On Sun, May 13, 2018 at 2:54 PM Matt Arcidy <marcidy@gmail.com> wrote:


On Sun, May 13, 2018, 11:28 Brendan Barnwell <brenbarn@brenbarn.net> wrote:
On 2018-05-13 04:23, Steven D'Aprano wrote:
> In my experience mathematicians put the given *before* the statement:
>
>     Given a, b, c three sides of a triangle, then
>
>         Area = sqrt(s*(s-a)*(s-b)*(s-c))
>
>     where s = (a + b + c)/2 is the semi-perimeter of the triangle.
>
> For the record, that is almost exactly what I wrote for a student
> earlier today, and its not just me, it is very similar to the wording
> used on both Wolfram Mathworld and Wikipedia's pages on Heron's Formula.
>
> http://mathworld.wolfram.com/HeronsFormula.html
>
> https://en.wikipedia.org/wiki/Heron%27s_formula
>
>
> Putting "given" after the expression is backwards.

I usually read the vertical bar "given" in

set-builder notation:  {x | 10 < x < 100, x is prime}

Conditional probabilities, expectations, entropy, etc.: P(X | Y), E(X| Y), H(X | Y), 

And, the so-called "evaluation bar": https://math.stackexchange.com/questions/52651/what-is-the-name-of-the-vertical-bar-in-x21-vert-x-4-or-left-left

In words, I agree that where is probably better in text because writing "given the gravitational constant G" puts the subject last, unlike "where G is the gravitational constant".  However, the given proposal for Python is putting the subject first: "given x = y".


        Yes, but that's because we're ruling out the use of "where".  At this
point I would be fine with "snicklefritz" as the keyword.  The point is
that I want to put SOMETHING after the expression, and this is not at
all unusual.  See for instance Wikipedia pages on the Reimann zeta
function
(https://en.wikipedia.org/wiki/Riemann_zeta_function#Definition),
gravitation equation
(https://en.wikipedia.org/wiki/Gravity#Newton%27s_theory_of_gravitation), and
compound interest
(https://en.wikipedia.org/wiki/Compound_interest#Mathematics_of_interest_rate_on_loans).
  If we have to use the word "given" even though the word mathematicians
would use in that position is "where", that's not such a big deal.

it is a big deal.  postfix requires more cognitive load, we will have no idea up front what's going on except for trivial exames.  more givens, more cognitive load.

if you think spending that is fine for you, I can't argue, but to say it doesn't matter isn't correct.

2.exames which get far worse for complex cases.  left for the for can be as complex.as.you wish.
1:
[ x + y for t in range(10)  ... ]

2:
x = 10
y = 20
[ x + y for t in range(10) ...]

up till you read ... you have no idea there even will be a substitution.  The lower is even worse, you think you know, but then have to redo the whole problem with new information.

also :
mathematicians don't just put the _word_ "given", they put givens, things that are known or assumed to be true.  Axioms and definitions, where definitions assign names to values.  This is for formal arguements.  reassigning values is handled in post fix occasionally once it is clear what x and y are.  but that's not what we are talking about if the name doesn't exist already.

Most (if not all) uses of the vertical are read as "given" and they all put the givens to the right of it.

again, you want to use given, that's fine, but the math argument is wrong, as is the "it doesn't matter" argument, assuming the current neurological model for working memory continues to hold.

 Maybe the difference is small, especially after familiarity sets in, but that doesn't mean the difference in load isn't there.  it will only increase for more complex statements with more givens.

--
Brendan Barnwell
"Do not follow where the path may lead.  Go, instead, where there is no
path, and leave a trail."
    --author unknown
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