The most widely circulated definition of magick today is attributed to Aleister Crowley:
Magick is the art and science of causing change in conformity with will
The problem with this definition, unqualified, is that it means virtually every act is magical; say using a can opener to open a can of tomatoes, or crossing the road to get to the other side, etc. Understanding Crowley’s actual meaning requires delving into Thelema (a Greek word meaning “will”) and the associated principles he espoused throughout his corpus. However, his basic statement about what magick is has been circulated so often over the past hundred years that it’s developed a life of its own, so to speak, independent of Crowley’s favored dogma.
Crowley aside, historically and across virtually every culture, the notion of “magick” has always been of a special, decidedly non-ordinary sort of activity, virtually never applied to such mundane acts as turning a knob to open a door. Modern authors, such as Donald Michael Kraig, agreeing that magick is a matter of causing change in conformity with will, have sought to rectify the discrepancy by appending statements like, through means not currently understood by Western science, to Crowley’s minimalistic definition.
Other authors have adapted Crowley’s basic definition in other ways. Most notably, Dion Fortune added the idea that the changes caused by magical acts are first and foremost changes in consciousness, which presumably translate into real word effects in one way or another.
From the neuromagick perspective, magick is indeed primarily a matter of initiating desired change, so Crowley's base definition remains a good starting point. Further, the term magick, if it is to have a unique meaning and not refer to any ol' mundane effort, should refer to something special, to some unique approach to initiating change. Therefore, the implied intention behind Kraig's amendment is consistent with the neuromagick point of view. However, a key feature the Neuromagick Initiative is to promote a model of magick that can be specified within the parameters of modern science, so Kraig's specific solution is at variance with the Initiative.
What Kraig seemed to be aiming for was expressing that magick operates by mysterious means, or stated with more specificity, resulting from occult (unseen) influences in and around the target situation, a general idea that is both historically consistent and in harmony with the neuromagick perspective. The challenge of the Initiative, then, is to specify, within scientifically valid parameters, occult influences that a practitioner can initiate by intentional act, but that remain mysterious as they operate on any given situation, from an outside observer's point of view certainly, but even to the practitioner.
Fortune's amendment, that the changes directly caused by magical acts are first and foremost changes in the consciousness of the operator, is consistent with the neuromagick perspective in spirit, but likewise requires some updating, or at least better specification. Fortune, a contemporary of Signund Freud and Carl Jung, famously studied the generalized psychoanalytic model of the human psyche, and even practiced as a psychoanalyst for many years. Her writing on magick and Hermeticism clearly reflects the goal of fusing magical practice and her personal take on psychoanalytic principles, a trend mirrored and carried forth by Isreal Regardie (see The Middle Pillar), who also practiced as a Freudian-style analyst late in his career, and who strove to interpret the workings of magick through the lens of the Freudian-Jungian model.
Current psychological and psychiatric science have long since moved away from the Freudian-Jungian model of the psyche in favor of more supportable models, and in keeping, Freudian-Jungian notions are generally not consistent with the neuromagick conception of consciousness or related notions of an unconscious/subconscious entity residing within the psyche. More current and better-specified models tend to emphasize cognitive processes, some of which we are aware of as they operate (ostensibly termed explicit processes) and some of which we are not (alternatively termed implicit processes), which together could be considered as the consciousness, though modern usage of that term in popular culture leaves its actual meaning somewhat ambiguous for a variety of reasons. Therefore, the term is best avoided, and the more descriptive and more current term, cognitive processes, is a reasonable alternative.
To specify the Fortune amendment further, the initial changes caused by magical acts are on the cognitive process of the practitioner, AND, any effects on the world at large are a function of subsequent changes in the thinking and behavior of the practitioner. Specifying the mode of effect on the world at large in this manner is necessary because any direct effect on the world that does not rely on preceding changes in the behavior of the practitioner would require amending the currently accepted laws of physics. As stated in Taking the Initiative, the neuromagick effort, at present at least, looks to psychology, cognitive science, and especially cognitive neuroscience rather than physics for its scientific support.
Finally, in bringing the updated versions of Fortune and Kraig's amendments of Crowley's base definition together, we arrive at a definition of magick that nicely suits the neuromagick philosophy.
Magick is a specialized method for initiating desired change, which first impacts implicit cognitive processes, thereby altering the thinking and behavior of the practitioner, which in turn instantiates changes in the world at large.
Some may argue that this definition is too specific, and/or lacks the mystery and romance that for some is the allure of magick and occult studies in the first place. While that may be so, this definition is at least consistent with the Initiative's aims of establishing a model of magick that, theoretically, could be tested and validated through standard scientific methods.