over the second one is that the whole class is
    defined inside the class.

    --

    DaveA
     
    Dave Angel, Nov 10, 2012
    #6
  7. On Sat, 10 Nov 2012 20:33:05 +0100, Jennie wrote:

    [...]
    > I propose three solutions. The first one:
    >
    > >>> class Point:

    > ... def __init__(self, x=0, y=0):
    > ... self.x = x
    > ... self.y = y
    > ... def __sub__(self, other):
    > ... return Point(self.x - other.x, self.y - other.y)


    Don't do this, because it breaks subclassing. Your instance should
    dynamically get it's own class, not hard-code the name of Point.

    return self.__class__(self.x - other.x, self.y - other.y)

    That way, when you subclass Point, you can do arithmetic on the subclass
    instances and they will do the Right Thing.

    Note: Python's builtin numeric types don't do this, and it is a damned
    nuisance:

    py> class MyInt(int):
    .... pass
    ....
    py> a, b = MyInt(23), MyInt(42)
    py> assert type(a) is MyInt and type(b) is MyInt
    py> type(a + b)
    <type 'int'>


    Back to your class:

    > ... def distance(self, point=None):
    > ... p = point if point else Point()
    > ... return math.sqrt((self - p).x ** 2 + (self - p).y ** 2)


    Almost but not quite. I assume that, in a full Point class, you would
    want Point(0, 0) to count as false in a boolean context. (A "falsey"
    value, like None, [], 0.0, etc.) So change the test to an explicit test
    for None, not just any falsey value:

    if point is None:
    point = self.__class__() # Allow subclassing to work.


    > The second one:
    >
    > >>> class Point:

    > ... def __init__(self, x=0, y=0):
    > ... self.x = x
    > ... self.y = y
    > ... def __sub__(self, other):
    > ... return Point(self.x - other.x, self.y - other.y)
    > ...
    > >>> def distance(self, point=Point()):

    > ... return math.sqrt((self - point).x ** 2 + (self - point).y ** 2)
    > ...
    > >>> Point.distance = distance


    Cute, but ugly and messy. You can inject methods into a class, of course,
    but that's an awfully big hammer to crack this tiny little nut. Your
    first solution is better.

    Here is a variation which, according to your tastes, may count as more or
    less ugly: inject the default value into the method:

    class Point:
    def distance(self, other=None): # None is a placeholder
    delta = self - other
    return math.sqrt(delta.x ** 2 + delta.y ** 2)

    Point.distance.__defaults__ = (Point(),)
    # In Python 2, use:
    # Point.distance.__func__.func_defaults = (Point(),)



    --
    Steven
     
    Steven D'Aprano, Nov 11, 2012
    #7
  8. On 10 November 2012 19:33, Jennie <> wrote:
    > What is the best solution to solve the following problem in Python 3.3?
    >
    > import math
    >>>> class Point:

    > ... def __init__(self, x=0, y=0):
    > ... self.x = x
    > ... self.y = y
    > ... def __sub__(self, other):
    > ... return Point(self.x - other.x, self.y - other.y)
    > ... def distance(self, point=Point()):
    > ... """Return the distance from `point`."""
    > ... return math.sqrt((self - point).x ** 2 + (self - point).y ** 2)
    > ...
    > Traceback (most recent call last):
    > File "<stdin>", line 1, in <module>
    > File "<stdin>", line 5, in Point
    > NameError: name 'Point' is not defined


    I would use namedtuple and make it so that an ordinary tuple could be
    used as in place of a Point instance:

    >>> import math
    >>> from collections import namedtuple
    >>> class Point(namedtuple('Point', ['x', 'y'])):

    .... def distance(self, other=(0, 0)):
    .... (myx, myy), (theirx, theiry) = self, other
    .... return math.sqrt((myx - theirx) ** 2 + (myy - theiry) ** 2)
    ....
    >>> p = Point(3, 4)
    >>> p.distance()

    5.0
    >>> p2 = Point(4, 5)
    >>> p.distance(p2)

    1.4142135623730951


    Oscar
     
    Oscar Benjamin, Nov 11, 2012
    #8
  9. On Sun, Nov 11, 2012 at 12:13 PM, Steven D'Aprano
    <> wrote:
    > Almost but not quite. I assume that, in a full Point class, you would
    > want Point(0, 0) to count as false in a boolean context. (A "falsey"
    > value, like None, [], 0.0, etc.)


