Historical definitions include:
"... the Science and Art of causing Change to occur in conformity with Will." Aleister Crowley
"...the art of changing consciousness at will" Dion Fortune
"...an art and a science for dealing with particular types of knowledge, the manipulation of which will produce results that will astound and amaze the uninformed" Isaac Bonewits
There is no contradiction between science and magic. All the various systems of magic are maps and periscopes into the unconscious activity of our individual and collective selves. Sure, the maps are inaccurate in some places and the field of view is limited. Sure, the results of psychic activity and magic spells are not reproducible or reliable. That is not the point. The point is that through magic (and only through magic --- if you have the right definition of magic) does life have meaning. Magic is (at least, in my definition) the process of manifesting reality in accordance to your Will.

You wake up in a darkened room and flip on the light-switch to see. That action is, by my definition, magic. Magic does not always work: sometimes the light-bulb is burned out or the power is out. Nevertheless, it works frequently enough for us to have the sense that, thanks to science and power-companies and light-bulb manufacturers and electricians, we can manifest light in our rooms whenever we want it. What amazing magicians we are to have manifested science and power-companies and light-bulb manufacturers and electricians so that we might have the karma of making light whenever we want!

O.K., O.K., but how do you make the leap from the finger-on-the-switch kind of magic to the chants-and-prayers-and-candles-and-bizarre-paraphernalia kind of magic? The purpose of this latter magic is to communicate with the unconscious processes that we use to manifest reality just like we use conscious processes to flip on light-switches.

I believe that we are largely responsible for the reality we create around ourselves. That statement is really harsh and hard to accept for anyone in a system of abuse or the midst of tragedy. But if our definition of self includes the entirety of the unconscious processes that are operent in our lives including the dark, violent parts of ourselves that we wish to deny or hide from ourselves (Jung's idea of the shadow), then the manifestation of terrible things can be seen as the result of processes within ourselves that are beyond our conscious control.

The point of the candle-and-pentagram kind of magic is, therefore, to achieve a similar level of control and accord with our unconscious processes that we have with our conscious processes, and to be able to manifest reality through our unconscious abilities in the same way that we can manifest reality through our conscious abilities. Sometimes we are not smart enough or capable enough or wise enough to make consciously the changes in our lives that we would like to create, and even if we were smart enough and capable enough and wise enough to accomplish what we want to accomplish, doing so would be pointless and hollow if we can not find fulfillment in reaching our goals. Magic is a way of both tapping into powers that go beyond our conscious limitations and finding joy in what we do.

(Note: there is a rather pointless disctinction made between stage magic and the magic practiced by ceremonial magicians and witches. The different uses of the word are completely obvious by context, and, therefore, I did not node this write-up under magick or magik.)