Adjustable-length metal crutches click with each ground contact and lifting, which some people find annoying. The reason for the clicks is that the push button used to adjust the length of the crutch is not snug in its hole, but pushes against the top of its hole when the crutch is pressed against the ground and against the bottom of the hole when the crutch is lifted.
The push button length adjustment system consists of two pipes inside each other, with holes in the outer pipe and a spring-loaded button on the inner one. Pushing the button in allows the pipes to slide relative to each other. When the button is released and pops out into a hole, it locks the pipes together. Similar push button systems are used to adjust the handle length of rolling luggage and the weight stacks of gym equipment.
To silence the clicks, the button should push against the same side of the hole at all times, which can be achieved by adding one spring. The spring should pull the inner pipe of the adjustable part of the crutch in the direction of shortening the crutch, i.e. the same direction as ground contact. Then the button always stays in contact with the same side of its hole instead of alternately hitting the two opposing sides. The reason the spring should pull in the same direction as ground contact is that the upward force on the adjustable inner pipe when the crutch bears the weight of the user is much greater than the downward force of the weight of the inner pipe when the crutch is lifted. Thus it is easier to overcome the downward force using a spring.
A homemade version of the spring is to tie a rubber band under tension to above and below the adjustment button. A bungee cord or bicycle inner tube would work as well.
The length adjustment of the crutch with a spring would be similar to that of an office chair – automatic in one direction, but requiring force in the other. When the button is pushed, the crutch shortens automatically by one hole. To lengthen the crutch, one has to push the button in and then pull the crutch in two opposing directions.
Empirically, articles with more authors are cited more, according to Wuchty et al. (2007). The reasons may be good or bad. A good reason is that coauthored papers may have higher quality, e.g. due to division of labour increasing the efficiency of knowledge production. I propose the following bad reasons, independent of potential quality differences between coauthored and solo articles. Suppose that researchers cite the works of their friends more frequently than warranted. A given scientist is more likely to have a friend among the authors of an article with a greater number of collaborators, which increases its probability of getting a „friendly citation”.
Another reason is defensive citing, i.e. including relatively unrelated papers in the reference list before submitting to a journal, in case the referees happen to be the authors of those works. The reason for adding these unnecessary citations is the belief, warranted or not, that a referee is more likely to recommend acceptance of a paper if it cites the referee’s publications. The probability that the set of referees overlaps with the set of authors of a given prior work increases in the number of authors of that work. Thus defensive citing is more effective when targeted to collaborative instead of solo papers.
The referees may also directly ask the author to cite certain papers in the revision (I have had this experience). If the referees are more likely to request citations to their own or their coauthors’ work, then articles with more authors are again referenced more.
Valderas et al. (2007) offer some additional explanations. One is measurement error. Suppose that letters to the editor, annual reports of the learned society, its presidential inaugural addresses, and other non-research in scientific journals are counted as publications. These have both fewer authors and citations than regular research articles, which creates a positive correlation between the popularity of a piece of writing and its number of authors.
If self-citations are not excluded and researchers cite their own work more frequently than that of others, then papers with more authors get cited more.
Articles with more collaborators are presented more frequently, thus their existence is more widely known. Awareness of a work is a prerequisite of citing it, so the wider circulation of multi-author publications gives them a greater likelihood of being referenced, independent of quality.