Everybody seems to be talking about the Kardashian index (call it K) these days. It is a rather useless number that you compute as a ratio between the number of twitter followers you have and the number of citations that your papers got.

Here is a quote from its inventor Neil Hall:

“I am concerned that phenomena similar to that of Kim Kardashian may also exist in the scientific community,” wrote Hall. “I think it is possible that there are individuals who are famous for being famous (or, to put it in science jargon, renowned for being renowned). We are all aware that certain people are seemingly invited as keynote speakers, not because of their contributions to the published literature but because of who they are.”
This article notes:

Essentially, Hall’s efforts (done in the name of having “a bit of fun,” he clarified) point out that some scientists seem to be reaping the benefits of high social media engagement, regardless of their actual contributions to the scientific community. By “shouting louder” than others, these social media-savvy scientists are instantly perceived as thought leaders and subject matter experts, without the need for published work to back up their reputations.

Of course a K index can only be meaningful if you are a scientist publishing papers - otherwise your number of citations is zero and K is infinite. For researchers, the idea is that the two inputs should roughly balance each other, and a large ratio would imply that you have too large a following for the kind of scientific merits you actually have, based on the papers you published and how much they were mentioned in other publications.

To evaluate scientists a wide range of metrics have been proposed. The sheer number of papers one wrote is one example; it has the drawback that it does not account for the fact that you may be able to publish papers in obscure journals that nobody reads. So one better way to judge if your work is of some impact in the progress of science is to count the number of citations your papers receive: the more people mention your work, the better a scientist you are. Again, such a number has drawbacks: you might have written a widely cited paper and then stopped doing anything, and your citation number might be higher than that of a productive researcher with several papers cited a few times each.

A better metric is the Hirsch index, which combines number of papers and number of citations: it is the number N of papers you authored which have collected at least N citations. The higher N is, the more highly cited papers you have. The H-index is smarter as a metric, but it also has its own drawbacks - for instance, it hardly allows to compare the productivity of scientists in different disciplines, as the total volume of publications might differ and so would the average number of citations. Not to mention, of course, the fact that a paper with one single author must be valued much more than a paper with 3000 authors (as the CMS and ATLAS publications...).

So what is the business with the number of twitter followers and the K index? Of course, it's a joke. One may have many followers because one is writing a lot of funny things in twitter, or for dozens of other reasons not connected to the scientific research one does. Hence I do not think such a simple-minded metric deserves much discussion, but I will take my own example to demonstrate how silly this is. I do use twitter mostly for scientific topics, as opposed to Facebook (where I do let go with humorous stuff or personal pics as any other human being); and yet the number of twitter followers I have (166) is not really a measure of how much of a trend I set. In fact, this blog shows that 166 twitter followers are a little too few - I have ten times more daily readers here, e.g.

From the number of citations that the 800-or-so publications I authored have so far collected, which is a number in the upper 50 thousand, one gets that my K-index is 0.003. I leave it to you to decide what to make of such a number. It has been suggested that I should pay more attention to twitter and collect at least 10000 followers there, but I do not consider the raising to 1 of that silly metric a goal worth my time.

On the other hand, if you want to follow my twitter account, you're welcome to do it :-) ! I promise a very low-background feed.