Sadly, I have no statistics, just a few anecdotes—which is unhelpful to answer the question.
After more thinking, maybe this is a question of having a platform. Like, maybe there are many experts who have crazy opinions outside their area of expertise, but we will never know, because they have proper channels for their expertise (publish in journals, teach at universities), but they don’t have equivalent channels for their crazy opinions. Their environment filters their opinions: the new discoveries they made will be described in newspapers and encyclopedias, but only their friends on Facebook will hear their opinions on anything else.
Heterodox people need to find or create their own alternative platforms. But those platforms have weaker filters, or no filters at all. Therefore their crazy opinions will be visible along their smart opinions.
So if you are a mainstream scientist, the existing system will publish your expert opinions, and hide everything else. If you are not mainstream, you either remain invisible, or if you find a way to be visible, you will be fully visible… including those of your opinions that are stupid.
But as you say, fame will have the side effect that now people pay attention to whatever you want to say (as opposed to what the system allows to pass through), and some of that is bullshit. For a heterodox expert, the choice is either fame or invisibility.
Sadly, I have no statistics, just a few anecdotes—which is unhelpful to answer the question.
After more thinking, maybe this is a question of having a platform. Like, maybe there are many experts who have crazy opinions outside their area of expertise, but we will never know, because they have proper channels for their expertise (publish in journals, teach at universities), but they don’t have equivalent channels for their crazy opinions. Their environment filters their opinions: the new discoveries they made will be described in newspapers and encyclopedias, but only their friends on Facebook will hear their opinions on anything else.
Heterodox people need to find or create their own alternative platforms. But those platforms have weaker filters, or no filters at all. Therefore their crazy opinions will be visible along their smart opinions.
So if you are a mainstream scientist, the existing system will publish your expert opinions, and hide everything else. If you are not mainstream, you either remain invisible, or if you find a way to be visible, you will be fully visible… including those of your opinions that are stupid.
But as you say, fame will have the side effect that now people pay attention to whatever you want to say (as opposed to what the system allows to pass through), and some of that is bullshit. For a heterodox expert, the choice is either fame or invisibility.