I think that how "connected to reality" scientists are has to do with this trend.
In older times, being a scientist or an engineer meant being able to exert real, measurable, almost magical force upon your (and people around your's) surroundings. You made a bridge come to existence, you created a vaccine.
Nowadays, being a scientist or an engineer is associated with spending long days holed up in a room doing work which is incredibly complex and expensive, yet does not seem to create net benefit except in rare occasions. Furthermore, this isolation is considered to reduce social aptitude (which is high-status). Compare this to people with capital or social skills, who can almost magically navigate and cause things to happen in our modern very-social world.
The two castes of scientists or engineers which can still "make things happen" are the mad scientist (going against social rules) or the startupist (and his friend, the DIY Maker), and from my local zeitgeist, they are considered positions with status.
Also, this trend is supported by the fact that (As Mitchell_Porter pointed out) scientists get payed to research obscure subjects with questionable value to the world at large. I'm not saying this is bad, but I'm saying that it makes people correlate scientists with obscure subjects.
And how do we fix it? I have two ideas (both of which I actively pursue, and (I believe) let me enjoy a high status life as an engineer and science-lover (Given, I live in Tel Aviv, Israel, where engineers and scientists (I feel) are higher status than the US).
Yes, this isn't as rewarding as learning more about your favorite subject and requires taking risks, but (and sadly I can't find the reference for this right now) doing hard, risky, not very rewarding work is in itself a way to create status.
Or, in other words, go out and do stuff :) We'll all benefit from it.
[Feel free to read this poor little unrigorous and unsourced post in JK Simmons' voice. That is entirely optional and you are of course free to read it in any voice you like; I only thought it might be interesting in the light of what is mentioned in the edit at the bottom of the text]
Nowadays, it seems that the correlation between sciency stuff, social ineptitude, and uncoolness, is cemented in the mind of the public. But this seems to be very era-specific, even time-specific.
As a lesswronger, I find what follows ironic: In Islamic countries, "scientists" are called with the same word use for religious leaders and other teachers, "olama", literally "knowers"; historically, there's been a huge overlap between the two, and, when one of these folks speaks, you're supposed to shut up and listen. This is still true to this day. There might not be much wealth to be gained from marrying a scientist, but there was status; amusingly enough, it's in modern-day materialism that is pushing them into irrelevance as money becomes, more and more, the sole measure of status.
In the West, in the XIXth century, Science and Progress were hip and awesome. Being a scientist of some sort was practically a requirement for any pulp hero. In the USA, an era of great works of engineering that had a dramatic impact on life quality made engineers heroes of popular fiction, men of knowledge and rigour who would not bow down to money and lawyer-cushioned bourgeois, or to corrupt and fickle politicians, men who would stand up against injustice and get the job done no matter what. Everyone wanted to call themselves an engineer, and the word was rampantly abused into meaninglessness; florists called themselves "flower engineers"! That's how cool being an engineer was.
In the Soviet Union, as long as they didn't step on the toes of the Party, scientists were highly acclaimed and respected, they got tons of honour and status. There was a huge emphasis on technological progress, on mankind reaching its full potential (at least on paper).
Nowadays, nearly the entire leadership of China is made of technicians and engineers. Not lawyers, or economists, or literati. These people only care about one thing, getting the job done - and that's what Science does.
So, I've really got to ask, when and *how* did Science and Engineering become "uncool", and why are they termed "geek", the term used for sideshow circus performers whose speciality was eating chickens alive (or something like that), and which, before that, used to be synonymous with freak and fook? When and how did we become worse than clowns in the eyes of society? Most importantly: how can the process be reversed?
After all, from a utilitarian standpoint, Science being cool and appreciated and respectable is kind of important.
EDIT: There's also the strange relationship, in the public mind, between science and dangerous, callous, abusive insanity, with a long tradition in popular fiction from Victor Von Frankenstein and Captain Nemo to Tony Stark and GLaDOS, and some Real Life counterparts, especially in brutal totalitarian regimes. Wikipedia has an interesting article on the topic, and how the characterization and prevalence of the Mad Scientist related to time-pertinent perceptions of Science.
For some reason, that aspect is often treated as cool and dramatic and impressive (besides being characterized as repulsive), perhaps because it involves displays of power over others, which is a high-status thing to do. Is that one of the existing paths to social prestige? Achieving power, and being inconsiderate about flaunting it? I'd like to hear more constructive alternatives, because that one doesn't seem viable, from where I stand.