4 ms·

Metcalfe’s Law is Wrong (2006)

39 points by hapnin 9y ago

dmoy 9y ago
Hah from the title I guessed this was an Odlyzko paper. If you liked this one, also read Content is not King
nordsieck 9y ago
I think one of the best ways to understand network scaling (in the human sense) is the warrens and plazas metaphor [0] Warrens are venues with relatively small size, that are relatively opaque to the outside. In principle, there is no scalability limit to warrens, as warrens scale horizontally. Plazas are venues with relatively large size that are relatively transparent to the outside. Plazas scale vertically, and so run into all sorts of size based scaling difficulties [1][2]. I'd expect networks like facebook which are very warren-y to have a much lower value growth curve relative to the number of nodes. While it's true that Facebook has created plaza-ish features like Pages, the core function of the network is explicitly warren-y, with a cap to the number of friends any profile can have. In contrast, a network like twitter should have a value growth curve much closer to Metcalf's law since it is almost completely plaza-ish. [0] https://www.ribbonfarm.com/2010/10/27/warrens-plazas-and-the-edge-of-legibility/ https://www.ribbonfarm.com/2010/10/27/warrens-plazas-and-the... [1] https://en.wikipedia.org/wiki/Dunbar%27s_number https://en.wikipedia.org/wiki/Dunbar%27s_number [2] https://pjammer.livejournal.com/61330.html https://pjammer.livejournal.com/61330.html
QML 9y ago
I'm surprised the Erdős–Rényi model [1] isn't mentioned in this article along with Metcalfe's Law and Zipf’s Law. There's a nice phenomenon with random graphs: if the probability of two users being connected > log n / n, then the graph is "surely" connected. [1] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...
- abetusk 9y ago
  Erdos-Renyi random graphs aren't mentioned probably because they hold almost no relevance to social graphs and networks, like the ones being addressed by Metcalfe's and Zipf's law. Erdos-Renyi random graphs have a Gaussian degree distribution (or maybe Poissonian degree distribution) [1] which effectively makes the number of edges a proportion of the number of vertices with a narrow band of variation as a result of the finite variance. Social networks tend to have some type of power law or "long tailness" to them, giving them unbounded variance of degree and often giving them unbounded mean degree [2] [3]. Another way to say this is Erdos-Renyi random graphs are not long tailed, power law degree distributed or scale free, which Metcalf's law and Zipf distributions address in one form or another. [1] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model#Properties_of_G(n,_p) https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_... [2] https://en.wikipedia.org/wiki/Long_tail https://en.wikipedia.org/wiki/Long_tail [3] https://en.wikipedia.org/wiki/Stable_distribution https://en.wikipedia.org/wiki/Stable_distribution
  - QML 9y ago
    After rereading this article [1], I’d have to agree the Erdos model is ill-fitting — but still disappointed no model was mentioned. [1] https://www.quantamagazine.org/scant-evidence-of-power-laws-found-in-real-world-networks-20180215/ https://www.quantamagazine.org/scant-evidence-of-power-laws-...
imglorp 9y ago
Metcalfe is an interesting character, still sharp and full of stories. Ferriss did a nice, non-technical, long form interview with him that covers his time at Xerox and 3Com and what he learned about leadership and business. They do discuss his law, if you want to hear it from the horse. https://tim.blog/2018/02/14/bob-metcalfe https://tim.blog/2018/02/14/bob-metcalfe
toss1 9y ago
These 'laws' of network value address only the potential value -- each node could make n*(n-1) connections. However, the network will never actually make all of those connections. None of us will ever call anything close to everyone on the telephone network, contact everyone on FB or Twitter, etc. Yes, there is value in the larger network of addressable nodes that could potentially be connected, but it seems to me that the yield of connections made also counts. So, the value of a network should first include the available resources of the nodes connecting, such as time. A telephone network has a different value from a broadcast network. The telephone users can only physically call other people for 86400 seconds/day, etc., so the yield of connectsion made is capped. Vs a broadcast network that can simultaneously reach millions, but only one-way. Similarly, the friction in making connections needs to be considered. E.g., a telephone network with speed dial has more net available connection time than a network requiring everyone to talk to the operator and get literally patched thru. Search functions, and discover-ability also come into play. Having the White Pages where everyone was listed in the US would have made its telephone network much more valuable than a Russian network of exactly the same size where no numbers were published. Similarly, DNS adds zero new connections to the Internet, but makes it enormously more valuable. Obviously, this lacks quantative measures, but these are the sorts of factors I'd want to see in an improved algorithm.
- EGreg 9y ago
  Very well said. One would probably have O(log N) potential partners for activities they care about.
beefman 9y ago
My response to this article, written in 2006: http://lumma.org/microwave/#2006.08.23 http://lumma.org/microwave/#2006.08.23
caseysoftware 9y ago
Metcalfe lives here in Austin and is involved in the local startup community in a variety of ways. One time I asked him how he came up with the law and he said something close to: "It's simple! I was selling network cards! If I could convince them it was more valuable to buy more, they'd buy more!" As an EE who studied networks, etc in college, it was jarring but audacious and impressive. He was either BSing all of us ~40 years ago or in that conversation a few years ago.. but either way, he helped make our industry happen.
- heisenbit 9y ago
  Build it and they will come. Scale it up and it will turn to gold. IPO before reality catches up.
andreareina 9y ago
I was initially skeptical about the n log(n), but the arguments are persuasive. Specifically about not all connections being worth the same. That they follow Zipf's law specifically is a minor point I think, the overall shape seems right.
- sitkack 9y ago
  > Specifically about not all connections being worth the same Kicker right here. If don't know what makes a network interesting, it is best to just add more links as fast as possible. In a network like Quora, they were initially successful because they curated the link quality.
stretchwithme 9y ago
I think you can't even trace all of the effects, so it can be neither proven nor disproven. You would need to study something much simpler than human beings. And it might be more accurate to say the POTENTIAL is what scales. And this is one more technology that some people don't exploit at all and that others make the most of. But it is right enough to describe the gist of the situation.

