Re: Epistemology 201: The Science of Science

stephen_at_nomail.com
Date: 03/14/05 

Date: 14 Mar 2005 17:25:47 GMT

In sci.math Tony Orlow (aeo6) <aeo6@cornell.edu> wrote:
: stephen@nomail.com said:
:> In sci.math Allan C Cybulskie <allan.c.cybulskie@yahoo.ca> wrote:
:>
:> : <stephen@nomail.com> wrote in message
:> :> Consider a 2 cup measure. The possible values you could
:> :> measure with it are in the range [0,2]. Consider a 1 pint
:> :> measure. The possible values you could measure with it
:> :> are in the range [0,1]. Of course, 2 cups equals 1 pint in the
:> :> English system, and it is clear that any amount that fits
:> :> in the 2 cup measure also fits in the 1 pint measure. There
:> :> are not twice as many measurements possible with the 2 cup
:> :> measure. Similarly, using meters instead of feet does
:> :> not result in fewer possible results. The fact that
:> :> the number of possible measurements is independent of the
:> :> units used is quite intuitive.
:>
:> : The example is also totally wrong. I can get far more accuracy of
:> : measurement from the 2 cup example than the pint example. Why? Because
:> : there are more numbers that I can retrieve from the 2 cup measure than the 1
:> : cup measure, allowing me to subdivide the measure further than I can with
:> : the pint measure.
:>
:> You are assuming your conclusion. Do you really believe there are more
:> possible quantities that fit into a 2 cup measure than a 1 pint measure?
:> They are exactly the same size. Any quantity you can fit in one
:> will fit in the other. Any lines you mark on a 2 cup measure you
:> can also mark on a 1 cup measure, because they are exactly the same
:> size. Apparently you think there is some quantity of y cups such that
:> y/2 pints is an impossibility. I think most people intuitively recognize
:> that the units used in measuring do not affect the number of possible
:> measurements. Anything I can measure in feet I can measure in meters and vice
:> versa. Anything I can measure in Celsius I can measure in farenheit. It
:> does not matter that the ranges of the measurements differ, because each
:> measurement can be translated into any appropriate units. It is clearly
:> true in the world of finite precision and only a finite number of possible
:> measurements that anything measurable with a 2 cup measure is measurable
:> with a 1 pint measure.
:>
:> Stephen
:>
: Stephen -

: If I can draw a 1-1 correspondence between cups in a pint, and pints in a
: quart, does that prove a pint=a quart? Or, do I somehow lose some information
: by ignoring units of measure?

Why do you even ask the question? Noone ever said that a mapping
implies anything other than a mapping. You keep conflating it
with "equivalence". People have repeatedly corrected you on this,
but you keep making the same mistake.

The whole point of my example was there are cases where cardinality agrees
with our intuitions. Anything we can measure with a 2 cup measure we can
measure with 1 pint measure. In the first case we will get an answer in [0,2].
In the second case we will get an answer in [0,1], but there are not "more"
possible answers when we use cups instead of pints. Is that
really so hard for you to understand?

And this was just meant as an example of an instance where
cardinality agrees with our naive intuitions. I will be
the first to admit there are plenty of places where it is
not intuitive. For example, consider a 1 cup measure and a
2 cup measure. With the first I will get an answer in [0,1]
and with the second I will get an answer in [0,2], and clearly
there are lots of quantities I can measure with a 2 cup
measure that I cannot measure with a 1 cup measure (at least
not all at once). When dealing with infinite sets, no
single definition of "size" is going to capture both
intuitions simultaneously.

You keep repeating the same mistake of thinking that
"same cardinality" somehow implies the sets are equivalent
or that their elements are somehow equivalent. It does not,
and noone has ever said that it does. In another post you
made the utterly ridiculous claim that cardinality implies
that volumes can fit inside of lines. Claiming that there
are the same number of lines as volumes in no way implies
that volumes fit inside of lines. That is like claiming
that if I have 5 elephants and 5 envelopes I must be able
fit each elephant in an envelope. You keep making these
ridiculous leaps in logic.
 
Stephen
: Tony

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... :>:> are not twice as many measurements possible with the 2 cup ... :>: measurement from the 2 cup example than the pint example. ... Any quantity you can fit in one ... cardinality agrees with our naive intuitions. ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... :>:> are not twice as many measurements possible with the 2 cup ... :>: measurement from the 2 cup example than the pint example. ... Any quantity you can fit in one ... cardinality agrees with our naive intuitions. ...
    (sci.physics)
  • Re: Epistemology 201: The Science of Science
    ... :> in the 2 cup measure also fits in the 1 pint measure. ... :> are not twice as many measurements possible with the 2 cup ... Any quantity you can fit in one ... true in the world of finite precision and only a finite number of possible ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... :> in the 2 cup measure also fits in the 1 pint measure. ... :> are not twice as many measurements possible with the 2 cup ... Any quantity you can fit in one ... true in the world of finite precision and only a finite number of possible ...
    (sci.physics)
  • Re: Epistemology 201: The Science of Science
    ... :> in the 2 cup measure also fits in the 1 pint measure. ... :> are not twice as many measurements possible with the 2 cup ... Any quantity you can fit in one ... true in the world of finite precision and only a finite number of possible ...
    (sci.math)
Quantcast