Metcalfe's law

 

The London Underground is a dense, connected network, which makes it extraordinarily valuable
 to London and Southern England. 

From History-Computer

Metcalfe’s Law is one of the foundational principles of network economics. It suggests that as a network grows, its value grows much faster than its user base.

The idea behind Metcalfe’s Law is that, while a network’s cost generally grows as a direct proportion of its total number of nodes, its value grows in proportion to the square of that number. Network value grows fast because it’s related to the number of connections between nodes rather than the number of nodes. Metcalfe’s idea implies that node connectivity is the real source of utility in a network.

The word node comes from a Latin word that means knot. In this context, we use it to mean any endpoint in a network. Telephones, computers, train stations, or individual people can all act as nodes in different kinds of networks.

A network with 10 of these nodes might cost about 10 times the price of one node, but Metcalfe’s Law suggests that the network’s inherent value will be closer to 100 times the value of one node. If you add a node, the cost will jump to 11, but the value will jump to 121, the square of 11. In mathematical terms, network cost grows linearly, but network value seems to grow nonlinearly as an exponential function of the total number of nodes in the network.

Metcalfe’s Law isn’t a physical or perfect law of network value. Just like economics has the idea of supply and demand that works perfectly only under perfect conditions, Metcalfe’s idea of network effects is more of an approximation rather than an exact formula. It’s most useful as a conceptual model that you can use to think about network economics in general terms.

Metcalfe’s Law observes that any network’s value is a proportion of the square of the network’s total number of connected nodes.

The mechanics of Metcalfe’s Law are simple. If a network gains new nodes that can connect with all its existing nodes, then the amount of connections grows much quicker than the number of nodes. Every single new node adds as many connections to the network as there are existing nodes.

When Metcalfe first came up with the idea, he indicated that the formula for a network’s value worked best as an exponential function of its total number of nodes. He and other researchers like Bob Briscoe later scaled it back, calculating that the network value was closer to a logarithmic function of its number of nodes.

In 2013, data analysts from the Netherlands released a broad study of seven years of internet use across 33 European countries. They concluded that the growth patterns of smaller and newly launched networks do seem to follow Metcalfe’s exponential estimation. As a network grows, however, the growth of its value seems to taper off into a logarithmic rather than exponential function of its number of nodes.

Other recent studies involving data from the past decade from Facebook, Tencent, Bitcoin, and Ethereum networks also indicate that these networks seem to fit Metcalfe’s observation in their initial phases and then slow down as they reach widespread adoption.

The network effects of this value escalation tend to be both direct and indirect.  

We call network effects symmetric or direct when a node increase provides direct utility to the other nodes. We can see direct network effects in social networks like Twitter or Tinder, where additional users joining directly improves the user experience of the existing users, giving them the possibility of more followers or matches.

We call networks effects asymmetric or indirect when there is more than one type of node and a node increase provides indirect utility to other types of nodes. Indirect network effects show up in networks like Uber or Airbnb, where more drivers and hosts indirectly improve the experience of the riders and guests, and vice versa. Indirect effects often look like increased supply encouraging increased demand, which then encourages even more supply.

Metcalfe’s Law seems to work best when all the nodes in a network have equal value and provide equal benefit. Nodes with fewer connections are less valuable than highly connected nodes.

Many networks don’t match Metcalfe-style growth because some new nodes don’t create connections with all existing nodes. This can happen when, for instance, new users of a network speak different languages or have interests and expertise in areas that don’t overlap.

To estimate network effects accurately, we have to take into account not only the number of nodes but also the affinity between nodes. If a network’s cost per user is fixed and later users use the network less than the trailblazers, the newer users will be less valuable to the network, and the network will become less efficient.

While experts in network economics and computer science continue to battle over whether the correct formula for calculating network effects should be exponential, logarithmic, or some other function, Metcalfe’s general point is clear. A network’s overall value tends to grow much quicker than its size.

Metcalfe’s Law of network effects seems to have the strongest applications in these four main kinds of networks:

• Physical networks
• Protocol networks
• Personal networks
• Market networks

Physical networks are composed of physical nodes connected by physical links. These include electrical grids, roads, railroads, sewer systems, and broadband internet services.

Thanks to Metcalfe’s Law, it’s not uncommon to see these physical networks grow so powerful that they overwhelm smaller competing networks and turn into monopolies or duopolies. When that happens, governments tend to nationalize them and call them utilities.

Protocol networks are standards of use for digital or communications networks. They layout sets of rules for how nodes in a network must format and process data.

Nodes in protocol networks are generally digital devices rather than humans, so you can think of protocol networks as computer languages. Just like a human language, once a protocol network has been widely adopted, it’s nearly impossible to replace.

Ethernet is an example of a protocol network. When Metcalfe and Boggs came up with the Ethernet standard, other local area network protocols existed. Thanks to Metcalfe’s Law, however, the more market share Ethernet captured, the less valuable the competition became until it dwindled to almost nothing. More recent examples of protocol networks include Bitcoin, Ethereum, and other cryptocurrencies.

A network is considered personal when the nodes are people. Human nodes may be anonymous or may have their real identities tied to their usernames.

Personal networks generally grow when real-life people find value in them and influence their inner circles to join as well. When a large number of people who you like and respect are using a network, you’ll usually find a lot of value in joining it too.

Examples of personal networks include TikTok and Facebook.

