Most people have trouble intuitively grasping the scale of the universe.
Its not that we have problems with the numbers. Most people can bandy the facts and figures around pretty easily. Approximately 238,000 miles to the Moon, 93 million miles to the Sun, 4.3 light years to Proxima Centauri, and so on. Not too much difficulty there.
But visualizing those distances accurately is not instinctive at all. In a way, we're built against that--we have only these analog animal brains of ours, after all. Our minds are hardwired by evolution to deal with things on a human scale, and as a result we tend to mentally shrink everything down to that scale so we can more easily handle it, no matter how inaccurate that view may be.
You can see this popping up a lot in science fiction. The popularity of Space Opera science fiction, for example, can at least partially be credited to how it shrinks travel to other solar systems down to a human scale, with interstellar travel taking days or weeks at the most and entire planets usually represented by over-simplified sets of cities and environments. Space-borne disaster movies such as Armageddon or the more recent Moonfall suffer from this as well, portraying human nuclear weapons as being able to do more than imperceptibly nudge massive celestial objects like the Moon or a moon-sized asteroid. Trying to move the Moon with nuclear weapons would be like trying to propel an aircraft carrier out to sea by hitting it in the stern with a handful of firecrackers.
But I think this lack of understanding scale also colors how the public perceives a lot of scientific endeavors, and usually not for the better. For example, there recently have been a rash of blogs and opinions online complaining about how NASA has waited so long to return to the Moon or to mount an expedition to Mars...almost as if the Moon were right next door and Mars was just a jaunt down the street.
But the failure here is really in understanding just how far away even the Moon is, and how difficult it currently is to send people there. A round trip would cover a distance of roughly 20 times the circumference of Earth. When was the last time any one of us circumnavigated the globe even once? Even with modern commercial jets, how much would 20 such trips cost you in terms of time (both in preparation and in actual flight), resources, and money? And that would just be a taste of the raw distance involved. A trip to the Moon, performed entirely in hard vacuum and microgravity, would be far more difficult and expensive than that.
It was done before during the Apollo program, of course, with great difficulty and risk. But the problem is, we found nothing on the Moon that made it worth the expense for astronauts to return. Its not that the Moon doesn't have valuable resources we can use, its just that with our current level of technology we can't build up the infrastructure there to profitably exploit them. Why? Because the Moon is just too damn far away, and sending things there has proven just too expensive so far as a result.
And Mars is much, much worse. At its closest approach, Mars is about 36 million miles from Earth, or about 1440 times the circumference of Earth. How long and how expensive would 1440 trips around the world on commercial airlines be to you? Now imagine doing it twice, as you'd probably want a return trip back to Earth as well. Now imagine how difficult and expensive a flight that distance through a hostile, deadly void would be in a spacecraft using current technology.
Like the Moon, its not as if Mars isn't ripe with valuable resources and potential scientific discoveries. But we just don't have the technology yet to reach all that distance and set up all the infrastructure that would be needed to make it worth the expense.
In the future, of course I think things will turn around, with the development of faster, better propulsion ssystems and more long-enduring and reliable life support systems. But as much as we may want that to happen in the near future, its much more likely that it will not happen for decades yet.
If people, especially those controlling the purse strings in Congress, understood just how vast the distances were out in space, I think they'd understand the need for more long-term planning and execution in the space program. We have to break out of the short-sighted cycle of trying to restart the space program every 4 or 8 years whenever we have a new president.
And I think the public in general would be more supportive of space efforts, knowing how daunting the task faced by NASA and other space agencies are. I think educating people on the true scale of things should begin in the science classroom, and science writers--and even science fiction creators--should be mindful of trying to convey that when it comes up.