there are a bunch of laws of the value, or utility of a network - all these assume a set of n nodes (presumably owned each by one user), all effectively connected to all other users. That doesn't mean there is a "full mesh" network (with n^2 links) - just the capability of communication from each to every other node.
i'm not stuck on any particular "layer" of communications here - for those not familiar with the marvellous seven layer model of communications (or variants) we could be talking about physical or internet or application layer here - if you like, we're talking wires, versus who's in your contact list, versus who you can get to on facebook or zoom or whose blog you can read, etc
Lets leave aside annoying things like NATs (and ADSL and most cellular links) that are asymmetric - there are workarounds for that anyhow. Well, let's not leave that aside, as asymmetry of a communications service is part of why there are different laws. this matters, as constraints on who you can talk to aren't just about censorship. they create "walled gardens" - a phrase I hate as the implication is that all is well in the garden : it isn't - there's no supply of water or seeds or bees or anything to keep the garden alive. it isn't a garden. its a desert. facebook is a desert. or an elephants graveyard, where old things go to die.
n^2
so if you have a network of 12 people, its utility is 144
since that's the total number of connections possible - for each of the 12 people,
they can talk to 12 other people. They may not want to, but they could. I think metcalfe was getting at something more nuanced than this - I think he has been a proponent of super-linear economic growth that underpinned some teechno-evangelism from the left coast. I like it because it captures an essential idea of the Internet inherrent in always on, always reachable, and extensible. Anyone could run a server. anyone could write a server. my interpretation of this model is that it is about affordance of the capability of endless addition of new applications from anyone anywhere anytime, that anyone else can use.
reed's law
2^n
so if you have a network of 12 people, its collective potential is 4096
since thats the set of all possible subsets of people that can form.
I think reed took the same interprretation that I have, but is even more enthusiastic, but at the same time, captures the idea that new applications may be of niche interest. the value of the network in both metcalfe and reed's models is a value that accrues to all the users - providers ('lower levels') cannot explicit this value in the same scale, because that would kill the incentive for people to create all these new apps - the entry cost would be too high, the return too low. there is no tax levy on service that could be set which would do anything else. kill the goose that laid the golden egg. I'd note that there's still a golden egg (see next laws) because more people still means more revenue as each still pay a recurrent fee, and more apps may mean more bandwidth so capacity deployed still always (in the end) will make money.
briscoe's law
n*log(n)
with a network of 12 people, your service utility is 29.82 (approx)
briscoe's taking a plausible model which I think is more about revenue that can be made by a serrvice provider, offereing connectivity to a higher layer. Note it is still super-linear, and I am not completely convinced this makes sense.
jon's complaint (sarnoff's law)
n
so with a network of 12 people, the provider's service is worth 12 units. sarnoff devised this for broadcast networks. Broadcast systems are massively asymmetric - there's a broadcaster (often using radio/tv/satellite etc) that reaches a lot of people. hHey often get in the business of content creation (or at least sponsorship - e.g. for sports, but nowadays, for internet streaming/download too - Amazon, Netflix join the BBC, Disney etc - securing their supply chain, etc)
I'm going to try to explain why these are all not wrong, although, like many models, they may or may not be useful.
I claim that the internet is mostly behaving like Sarnoff's law now. we can't create new services. Not because of network effects (people on old services can't shift to the new one is not a strictly correct barrier - people went from myspace to facebook, from twitter to tiktok, but they had to do so additively. not multiplicatively - having 10 social networks or 10 video conferencing apps is 100 times less valuable than having 1 that reaches all the people that are divided by those barriers. (insert old joke about america and england being two great nations divided by a common language).
the cost of writing a new app, creating a new service is tiny. it immediately would get value if it was possible to deploy, but long gone are the days of Metcalfe or Reed's idealised Internet. barriers to deployment exist at all levels. the wires are not open, the address books are not all equal. Apps to not afford access to other apps the way email and the web permitted arbitrary extensibility and innovation.
what's more, the stultification of the growth in new systems that can reach anyone and everyone also means that the very bottom of the system, the wires, where there is never any hope of getting more value than n for n users, is getting less. that is a great example of the poisoning of the geese.
...and they aren't laws, they are models...
I'm going to try to explain why these are all not wrong, although, like many models, they may or may not be useful.
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