    I would not assume that. The origin is a point, just like any other.
    With a Line class, you could deem a zero-length line to be like a
    zero-element list, but Point(0,0) is more like the tuple (0,0) which
    is definitely True. In any case, this would not even matter, beyond
    unnecessary work; the bug would occur only if you seek the distance to
    Point(0,0), at which point[1] the code would throw out the incoming
    Point and go with the default of 0,0. So it'd result in the same
    distance.

    ChrisA

    [1] Sorry, couldn't resist
     
    Chris Angelico, Nov 11, 2012
    #9
  10. Jennie

    Ian Kelly Guest

    On Sat, Nov 10, 2012 at 7:13 PM, Chris Angelico <> wrote:
    > I would not assume that. The origin is a point, just like any other.
    > With a Line class, you could deem a zero-length line to be like a
    > zero-element list, but Point(0,0) is more like the tuple (0,0) which
    > is definitely True.


    It's more like the number 0 than the tuple (0,0).

    0 is the origin on a 1-dimensional number line.
    (0,0) is the origin on a 2-dimensional number plane.

    In fact, it might be pointed out that Point(0, 0) is a generalization
    of 0+0j, which is equal to 0.
     
    Ian Kelly, Nov 11, 2012
    #10
  11. Jennie

    Roy Smith Guest

    In article <>,
    Ian Kelly <> wrote:

    > On Sat, Nov 10, 2012 at 7:13 PM, Chris Angelico <> wrote:
    > > I would not assume that. The origin is a point, just like any other.
    > > With a Line class, you could deem a zero-length line to be like a
    > > zero-element list, but Point(0,0) is more like the tuple (0,0) which
    > > is definitely True.

    >
    > It's more like the number 0 than the tuple (0,0).
    >
    > 0 is the origin on a 1-dimensional number line.
    > (0,0) is the origin on a 2-dimensional number plane.


    > In fact, it might be pointed out that Point(0, 0) is a generalization
    > of 0+0j, which is equal to 0.



    If (0,0) is the origin on a plane, then (0,) should be the origin on a
    line. If you consider 0 + 0j to be the origin of a plane, then 0 is the
    origin of a line. Either way is plausible, but you need to be
    consistent.
     
    Roy Smith, Nov 11, 2012
    #11
  12. Jennie

    Ian Kelly Guest

    On Sat, Nov 10, 2012 at 11:43 PM, Ian Kelly <> wrote:
    > Where I wrote "(0,0) is the origin" above I was not referring to a
    > point, not a tuple, but I can see how that was confusing.


    What I meant to say is I *was* referring to a point. Gah!
     
    Ian Kelly, Nov 11, 2012
    #12
  13. On 11 November 2012 02:47, Chris Angelico <> wrote:
    > On Sun, Nov 11, 2012 at 1:43 PM, Ian Kelly <> wrote:
    >> On Sat, Nov 10, 2012 at 7:13 PM, Chris Angelico <> wrote:
    >>> I would not assume that. The origin is a point, just like any other.
    >>> With a Line class, you could deem a zero-length line to be like a
    >>> zero-element list, but Point(0,0) is more like the tuple (0,0) which
    >>> is definitely True.

    >>
    >> It's more like the number 0 than the tuple (0,0).
    >>
    >> 0 is the origin on a 1-dimensional number line.
    >> (0,0) is the origin on a 2-dimensional number plane.
    >>
    >> In fact, it might be pointed out that Point(0, 0) is a generalization
    >> of 0+0j, which is equal to 0.

    >
    > Ah, good point. In any case, though, it'd be an utterly inconsequential bug.


    You were right the first time, Chris. A point that happens to coincide
    with the arbitrarily chosen origin is no more truthy or falsey than
    any other. A vector of length 0 on the other hand is a very different
    beast.

    The significance of zero in real algebra is not that it is the origin
    but rather that it is the additive and multiplicative zero:

    a + 0 = a for any real number a
    a * 0 = 0 for any real number a

    The same is true for a vector v0, of length 0:

    v + v0 = v for any vector v
    a * v0 = v0 for any scalar a

    There is however no meaningful sense in which points (as opposed to
    vectors) can be added to each other or multiplied by anything, so
    there is no zero point.

