Science has, many times in the past, embarked upon a path to which there was no obvious benefit, yet ultimately came upon a discovery or application which improved the lives of humans immeasurably. Could Halley have had any idea how large the impact would be when he coerced Newton to record calculus and the laws of gravity in a book? What about Michael Faraday's fascination with electricity, generously supported by the Royal Society?
People aren't, as a whole, equipped to understand the long-term consequences of our actions. Predicating funding for something so essential to all of the progress made in the last few centuries on this faulty understanding would cripple our development. A government which attempts to offset the massive social cost of such a missed opportunity with speculative research is doing its duty to its citizens. We don't know what we don't know; evaluating scientific research with your limited cost/benefit analysis fails to take into account the enormous opportunity cost of a lost discovery.
As others have noted, taxation which funds things you don't agree with is a basic fact of modern life, but it has benefited you immensely - complaining about this funding model while you enjoy its output seems disingenuous.
