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In considering the nature of genius, it is not possible to define it in terms of a single variable - but requires several factors: the three Ps - power, preeminence, and associated with a personality.
1. Genius is a form of power
It is indeed a new source of power that adds to human capability.
An analogy would be that genius is like discovering a new supply of fuel - a new forest, coal seam or oil field. This new power can be used constructively, or destructively - for tools or for weapons.
Genius is somewhat like a local reorganization of reality to create new capability or efficiency, the insights and theory necessary for such a reorganization, or a technology or tool that enables such a reorganization.
But if the primary reality of genius is a new source of power, the secondary effect is to redistribute power - specifically to concentrate power around the results of genius (not necessarily around the genius himself, but concentrate power around the product of genius).
But is should be noticed that the tendency is for this power to diffuse and dilute - so that the consequences of genius spread much more widely than the situation or society in which the originating genius dwelt.
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2. That power is associated with preeminence
A genius must also be preeminent is his field, must be a person of high ability. Thus, it is not genius when a person is of mediocre ability but merely has power conferred upon him or has a large effect but by accident.
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3. Genius is personal, that is it originates in a specific person
The power and preeminence of a genius must also be derived from within themselves, must originate from the person - and not merely from his position in a system or institution or from headship of a team (or from some other person - as when somebody else's work is appropriated).
I think the only exception to this is that sometimes genius seems to be genuinely dyadic - a product of the close interaction of two persons neither of who is necessarily a genius alone. Gilbert and Sullivan would be one instance, Crick and Watson is perhaps another. But - as far as I know - this does not scale-up to higher numbers: genius may occasionally be a dyad, but never triadic or more.
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These criteria are similar to those for a Nobel Prize - a prize is awarded (in general) when an influential breakthrough (corresponding to power) is associated with a particular individual and is the achievement of that person; or up to three people when the prize is awarded for either for establishing a new field via more than one discovery, or awarded for the two or three most significant steps towards as discovery.
However, the Nobel does not have direct reference to preeminence, and some prizes have been given to people who were exceptionally hard-working, or in the right place at the right time, or lucky rather than exceptionally able.
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