39 points by hapnin 9y ago

dmoy 9y ago

Hah from the title I guessed this was an Odlyzko paper. If you liked this one, also read Content is not King

I think one of the best ways to understand network scaling (in the human sense) is the warrens and plazas metaphor [0] Warrens are venues with relatively small size, that are relatively opaque to the outside. In principle, there is no scalability limit to warrens, as warrens scale horizontally. Plazas are venues with relatively large size that are relatively transparent to the outside. Plazas scale vertically, and so run into all sorts of size based scaling difficulties [1][2]. I'd expect networks like facebook which are very warren-y to have a much lower value growth curve relative to the number of nodes. While it's true that Facebook has created plaza-ish features like Pages, the core function of the network is explicitly warren-y, with a cap to the number of friends any profile can have. In contrast, a network like twitter should have a value growth curve much closer to Metcalf's law since it is almost completely plaza-ish. [0] https://www.ribbonfarm.com/2010/10/27/warrens-plazas-and-the-edge-of-legibility/ https://www.ribbonfarm.com/2010/10/27/warrens-plazas-and-the... [1] https://en.wikipedia.org/wiki/Dunbar%27s_number https://en.wikipedia.org/wiki/Dunbar%27s_number [2] https://pjammer.livejournal.com/61330.html https://pjammer.livejournal.com/61330.html

QML 9y ago

I'm surprised the Erdős–Rényi model [1] isn't mentioned in this article along with Metcalfe's Law and Zipf’s Law. There's a nice phenomenon with random graphs: if the probability of two users being connected > log n / n, then the graph is "surely" connected. [1] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...

