Does this compute?

I often compare the Law of Mobility to Moore’s Law and Metcalfe’s Law.  Like those other laws, the LoM explains the economic realities that are bringing about a new set of dynamics that will radically change how businesses operate.

But several folks have asked “what’s the equation?” 

Their point is that it’s easy to figure out an equation that goes along with Moore’s Law and Metcalfe’s Law.  This is especially important if you’re working on a powerpoint presentation or a whitepaper (like this one) where you want to show impressive graphs of how things have changed over time.

The equation for Moore’s Law looks something like this:

processing power = original power *2^ ((# of years since original)/2)

The equation for Metcalfe’s Law looks something like this:

network value = some constant *(# of users)^2

 So – what is the equation for the Law of Mobility?  I doubt that we could prove the validity of any equation, but I think this one reasonably represents the truth captured in the Law:

product value = theoretical maximum value * (% of time product is fully available)^2

If the product is available 100% of the time, then the value of the product is its theoretical maximum.  If the product is avaliable half the time, then its value is about 1/4 the theoretical maximum.  If the product is only available 10% of the time, then it’s value is only 1% of the theoretical maximum.

That feels about right to me.  What do you think?

4 Responses to “Does this compute?”

  1. David Cordeiro says:

    I think the percentage of availability is the right metric. It might be possible to phrase this in terms of fuzzy logic (http://en.wikipedia.org/wiki/Fuzzy_logic).

    My understanding of fuzzy logic is still rudimentary, but I believe it is a modification to traditional set theory which acknowedges that a given element can be a partial element of a set (as opposed to the traditional binary logic of sets.)

    Thus at any given time a device can be a part of the set “accessible” and yet partially “inaccesible” (it contains its own negation).

    Determining the exact contours between these two sets is where fuzzy engineers seem to spend a great deal of their time. While fuzzy logic is still a rather new discipline I understand it is already finding many practical uses in consumer electronics and AI research.

  2. RAS says:

    It feels right to me, too. But…how does low battery power impact the concept of 100% availability? It may be available, but inaccessible. Is that part of David’s fuzzy logic? Or would I need to be a fuzzy engineer to know?

  3. David Cordeiro says:

    My expertise in fuzzy logic consists of reading one book but I do think battery life is a good illustration. We tend to think of it in binary terms of “battery is live” or “battery is dead.”

    But in reality, I will adjust my behavior and thus derive different utility depending on my knowledge of the relative battery life. If I am away from a recharger and I know my battery is running low, I might refrain from making a marginal call or using a marginal service.

    Thus there may be a fuzzy frontier of utility between a fully charged battery and a fully discharged one.

  4. Russ says:

    I’m a strategy guy – all my logic is fuzzy! Oh, that’s not what you meant?

    When I was in school, studying electrical engineering, I really liked digital stuff. Everything was a zero or a one. I really didn’t like analog stuff. And then there was that semi-conductive material. It all just made my brain hurt. Give me zeros and ones anyday.

    I think I can work with an equation for the value of mobility if I only have to deal with ones and zeros (either “fully available” or “not fully available”). Don’t bog me down with realities like battery life, roaming, voice but not data coverage, 1xRTT but not EV-DO, no connection but synced data on my device, etc.

    Did Gordon and Bob have to deal with this stuff?

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