    The relationship between points and vectors is analogous to the
    relationship between datetimes and timedeltas. Having Vector(0, 0)
    evaluate to False is analogous to having timedelta(0) evaluate to
    False and is entirely sensible. Having Point(0, 0) evaluate to False
    is precisely the same conceptual folly that sees midnight evaluate as
    False.


    Oscar
     
    Oscar Benjamin, Nov 11, 2012
    #13
  14. On Sun, 11 Nov 2012 14:21:19 +0000, Oscar Benjamin wrote:

    > On 11 November 2012 02:47, Chris Angelico <> wrote:
    >> On Sun, Nov 11, 2012 at 1:43 PM, Ian Kelly <>
    >> wrote:
    >>> On Sat, Nov 10, 2012 at 7:13 PM, Chris Angelico <>
    >>> wrote:
    >>>> I would not assume that. The origin is a point, just like any other.
    >>>> With a Line class, you could deem a zero-length line to be like a
    >>>> zero-element list, but Point(0,0) is more like the tuple (0,0) which
    >>>> is definitely True.


    Don't conflate the set of all tuples of arbitrary length with points,
    which have fixed length. Points are not *sequences* -- in Python, we
    treat tuples as sequences first and records second, because that is a
    useful thing to do. (But it is not the only useful thing to do: if we
    treated them as records first and sequences second, we might want to say
    that a tuple t was falsey if all the fields in t were falsey.)

    In the case of a Point class, a Point is definitely not a sequence. That
    we put the x-coordinate first and the y-coordinate second is a mere
    convention, like writing left to right. The mathematical properties of
    points do not depend on the x-coordinate coming first. Since points
    should not be treated as sequences, the requirement that non-empty
    sequences be treated as truthy is irrelevant.


    >>> It's more like the number 0 than the tuple (0,0).
    >>>
    >>> 0 is the origin on a 1-dimensional number line. (0,0) is the origin on
    >>> a 2-dimensional number plane.
    >>>
    >>> In fact, it might be pointed out that Point(0, 0) is a generalization
    >>> of 0+0j, which is equal to 0.

    >>
    >> Ah, good point. In any case, though, it'd be an utterly inconsequential
    >> bug.

    >
    > You were right the first time, Chris. A point that happens to coincide
    > with the arbitrarily chosen origin is no more truthy or falsey than any
    > other. A vector of length 0 on the other hand is a very different beast.


    Nonsense. The length and direction of a vector is relative to the origin.
    If the origin is arbitrary, as you claim, then so is the length of the
    vector.

    Just because we can perform vector transformations on the plane to move
    the origin to some point other that (0,0) doesn't make (0,0) an
    "arbitrarily chosen origin". It is no more arbitrary than 0 as the origin
    of the real number line.

    And yes, we can perform 1D vector transformations on the real number line
    too. Here's a version of range that sets the origin to 42, not 0:

    def myrange(start, end=None, step=1):
    if end is None:
    start = 42
    return range(start, end, step)


    Nevertheless, there really is something special about the point 0 on the
    real number line, the point (0,0) on the complex number plane, the point
    (0,0,0) in the 3D space, (0,0,0,0) in 4D space, etc. It is not just an
    arbitrary convention that we set the origin to 0.

    In other words: to the extent that your arguments that zero-vectors are
    special are correct, the same applies to zero-points, since vectors are
    defined as a magnitude and direction *from the origin*.

    To put it yet another way:

    The complex number a+bj is equivalent to the 2D point (a, b) which is
    equivalent to the 2D vector [a, b]. If (0, 0) shouldn't be considered
    falsey, neither should [0, 0].


    > The significance of zero in real algebra is not that it is the origin
    > but rather that it is the additive and multiplicative zero:
    >
    > a + 0 = a for any real number a
    > a * 0 = 0 for any real number a


    I'm not sure what you mean by "additive and multiplicative zero", you
    appear to be conflating two different properties here. 0 is the additive
    *identity*, but 1 is the multiplicative identity:

    a + 0 = a
    a * 1 = a
    for any real number a.

    If the RHS must be zero, then there is a unique multiplicative zero, but
    no unique additive zero:

    a * 0 = 0 for any real number a
    a + -a = 0 for any real number a


    > The same is true for a vector v0, of length 0:
    >
    > v + v0 = v for any vector v
    > a * v0 = v0 for any scalar a


    Well that's a bogus analogy. Since you're talking about the domain of
    vectors, the relevant identify for the second line should be:

    v * v0 = v0 for any vector v

    except that doesn't work, since vector algebra doesn't define a vector
    multiplication operator.[1] It does define multiplication between a
    vector and a scalar, which represents a scale transformation.