abetusk 9y ago
Erdos-Renyi random graphs aren't mentioned probably because they hold almost no relevance to social graphs and networks, like the ones being addressed by Metcalfe's and Zipf's law. Erdos-Renyi random graphs have a Gaussian degree distribution (or maybe Poissonian degree distribution) [1] which effectively makes the number of edges a proportion of the number of vertices with a narrow band of variation as a result of the finite variance. Social networks tend to have some type of power law or "long tailness" to them, giving them unbounded variance of degree and often giving them unbounded mean degree [2] [3]. Another way to say this is Erdos-Renyi random graphs are not long tailed, power law degree distributed or scale free, which Metcalf's law and Zipf distributions address in one form or another. [1] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model#Properties_of_G(n,_p) https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_... [2] https://en.wikipedia.org/wiki/Long_tail https://en.wikipedia.org/wiki/Long_tail [3] https://en.wikipedia.org/wiki/Stable_distribution https://en.wikipedia.org/wiki/Stable_distribution
- QML 9y ago
  After rereading this article [1], I’d have to agree the Erdos model is ill-fitting — but still disappointed no model was mentioned. [1] https://www.quantamagazine.org/scant-evidence-of-power-laws-found-in-real-world-networks-20180215/ https://www.quantamagazine.org/scant-evidence-of-power-laws-...

imglorp 9y ago

Metcalfe is an interesting character, still sharp and full of stories. Ferriss did a nice, non-technical, long form interview with him that covers his time at Xerox and 3Com and what he learned about leadership and business. They do discuss his law, if you want to hear it from the horse. https://tim.blog/2018/02/14/bob-metcalfe https://tim.blog/2018/02/14/bob-metcalfe

toss1 9y ago

These 'laws' of network value address only the potential value -- each node could make n*(n-1) connections. However, the network will never actually make all of those connections. None of us will ever call anything close to everyone on the telephone network, contact everyone on FB or Twitter, etc. Yes, there is value in the larger network of addressable nodes that could potentially be connected, but it seems to me that the yield of connections made also counts. So, the value of a network should first include the available resources of the nodes connecting, such as time. A telephone network has a different value from a broadcast network. The telephone users can only physically call other people for 86400 seconds/day, etc., so the yield of connectsion made is capped. Vs a broadcast network that can simultaneously reach millions, but only one-way. Similarly, the friction in making connections needs to be considered. E.g., a telephone network with speed dial has more net available connection time than a network requiring everyone to talk to the operator and get literally patched thru. Search functions, and discover-ability also come into play. Having the White Pages where everyone was listed in the US would have made its telephone network much more valuable than a Russian network of exactly the same size where no numbers were published. Similarly, DNS adds zero new connections to the Internet, but makes it enormously more valuable. Obviously, this lacks quantative measures, but these are the sorts of factors I'd want to see in an improved algorithm.

EGreg 9y ago
Very well said. One would probably have O(log N) potential partners for activities they care about.

beefman 9y ago

My response to this article, written in 2006: http://lumma.org/microwave/#2006.08.23 http://lumma.org/microwave/#2006.08.23

caseysoftware 9y ago

Metcalfe lives here in Austin and is involved in the local startup community in a variety of ways. One time I asked him how he came up with the law and he said something close to: "It's simple! I was selling network cards! If I could convince them it was more valuable to buy more, they'd buy more!" As an EE who studied networks, etc in college, it was jarring but audacious and impressive. He was either BSing all of us ~40 years ago or in that conversation a few years ago.. but either way, he helped make our industry happen.

heisenbit 9y ago
Build it and they will come. Scale it up and it will turn to gold. IPO before reality catches up.

andreareina 9y ago

I was initially skeptical about the n log(n), but the arguments are persuasive. Specifically about not all connections being worth the same. That they follow Zipf's law specifically is a minor point I think, the overall shape seems right.

sitkack 9y ago
> Specifically about not all connections being worth the same Kicker right here. If don't know what makes a network interesting, it is best to just add more links as fast as possible. In a network like Quora, they were initially successful because they curated the link quality.

stretchwithme 9y ago

I think you can't even trace all of the effects, so it can be neither proven nor disproven. You would need to study something much simpler than human beings. And it might be more accurate to say the POTENTIAL is what scales. And this is one more technology that some people don't exploit at all and that others make the most of. But it is right enough to describe the gist of the situation.