
A Note on Two Problems in Connexion with Graphs (1959) [pdf] - guiambros
http://www-m3.ma.tum.de/foswiki/pub/MN0506/WebHome/dijkstra.pdf
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punnerud
Is there a visualization showing this?

~~~
Someone
Heresy :-)

[https://www.cs.utexas.edu/users/EWD/transcriptions/EWD06xx/E...](https://www.cs.utexas.edu/users/EWD/transcriptions/EWD06xx/EWD696.html):

 _" The habit of using pictorial aids, like any habit, is very difficult to
get rid of. If, however, we take any responsibility for the effectiveness of
our thinking habits, we should try to get rid of the habit as quickly as
possible, for it is a bad habit, confusing and misleading up to the point of
being paralysing"_

~~~
daralthus
"One of the bad things about pictures is that they are almost always
overspecific. One cannot make a picture of "an arbitrary triangle": as soon as
one has made it, it has either an obtuse angle or not, whereas for "the
arbitrary triangle" the property of having an obtuse angle is explicitly
undefined."

Still one can make a picture of all the arbitrary triangles at the same time
and in an interactive visualization explore them to get the complex behaviour
and constrains the notion "arbitrary triangle" actually represent. For a good
example have a look at:
[http://worrydream.com/LadderOfAbstraction/](http://worrydream.com/LadderOfAbstraction/)

~~~
Someone
But how do you know that, while playing with such an interactive
visualization, you looked at all possible cases?

Also, let's say a theorem says two lines are parallel, two distances are
equal, or three lines intersect in a single point, how are you going to judge
that that's the case from such a display, even for one particular choice of
points?

