Order in writing composed morphisms When we have a function $f: A \rightarrow B$ between two sets, and we want to explicit that we are applying it to some element $x \in A$, we write $f(x)$. After this, is natural to write $f(g(x))$ when we are compounding functions, and when we use the $\circ$ symbol, $f \circ g$. 
The reason why write $f(x)$ instead $(x)f$ is unknown to me; but, of course, after learned the entire life to write in the first way, I use this way.
But, when you start to compound arrows in a sistematically way (i.e. studying category theory) you start to think that this was a bad choice.

Bother me this compose be $g\circ f$ instead of the (much more comfortable to the brain) $f \circ g$. Of course, you can kill the circle too, and write the even more confortable $fg$. We are talking about arrows, and arrows have direction! 
But is not a good choice to use at the same time the "natural" and nonstandard compose and the notation $f(x)$; The first time I realized it was when I was writing a report, and I was going to talk about group action, and representations of the group of automorphisms (was a disaster). After, I partially understood why it was a bad idea:
On the category of sets, Set, we call a point an final object $P$. Of course, these are the sets with only one element, and are all isomorphic. An element on a set $S$ is an morphism $x:P \rightarrow S$; if we have a morphism $f:S \rightarrow T$, so the image of $x$ by $f$ is an element of $T$, and, of course, this guy is the compose of both $x$ and $f$.

and, if we want to use the confortable nonstandard notation of composed, we have to write $xf$ instead $fx$. I have no doubt that this way to write composed morphism is much better, allowing the brain to think on more interesting and important stuff instead "how to write this and what are the domain and codomain". But I admit that I fell like a goddamn fundamentalist having to write $xf$, since $f(x)$ by itself don't bother at all.
So the questions are:
There exists more people awkward with the standard way of write composed functions/arrows/morphisms?
There are more arguments in favor to some notation or another?
Thanks in advance
 A: Yes, the usual order of composition is awkward. Unfortunately, it is hard to imagine how to change this mistake. Here are some links which are related to your question:


*

*Category theory text that defines composition backwards?

*http://ncatlab.org/nlab/show/composition#Notation

*https://en.wikipedia.org/wiki/Reverse_Polish_notation
For example, you will find that "reverse Polish has been found to lead to faster calculations", and that "Many people who agree that diagrammatic order is 'better' on its own merits nevertheless believe that trying to change the established 'classical' order of composition creates more confusion than it removes".
By the way, I have recently written an introduction to (weak) $2$-categories with the usual composition notation, and it was really just a big mess. For instance, try to write down the interchange law without confusing yourself or the reader! I was really wondering why in their texts almost all category theorists just cope with this mess instead of changing it. Then I chose the diagrammatic order of composition and have written $f * g$ (not $f;g$ which is kind of ugly) for the composition (first $f$, then $g$). I also wrote $(x)f$ instead of $f(x)$, because then we have $(x)(f * g)=((x)f)g$. The result was unusual, but also enlightening, because now every formula and every part of a formula could be read and simultaneously evaluated from left to right, which is what we do anyway in most countries around the world.
Notice how natural $(x)f$ really is: First, I have my $x$, and then I plug this $x$ into $f$. This is how calculations work. The notation $f(x)$ is not so good because we have to put $f$ on a stack while evaluating this expression (either by our mind, or by a parser).
Actually RPN (Reverse Polish Notation) is completely free of brackets, but I would suggest to add brackets for readability and also still use infix notation for binary opaerations. I would prefer $2+3$ to $2 \,3 + $.
