I try to make an isolated example to show how difficult the problem of "Knowing" and "Persuasion" is in the personal domain.
Let us look at this question:
is living next to power lines dangerous?
It is established scientifically that non-ionizing electromagnetic radiations are not carcinogenic (do not lead to cancer or other disease), for example, electromagnetic radiation from power lines and cell phones.
There was a research decades ago that linked living near power lines to blood cancer. This research however later was shown to be invalid.
I am an electrical engineer by education and my wife is a physics graduate so both of us should be able to follow the reasoning fairly well, as long as it is related to electromagnetic and not biology.
My wife, however, opposes to buy a house within a visible distance of high voltage power lines and whatever I did I could not persuade her that this is harmless. She is not alone as I heard this from many highly educated engineers around me. They just prefer to stay on the safe side which might be wrong. They always combine it with the argument of 'there are things that we don't know'. This is even reflected in the market price of houses near power lines.
Now how can you prove that living near power lines is safe and more importantly persuade someone else? Can you run your own tests? Can you follow the health of people living near power lines? If your full-time job is not that then this would be impossible.
When I google the question I get a boxed search result from a "snake oil seller" feeding on the fears of people:
Hundreds of studies worldwide have shown that living next to high voltage power lines and other parts of the power transmission network increases your risk of cancer and other health problems. The closer you are the more you are bombarded with dangerous EMFs www.safespaceprotection.com › emf-health-risks › emf-health-effects
So much praise should go to the power of page-rank and other algorithms in google search to bring this up. I am certain that the majority of people won't go further than the boxed results.
Now, this seems like a trivial and not so important example. But we are just following the same line of reasoning for many more decisions in everyday life.