    > There is however no meaningful sense in which points (as opposed to
    > vectors) can be added to each other or multiplied by anything, so there
    > is no zero point.


    I think that the great mathematician Carl Gauss would have something to
    say about that.

    Points in the plane are equivalent to complex numbers, and you can
    certainly add and multiply complex numbers. Adding two points is
    equivalent to a translation; multiplication of a scalar with a point is
    equivalent to a scale transformation. Multiplying two points is
    equivalent to complex multiplication, which is a scale + a rotation.

    Oh look, that's exactly the same geometric interpretation as for vectors.
    Hardly surprising, since vectors are the magnitude and direction of a
    line from the origin to a point.


    > The relationship between points and vectors is analogous to the
    > relationship between datetimes and timedeltas. Having Vector(0, 0)
    > evaluate to False is analogous to having timedelta(0) evaluate to False
    > and is entirely sensible. Having Point(0, 0) evaluate to False is
    > precisely the same conceptual folly that sees midnight evaluate as
    > False.


    If you are dealing with datetimes, then "midnight 2012-11-12" is not
    falsey. The only falsey datetime is the zero datetime. Since it would be
    awfully inconvenient to start counting times from the Big Bang, we pick
    an arbitrary zero point, the Epoch, which in Unix systems is midnight 1
    January 1970, and according to the logic of Unix system administrators,
    that is so far in the distant past that it might as well be the Big Bang.

    (People with more demanding requirements don't use Unix or Windows
    timestamps for recording date times. E.g. astronomers use the Julian
    system, not to be confused with the Julian calendar.)

    The midnight problem only occurs when you deal with *times* on their own,
    not datetimes, in which case the relationship with timedeltas is not
    defined. How far apart is 1:00am and 2:00am? Well, it depends, doesn't
    it? It could be 1 hour, 25 hours, 49 hours, ...

    In any case, since times are modulo 24 hours, they aren't really relevant
    to what we are discussing.



    [1] There is no single meaningful definition of vector multiplication
    that works for all dimensions. In two dimensions, you can define the dot
    product of two vectors to give a scalar; in three dimensions you have a
    dot product and a vector product.

    Since vectors are equivalent to points, and points are equivalent to
    complex numbers, one could define a vector operation equivalent to
    complex multiplication. There is a natural geometric interpretation of
    this multiplication: it is a scaling + rotation.


    --
    Steven
     
    Steven D'Aprano, Nov 11, 2012
    #14
  15. On 11 November 2012 22:31, Steven D'Aprano
    <> wrote:
    > On Sun, 11 Nov 2012 14:21:19 +0000, Oscar Benjamin wrote:
    >
    >> On 11 November 2012 02:47, Chris Angelico <> wrote:
    >>> On Sun, Nov 11, 2012 at 1:43 PM, Ian Kelly <>
    >>> wrote:
    >>>> On Sat, Nov 10, 2012 at 7:13 PM, Chris Angelico <>
    >>>> wrote:
    >>>>> I would not assume that. The origin is a point, just like any other.
    >>>>> With a Line class, you could deem a zero-length line to be like a
    >>>>> zero-element list, but Point(0,0) is more like the tuple (0,0) which
    >>>>> is definitely True.
    >>>> It's more like the number 0 than the tuple (0,0).
    >>>>
    >>>> 0 is the origin on a 1-dimensional number line. (0,0) is the origin on
    >>>> a 2-dimensional number plane.
    >>>>
    >>>> In fact, it might be pointed out that Point(0, 0) is a generalization
    >>>> of 0+0j, which is equal to 0.
    >>>
    >>> Ah, good point. In any case, though, it'd be an utterly inconsequential
    >>> bug.

    >>
    >> You were right the first time, Chris. A point that happens to coincide
    >> with the arbitrarily chosen origin is no more truthy or falsey than any
    >> other. A vector of length 0 on the other hand is a very different beast.

    >
    > Nonsense. The length and direction of a vector is relative to the origin.
    > If the origin is arbitrary, as you claim, then so is the length of the
    > vector.


