Theoretical research, with supporting experimental data, has proven to be one of the most important endevours of the human species. There are three main reasons I believe in the importance of theoretical research.
The first major benefit of theoretical research is provide a way of describing natural phenomena. It also allows for us to build properly supported models and theories that describe nature. Previous to the scientific endevour, fantasy and reality had no clear dividing line and superstitions were considered just as valid as most human knowledge. Theoretical research has, since its inception, provided the means to seperate fact from fiction, and to explain real phenomena as logically as possible. It also provides guidance to new areas of reasearch and understanding that can't be obtained by simple trial-and-error methodology.
Secondly, theoretical research, especially in the last century, has been the backbone of almost all modern technology. I think it important to point out that until recentally, technical invention and technology was based of trial and error, and not solid scientific principles in most cases. Alot of architecture was build on the premise that similar structures worked, and if the building kept standing after it was built, the design was good enough to be used again. Eyeglasses and the telescope were invented long before newton's treastise on optics. However, this was close relationship between the two. Progress in technology allowed new experimentation and research, which allowed theoretical research to progress with new data. Likewise, new theoretical theories would often explain why certain devices worked, and would be useful in improving such devices based on theories, not guess and check. However, the last century has seen this bond become not only closer, but irrevocably linked. Modern electronics, pharmecuticals, medicine, etc, have progressed because of the progress of theoretical research. Without abstract research into QM, modern solid state electronics wouldn't exist. Without QM, and the development of physical chemistry, biology, etc, modern pharmecutical and medicine wouldn't exist. Modern technical marvels such as the MRI, X-ray machine, CT scanner, etc only exist because of theoretical research. The advances in biology and biochemistry research have led to such solid understand of DNA that it has become possible to tailor make cures (still in infancy as an application.), allowed the design of crops that provide yields significantly higher than unmodified crops (saving billions from starvation), and provided medical advances such that the average human lifespan in the US is almost 40 years longer than it was 100 years ago. Also, the immediate positive benefits of technical research are dependant on the continued development of theoretical research to provide the backbone for future technical achievements.
Finally, and most importantly in my opinion, theoretical research gives us one of the best tools for understanding reality. Mankind has looked at the world around him (and her) for ages in wonder and bewilderment. Theoretical research has provided the means to alleviate some of the bewilderment and only increase our wonder. New unimagined frontiers are being seen that would never have come to light without theoretical research. From an understanding of how the sun, and suns like it everywhere, function to how the subatomic world behaves in ways counter-intuitive to our macroscopic world (yet provides the mechanisms that makes our macroscopic world function.), new venues of wonder and understanding, and new bewilderment are constandly cropping up.
That said, I think the best way to encourage support for theoretical research is to intruige people with the knowledge that it provides. I think almost everyone is curiuos about how the world works, but a lack of emphasis on scienfic education has left the average person with no inkling of what billions of dollars in theoretical research provides. All they see are the marvels of technology based on the research and take it for granted. Of course, that is a seperate thread all together.
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