What is the result of effecting permutation $(124)$ on $\{1, 2, 3, 4, 5, 6\}$? This article claims:

we simply replace the number 1 by 2, the number 2 by 4, and the number 4 by 1
....I start with the numbers arranged as follows: 1 2 3 4 5 6. After doing the permutation (124) the numbers are arranged as 2 4 3 1 5 6.

I always thought $(124)$ was read left to right as "1 goes to 2, 2 goes to 4, and 4 goes to 1" and therefore the outcome should be 4, 1, 3, 2, 5, 6.
According to my understanding, the article did the permutation reading from right to left. Is the blog following a convention of reading right to left, or do I just have it wrong?
 A: The text says "Let me illustrate this with $n=6$ and those two permutations. I start with the numbers arranged as follows: 1 2 3 4 5 6. After doing the permutation $(124)$ the numbers are arranged as 2 4 3 1 5 6." So indeed $1$ goes to $2$, and $2$ goes to $4$, and $4$ goes to $1$, if you read this top-down:
$$
\begin{matrix} 1 & 2 & 3 & 4 & 5 & 6\cr 2 & 4 & 3 & 1 & 5 & 6\end{matrix}
$$
A: You seem to be reading it as saying "1 goes to position 2", but the convention is that it should be read as "1 gets replaced by 2", or "object 1 becomes object 2". It helps to view these permutations in an alternate form (where for each number, we write the image underneath).
$$\begin{pmatrix} 
1 & 2 & 3 & 4 & 5 & 6\\
2 & 4 & 3 & 1 & 5 & 6
\end{pmatrix}$$
If we think of having the numbers in front of us as physical objects, laid out in order, after applying the permutation to these objects $2 \ 4 \ 3 \ 1 \ 5 \ 6$ is what we will see in front of us.
A: The third paragraph states that: 

$\ldots$ If we want to apply the permutation $(124)$, we simply replace the number $1$ by $2$, the number $2$ by $4$, and the number $4$ by $1$ $\ldots$.

Following the rule (reading from left to right), gives us the required result.
A: Perhaps a better example would be:
If you apply the permutation $(1\,2\,4)$ to (each element of) the sequence "6, 5, 3, 1, 2, 4" you get "6, 5, 3, 2, 4, 1".
The 6, 5, and 3 are unchanged by the permutation, 1 becomes 2, 2 becomes 4, and 4 becomes 1.