    Wrong on all counts. Neither the length not the direction os a vector
    are relative to any origin. When we choose to express a vector in
    Cartesian components our representation assumes an orientation for the
    axes of the coordinate system. Even in this sense, though, the origin
    itself does not affect the components of the vector.

    I have spent a fair few hours in the past few weeks persuading
    teenaged Engineering students to maintain a clear distinction between
    points, vectors and lines. One of the ways that I distinguish vectors
    from points is to say that a vector is like an arrow but its base has
    no particular position. A point on the other hand is quite simply a
    position. Given an origin (an arbitrarily chosen point) we can specify
    another point using a "position vector": a vector from the origin to
    the point in question.

    > Just because we can perform vector transformations on the plane to move
    > the origin to some point other that (0,0) doesn't make (0,0) an
    > "arbitrarily chosen origin". It is no more arbitrary than 0 as the origin
    > of the real number line.


    (0, 0) are the coordinates of the origin *relative to itself*. Had we
    chosen a different origin, the point that was previously called (0, 0)
    would now be called (a, b) for some other numbers a and b.

    > And yes, we can perform 1D vector transformations on the real number line
    > too. Here's a version of range that sets the origin to 42, not 0:
    >
    > def myrange(start, end=None, step=1):
    > if end is None:
    > start = 42
    > return range(start, end, step)


    This is lost on me...

    > Nevertheless, there really is something special about the point 0 on the
    > real number line


    Agreed.

    > , the point (0,0) on the complex number plane,


    Also agreed.

    > the point
    > (0,0,0) in the 3D space, (0,0,0,0) in 4D space, etc. It is not just an
    > arbitrary convention that we set the origin to 0.


    Wrong. The point (0,0,0,...) in some ND space is an arbitrarily chosen
    position. By this I don't mean to say that the sequence of coordinates
    consisting of all zeros is arbitrary. The choice of the point *in the
    real/hypothetical space* that is designated by the sequence of zero
    coordinates is arbitrary.

    > In other words: to the extent that your arguments that zero-vectors are
    > special are correct, the same applies to zero-points, since vectors are
    > defined as a magnitude and direction *from the origin*.


    Plain wrong. Vectors are not defined *from any origin*.

    > To put it yet another way:
    >
    > The complex number a+bj is equivalent to the 2D point (a, b) which is
    > equivalent to the 2D vector [a, b]. If (0, 0) shouldn't be considered
    > falsey, neither should [0, 0].


    a+bj is not equivalent to the 2D point (a, b). It is possible to
    define a mapping between complex numbers and a 2D space so that a+bj
    corresponds to the point (a, b) *under that map*. However there are an
    infinite number of such possible mappings between the two spaces
    including a+bj -> (a+1, b+1).

    >> The significance of zero in real algebra is not that it is the origin
    >> but rather that it is the additive and multiplicative zero:
    >>
    >> a + 0 = a for any real number a
    >> a * 0 = 0 for any real number a

    >
    > I'm not sure what you mean by "additive and multiplicative zero", you
    > appear to be conflating two different properties here. 0 is the additive
    > *identity*, but 1 is the multiplicative identity:


    I mean that it has the properties that zero has when used in addition
    and multiplication:
    http://en.wikipedia.org/wiki/0_(number)#Elementary_algebra

    >
    > a + 0 = a
    > a * 1 = a
    > for any real number a.


    No. I meant the two properties that I listed.

    >
    > If the RHS must be zero, then there is a unique multiplicative zero, but
    > no unique additive zero:
    >
    > a * 0 = 0 for any real number a
    > a + -a = 0 for any real number a


    That is not the same as:

    a + 0 = a

    >> The same is true for a vector v0, of length 0:
    >>
    >> v + v0 = v for any vector v
    >> a * v0 = v0 for any scalar a

    >
    > Well that's a bogus analogy. Since you're talking about the domain of
    > vectors, the relevant identify for the second line should be:
    >
    > v * v0 = v0 for any vector v
    >
    > except that doesn't work, since vector algebra doesn't define a vector
    > multiplication operator.[1] It does define multiplication between a
    > vector and a scalar, which represents a scale transformation.


    That is precisely the multiplication operation that I was referring
    to. There are other senses of vector multiplication between vectors
    for which v0 will also behave as a "zero" under multiplication:

    v . v0 = 0 for any vector v
    v x v0 = 0 for any vector v

    >> There is however no meaningful sense in which points (as opposed to
    >> vectors) can be added to each other or multiplied by anything, so there
    >> is no zero point.