Market networks take the identity-based format of personal networks and combine it with the transactional focus of marketplaces to facilitate mass transactions from many buyers and sellers. Instead of optimizing for quick transactions, market networks generally encourage long-term projects that allow users to improve their reputation with each successful purchase or sale.

Market networks provide value in both directions, from the sellers to the buyers, and vice versa. In double-sided systems like these, the value is derived from the network connectivity not from the specific system itself. Once a market network is established, the two sides tend to cement the network in place. To get users to move, you have to find a way to provide more value to both sides at once than what they’re getting from the existing network.

I'd never heard of Metcalfe's Law before I read this article, but I realise now that I'd always understood it without being aware of it.  

In particular, I thought of it as it applies to public transport networks.  Think of the extraordinary network of the London Tube, including the Underground, the Overground, the new Elizabeth line (Crossrail), the tram network, and mainline trains and airports, where almost every line connects with several other lines.  

In Victoria, the tram (light rail) and transit networks don't connect very well.  There are connections at the main downtown termini, but in the suburbs, because the tramways and railways were owned by different companies, their stops at the end of the line are sometimes far apart.  It has been suggested to the public transport authorities that tram lines should be extended to the nearest railway station to improve network connectivity.  Alas, this still hasn't happened.  Although the Labor government has committed to a new outer circle rail line, which will connect all the radial suburban branch lines.  Predicatbly, the LNP opposition doesn't want it.

Air pollution linked to mental illness

Pollution in London. Photograph: Toby Melville/Reuters

From The Guardian

 

Exposure to air pollution is linked to an increased severity of mental illness, according to the most comprehensive study of its kind.

The research, involving 13,000 people in London, found that a relatively small increase in exposure to nitrogen dioxide led to a 32% increase in the risk of needing community-based treatment and an 18% increase in the risk of being admitted to hospital.

The researchers said the findings were likely to apply to most cities in developed nations, and cutting air pollution could benefit millions of people.

The study used the frequency of admission to hospital or visits to community doctors and nurses as a measure of severity. The researchers calculated that a small reduction in one pollutant alone could reduce illness and save the NHS tens of millions a year.

Levels of air pollution in London have fallen in recent years but there is no safe level, said Ioannis Bakolis, of King’s College London, who was part of the research team. “Even at low levels of air pollution, you can observe this kind of very important effect.”

Recent research has shown that small increases in air pollution are linked to significant rises in depression and anxiety. It has also linked dirty air to increased suicides and indicated that growing up in polluted places increases the risk of mental disorders. Other research has found that air pollution causes a “huge” reduction in intelligence and is linked to dementia. A global review in 2019 concluded that air pollution may be damaging every organ in the human body.

The new study, published in the British Journal of Psychiatry, tracked patients in south London from their first contact with mental health services and used high-resolution estimates of air pollution at their homes.

The quarterly average NO2 levels in the study area varied by between 18 and 96 micrograms per cubic metre (µg/m³). The researchers found that people exposed to 15µg/m³ higher levels of pollution had an 18% higher risk of being admitted to hospital and a 32% higher risk of needing outpatient treatment after a year.

The link was strongest for NO2, which is largely emitted by diesel vehicles, but was also significant for small particle pollution, which is produced by burning all fossil fuels. The small particle levels varied from 9 to 25 µg/m³ and an increased exposure of 3 units increased hospital admission risk by 11% and outpatient treatment risk by 7%.

The scientists assessed the patient data again seven years after the first treatment and found the link to air pollution was still apparent. The findings were not explained by a range of possible other factors including age, sex, ethnicity, deprivation or population density, although unidentified factors might still play an important role.

“Identifying modifiable risk factors for illness severity and relapse could inform early intervention efforts and reduce the human suffering and high economic costs caused by long-term chronic mental illness,” the researchers said.

The study was not designed to prove a causal link between air pollution and the severity of mental illness – that requires difficult experimental work. But the link is “biologically plausible”, the researchers said, as air pollutants are known to have potent inflammatory properties and inflammation is believed to be a factor in psychotic and mood disorders.

The World Bank has estimated that air pollution costs the global economy $5tn a year, but this includes only the well-known damage caused to heart and lungs.

“Cost evaluations currently only factor in physical health, but we’re seeing more studies demonstrating links with mental health,” said Newbury. “We think it can be important to include these, because it could tip the scales and make it clearer that investing in reducing air pollution is cost-effective.”

The researchers estimated that reducing the exposure of the UK’s urban population to small particle pollution alone by just a few units, to the World Health Organization’s annual limit of 10µg/m³, would cut the use of mental health services by about 2% and save tens of millions of pounds each year.

Prof Kevin McConway of the Open University, who was not part of the study team, said: “This is a good study. The statistical analysis is generally appropriate [and] does increase confidence that there’s at least some element of cause and effect in the association between pollution and mental health.

“But it’s not easy for people to avoid pollution. Reducing air pollution in cities needs communal action on a broad scale.”

A separate new study has shown that heart attacks rise as the level of air pollution rises. The research examined data from southern Lombardy in Italy, an area with 1.5 million inhabitants.

Francesca Gentile, of the IRCCS Policlinico San Matteo Foundation in Pavia, said: “The results could be used to predict the incidence of this life-threatening condition [and] improve health service efficiency by being factored into ambulance forecasting models and warning systems.” The study was presented at the European Society of Cardiology 2021 congress.

We all know what the solution to air pollution is.  It's the rapid transition of land transport to EVs and of electricity generation to renewables.  It's that simple.  Why aren't governments acting?