# Proving by algebra

This mixes up the concepts, I believe, but for amusement and because it fits my thesis of digital networks as extensions or mirrors of networks found in nature, following similar properties and therefore governed by similar principles…

On that basis, and just to play around…

Two energy equations, E = mc2 (mass-energy equivalence) and E = hv (Planck–Einstein relation) – where E is energy, m is mass, c is the speed of light, v is wave frequency, and h is the Planck Constant – can be combined, thus…

mc2 = hv

And, since both c2 and h are constants, a further step can isolate these as a fixed value combined, and represent both of the surviving variables, m and v, as functions of each other…

m = f(v)

or

v = f(m)

But the representation is just doodling, and, like I said, in support of a preconception. It’s meant as a symbolic illustration, by way of analogy and loose interpretation.

The takeaway, on that basis, is as follows:

If in the network context m (mass) is equivalent to, say, network density (and, by extension, value), while v (frequency) is equivalent to engagement between nodes, then it is shown that network value and engagement are correlated. What’s more, as functions of each other and the relationship mutual, the dual reinforcement of value and engagement is, mathematically speaking, the network effect.

Additionally, before concluding: The constant speed of light (c) in the famous formula, could in the digital network context be seen as analogous to network speed, a qualitative signal of robustness, security, and efficiency in the underlying infrastructure. This isn’t fixed, like traveling light, but variable in actuality, adding another wrinkle to the illustrated functions.

The bottom line of the conceptuals and analogs is this: “He proves by algebra” that the principal value driver of digital networks is engagement, which is in turn dependent (among other things) on the enabling technology.

This was my preconception going in, the fudged math notwithstanding.