    >
    > I think that the great mathematician Carl Gauss would have something to
    > say about that.


    Is the text below a quote?

    > Points in the plane are equivalent to complex numbers, and you can
    > certainly add and multiply complex numbers. Adding two points is
    > equivalent to a translation; multiplication of a scalar with a point is
    > equivalent to a scale transformation. Multiplying two points is
    > equivalent to complex multiplication, which is a scale + a rotation.


    The last point is bizarre. Complex multiplication makes no sense when
    you're trying to think about vectors. Draw a 2D plot and convince
    yourself that the square of the point (0, 1) is (-1, 0).

    > Oh look, that's exactly the same geometric interpretation as for vectors.
    > Hardly surprising, since vectors are the magnitude and direction of a
    > line from the origin to a point.


    Here it becomes clear that you have conflated "position vectors" with
    vectors in general. Let me list some other examples of vectors that
    are clearly not "from the origin to a point":

    velocity
    acceleration
    force
    electric field
    angular momentum
    wave vector

    (I could go on)

    >> The relationship between points and vectors is analogous to the
    >> relationship between datetimes and timedeltas. Having Vector(0, 0)
    >> evaluate to False is analogous to having timedelta(0) evaluate to False
    >> and is entirely sensible. Having Point(0, 0) evaluate to False is
    >> precisely the same conceptual folly that sees midnight evaluate as
    >> False.

    >
    > If you are dealing with datetimes, then "midnight 2012-11-12" is not
    > falsey. The only falsey datetime is the zero datetime. Since it would be
    > awfully inconvenient to start counting times from the Big Bang, we pick
    > an arbitrary zero point, the Epoch, which in Unix systems is midnight 1
    > January 1970, and according to the logic of Unix system administrators,
    > that is so far in the distant past that it might as well be the Big Bang.
    >
    > (People with more demanding requirements don't use Unix or Windows
    > timestamps for recording date times. E.g. astronomers use the Julian
    > system, not to be confused with the Julian calendar.)
    >
    > The midnight problem only occurs when you deal with *times* on their own,
    > not datetimes, in which case the relationship with timedeltas is not
    > defined. How far apart is 1:00am and 2:00am? Well, it depends, doesn't
    > it? It could be 1 hour, 25 hours, 49 hours, ...
    >
    > In any case, since times are modulo 24 hours, they aren't really relevant
    > to what we are discussing.


    They are relevant. The point is that conflating points and vectors is
    the same as conflating datetime and timedelta objects. The zero of
    datetime.timedelta objects is not arbitrary but the zero of
    datetime.time objects is.

    > Since vectors are equivalent to points, and points are equivalent to
    > complex numbers, one could define a vector operation equivalent to
    > complex multiplication. There is a natural geometric interpretation of
    > this multiplication: it is a scaling + rotation.


    Vectors, points and complex numbers are not equivalent. There are
    cases in which it is reasonable to think of them as equivalent for a
    particular purpose. That does not diminish the fundamental differences
    between them.


    Oscar
     
    Oscar Benjamin, Nov 12, 2012
    #15
  16. Jennie

    Steve Howell Guest

    On Nov 10, 11:33 am, Jennie <> wrote:
    > What is the best solution to solve the following problem in Python 3.3?
    >
    > import math
    >  >>> class Point:
    > ...     def __init__(self, x=0, y=0):
    > ...         self.x = x
    > ...         self.y = y
    > ...     def __sub__(self, other):
    > ...         return Point(self.x - other.x, self.y - other.y)
    > ...     def distance(self, point=Point()):
    > ...         """Return the distance from `point`."""
    > ...         return math.sqrt((self - point).x ** 2 + (self - point).y ** 2)


    Before you do anything else, introduce a Vector class into your app.
    The difference between two Points is not a Point; it's a Vector.
    Create a magnitude() method in your Vector class, then make your
    Point.distance return the results of Vector.magnitude(self - other).
    To define the distance of a point from the origin, don't make your
    distance() method have default arguments; instead, define another
    method called distance_from_origin().
     
    Steve Howell, Nov 12, 2012
    #16
  17. Jennie

    Steve Howell Guest

    On Nov 11, 4:31 pm, Oscar Benjamin <> wrote:
    > On 11 November 2012 22:31, Steven D'Aprano


    > > Nonsense. The length and direction of a vector is relative to the origin.
    > > If the origin is arbitrary, as you claim, then so is the length of the
    > > vector.

    >
    > Wrong on all counts. Neither the length not the direction os a vector
    > are relative to any origin. When we choose to express a vector in
    > Cartesian components our representation assumes an orientation for the
    > axes of the coordinate system. Even in this sense, though, the origin
    > itself does not affect the components of the vector.
    >


    Thank you for pushing back on Steven's imprecise statement that the
    "direction of a vector is relative to the origin."

    You can't find an angle between two points. That's absurd. You need
    axes for context.


    > Vectors, points and complex numbers are not equivalent. There are
    > cases in which it is reasonable to think of them as equivalent for a
    > particular purpose. That does not diminish the fundamental differences
    > between them.
    >


    I looked to wikipedia for clarity, but the definition of a Euclidean
    vector is somewhat muddy:

    http://en.wikipedia.org/wiki/Euclidean_vector

    They say that the formal definition of a vector is a directed line
    segment. But then they define a "free vector" as an entity where only
    the magnitude and direction matter, not the initial point.

    As you say, it's not unreasonable to treat vectors, points, and
    complex numbers as equivalent in many circumstances. But, if you're
    gonna be pedantic, they really are different things.
     
    Steve Howell, Nov 12, 2012
    #17
  18. On 12/11/2012 00:31, Oscar Benjamin wrote:
    >
    > Plain wrong. Vectors are not defined *from any origin*.
    >


    So when the Captain says "full speed ahead, steer 245 degrees", you
    haven't the faintest idea where you're going, because you have no origin?

    --
    Cheers.

    Mark Lawrence.
     
    Mark Lawrence, Nov 12, 2012
    #18
  19. Jennie

    Roy Smith Guest

    In article <>,
    Mark Lawrence <> wrote:

    > On 12/11/2012 00:31, Oscar Benjamin wrote:
    > >
    > > Plain wrong. Vectors are not defined *from any origin*.
    > >

    >
    > So when the Captain says "full speed ahead, steer 245 degrees", you
    > haven't the faintest idea where you're going, because you have no origin?


    Vectors have a length ("full speed ahead") and a direction ("245
    degrees"). What they don't have is a fixed location in space. The
    captain didn't say, "Full speed ahead, steer 245 degrees, from 45.0N,
    20.0W".

    In other words, you are correct. The order, "full speed ahead, steer
    245 degrees", doesn't give you the faintest idea of where you're going.
    If you were the helmsman, after you executed that order, without any
    additional information (such as your current location), you would have
    no idea what piece of land you will hit, or when you will hit it, if you
    maintain your current course and speed.
     
    Roy Smith, Nov 12, 2012
    #19
  20. On 12 November 2012 01:10, Mark Lawrence <> wrote:
    > On 12/11/2012 00:31, Oscar Benjamin wrote:
    >>
    >>
    >> Plain wrong. Vectors are not defined *from any origin*.
    >>

    >
    > So when the Captain says "full speed ahead, steer 245 degrees", you haven't
    > the faintest idea where you're going, because you have no origin?


    As Steve has just explained, the origin has nothing to do with the
    orientation of the coordinate system.

    But then I'm assuming you meant that 245 degrees was a bearing
    relative to North. Was it supposed to be relative to my current angle?
    Truthfully I wouldn't know what to do without asking the captain a
    couple more questions.


    Oscar
     
    Oscar Benjamin, Nov 12, 2012
    #20
    1. Advertising

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

It takes just 2 minutes to sign up (and it's free!). Just click the sign up button to choose a username and then you can ask your own questions on the forum.
Similar Threads
  1. Charles
    Replies:
    6
    Views:
    13,964
  2. mike
    Replies:
    5
    Views:
    339
    Ben Pope
    Feb 22, 2006
  3. Hicham Mouline
    Replies:
    1
    Views:
    356
    Vladyslav Lazarenko
    Mar 27, 2009
  4. programmingzeal
    Replies:
    0
    Views:
    1,131
    programmingzeal
    May 6, 2012
  5. Ryan Dupuis
    Replies:
    8
    Views:
    1,265
    Eric Sosman
    Oct 2, 2013
Loading...

Share This Page